Low-voltage power grid real topology identification method based on power flow constraint

Abstract

The application discloses a low-voltage power grid real topology identification method based on power flow constraints and relates to the field of low-voltage power grid topology. The application can effectively avoid the misjudgment problem based on only statistical correlation by coupling analysis of node measurement data and network physical operation rules and performing consistency evaluation on the topology structure under the premise of meeting electrical operation constraints. Meanwhile, the stability of the identification result under the condition of load fluctuation is improved by comprehensively evaluating the measurement results at multiple times. In addition, the application can realize accurate identification of the connection relationship of the user access point, phase type and branch without relying on manual checking, can significantly improve the authenticity and consistency of the low-voltage distribution network topology data, and provides a reliable basis for fine operation and maintenance and line loss analysis.

Description

Technical Field

[0001] This invention relates to the field of low-voltage power grid topology, specifically a method for identifying the true topology of low-voltage power grids based on power flow constraints. Background Technology

[0002] Topology identification in existing low-voltage distribution networks is typically based on ledger data, manual inspection, and switch status information from distribution automation systems. In scenarios with measurable data, some technical solutions employ voltage correlation coefficient analysis, phase difference discrimination, or graph matching methods based on measured data to infer the electrical relationships between nodes. Other technologies construct node voltage similarity matrices or power fluctuation correlation models, combining statistical thresholds to determine the phase and branch affiliation of users. Regarding power flow analysis, existing technologies usually assume a known network topology and perform one or more power flow calculations under a given topology for voltage assessment or line loss analysis, but rarely use the results of power flow calculations in reverse for topology identification.

[0003] However, in low-voltage power grids, discrepancies often exist between the actual topology and system records due to frequent user relocations, unauthorized connections, and failure to update phase adjustment records in a timely manner. Relying solely on voltage or power correlation indicators makes it difficult to distinguish nodes that are physically close but have different electrical paths. When network load fluctuations are small or multiple nodes exhibit similar power consumption behaviors, correlation identification is prone to misjudgment. Furthermore, existing methods typically do not incorporate the physical constraints between node voltage, current, and branch impedance into a unified discrimination framework. This results in identification results that are sensitive to noise and lack stability under conditions of weak measurement errors or local imbalances, and they cannot effectively eliminate electrically impossible connections. Consequently, the identification accuracy fails to meet the requirements of refined power distribution management. Summary of the Invention

[0004] This invention proposes a power flow constraint-based method for identifying the true topology of a low-voltage power grid. It aims to address the problem that it is difficult to accurately identify the actual user access point, phase, and branch connection relationship when the actual operating topology of the low-voltage power grid is inconsistent with the system ledger topology, under conditions of measurement error and load fluctuation. In particular, it solves the problem that existing methods based on correlation or static information cannot simultaneously meet the requirements of electrical and physical constraint consistency and multi-time period stability, and are prone to misjudgment and unrealizable topology structures.

[0005] The method for identifying the true topology of a low-voltage power grid based on power flow constraints includes the following steps: S1. Perform synchronous measurements on the root node and each node to be identified in the distribution network to obtain a measurement data set, wherein the measurement data set includes at least the voltage measurement value, active power measurement value and reactive power measurement value of each node; Specifically, existing low-voltage distribution area topology identification technologies typically rely on historical archives or manual checks. Measurement data is often scattered and asynchronous, making it difficult to form a unified data benchmark for topology inversion. This step deploys smart metering terminals or distribution IoT acquisition units with time synchronization capabilities at the root node and all nodes to be identified, constructing a measurement data set under a unified time coordinate. This ensures that the voltage, active power, and reactive power data of all nodes are strictly aligned at the same sampling time, thereby eliminating phase errors and power fluctuation errors caused by sampling time misalignment. Compared with traditional methods based on single-point meter reading or asynchronous data splicing, this step ensures the consistency and physical closure of the boundary conditions required for power flow calculation from the source, making subsequent topology hypothesis verification comparable and repeatable. At the same time, by directly introducing the original measured values ​​of node power and voltage instead of estimating the load model, it avoids relying on typical load curves or empirical correction coefficients, improving the accuracy of characterizing the actual operating state. This allows topology identification to be based on the real operating power flow state, thereby enhancing the adaptability of the method in scenarios with load fluctuations, three-phase imbalance, and distributed power supply access.

[0006] S2. Based on the geographical location of the node to be identified and the preset connection rules, construct a set of topology assumptions that includes user access points, phases and branch connection relationships, and establish a corresponding topology constraint space for each assumed topology structure in the set of topology assumptions; Specifically, most existing topology identification methods rely on statistical correlation or voltage similarity for inference, lacking physical structural constraints. This easily leads to the retention of a large number of combinations in candidate structures that do not conform to actual power supply logic, resulting in search space explosion or misidentification. This step first constructs a set of topology hypotheses by combining node geographical locations and preset physical connection rules. At the spatial level, candidate access points are constrained by physical connection radius, tower path, and known trunk line direction. At the logical level, a combination structure is formed by phase affiliation and branch hierarchy. Then, a corresponding topology constraint space is established for each hypothetical structure, so that each set of hypotheses is not just a simple enumeration of connection relationships, but a physically computable structure with a complete node-branch association matrix and parent-child hierarchy. Compared with the unconstrained exhaustive search method, this step significantly compresses the hypothetical scale through spatial constraints and graph theory rules pre-screening, while ensuring that each retained topology structure meets the basic power supply characteristics of a radial distribution network. This provides a strict, standardized, and computable structural foundation for subsequent power flow consistency verification, thereby effectively reducing computational complexity while ensuring coverage of all reasonable possibilities.

