Data-driven power distribution network topology and line parameter identification method

Abstract

The invention relates to a data-driven power distribution network topology and line parameter identification method, which comprises the following steps of: 1, constructing a linear power flow model, obtaining an initial estimation value of a network parameter of a power distribution network based on an initial identification method of linear regression, and further obtaining an initial identification result of a power distribution network admittance matrix; and step 2, introducing the voltage phase angle change between nodes, and correcting the initial identification result of the admittance matrix of the power distribution network obtained based on the step 1 through an accurate power flow iteration model to obtain a final topology identification result. According to the method, the limitation of a traditional method is broken through, and topology and parameter estimation completely without phase angle measurement is realized through a strategy of combining linear regression and iterative calculation under the condition that the voltage phase angle and topological information do not need to be known in advance.

Description

Technical Field

[0001] This invention belongs to the field of distribution network topology identification technology, and relates to a method for identifying distribution network topology and line parameters, particularly a data-driven method for identifying distribution network topology and line parameters. Background Technology

[0002] The distribution network is responsible for receiving electrical energy from the transmission network or regional power plants and distributing it to users locally or tiered according to voltage levels through distribution facilities. As the core bridge connecting the transmission network and power users, its operational status directly affects the reliability and economy of electricity consumption. In recent years, with the widespread integration of renewable energy and distributed generation equipment, the operational complexity of the distribution system has increased significantly, placing higher demands on the efficiency and precision of operation control. Topology connectivity and line parameters are crucial foundations for supporting the refined planning, intelligent operation, and coordinated control of the distribution network, and are widely used in power flow calculation, optimal scheduling, demand-side response, and system resilience enhancement. In transmission systems, topology information can generally be obtained through periodic testing and verification, and is usually equipped with a mature state estimation system. However, due to the large number of feeders and switches and limited monitoring point coverage in the distribution network, most topology and line parameters have errors or are incompletely recorded, posing significant challenges to their accurate acquisition.

[0003] Distribution network topology identification, line parameter estimation, and voltage phase angle recovery are fundamental prerequisites for realizing advanced applications such as active power distribution and fault location. Their accuracy directly determines the safety and economy of power grid operation.

[0004] However, existing data-driven methods for identifying distribution network topology and line parameters still have significant limitations and are difficult to meet actual engineering needs: (1) The measurement dependence is too high. Most methods rely on synchronous phasor measurement units (PMU) to obtain voltage phase angle data, or require the configuration of a large number of current transformers and other special equipment, which leads to a sharp increase in deployment costs. Moreover, the coverage of PMU at the end nodes of the distribution network is extremely low, making it difficult to promote on a large scale. Some methods that rely on smart meter data are limited to only being able to estimate the topology or parameters, and cannot take into account the collaborative solution of multiple tasks.

[0005] (2) Insufficient robustness and practicality. Existing data-driven methods mostly assume that the measurement data is noise-free or has a low noise level. However, the data of smart meters in actual distribution networks are easily affected by communication interference and equipment errors, which leads to a significant decrease in the estimation accuracy of the algorithm in noisy environments. At the same time, although model-driven methods rely on physical constraints such as power flow equations to ensure stability, they are sensitive to initial values. If there is a lack of prior information on voltage phase angle, they are prone to getting trapped in local optima and are difficult to adapt to complex distribution network structures containing ring networks.

[0006] (3) The lack of a multi-objective collaborative solution mechanism means that existing studies often separate topology identification and parameter estimation into independent tasks and execute them step by step, ignoring the strong coupling relationship between the two. Topology error will be transmitted to the parameter estimation result, and parameter deviation will affect the correct topology structure, forming an "error accumulation" effect, which will ultimately affect the overall estimation performance.

[0007] The aforementioned problems make it difficult for existing methods to achieve efficient and accurate estimation of topology, parameters, and phase angles in actual distribution networks that are "without special measurement equipment and subject to noise interference".

[0008] To address the aforementioned technical problems, this invention proposes an integrated data-driven method for identifying distribution network topology and line parameters that is low in measurement dependence and highly robust.

[0009] A search revealed no publicly available literature of the same or similar prior art as this invention. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention proposes a data-driven method for identifying distribution network topology and line parameters. Using node voltage amplitude, injected active power, and reactive power as the basic dataset, a parameter identification model is constructed. First, a linear power flow model is established, ignoring voltage phase angles. Initial identification results of the distribution network admittance matrix are quickly obtained through linear regression and denoising. Based on this, pseudo-power flow calculations and the Adam algorithm are alternately performed to refine the node admittance matrix, ultimately yielding accurate distribution network topology and line parameters.

