Power distribution network model-free state estimation method and system based on canonical multi-linear decomposition, and storage medium

Abstract

The invention discloses a model-free state estimation method and system for a power distribution network based on canonical multi-linear decomposition and a storage medium in the field of state estimation of a power system, and aims to solve the technical problem that the power distribution network cannot execute state estimation under the condition that real-time topological information of the power distribution network is lost. The method comprises the following steps: acquiring historical measurement data of a power distribution network and preprocessing the historical measurement data, constructing a three-dimensional tensor according to a time dimension, a node dimension and a measurement type dimension, and performing tensor decomposition on the three-dimensional tensor through an alternating least square algorithm to obtain an optimal decomposition factor matrix, and reconstructing a measurement tensor by using an optimal decomposition factor matrix to realize filtering of historical measurement data in an original three-dimensional tensor and complementation of missing measurement data, and finally extracting a voltage sub-tensor in the reconstructed measurement tensor and performing reverse normalization processing to obtain a voltage amplitude estimated value. The method is applied to state estimation of the power distribution network, and stable and accurate state estimation calculation can be achieved under the condition that topological information is not used.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network, and in particular to a distribution network model-free state estimation method, system and storage medium based on canonical multilinear decomposition. Background Art

[0002] Distribution network state estimation refers to the process of inferring the operating status of the entire distribution network system based on measurement data. It is an important basis for distribution network monitoring, control and optimization.

[0003] Currently, common distribution network state estimation methods include weighted least squares (WLS) based on power flow models and forward-backward substitution based on the system impedance matrix. These methods establish explicit relationships between system measurements and state variables and apply mathematical optimization techniques to obtain optimal state estimates. However, these methods require detailed network topology and parameter information. In actual distribution network operation, due to frequent changes in network structure and parameter uncertainty, model accuracy is difficult to guarantee.

[0004] In recent years, with the development of data-driven technologies, several state estimation methods based on historical data mining have gradually emerged. These methods utilize historical measurement data to construct state estimation models and achieve state estimation through machine learning and other means, without requiring detailed network topology and parameter information. However, existing data-driven methods have significant limitations when dealing with incomplete measurement data: first, they struggle to effectively handle large amounts of missing data; second, estimation accuracy is significantly affected by the quality of historical data; and third, computational complexity increases dramatically with system scale.

[0005] Therefore, there is an urgent need for a distribution network state estimation method that can effectively process incomplete measurement data, has high computational efficiency, and does not rely on detailed network models. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a distribution network model-free state estimation method, system and storage medium based on canonical multilinear decomposition, which can effectively handle large-scale missing data and has high computational efficiency.

[0007] To achieve the above object, the present invention is implemented by adopting the following technical solutions: In a first aspect, the present invention provides a distribution network model-free state estimation method based on canonical multilinear decomposition, characterized by comprising: Obtain historical measurement data of the distribution network, and process the historical measurement data to obtain pre-processed measurement data; Based on the preprocessed measurement data, a three-dimensional tensor is constructed according to the time dimension, node dimension, and measurement type dimension, and a missing marker matrix with the same dimension as the three-dimensional tensor is generated based on the three-dimensional tensor; The random number initialization method is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension; The objective function is constructed based on the three-dimensional tensor, the missing marker matrix, and the initialization decomposition factor matrix. The objective function is iteratively optimized through alternating least squares to obtain the optimal decomposition factor matrix in the time dimension, node dimension, and measurement type dimension. Reconstructing the optimal decomposition factor matrix using the time dimension, node dimension and measurement type dimension to obtain a measurement tensor, and extracting the voltage sub-tensor from the measurement tensor; The voltage sub-tensor is denormalized based on historical measurement data and measurement tensor to obtain the voltage state estimation value of the distribution network.

[0008] Optionally, the processing of historical measurement data to obtain pre-processed measurement data includes: Identify abnormal data in historical measurement data through 3σ data processing method; Replace the abnormal data with the average value of the normal historical measurement data at the adjacent two moments of the abnormal data to obtain the measurement data after the abnormal value is processed; The measured data after outlier processing is normalized to obtain preprocessed measured data.