[0007] S3. Within the topological constraint space, the power flow equations are constructed using the acquired measurement data set and the forward-backward substitution method. Power flow calculations are performed on each assumed topology to obtain the calculated voltage values ​​of each node and the calculated current values ​​of each branch. Specifically, traditional topology identification often uses static voltage difference comparison or equivalent impedance back-calculation, without incorporating the complete power flow physical equations into the verification process, resulting in a lack of electrical consistency verification. This step constructs a complete distribution network power flow equation system for each hypothetical topology within the established topology constraint space, and uses the forward-backward substitution method for iterative solution, ensuring that node voltages and branch currents simultaneously satisfy the power balance equation and line voltage drop equation. Compared to methods based on linearized models or DC power flow approximations, this step uses a forward-backward substitution algorithm suitable for low-voltage, high R / X ratio networks, which can accurately reflect the voltage change law under three-phase load imbalance and line resistance-dominated characteristics. By iteratively updating node voltages until the convergence condition is met, the calculation results truly conform to the physical operating law, thereby transforming each topology hypothesis into a verifiable electrical state solution. When a hypothetical structure fails to converge or produces abnormal voltage distributions during the iteration process, it can be naturally excluded.

[0008] S4. Establish an optimization model with the goal of minimizing power flow consistency deviation. By comparing the deviation between the calculated voltage value and the measured voltage value, solve for the minimum topology from the set of topology assumptions. Use the connection relationship corresponding to the minimum topology as the actual user access point, phase and branch connection relationship. Specifically, existing technologies often rely on the principle of minimizing single-moment error or empirical thresholds for topology determination, lacking a full-time consistency optimization framework and being susceptible to instantaneous load fluctuations. This step constructs an optimization model with the goal of minimizing power flow consistency deviation, uniformly measuring the difference between the calculated and measured voltages of each node, and performing a global comparison among all hypothetical topologies. The actual topology is determined by minimizing the objective function. Compared to simple error sorting methods, this step incorporates voltage deviation into a unified optimization model framework, making topology selection a clear mathematical optimization problem. It can also be extended to a multi-moment cumulative form, improving the ability to resist short-term disturbances. By traversing and calculating all candidate structures under the same evaluation index, the result is guaranteed to have global optimality rather than local optimality. The final output connection relationship satisfies both physical power flow balance and is statistically most consistent with the actual measured data, thereby achieving accurate identification of the actual user access point, phase, and branch connection relationship from both data consistency and electrical rationality dimensions.

[0009] The beneficial effects of the invention are: This invention couples node measurement data with network physical operation patterns for analysis, enabling a consistency assessment of the topology while meeting electrical operation constraints. This effectively avoids misjudgments based solely on statistical correlation. Furthermore, by comprehensively evaluating measurement results from multiple time points, it improves the stability of the identification results under load fluctuation conditions. This invention achieves accurate identification of user access points, phases, and branch connections without relying on manual verification, significantly improving the authenticity and consistency of low-voltage distribution network topology data and providing a reliable foundation for refined operation and maintenance and line loss analysis. Attached Figure Description

[0010] Figure 1 This is a flowchart of the low-voltage power grid real topology identification method based on power flow constraints proposed in this embodiment of the invention. Detailed Implementation

[0011] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, and not all of them. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0013] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0014] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or machine that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or machine. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or machine that includes said element.

[0015] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0016] Example 1 Among them, such as Figure 1 A method for identifying the true topology of a low-voltage power grid based on power flow constraints, characterized by the following steps: S1. Perform synchronous measurements on the root node and each node to be identified in the distribution network to obtain a measurement data set, wherein the measurement data set includes at least the voltage measurement value, active power measurement value and reactive power measurement value of each node; S2. Based on the geographical location of the node to be identified and the preset connection rules, construct a set of topology assumptions that includes user access points, phases and branch connection relationships, and establish a corresponding topology constraint space for each assumed topology structure in the set of topology assumptions; S3. Within the topological constraint space, the power flow equations are constructed using the acquired measurement data set and the forward-backward substitution method. Power flow calculations are performed on each assumed topology to obtain the calculated voltage values ​​of each node and the calculated current values ​​of each branch. S4. Establish an optimization model with the goal of minimizing power flow consistency deviation. By comparing the deviation between the calculated voltage value and the measured voltage value, solve for the minimum topology from the set of topology assumptions. Use the connection relationship corresponding to the minimum topology as the actual user access point, phase and branch connection relationship.