[0011] The above-mentioned objective of this invention is achieved through the following technical solution: A data-driven method for identifying distribution network topology and line parameters includes the following steps: Step 1: Construct a linear power flow model, obtain preliminary estimates of the distribution network parameters based on the initial identification method of linear regression, and then obtain the initial identification results of the distribution network admittance matrix. Step 2: Introduce the voltage phase angle change between nodes, and correct the initial identification result of the distribution network admittance matrix obtained in Step 1 through an accurate power flow iteration model to obtain the final topology identification result.

[0012] Furthermore, the specific steps of step 1 include: (1) Construct a linear power flow model. By constructing a simplified power flow equation that ignores the influence of phase angle, the node power-voltage magnitude relationship is expressed as a linear regression problem. (2) Based on the linear power flow model constructed in sub-step (1), design an initial identification method based on linear regression, and then obtain preliminary estimates of the distribution network parameters. Use voltage and power measurement data to iteratively calculate the admittance matrix, set residual thresholds to screen out non-existent branches, and apply matrix symmetry constraints to obtain the initial identification results of the distribution network admittance matrix.

[0013] Moreover, the specific steps of step 1 (1) include: For the distribution network, establish the power flow equations in polar coordinates: (1) In the formula: p i , q i and v i Representing nodes respectively i The injected active power, reactive power, and voltage amplitude; G ij , B ij Representing branch roads ij Branch conductance and susceptance; θ ij express i , j The phase angle difference between the voltages at the two nodes, ; n This represents the total number of nodes.

[0014] Rewrite the above equation in matrix form, where # denotes an approximation: (2) (3) In the formula: It is a voltage magnitude vector, without phase angle information; ; ; , Represented as: (4) (5) in, , .

[0015] Based on the characteristics of the power distribution network, equations (4) and (5) can be approximated as follows: (6) (7) This leads to the construction of a linear power flow model; If it exists, it contains P , Q , V Information M 0 For group measurement data, the linear regression method can be used to estimate... G ij and B ij Then formulas (2) and (3) can be rewritten as: (8) (9) Moreover, the specific steps of step 1, step (2) include: Based on the linear power flow model constructed in sub-step (1), an initial identification method based on linear regression was designed. First, the least squares method was used to solve equations (8) and (9) to obtain preliminary estimates of the distribution network parameters, and then the admittance matrix was obtained. and The expression is: (10) (11) The admittance matrix must maintain symmetry: (12) (13) The diagonal element value in the matrix is ​​equal to the negative of the sum of the conductances of all branches connected to that node, calculated as follows: (14) Branch weights Defined as and The ratio: (15) If the weight of a certain branch Less than the set threshold If so, the branch is removed, and the corresponding conductance value for that branch is set. The result is zero. This method can be expressed using a constrained linear least squares problem, as shown below: (16) After zeroing some elements, linear regression is performed again on each node using the measurement data of the remaining branches to update the matrix elements. This process of "calculating branch weights - threshold judgment - zeroing - re-regression" is repeated until the topology no longer changes. This result is the initial identification result of the distribution network admittance matrix.

[0016] Furthermore, the specific steps of step 2 include: (1) First, the voltage phase angle change between nodes is introduced, and the voltage phase angle estimate corresponding to the power measurement is obtained by pseudo power flow calculation; (2) Based on the voltage phase angle estimate corresponding to the power measurement obtained in step (1), combined with the measurement data and phase angle information, the Adam optimization algorithm and noise reduction processing are used to correct the initial identification result of the distribution network admittance matrix obtained in step 1, so as to ensure the identification accuracy and calculation stability. The iteration ends after the convergence condition is met, and the final topology identification result is obtained.

[0017] Moreover, the specific steps of step 2 (1) include: The admittance estimation matrix obtained from the initial identification is used as an initial value and then corrected using an accurate power flow iterative model. The admittance is obtained from the preliminary estimation result in step 1, and the phase angle is obtained from pseudo-power flow calculation.

[0018] Constructing the Adam optimization model: (17) Calculate the loss function with respect to variables g , b , gradient: (18) Update parameters using the Adam algorithm.

[0019] Update learning rate: (19) In the formula, , Set the upper and lower bounds of the learning rate to be respectively; Total number of iterations per cycle; Show the current iteration number t Divide by period length T The remainder obtained after maxing out.