[0009] Optionally, constructing a three-dimensional tensor based on the pre-processed measurement data according to the time dimension, the node dimension, and the measurement type dimension includes: Divide the preprocessed measurement data into time series to obtain time dimension data; Map the pre-processed measurement data to the monitoring point position to obtain node dimension data; Classifying the voltage amplitude, phase angle, active power, and reactive power in the preprocessed measurement data to obtain measurement type dimension data; The three-dimensional tensor is constructed by combining the time dimension data, the node dimension data and the measurement type dimension data.

[0010] Optionally, generating a missing marker matrix having the same dimension as the three-dimensional tensor based on the three-dimensional tensor includes: Identifying known measurement data locations and missing measurement data locations in a three-dimensional tensor; A binary mapping method is used to assign a value of 1 to the position of the known measurement data and a value of 0 to the position of the missing measurement data, thereby constructing the missing marker matrix.

[0011] Optionally, constructing the objective function based on the three-dimensional tensor, the missing marker matrix, and the initialized decomposition factor matrix includes: Obtaining a reconstruction error term based on the missing marker matrix and the initialization decomposition factor matrix; Obtaining a regularization term based on the norm calculation of the initialized decomposition factor matrix; The objective function is obtained based on the reconstruction error term and the regularization term.

[0012] Optionally, the reconstruction error term is ‖W⊙(XT)‖F², where ‖•‖F represents the square root of the sum of the squares of all elements in the tensor, and T is the tensor reconstructed by the initialization factorization matrix. The calculation formula is , aᵣ, bᵣ, cᵣ are the rth columns of the initialization factor matrices A, B, and C for the time dimension, node dimension, and measurement type dimension, respectively. ⊙ represents the Hadamard product (element-wise multiplication). The regularization term is λ(‖A‖F 2 +‖B‖F 2 +‖C‖F 2 ), where λ is the regularization parameter; Then combine the two items to form the objective function: f(A,B,C) = ‖W⊙(XT)‖F² + λ(‖A‖F²+‖B‖F²+‖C‖F²).

[0013] Optionally, a tensor index mapping method is then used to extract the voltage sub-tensor from the measurement tensor.

[0014] Optionally, the performing denormalization processing on the voltage sub-tensor based on the historical measurement data and the measurement tensor includes: Obtaining a maximum value of voltage measurement data and a minimum value of voltage measurement data in the measurement data by using a data distribution analysis method; The voltage sub-tensor is restored to a value between the maximum value and the minimum value of the voltage measurement data by a linear mapping method, so as to obtain an estimated value of the voltage state of the distribution network.

[0015] In a second aspect, the present invention provides a distribution network model-free state estimation system based on canonical multilinear decomposition, comprising: The data preprocessing module is used to obtain historical measurement data of the distribution network and process the historical measurement data to obtain preprocessed measurement data; A tensor construction module is used to construct a three-dimensional tensor based on the preprocessed measurement data according to the time dimension, node dimension, and measurement type dimension, and generate a missing marker matrix with the same dimension as the three-dimensional tensor based on the three-dimensional tensor; A matrix initialization module is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension using a random number initialization method; Iterative optimization module, which is used to construct the objective function based on the three-dimensional tensor, the missing marker matrix and the initial decomposition factor matrix, and solve the objective function by alternating least squares method to obtain the optimal decomposition factor matrix in the time dimension, node dimension and measurement type dimension; A tensor reconstruction module is used to reconstruct the measurement tensor based on the optimal decomposition factor matrix of the time dimension, the node dimension, and the two-side type dimension, and extract the voltage sub-tensor from the measurement tensor; The state estimation module is used to perform denormalization on the voltage sub-tensor based on historical measurement data and the measurement tensor to obtain the voltage state estimation value of the distribution network.

[0016] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the distribution network model-free state estimation method based on canonical multilinear decomposition described in the first aspect.