[0017] Specifically, in step S1, the method proposed in this embodiment performs network-wide synchronous sensing. Using concentrators or smart terminals deployed on the low-voltage side of the distribution transformer and smart meters on the user side, electrical characteristic data, including voltage amplitude, active power, and reactive power, are collected at a unified time point. This data constitutes the "fingerprint" information for topology identification. Further, in step S2, based on spatial location data provided by the geographic information system and combined with the physical limitations of the low-voltage power supply radius, a set of topology hypotheses containing all potential connection relationships is constructed by exhaustively enumerating the possible access point locations (such as poles and junction boxes) and possible phase assignments (A / B / C phases) of the user to be identified. A corresponding mathematical model, i.e., a topology constraint space, is established for the topology structure generated by each hypothesis. This space defines the current flow path and electrical constraints between nodes. In step S3, the system injects the collected power data into the topology constraint space of each hypothesis and runs a forward-backward power flow algorithm for simulation calculation. This algorithm simulates the voltage distribution and current flow state of the power grid under the premise that the assumed connection relationships are valid, thereby outputting the theoretical calculated voltage value of each node and the calculated current value of each branch. Step S4 constructs an optimization solution model with the objective function of minimizing the power flow consistency deviation. This involves comparing the calculated voltage value obtained from the simulation with the actual collected voltage measurement value and finding the topology structure corresponding to the smallest deviation between the two. This structure physically uniquely maps the real user access point, phase, and branch connection relationship, thereby achieving non-intrusive and accurate identification of the low-voltage power grid topology.

[0018] Furthermore, step S2 specifically includes the following sub-steps: S201. Based on the geographical coordinates of the node to be identified, calculate the Euclidean distance between the node and known potential access points in the distribution network, filter out potential access points whose distance is less than the preset physical connection radius, and form a candidate access association set; S202. Traverse the candidate access association set, and for each node to be identified, enumerate the possibility that the node to be identified is connected to different potential access points and belongs to phase A, phase B or phase C, and generate an initial set of topological hypotheses through full permutation and combination; S203. Based on the principles of graph theory, perform a validity check on each hypothetical topology in the initial set of topological hypotheses, eliminate connections containing closed loops, and ensure that each node except the root node has only a unique parent node, retaining only valid topology structures that meet the verification conditions. S204. For each valid topology, establish a node-branch association matrix describing the connection relationship between network nodes and branches, and construct a topology constraint space for forward and backward iteration calculations.

[0019] Specifically, the above implementation reduces the topology search space through spatial location constraints, uses the geometric distance between the node to be identified and potential access points as the criterion for physical connectivity, and forms a candidate access set. Further, an initial topology hypothesis set is constructed by enumerating different access points and phase combinations. Then, the tree structure characteristics in graph theory are used for legality screening, eliminating structures that violate single-source power supply and acyclic constraints, retaining only valid topology structures that satisfy the radial operation characteristics of the distribution network, and converting them into a node-branch association matrix. In specific implementation, in step S201, the system calculates the spatial Euclidean distance based on the GPS coordinates of the user to be identified and the GIS coordinates of the power grid equipment. A preset physical power supply radius (exemplarily selected as 200 meters or 300 meters) is used as a screening threshold to filter out physically inaccessible invalid access points, generating a simplified candidate access association set. Further, in step S202, a full permutation and combination operation is performed on the candidate set, simultaneously enumerating the physical access point and phase attributes for each user node to generate an initial topology hypothesis set. Step S203 introduces a graph theory algorithm to clean the validity of the generated assumptions, eliminating those structures that violate the radial operation principle of the distribution network, ensuring that the generated topology does not contain closed loops and that each node except the root node has a unique parent node. Step S204 transforms the verified valid topology into a node-branch association matrix that can be recognized by a computer.

[0020] Furthermore, in step S203, the specific process of legality verification includes the following sub-steps: S2031. Transform the assumed topology into a directed graph model and construct a node adjacency matrix, where the matrix elements represent the parent-child connection direction between nodes; S2032. Traverse each column of the node adjacency matrix and calculate the in-degree of each node except the root node. If the in-degree of any node is greater than 1, it is determined that the topology has multiple power supply or logical conflict and is marked as an invalid topology. S2033. For the topology structure that has passed the unique parent node verification, perform a path backtracking check. If any path is detected that can start from a certain node and eventually return to the node itself, it is determined that the topology structure has a closed loop and is marked as an invalid topology.

[0021] Specifically, the above implementation formalizes the assumed topology into a directed graph model, expresses the parent-child relationship between nodes through an adjacency matrix, and determines whether a node has multiple parent node conflicts by using in-degree uniqueness, thereby ensuring that the network satisfies the radial power supply characteristics. Furthermore, a path backtracking algorithm is used to detect whether there is a closed path that can return to itself, so as to avoid forming a loop structure. Since the low-voltage distribution network is a radial network under normal operating conditions, in addition, the legality verification is used to ensure that each assumed topology satisfies the basic electrical operation constraints at the structural level.