[0020] Calculate the first-order momentum estimate : (20) Calculate the second-order momentum estimate : (twenty one) Deviation correction for calculating first-order momentum: (twenty two) Correction for deviation in calculating second-order momentum: (twenty three) Update parameters: (twenty four) Pseudo-power flow calculation updates voltage phase angle: Assuming all nodes except the reference bus are PQ nodes, calculate the new phase angle using the currently estimated admittance. The iteration that replaced Adam Value. Repeat the iteration until convergence.

[0021] After each Adam iteration, the voltage phase angle is corrected by pseudo-power flow calculation, and finally the voltage phase angle estimate corresponding to the obtained power measurement is obtained.

[0022] Moreover, the specific steps of step 2 (2) include: ① Clear erroneous parameters during iteration: After each parameter update, the estimated conductance *g* and susceptance *b* of all branches are checked. If g If the value is less than 0, then replace it with a value that follows a uniform distribution. Positive random numbers; if b If the value is greater than 0, then replace it with a value that follows a uniform distribution. Negative random numbers.

[0023] ② Modify the topology during the iteration process: Near the end of each iteration, all branches are traversed, and branches with admittance parameters less than a set threshold are identified and eliminated. The branches are used to obtain a new topology, and the modified topology is used in subsequent iterative calculations.

[0024] If the loss function value of the current iteration L (k) Satisfy | L (k) -L (k-1) ∣< If the topology does not change after multiple iterations, the iteration terminates; otherwise, return to step 2 (1) to continue optimization; when the convergence condition is met, the final topology identification result is obtained.

[0025] The advantages and beneficial effects of this invention are as follows: 1. This invention proposes a data-driven method for identifying distribution network topology and line parameters, which breaks through the limitations of traditional methods. Without prior knowledge of voltage phase angle and topology information, it achieves topology and parameter estimation without phase angle measurement by combining linear regression and iterative calculation.

[0026] 2. In step 1, the present invention introduces a noise filtering mechanism to effectively eliminate false connections; in step 2, it uses pseudo-power flow calculation to assist iterative convergence and adds a topology correction mechanism, so that it can still maintain high robustness and practicality when the measurement error is large. Attached Figure Description

[0027] Figure 1 is a flowchart of the processing of the present invention; Figure 2 is a topology diagram of the IEEE 33-node system of this invention; Figure 3 is a schematic diagram of the relative percentage error of the 33-node conductance g; Figure 4 is a schematic diagram of the relative percentage error of the susceptance b at node 33; Figure 5 is a topology diagram of the IEEE 123 node of the present invention; Figure 6 is a schematic diagram of the relative percentage error of the conductance g in the 123-node example; Figure 7 is a schematic diagram of the relative percentage error of susceptance b in the 123-node example; Detailed Implementation

[0028] The structure of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that these embodiments are descriptive and not limiting.

[0029] A data-driven method for identifying distribution network topology and line parameters includes the following steps: Step 1: Construct a linear power flow model and obtain preliminary estimates of the distribution network parameters based on the initial identification method of linear regression. The specific steps of step 1 include: (1) Construct a linear power flow model. By constructing a simplified power flow equation that ignores the influence of phase angle, the node power-voltage magnitude relationship is expressed as a linear regression problem. The specific steps of step 1 (1) include: For the distribution network, establish the power flow equations in polar coordinates: (1) In the formula: p i , q i and v i Representing nodes respectively iThe injected active power, reactive power, and voltage amplitude; G ij , B ij Representing branch roads ij Branch conductance and susceptance; θ ij express i , j The phase angle difference between the voltages at the two nodes, ; n This represents the total number of nodes.

[0030] Rewrite the above equation in matrix form, where # denotes an approximation: (2) (3) In the formula: It is a voltage magnitude vector, without phase angle information; ; ; , Represented as: (4) (5) in, , .