[0017] Compared with the prior art, the present invention has at least the following beneficial effects: Innovatively constructs historical distribution network measurement data into a three-dimensional tensor structure, which can effectively express the correlation between the three dimensions of time, space and measurement type; The tensor completion method using canonical multilinear decomposition can simultaneously process large-scale missing data, and its computational efficiency is higher than that of traditional matrix decomposition methods; The convergence and numerical stability of the factorization are improved by the alternating least squares (ALS) optimization algorithm; Without the need for distribution network topology and parameter information, pure data-driven state estimation is achieved, which has a wider range of applications; It can simultaneously estimate the system status at multiple time points and has the function of completing measurement data. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 1 is a structural block diagram of a distribution network model-free state estimation system based on canonical multilinear decomposition according to the present invention; Figure 2 This is a network diagram of the IEEE 34-node three-phase unbalanced distribution network system of the present invention; Figure 3 This is a simulation result diagram of the synchronous sampling moment of the present invention; Figure 4 This is a simulation result diagram of the present invention under the condition of high proportion missing of measurement data. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all of the embodiments. The components of the embodiments of the present disclosure generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present disclosure provided in the drawings is not intended to limit the scope of the disclosure for which protection is sought, but merely represents selected embodiments of the present disclosure. Based on the embodiments of the present disclosure, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present disclosure.

[0020] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0021] The term "and / or" herein simply describes an association relationship, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, and the existence of B alone. In addition, the term "at least one" herein refers to any combination of at least two of any one or more of a plurality of items. For example, "at least one of A, B, and C" can represent any one or more elements selected from the set consisting of A, B, and C. Example

[0022] See also Figure 1 The present invention provides a distribution network model-free state estimation method based on canonical multilinear decomposition, comprising the following steps: Obtain historical measurement data of the distribution network, and process the historical measurement data to obtain pre-processed measurement data; Based on the preprocessed measurement data, a three-dimensional tensor is constructed according to the time dimension, node dimension, and measurement type dimension, and a missing marker matrix with the same dimension as the three-dimensional tensor is generated based on the three-dimensional tensor; The random number initialization method is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension; The objective function is constructed based on the three-dimensional tensor, the missing marker matrix, and the initialization decomposition factor matrix. The objective function is iteratively optimized through alternating least squares to obtain the optimal decomposition factor matrix in the time dimension, node dimension, and measurement type dimension. Reconstructing the optimal decomposition factor matrix using the time dimension, node dimension and measurement type dimension to obtain a measurement tensor, and extracting the voltage sub-tensor from the measurement tensor; The voltage sub-tensor is denormalized based on the measurement data to obtain the voltage state estimation value of the distribution network.

[0023] Furthermore, the processing of the historical measurement data to obtain pre-processed measurement data includes: Identify abnormal data in historical measurement data through 3σ data processing method; Replace the abnormal data with the average value of the normal historical measurement data at the adjacent two moments of the abnormal data to obtain the measurement data after the abnormal value is processed; The measured data after outlier processing is normalized to obtain preprocessed measured data.

[0024] Historical measurement data refers to historical voltage amplitude measurement data, historical active power injection measurement data, and historical reactive power injection measurement data. (For example, the historical measurement data shown in the following test: the calculation example has 86 nodes, and historical data is collected for one day every 5 minutes. Therefore, there are 288 time sections of data in 24 hours, or 288 data sets. The time dimension of the constructed tensor refers to the total number of time sections, or 288; the node dimension is the number of nodes, or 86; the measurement type dimension is the measurement type. Here, voltage amplitude measurement values, active power injection measurement values, and reactive power injection measurement values ​​are used, so it is 3. The tensor constructed in this way has a 96×86×3 dimension.) In practice, for any measurement point i and measurement type j, the mean μᵢⱼ and standard deviation σᵢⱼ of the historical data are calculated. If the measurement value xᵢⱼᵗ at a certain time t satisfies |xᵢⱼᵗ - μᵢⱼ|>3σᵢⱼ, then xᵢⱼᵗ is marked as abnormal data. If the measurement value xᵢⱼᵗ at a certain time t is marked as abnormal data, the abnormal data is replaced by the average value of the adjacent time points on both sides, that is, xᵢⱼᵗ = (xᵢⱼ t-1 + xᵢⱼ t+1 ) / 2, and the measured data after outlier processing is obtained. If the data at a certain adjacent time is also an outlier, the time window is expanded until a normal value is found.

[0025] For the measurement data after outlier processing, the data of each measurement point i and measurement type j are normalized and mapped to the interval [0,1]: x'ᵢⱼᵗ = (xᵢⱼᵗ - min(xᵢⱼ)) / (max(xᵢⱼ) - min(xᵢⱼ)), where min(xᵢⱼ) and max(xᵢⱼ) are the minimum and maximum values ​​of the historical data of the corresponding measurement point and measurement type, respectively. The preprocessed measurement data is obtained.