[0022] Furthermore, step S3 specifically includes the following steps: S301. Initialize the network voltage variables, set the calculated voltage value of the root node to the voltage measurement value of the root node, and initialize the calculated voltage values ​​of the other nodes to their respective voltage measurement values. S302: Calculate the load injection current at each node by combining the active power measurement value and the reactive power measurement value with the current node voltage value; S303. Based on the connection relationship of the current assumed topology, and according to the obtained load injection current, calculate the branch current of each branch by stepping back from the end point of the network to the root node. S304. Based on the branch current and combined with the branch impedance parameters, push forward step by step from the root node to the end of the network and update the calculated voltage value of each node. S305. Determine whether the difference between the calculated voltage value updated in this round and the calculated voltage value in the previous round meets the convergence condition. If not, use the updated calculated voltage value to return to step S302 until the convergence condition is met.

[0023] Specifically, the principle of the above implementation method is to establish an iterative coupling relationship between node voltage and branch current based on the forward-backward power flow algorithm applicable to radial distribution networks. The root node voltage measurement value is used as a fixed input as a boundary condition, and the voltages of other nodes are initialized to the measured voltage values ​​to improve the initial value approximation. By converting the power measurement value into the load injection current as the source term for the back-substitution calculation, the branch current is summarized step by step from the end node of the network, so that the current of each upstream branch is equal to the sum of the currents of all its downstream loads. Then, based on the branch impedance parameters, the node voltage is updated step by step from the root node to the end. The voltage update result, in turn, affects the next round of load current calculation, forming a nonlinear coupling iterative process between voltage and current. Furthermore, the iteration is terminated by an error criterion, so that the calculation result satisfies the voltage balance and power conservation constraints, thereby verifying whether the assumed topology has physical feasibility at the electrical level. Furthermore, in radial distribution networks, there is a recursive relationship between node voltage and branch current. Load current depends on node voltage, which in turn depends on branch current and impedance voltage drop. Therefore, the forward-backward substitution method can solve nonlinear power flow equations while maintaining low computational complexity. The root node voltage is fixed as a boundary condition to give the network a definite reference phase. The voltages of the remaining nodes are initialized to measured values ​​to improve the accuracy of the initial guess. In the back-substitution stage, the downstream loads are summarized to form the branch current distribution. In the forward-substitution stage, the node voltages are corrected based on the impedance voltage drop. Through multiple iterations, the stable solution that satisfies power balance is gradually approximated. If the topology is assumed to be consistent with the actual structure, the iteration results can converge stably within the error tolerance. If there are incorrect connections in the topology, the calculated voltage will have a systematic deviation from the measured value due to the incorrect power path assumption, or even non-convergence. Therefore, the power flow iteration process is both a state calculation process and a topology rationality verification process.

[0024] Furthermore, in step S302, the specific process for calculating the load injection current of a node includes the following sub-steps: S3021. Extract the active power measurement value and reactive power measurement value of the node; S3022. Calculate the load injection current of the node based on the calculated voltage value of the node in the current iteration. The specific calculation process for the load injection current is expressed as follows: ; Among them, Indicates the first The load injection current of each node, the Indicates the first The active power measurement values ​​of each node, the Indicates the first The reactive power measurement values ​​of each node, the Indicates the first Calculated voltage values ​​of each node The conjugate of, the This represents the imaginary unit. Specifically, the precise conversion of power measurement data into current state variables is achieved through the definition of complex power. In AC systems, there is a complex phasor relationship between power, voltage, and current. Complex power S is equal to the conjugate product of voltage and current. The current expression is obtained through algebraic transformation, so that active power and reactive power jointly determine the current amplitude and phase angle direction. In each iteration, the current is recalculated based on the updated voltage value, thus forming a closed-loop coupling mechanism between voltage and current.

[0025] Furthermore, in step S303, the specific process for calculating the branch current includes the following sub-steps: S3031. Based on the current assumed topology, determine the terminal node of the branch to be calculated, and the set of all sub-branches with that node as the parent node; S3032. Vector superimpose the calculated load injection current with the branch current of all sub-branches in the branch set in the current iteration step. It should be noted that the above implementation method uses the principle of current conservation to ensure that the network current distribution conforms to physical laws. In a radial structure, the current of each upstream branch is equal to the sum of the currents of all its downstream loads. By vector superimposing the load injection current with the sub-branch current, it ensures that the superposition rules of magnitude and phase angle are satisfied simultaneously in the complex domain. The back-substitution process constructs the current convergence path from the leaf node to the root node, so that the branch current calculation result can accurately reflect the load distribution structure. If the topology assumption is incorrect, the current convergence path will be incorrect, which will lead to an increase in the estimation deviation of the upstream branch current, thereby amplifying the voltage drop error in the voltage forwarding stage.

[0026] Furthermore, in step S3032, the specific calculation process for the branch current is expressed as follows: ; Among them, the Indicates the first The current in each node branch, the Indicates the first The load injection current of each node, the This represents a summation operation, where, based on the topology, a node is determined to be a terminal point, and the branch set is empty. In this case, the branch current equals the load injection current. Iteration The branch current under the step.