[0031] Based on the characteristics of the power distribution network, equations (4) and (5) can be approximated as follows: (6) (7) This leads to the construction of a linear power flow model; If it exists, it contains P , Q , V Information M 0 For group measurement data, the linear regression method can be used to estimate... G ij and B ij Then formulas (2) and (3) can be rewritten as: (8) (9) (2) Based on the linear power flow model constructed in sub-step (1), design an initial identification method based on linear regression, and then obtain preliminary estimates of the distribution network parameters. Use voltage and power measurement data to iteratively calculate the admittance matrix, set a residual threshold to screen out non-existent branches, and apply matrix symmetry constraints to obtain the initial identification results of the distribution network admittance matrix. The specific steps of step 1, step (2) include: Based on the linear power flow model constructed in sub-step (1), an initial identification method based on linear regression was designed. First, the least squares method was used to solve equations (8) and (9) to obtain preliminary estimates of the distribution network parameters, and then the admittance matrix was obtained. and The expression is: (10) (11) The admittance matrix must maintain symmetry: (12) (13) The diagonal element value in the matrix is ​​equal to the negative of the sum of the conductances of all branches connected to that node, calculated as follows: (14) Branch weights Defined as and The ratio: (15) If the weight of a certain branch Less than the set threshold If so, the branch is removed, and the corresponding conductance value for that branch is set. The result is zero. This method can be expressed using a constrained linear least squares problem, as shown below: (16) After zeroing some elements, linear regression is performed again on each node using the measurement data of the remaining branches to update the matrix elements. This process of "calculating branch weights - threshold judgment - zeroing - re-regression" is repeated until the topology no longer changes. This result is the initial identification result of the distribution network admittance matrix.

[0032] The working principle of step 1 is as follows: Step 1: Initial Identification Based on Linear Regression 1.1 Construction of Linear Power Flow Model In power distribution networks, nonlinear power flow equations easily lead to nonconvex optimization problems, posing convergence challenges to conventional solution methods. Therefore, linearizing the power flow equations can effectively improve the convergence and robustness of the algorithm. In this stage, a linear approximation of the power flow equations is implemented. By constructing a simplified power flow equation that ignores the influence of phase angle, the node power-voltage magnitude relationship is expressed as a linear regression problem. The admittance matrix is ​​iteratively calculated using voltage and power measurement data, and a residual threshold is set to filter out non-existent branches, while matrix symmetry constraints are applied. Although this stage introduces biases in parameter estimation due to model simplification, it can quickly reduce the set of branches to be optimized, providing feasible initial values ​​for subsequent calculations.

[0033] For distribution networks, the power flow equations in polar coordinates are: (1) In the formula: p i , q i and v i Representing nodes respectively i The injected active power, reactive power, and voltage amplitude; G ij , B ij Representing branch roads ij Branch conductance and susceptance; θ ij express i , j The phase angle difference between the voltages at the two nodes, ; n This represents the total number of nodes.

[0034] Rewrite the above equation in matrix form, where # denotes an approximation: (2) (3) In the formula: It is a voltage magnitude vector, without phase angle information; ; ; , Represented as: (4) (5) Unlike transmission networks, the voltage amplitude at distribution network nodes is stable at 1. pu Around 1, the branch resistance / reactance ratio is relatively large, generally close to or greater than 1, and the voltage phase angle difference between the nodes at both ends of the branch is large. Smaller, usually Therefore, there is , .

[0035] Based on the characteristics of the power distribution network, equations (4) and (5) can be approximated as follows: (6) (7) We obtain the linearized power flow equations, at which point even θ ij It is large, but it can still provide a good initial value for subsequent accurate identification.

[0036] If it exists, it contains P , Q , V Information M 0 For group measurement data, the linear regression method can be used to estimate... G ij and B ij Then formulas (2) and (3) can be rewritten as: (8) (9) 1.2 Initial Identification Algorithm Design Based on the linear power flow model constructed in section 1.1, an initial identification method based on linear regression was designed. The specific process is as follows: First, the least squares method is used to solve equations (8) and (9) to obtain preliminary estimates of the distribution network parameters. Based on this, the admittance matrix is ​​obtained. and The expression is: (10) (11) Due to the reciprocity of admittance in a power grid, i.e., the admittance matrix of the power grid is based on the interactions between nodes, from the nodes... i To the node j Power flow and from node j To the node i The power flows are numerically equal, therefore the admittance matrix must remain symmetric.

[0037] (12) (13) Because the measured data itself contains instrument measurement errors, and an approximate linear model is used to represent the system power flow equations, the values ​​of conductance and susceptance in the estimated admittance matrix contain significant noise components. To eliminate these inaccurate branches, the estimated admittance matrix needs to be denoised. Traditional denoising methods reduce noise by removing terms below a certain fixed threshold; however, the lack of prior information on conductance and susceptance during branch parameter processing makes setting the upper limit of the threshold difficult. Furthermore, for nodes, the number of output branches is usually lower than the maximum number of connections. Based on this characteristic, a weighted ratio of branch admittance to node self-admittance is proposed. This serves as a judgment, thereby completing the noise processing of the admittance matrix and improving the accuracy of system analysis.