[0027] Furthermore, in step S304, the specific process for updating the calculated voltage value of the node is as follows: S3041. Obtain the calculated voltage value of the first node of the branch to be calculated; S3042. Based on the calculated branch current flowing through the branch, combined with the resistance and reactance of the branch, calculate the new calculated voltage value of the last node of the branch.

[0028] Furthermore, in step S3042, the specific process for calculating the new calculated voltage value of the branch terminal node is expressed as follows: ; Among them, the Indicates the first The new calculated voltage value of the terminal node of each node, the Indicates the first The current in each node branch, the The calculated voltage value of the first-end node is represented by the following: Indicates the first The branch resistance of each node, the Indicates the first The branch reactance of each node. Specifically, this step uses complex number formulas to calculate the terminal voltage, where the voltage drop is obtained by multiplying the branch current by the branch complex impedance (resistance plus imaginary reactance). Furthermore, this formula is used to reflect the combined impact of active power loss voltage drop caused by resistance and reactive power loss voltage drop caused by reactance on the node voltage amplitude and phase angle in AC distribution networks.

[0029] Furthermore, in step S305, the specific logic for determining the convergence condition is as follows: a maximum iteration count threshold and a voltage deviation tolerance threshold are preset; after each iteration, the maximum absolute error between the voltage values ​​calculated in the current iteration and the voltage values ​​calculated in the previous iteration is calculated for all nodes; if the maximum absolute error is less than the voltage deviation tolerance threshold, the convergence condition is satisfied; if the number of iterations reaches the maximum iteration count threshold and the maximum absolute error is still greater than the voltage deviation tolerance threshold, the power flow calculation of the current assumed topology is determined to be non-convergent. Specifically, the above implementation method determines whether the iteration has reached a stable state through an error control mechanism. In nonlinear power flow calculation, the voltage variable gradually tends to stabilize through repeated updates. When the maximum voltage difference between two iterations is lower than the set threshold, it indicates that the system has entered an approximate equilibrium state. If a stable error level cannot be reached within a limited number of iterations, it indicates that the topology cannot form a consistent power flow solution under the current measurement conditions. This criterion eliminates structures that do not conform to physical laws. For example, a specific implementation is given, wherein the system presets a maximum iteration threshold of 50 times and a voltage deviation tolerance threshold of 0.0001 pu. After each iteration, the system calculates the maximum absolute error between the voltage of all nodes in the network in the current round and the voltage in the previous round. If the error is less than the tolerance threshold, the power flow calculation is determined to be converged and the result is output. If the iteration count is exhausted and the error still exceeds the limit, the currently assumed topology is determined to be physically invalid (possibly due to the formation of a dead loop or voltage collapse caused by impedance anomalies), and it is directly marked as an invalid topology and will no longer participate in the subsequent optimization comparison.

[0030] Furthermore, in step S4, solving for the minimum topology specifically includes the following sub-steps: S401. Construct an objective function to characterize the degree of consistency between measurement data and computational data; S402. Traverse all topological structures in the set of topological assumptions, calculate the corresponding objective function value for each, and select the topological structure with the smallest objective function value as the recognition result.

[0031] Furthermore, the expression for the objective function is: ; Among them, the Describe the objective function. Represents a node The voltage measurement value, This represents the node calculated based on the current assumed topology. Calculate the voltage value.

[0032] Furthermore, step S402 specifically includes the following sub-steps: S4021. Select a continuous time window, acquire measurement data at multiple sampling times within the time window, calculate the objective function value at each time point, and accumulate them. S4022. Sort the topologies according to the accumulated objective function values, and select the topology with the smallest cumulative deviation as the final identification result.

[0033] Specifically, in the above implementation method, the voltage deviation corresponding to each topology is quantified into an objective function value. An error set is formed by traversing all legal topologies, and the optimal structure is determined using the minimum value selection principle. This method avoids subjective judgment, transforming topology identification into a comparable numerical problem, making the identification results deterministic and repeatable. Specifically, the sensitivity to abnormal deviations is enhanced by using a L2 norm square accumulation method. When the voltage error of some nodes is large, their squared terms will dominate in the overall objective function, making incorrect topologies significantly worse than correct structures in the overall evaluation. Simultaneously, the sum of squares form has continuous and differentiable characteristics. Furthermore, the impact of random fluctuations on the identification results is weakened by accumulating errors in the time dimension. In actual operating environments, loads exhibit randomness and measurement noise. Judging based solely on single-moment results may lead to misidentification. By selecting continuous time windows to accumulate errors from multiple moments, the accidental matching phenomenon is diluted in the time dimension, while the true topology maintains a low deviation under different load conditions. Therefore, the time window mechanism improves the stability and anti-interference capability of the identification results.

[0034] Example 2 Furthermore, as a preferred embodiment of the above embodiments, step S3 can also adopt a power-based forward-backward calculation method. This method is particularly suitable for low-voltage distribution network scenarios dominated by constant power load models, and can effectively avoid iteration failures caused by current calculation divergence when the voltage is too low using the current method. Specifically, in the execution of step S3 in this preferred embodiment, the power back-substitution process is first executed, namely step S311. This step is based on the assumption of "temporary voltage and power flow". Using the measured active and reactive power data, it calculates step by step from the end node of the network towards the root node. Its core is to accurately calculate the power loss on each branch and add it to the power at the beginning of the upstream branch. In this process, the system uses the physical parameters of the branch, resistance and reactance, combined with the apparent power flowing through the branch (composed of active and reactive power) and the currently assumed node voltage, to calculate the active line loss and reactive line loss of the branch according to the power form of Joule's law. These two loss values ​​are inversely proportional to the square of the voltage, reflecting the amplification effect of low voltage on line loss. Furthermore, based on the law of conservation of energy, the system accumulates the calculated branch losses with the load power of the terminal node of that branch and the power of the starting points of all downstream branches connected to that node, thereby obtaining the total active and reactive power required to be injected into the starting point of the next-level branch (i.e., the branch). This process is repeated level by level upwards until the total injected power of the root node is calculated, completing the preliminary estimation of the power distribution of the entire network. This method specifically includes the following steps: S311. Assuming that the voltage of each node remains constant, the power measurement values ​​in step S1 are accumulated step by step from the end of the network to the beginning to calculate the power loss of each branch and the power at the beginning. S312. Assuming that the power of each branch remains constant, using the power at the beginning obtained in step S311, calculate the voltage loss of each branch and the calculated voltage value of the node step by step from the beginning to the end of the network. S313. Verify the convergence of the calculation results. If convergence is not achieved, return to step S311.

[0035] Furthermore, the specific process for calculating the power loss of the branch and the power at the beginning is as follows: Utilizing the resistance of the branch Reactance and the active power flowing through this branch reactive power and node voltage Calculate active power line loss and reactive power line loss : ; ; The line loss is related to the load power of the downstream node, i.e., the active power of that node. and reactive power By summing the results, we can obtain the upstream branch. active power at the head end and reactive power : ; .

[0036] Furthermore, in step S312, the specific process for calculating the voltage value of the calculation node is as follows: Using the branch power obtained in step S311 , Combined with the known first-end node voltage and branch impedance parameters , The end node voltage is solved according to the following formula. : .

[0037] Specifically, this formula is based on Kirchhoff's voltage law and the complex power conservation equation for AC circuits. The system uses the known head-end node voltages. Active power flowing through the branch and reactive power and the resistance of the branch circuit. and reactance As a fixed input parameter, further, in the formula This component, in a physical sense, characterizes the longitudinal voltage drop along the line impedance during electrical energy transmission. It reflects the degree to which the loss of active power in resistance and reactive power in reactance weakens the node voltage amplitude. Furthermore, in the formula... The term is essentially the product of the square of the line impedance modulus and the square of the apparent power modulus flowing through the line. This related term is used in the equation to accurately compensate for the nonlinear errors caused by the neglected lateral voltage component and phase angle offset in the traditional approximate voltage drop formula. Furthermore, the mathematical essence of the formula is the root-finding analytical expression of the quadratic equation of power flow in the distribution network. The physical quantity accurately calculated on the right side of the equation by squaring, taking the square root, and performing algebraic addition and subtraction on the above-mentioned longitudinal voltage drop term and phase angle compensation term is essentially the square of the calculated voltage amplitude at the end node to be determined, i.e. Furthermore, after obtaining the algebraic analytical solution, the system performs a simple square root operation on it to extract the new calculated voltage value of the terminal node without error. .

[0038] It should be noted that after completing the power back-substitution, this preferred embodiment immediately executes the voltage forward-pushing process, i.e., step S312. This step is based on the assumption of "temporary power and voltage drop," and uses the power at the beginning of each branch calculated in step S311 to update the voltage amplitude of each node step by step from the root node with known voltage towards the end of the network. In this process, in order to accurately solve the nonlinear circuit equations, the system adopts an accurate voltage calculation formula derived from the longitudinal and transverse components of voltage drop. This formula uses the known voltage at the beginning node, the branch impedance parameters, and the power flow through the branch to directly analyze the value of the voltage at the end node by solving an algebraic equation containing the voltage square term. This formula not only considers the active voltage drop across the resistor and the reactive voltage drop across the reactance, but also covers the nonlinear effects caused by the change in voltage phase angle, ensuring the accuracy of voltage calculation under long-distance power supply or heavy load lines. Furthermore, step S313 serves as the control loop for the iteration, monitoring the convergence of the voltage of all network nodes. If the deviation between the voltage distribution calculated in this round and the previous round exceeds the allowable range, the system will use the newly calculated voltage value to update the network state and trigger step S311 again to perform the next round of power loss calculation until the system state stabilizes, thereby obtaining the accurate power flow distribution result under the assumed topology.