[0038] As can be seen from circuit principles, the node conductance matrix in an electrical system has the following characteristics: the diagonal element value in the matrix is ​​equal to the negative of the sum of the conductances of all branches connected to that node, and its calculation formula is: (14) Branch weights Defined as and The ratio: (15) If the weight of a certain branch Less than the set threshold If so, the branch is removed, and the corresponding conductance value for that branch is set. The result is zero. This method can be expressed using a constrained linear least squares problem, as shown below: (16) Step 2: Introduce the voltage phase angle change between nodes, and correct the initial identification result of the distribution network admittance matrix obtained in Step 1 through an accurate power flow iteration model to obtain the final topology identification result.

[0039] The specific steps of step 2 include: (1) First, the voltage phase angle change between nodes is introduced, and the voltage phase angle estimate corresponding to the power measurement is obtained by pseudo power flow calculation; The specific steps of step 2, step (1) include: The admittance estimation matrix obtained from the initial identification is used as an initial value and then corrected using an accurate power flow iterative model. The admittance is obtained from the preliminary estimation result in step 1, and the phase angle is obtained from pseudo-power flow calculation.

[0040] Constructing the Adam optimization model: (17) Calculate the loss function with respect to variablesg , b , gradient: (18) Update parameters using the Adam algorithm.

[0041] Update learning rate: (19) In the formula, , Set the upper and lower bounds of the learning rate to be respectively; Total number of iterations per cycle; Show the current iteration number t Divide by period length T The remainder obtained after maxing out.

[0042] Calculate the first-order momentum estimate : (20) Calculate the second-order momentum estimate : (twenty one) Deviation correction for calculating first-order momentum: (twenty two) Correction for deviation in calculating second-order momentum: (twenty three) Update parameters: (twenty four) Pseudo-power flow calculation updates voltage phase angle: Assuming all nodes except the reference bus are PQ nodes, calculate the new phase angle using the currently estimated admittance. The iteration that replaced Adam Value. Repeat the iteration until convergence.

[0043] After each Adam iteration, the voltage phase angle is corrected by pseudo-power flow calculation, and finally the voltage phase angle estimate corresponding to the obtained power measurement is obtained.

[0044] (2) Based on the voltage phase angle estimate corresponding to the power measurement obtained in step (1), combined with the measurement data and phase angle information, the Adam (Adaptive Moment Estimation) optimization algorithm and noise reduction processing are used to correct the initial identification result of the distribution network admittance matrix obtained in step 1, so as to ensure the identification accuracy and calculation stability. The iteration ends after the convergence condition is met, and the final topology identification result is obtained. The specific steps of step 2 (2) include: Clear erroneous parameters in iteration After each parameter update, the estimated conductance *g* and susceptance *b* of all branches are checked. If g If the value is less than 0, then replace it with a value that follows a uniform distribution. Positive random numbers; if b If the value is greater than 0, then replace it with a value that follows a uniform distribution. Negative random numbers.

[0045] Modify the topology during the iteration process Near the end of each iteration, all branches are traversed, and branches with admittance parameters less than a set threshold are identified and eliminated. The branches are used to obtain a new topology, and the modified topology is used in subsequent iterative calculations.

[0046] If the loss function value of the current iteration L (k) Satisfy | L (k) -L (k-1) ∣< If the topology does not change after multiple iterations, the iteration terminates; otherwise, return to step 2 (1) to continue optimization; when the convergence condition is met, the final topology identification result is obtained.

[0047] The working principle of step 2 is as follows: Step 2: Precise Identification Based on Iterative Optimization In the initial identification and establishment of the linear regression model, the influence of voltage phase angle on the power flow equation was ignored, resulting in some errors in the established linear regression model. Therefore, in this stage, the voltage phase angle variation between nodes is introduced, and the admittance estimation matrix obtained from the initial identification is used as an initial value to correct the model through an accurate power flow iterative model, thereby improving the accuracy of the identification results.

[0048] In the precise identification stage, both branch admittance parameters and node voltage phase angles are used as variables to be optimized. However, considering that optimizing all variables simultaneously may reduce the computational efficiency of the algorithm, or even lead to difficulties in iterative convergence. To enhance the robustness of the optimization algorithm, this stage uses branch admittance as the core optimization variable, and achieves efficient solution by alternately updating voltage phase angle information and branch admittance parameters. The specific implementation process is as follows: First, the voltage phase angle estimate corresponding to the power measurement is obtained through pseudo-power flow calculation; then, combining the measurement data and phase angle information, the admittance matrix is ​​corrected using the Adam (Adaptive Moment Estimation) optimization algorithm and noise reduction processing to ensure identification accuracy and computational stability, until the convergence condition is met and the iteration ends. The core of the Adam algorithm lies in calculating the exponential moving average of the first moment (mean) and second moment information (uncentered variance) of the gradient, and using the estimates of these moments to adjust the learning rate of each parameter, which significantly improves the stability and efficiency of the optimization process.