[0039] Example 3 Furthermore, as a preferred embodiment of the above-described embodiment one, an implementation scenario for a low-voltage power grid real topology identification method based on power flow constraints is provided. This scheme is specifically implemented in a real wiring verification scenario of a suburban mixed low-voltage distribution area. The application object is a 0.4kV three-phase four-wire low-voltage distribution area under a 10kV distribution line. The system includes one 400kVA distribution transformer with a rated line voltage of 400V and a phase voltage of 230V on the low-voltage side. The low-voltage side of the transformer serves as the root node. There are 68 user nodes, 17 main branches, and several branch lines within the distribution area, with a total line length of approximately 2.3. The network spans km, with conductors of mixed JKLYJ-70 and JKLYJ-50 types. Typical branch resistance parameters range from 0.18Ω / km to 0.52Ω / km, and reactance parameters range from 0.08Ω / km to 0.31Ω / km. Single branch lengths range from 35m to 210m. The theoretical network structure is a radial tree structure, but historical records contain discrepancies. In actual operation, issues exist such as unauthorized connections by users, outdated records after branch modifications, and mixed phase connections. Approximately 6-10 nodes to be identified have uncertain access points or phases. The system is equipped with synchronous measurement devices. At the low-voltage side of the transformer and all user smart meters, the measurement sampling period is 1 minute, with a synchronization error of less than 20ms. Seven consecutive days of operating data are used as the identification time window. The typical active power measurement range for a single node is 0.3kW~8.5kW, the reactive power measurement range is 0.1kVar~3.2kVar, the power factor is distributed between 0.82 and 0.99, the node voltage measurement fluctuation range is 210V~238V, and the line loss rate is approximately 4.2%. During the topology hypothesis generation stage, the physical connection radius is set to 80m based on GIS coordinates, using an Euclidean distance sieve. A candidate access set is selected, with an average of 2-3 potential access points per node to be identified. Considering the three-phase attribution probability, the number of topology combinations per node is 6-9. The overall initial topology assumption size is approximately 3^6 × 2^4. After graph theory validity verification, the effective topology size is compressed to approximately 120-350. Power flow calculation adopts the forward-backward substitution method, with the initial voltage set as a measured value, the convergence threshold set as 1 × 10^-4 p.u., and the maximum number of iterations set as 50. Under normal operating conditions, convergence can be achieved in 8-15 iterations. Branch impedances are used in the calculation in complex form, and node load injection current is calculated according to... The calculation of branch currents uses the method where the parent node current equals the vector sum of the load current of this node and the currents of all its sub-branches. Node voltages are calculated according to... Update: During the objective function construction phase, a continuous 72-hour time window was selected, totaling 4320 sampling times. For each assumed topology, the sum of squared voltage deviations was calculated at each time point and accumulated over time. The objective function is expressed as follows: The topology with the smallest cumulative deviation is determined to be the true user access point, true phase, and true branch connection relationship. Through actual engineering verification, when there are 3 users with incorrect phases and 2 users with incorrect branch connections, this method can accurately locate the true topology in the entire set of assumptions. The root mean square error of voltage fitting of the final identification result can be controlled within 0.35V, which is about 78% lower than the original file topology. It can be directly used for transformer area line loss analysis, phase balance optimization, and refined load management.

[0040] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for identifying the true topology of a low-voltage power grid based on power flow constraints, characterized in that, Includes the following steps: S1. Perform synchronous measurements on the root node and each node to be identified in the distribution network to obtain a measurement data set, wherein the measurement data set includes at least the voltage measurement value, active power measurement value and reactive power measurement value of each node; S2. Based on the geographical location of the node to be identified and the preset connection rules, construct a set of topology assumptions that includes user access points, phases and branch connection relationships, and establish a corresponding topology constraint space for each assumed topology structure in the set of topology assumptions; S3. Within the topological constraint space, the power flow equations are constructed using the acquired measurement data set and the forward-backward substitution method. Power flow calculations are performed on each assumed topology to obtain the calculated voltage values ​​of each node and the calculated current values ​​of each branch. S4. Establish an optimization model with the goal of minimizing power flow consistency deviation. By comparing the deviation between the calculated voltage value and the measured voltage value, solve for the minimum topology from the set of topology assumptions. Use the connection relationship corresponding to the minimum topology as the actual user access point, phase and branch connection relationship. Step S2 specifically includes the following sub-steps: S201. Based on the geographical coordinates of the node to be identified, calculate the Euclidean distance between the node and known potential access points in the distribution network, filter out potential access points whose distance is less than the preset physical connection radius, and form a candidate access association set; S202. Traverse the candidate access association set, and for each node to be identified, enumerate the possibility that the node to be identified is connected to different potential access points and belongs to phase A, phase B or phase C, and generate an initial set of topological hypotheses through full permutation and combination; S203. Based on the principles of graph theory, perform a validity check on each hypothetical topology in the initial set of topological hypotheses, eliminate connections containing closed loops, and ensure that each node except the root node has only a unique parent node, retaining only valid topology structures that meet the verification conditions. S204. For each valid topology, establish a node-branch association matrix describing the connection relationship between network nodes and branches, and construct a topology constraint space for forward and backward iteration calculations. In step S203, the specific process for legality verification includes the following sub-steps: S2031. Transform the assumed topology into a directed graph model and construct a node adjacency matrix, where the matrix elements represent the parent-child connection direction between nodes; S2032. Traverse each column of the node adjacency matrix and calculate the in-degree of each node except the root node. If the in-degree of any node is greater than 1, it is determined that the topology has multiple power supply or logical conflict and is marked as an invalid topology. S2033. For the topology that has passed the unique parent node verification, perform a path backtracking check. If any path is detected that can start from a certain node and eventually return to the node itself, it is determined that the topology has a closed loop and is marked as an invalid topology.

2. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 1, characterized in that, Step S3 specifically includes the following steps: S301. Initialize the network voltage variables, set the calculated voltage value of the root node to the voltage measurement value of the root node, and initialize the calculated voltage values ​​of the other nodes to their respective voltage measurement values. S302: Calculate the load injection current at each node by combining the active power measurement value and the reactive power measurement value with the current node voltage value; S303. Based on the connection relationship of the current assumed topology, and according to the obtained load injection current, calculate the branch current of each branch by stepping back from the end point of the network to the root node. S304. Based on the branch current and combined with the branch impedance parameters, push forward step by step from the root node to the end of the network and update the calculated voltage value of each node. S305. Determine whether the difference between the calculated voltage value updated in this round and the calculated voltage value in the previous round meets the convergence condition. If not, use the updated calculated voltage value to return to step S302 until the convergence condition is met.

3. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 2, characterized in that, In step S302, the specific process for calculating the load injection current of a node includes the following sub-steps: S3021. Extract the active power measurement value and reactive power measurement value of the node; S3022. Calculate the load injection current of the node based on the calculated voltage value of the node in the current iteration. The specific calculation process for the load injection current is expressed as follows: ； Among them, Indicates the first The load injection current of each node, the Indicates the first The active power measurement values ​​of each node, the Indicates the first The reactive power measurement values ​​of each node, the Indicates the first Calculated voltage values ​​of each node The conjugate of, the It represents the imaginary unit.

4. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 2, characterized in that, In step S303, the specific process for calculating the branch current includes the following sub-steps: S3031. Based on the current assumed topology, determine the terminal node of the branch to be calculated, and the set of all child branches with that node as the parent node; S3032. The calculated load injection current is vector-superimposed with the branch current of all sub-branches in the branch set at the current iteration step.

5. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 4, characterized in that, In step S3032, the specific calculation process for the branch current is as follows: ； Among them, the Indicates the first The current in each node branch, the Indicates the first The load injection current of each node, the This represents a summation operation, where, based on the topology, a node is determined to be a terminal point, and the branch set is empty. In this case, the branch current equals the load injection current. Iteration The branch current under the step.

6. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 2, characterized in that, In step S304, the specific process for updating the calculated voltage value of the node is as follows: S3041. Obtain the calculated voltage value of the first node of the branch to be calculated; S3042. Based on the calculated branch current flowing through the branch, and combined with the resistance and reactance of the branch, calculate the new calculated voltage value of the terminal node of the branch.

7. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 6, characterized in that, In step S3042, the specific process for calculating the new calculated voltage value of the branch terminal node is expressed as follows: ； Among them, the Indicates the first The new calculated voltage value of the terminal node of each node, the Indicates the first The current in each node branch, the The calculated voltage value of the first-end node is represented by the following: Indicates the first The branch resistance of each node, the Indicates the first Branch reactance of each node.

8. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 2, characterized in that, In step S305, the specific logic for judging the convergence condition is as follows: a maximum iteration number threshold and a voltage deviation tolerance threshold are preset; after each iteration, the maximum absolute error between the voltage value calculated in this round and the voltage value calculated in the previous round is calculated for all nodes. If the maximum absolute error is less than the voltage deviation tolerance threshold, then the convergence condition is satisfied. If the number of iterations reaches the maximum iteration threshold and the maximum absolute error is still greater than the voltage deviation tolerance threshold, then the power flow calculation of the current assumed topology is determined to be non-convergent.

9. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 1, characterized in that, Step S4, in which the minimum topology is solved, specifically includes the following sub-steps: S401. Construct an objective function to characterize the degree of consistency between measurement data and computational data; S402. Traverse all topological structures in the set of topological assumptions, calculate the corresponding objective function value for each, and select the topological structure with the smallest objective function value as the recognition result.

10. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 9, characterized in that, The objective function is expressed as follows: ； Among them, the Describe the objective function. Represents a node The voltage measurement value, This represents the node calculated based on the current assumed topology. Calculate the voltage value.

11. The method for identifying the true topology of a low-voltage power grid based on power flow constraints as described in claim 9, characterized in that, Step S402 specifically includes the following sub-steps: S4021. Select a continuous time window, acquire measurement data at multiple sampling times within the time window, calculate the objective function value at each time point, and accumulate them. S4022. Sort the topologies according to the accumulated objective function values, and select the topology with the smallest cumulative deviation as the final identification result.

Images