[0049] 2.1 Establishing an Adam-based optimization model As an optimization method that integrates momentum mechanisms and adaptive learning rate adjustment, the Adam algorithm has significant advantages in handling non-convex optimization problems. Furthermore, the algorithm exhibits good robustness to the selection of initial parameter values, which can improve the model's convergence speed and thus enhance the accuracy of topology parameter identification.

[0050] node voltage amplitude v Active power p and reactive power q As a known quantity, to be estimated g , b , As an optimization variable, g , b The initial values ​​are based on the preliminary estimates of the line parameters mentioned earlier. The initial value is obtained through power flow calculation, and the cosine annealing algorithm is used to adjust Adam's learning rate.

[0051] Cosine annealing is a method for dynamically adjusting the learning rate. By periodically changing the learning rate, it helps the optimization algorithm escape local minima and accelerate convergence. Its core idea is to adjust the learning rate between preset upper and lower bounds according to the pattern of a cosine function.

[0052] Constructing the Adam optimization model: (17) Calculate the loss function with respect to variables g , b , gradient: (18) The Adam algorithm uses first-order and second-order moment estimation combined with an adaptive learning rate to optimize parameters more effectively. The specific steps are as follows: Update learning rate: (19) In the formula, , Set the upper and lower bounds of the learning rate to be respectively; Total number of iterations per cycle; Show the current iteration number t Divide by period length T The remainder obtained after maxing out.

[0053] Calculate the first-order momentum estimate : (20) Calculate the second-order momentum estimate : (twenty one) Deviation correction for calculating first-order momentum: (twenty two) Correction for deviation in calculating second-order momentum: (twenty three) Update parameters: (twenty four) To further improve the convergence speed, after each Adam iteration, we use pseudo-power flow calculation to correct the voltage phase angle: (1) Assume that all busbars except the reference busbar are PQ Nodes, using the current estimate g、b Calculate the new voltage phase angle.

[0054] (2) The new result obtained by calculation θ Replace Adam after iteration θ value.

[0055] (3) Continue the next round of iteration optimization until the convergence condition is met.

[0056] The following are the convergence conditions: (1) The loss function converges, that is It drops to the threshold.

[0057] (2) The parameter update magnitude is small enough, i.e. and .

[0058] (3) Reaching the maximum number of iterations .

[0059] 2.2 Topology Correction Mechanism In this stage, a topology correction mechanism is introduced to overcome the problem of incorrect estimation caused by getting trapped in local optima during the iteration process.

[0060] (1) Eliminate errors in iteration g and b During the iterative process of optimizing the model, it is possible to get trapped in local optima, resulting in negative conductance and positive susceptance. This situation does not exist in real-world networks. To escape local optima, noise perturbations need to be added to the model to adjust these erroneous parameters.

[0061] In gradient descent algorithms, introducing noise perturbation is a common strategy to avoid getting trapped in local optima. This method adds a small parameter perturbation during the iteration process: when the detected conductance value is negative, it is modified to follow a uniform distribution. Smaller positive random values; when the susceptance is positive, the value follows a uniform distribution. Smaller negative random values.

[0062] (2) Modify the topology during the iteration process During iterative optimization, some branches with sufficiently small admittances may be incorrectly identified as correct branches by the model. To further correct the topology, at the end of each iteration, all branches are traversed to identify and remove those with admittance parameters less than a set threshold. The branches are identified, resulting in a new topology, which is then used in subsequent iterative calculations. This mechanism of embedding topology verification during the convergence phase effectively improves the accuracy of network structure identification.

[0063] The innovation of this invention lies in: The core innovation of this invention lies in proposing a distribution network topology identification and parameter estimation method that is free from voltage phase angle and relies solely on smart meter data. Through a two-step identification framework, it achieves high-precision, robust, and real-time feasible estimation capabilities, providing a practical solution for state awareness and optimized operation of non-PMU distribution networks.

[0064] Example 1 This invention uses IEEE 33-node and IEEE 123-node distribution network examples to verify the effectiveness of the proposed topology and line parameter identification method. The IEEE 33-node distribution network topology is as follows: Figure 2As shown, the system contains 33 nodes and 37 possible branches (32 transmission lines and 5 connection lines within the system). The case study uses Monte Carlo simulations of the distribution system's operational measurement data. In the Monte Carlo simulation, the node injected power is calculated by multiplying a preset injected power by a coefficient randomly selected from a uniform distribution range. The range for both active and reactive power injection is [0.9, 1.1], with fluctuations generated by random variations. The node voltage amplitudes in the distribution network (except for slack nodes) are generated using the Matpower toolbox in MATLAB. Since the voltage at slack nodes in the distribution network is always equal to 1, there is... V 0 =1. Thus, the following has been constructed. P , Q and V Dataset. We then used 120 sets. P , Q and V The dataset is used to identify the topology and line parameters of the IEEE 33-node distribution network. After basic topology identification in step 1, the conductance ( g ) and susceptance ( b The mean absolute errors of the conductance matrix were 35.38% and 50.94%, respectively, which verifies the hypothesis that the conductance matrix... G ijS and conductance matrix G ij The differences between the two matrices are not significant, indicating a high degree of consistency between them.

[0065] In step 2, the same data as in step 1 is used for precise identification. The key parameters ξ, ζ, and... Set to 0.05, 0.01, and 1×10 respectively. -8 And. Parameter settings for the Adam algorithm. , and The values ​​are 0.01, 0.9, and 0.999 respectively. (Cosine annealing) and Set to 10 respectively -3 and 10 -5 ; Set to 15. These settings help optimize the convergence of the algorithm and improve the accuracy of the results. After step two, the mean absolute percentage errors of conductance g and susceptance b decreased to 0.55% and 0.76%, respectively. The comparison of branch admittance identification values ​​and errors is as follows: Figure 3 Figure 4 As shown. Considering the 0.5% additional error in the measurement data, the results still demonstrate that the proposed method can accurately estimate the conductance and susceptance of the distribution network, reflecting the effectiveness of the method.

[0066] In the 123-node test case, the IEEE 33-node distribution network topology is as follows: Figure 5 As shown, this is a large-scale distribution network test system containing 123 nodes. Its structure includes multiple ring networks and branches, effectively simulating the complex topology of a real distribution network. The experiment uses 24-hour measurement data; step one uses the complete dataset, and step two uses the last 50 samples from the complete dataset. The parameter settings are as follows: γTop=4%, ξ=0.05, ζ=0.001. =1 × 10⁻⁸. Cosine annealing. and Set to 10 respectively -3 and 10 -5 ; Set to 50. And by adding 0.2% Gaussian noise to the measurement data (P and Q), 360 datasets were tested. The relative percentage error plots of the admittance after identification in steps 1 and 2 are shown below. Figure 6 , Figure 7 As shown, their MAPE values ​​are 0.65% and 0.45%, respectively.

[0067] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A data-driven method for identifying distribution network topology and line parameters, characterized in that: Includes the following steps: Step 1: Construct a linear power flow model, obtain preliminary estimates of the distribution network parameters based on the initial identification method of linear regression, and then obtain the initial identification results of the distribution network admittance matrix. Step 2: Introduce the voltage phase angle change between nodes, and correct the initial identification result of the distribution network admittance matrix obtained in Step 1 through an accurate power flow iteration model to obtain the final topology identification result.

2. The data-driven method for identifying distribution network topology and line parameters according to claim 1, characterized in that: The specific steps of step 1 include: (1) Construct a linear power flow model. By constructing a simplified power flow equation that ignores the influence of phase angle, the node power-voltage magnitude relationship is expressed as a linear regression problem. (2) Based on the linear power flow model constructed in sub-step (1), design an initial identification method based on linear regression, and then obtain preliminary estimates of the distribution network parameters. Use voltage and power measurement data to iteratively calculate the admittance matrix, set residual thresholds to screen out non-existent branches, and apply matrix symmetry constraints to obtain the initial identification results of the distribution network admittance matrix.

3. The data-driven method for identifying distribution network topology and line parameters according to claim 2, characterized in that: The specific steps of step 1 (1) include: For the distribution network, establish the power flow equations in polar coordinates: (1) In the formula: p i , q i and v i Representing nodes respectively i The injected active power, reactive power, and voltage amplitude; G ij , B ij Representing branch roads ij Branch conductance and susceptance; θ ij express i , j The phase angle difference between the voltages at the two nodes, ; n Indicates the total number of nodes; Rewrite the above equation in matrix form, where # denotes an approximation: (2) (3) In the formula: It is a voltage magnitude vector, without phase angle information; ; ; , Represented as: (4) (5) in, , ; Based on the characteristics of the power distribution network, equations (4) and (5) can be approximated as follows: (6) (7) This leads to the construction of a linear power flow model; If it exists, it contains P , Q , V Information M 0 For group measurement data, the linear regression method can be used to estimate... G ij and B ij Then formulas (2) and (3) can be rewritten as: (8) (9)。 4. The data-driven method for identifying distribution network topology and line parameters according to claim 2, characterized in that: The specific steps of step 1, step (2) include: Based on the linear power flow model constructed in sub-step (1), an initial identification method based on linear regression was designed. First, the least squares method was used to solve equations (8) and (9) to obtain preliminary estimates of the distribution network parameters, and then the admittance matrix was obtained. and The expression is: (10) (11) The admittance matrix must maintain symmetry: (12) (13) The diagonal element value in the matrix is ​​equal to the negative of the sum of the conductances of all branches connected to that node, calculated as follows: (14) Branch weights Defined as and The ratio: (15) If the weight of a certain branch Less than the set threshold If so, the branch is removed, and the corresponding conductance value for that branch is set. The result is zero; this method can be expressed as a constrained linear least squares problem, as shown below: (16) After zeroing some elements, perform linear regression on each node using the remaining branch measurement data to update the matrix elements; repeat this process of "calculating branch weights - threshold judgment - zeroing - re-regression" until the topology no longer changes. This result is the initial identification result of the distribution network admittance matrix.

5. The data-driven method for identifying distribution network topology and line parameters according to claim 1, characterized in that: The specific steps of step 2 include: (1) First, the voltage phase angle change between nodes is introduced, and the voltage phase angle estimate corresponding to the power measurement is obtained by pseudo power flow calculation; (2) Based on the voltage phase angle estimate corresponding to the power measurement obtained in step (1), combined with the measurement data and phase angle information, the Adam optimization algorithm and noise reduction processing are used to correct the initial identification result of the distribution network admittance matrix obtained in step 1, so as to ensure the identification accuracy and calculation stability. The iteration ends after the convergence condition is met, and the final topology identification result is obtained.

6. The data-driven method for identifying distribution network topology and line parameters according to claim 5, characterized in that: The specific steps of step 2, step (1) include: The admittance estimation matrix obtained from the initial identification is used as the initial value and then corrected by an accurate power flow iterative model; the admittance is obtained from the preliminary estimation result in step 1, and the phase angle is obtained by pseudo power flow calculation. Constructing the Adam optimization model: (17) Calculate the loss function with respect to variables g , b , gradient: (18) Update parameters using the Adam algorithm; Update learning rate: (19) In the formula, , Set the upper and lower bounds of the learning rate to be respectively; Total number of iterations per cycle; Show the current iteration number t Divide by period length T The remainder obtained after maxing; Calculate the first-order momentum estimate : (20) Calculate the second-order momentum estimate : (21) Deviation correction for calculating first-order momentum: (22) Correction for deviation in calculating second-order momentum: (23) Update parameters: (24) Pseudo-power flow calculation updates voltage phase angle: Assuming all nodes except the reference bus are PQ nodes, calculate the new phase angle using the currently estimated admittance. The iteration that replaced Adam Value; repeat the iteration until convergence; After each Adam iteration, the voltage phase angle is corrected by pseudo-power flow calculation, and finally the voltage phase angle estimate corresponding to the obtained power measurement is obtained.

7. The data-driven method for identifying distribution network topology and line parameters according to claim 5, characterized in that: The specific steps of step 2 (2) include: ① Clear erroneous parameters during iteration: After each parameter update, the estimated conductance *g* and susceptance *b* of all branches are checked; if g If the value is less than 0, then replace it with a value that follows a uniform distribution. Positive random numbers; if b If the value is greater than 0, then replace it with a value that follows a uniform distribution. Negative random numbers; ② Modify the topology during the iteration process: Near the end of each iteration, all branches are traversed, and branches with admittance parameters less than a set threshold are identified and eliminated. The branches are used to obtain a new topology, and the modified topology is used in subsequent iterative calculations; If the loss function value of the current iteration L (k) Satisfy | L (k) -L (k-1) ∣< If the topology does not change after multiple iterations, the iteration terminates; otherwise, return to step 2 (1) to continue optimization; when the convergence condition is met, the final topology identification result is obtained.

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