[0026] Furthermore, the constructing of a three-dimensional tensor based on the pre-processed measurement data according to the time dimension, the node dimension, and the measurement type dimension includes: Divide the preprocessed measurement data into time series to obtain time dimension data; Map the pre-processed measurement data to the monitoring point position to obtain node dimension data; Classifying the voltage amplitude, phase angle, active power, and reactive power in the preprocessed measurement data to obtain measurement type dimension data; The time dimension data, the node dimension data and the measurement type dimension data are combined to construct the three-dimensional tensor.

[0027] In the specific implementation, the data is organized into a time series according to the time tag of the measurement data; the data is mapped to the corresponding node according to the spatial location information of the measurement point; and the data is divided into categories such as voltage amplitude, phase angle, active power and reactive power according to the different measurement types. Then, the three-dimensional data are combined into a three-dimensional tensor X∈R I×J×K , where I represents the number of time points, J represents the number of nodes, and K represents the number of measurement types.

[0028] Furthermore, generating a missing marker matrix having the same dimension as the three-dimensional tensor based on the three-dimensional tensor includes: Perform data detection on the three-dimensional tensor using a data scanning algorithm to identify the locations of known measurement data and missing measurement data in the three-dimensional tensor; A binary mapping method is used to assign a value of 1 to the position of the known measurement data and a value of 0 to the position of the missing measurement data, thereby constructing the missing marker matrix.

[0029] In the specific implementation, each element in the three-dimensional tensor X is scanned to determine whether it is a missing value; a missing mark matrix W∈R is constructed. I×J×K , the position with known measurement data is assigned a value of 1, and the position with missing measurement data is assigned a value of 0.

[0030] Furthermore, a random number initialization method is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension, wherein: the initialization processing adopts the mean and standard deviation initialization method; wherein, the mean adopts the second preset value and the standard deviation adopts the third preset value.

[0031] In the specific implementation, the random data are generated by the normal distribution with a mean of 0 and a standard deviation of 0.1, and three initialization factor matrices A∈R are obtained. I×R , B∈R J×R and C∈R K×R , the rank value R is a first preset value, where R=1.

[0032] Furthermore, the objective function is constructed based on the three-dimensional tensor, the missing marker matrix, and the initialized decomposition factor matrix, and the objective function is solved by alternating least squares method to obtain the optimal decomposition factor matrix of the time dimension, the node dimension, and the measurement type dimension, including: Obtaining a reconstruction error term based on the missing marker matrix and the initialization decomposition factor matrix; Obtaining a regularization term based on the norm calculation of the initialized decomposition factor matrix; The objective function is obtained based on the reconstruction error term and the regularization term.

[0033] In the specific implementation, first, calculate the reconstruction error term ‖W⊙(XT)‖F², where T is the tensor reconstructed by the initialization decomposition factor, and the calculation formula is , aᵣ, bᵣ, cᵣ are the rth columns of the initialization factor matrices A, B, and C respectively, and ⊙ represents the Hadamard product (element-wise multiplication); then, the regularization term λ(‖A‖F 2 +‖B‖F 2 +‖C‖F 2 ), where λ is the regularization parameter, usually 1; the two terms are combined to form the objective function f(A,B,C) = ‖W⊙(XT)‖F²+ λ(‖A‖F²+‖B‖F²+‖C‖F²).

[0034] Furthermore, the objective function is solved by alternating least squares method to obtain the optimal decomposition factor matrix of time dimension, node dimension and measurement type dimension, including: When solving the objective function A, keep B and C unchanged, substitute them into the objective function, and get the loss function for A. Then calculate the partial derivative of the loss function for A, and make the partial derivative of the loss function for A equal to 0, and get the formula for optimizing A. Similarly, we get the formula for optimizing B and the formula for optimizing C; The decomposition factor matrices of the iteration time dimension, node dimension, and measurement type dimension are updated through three formulas. When the difference between two adjacent iterations is less than the preset threshold (such as 10 -5 ), the iteration is considered to converge, that is, the optimal decomposition factor matrices A1, B1, and C1 are obtained.

[0035] In specific implementation, the formula for the optimization A is as follows: (ZᵀZ + λI1)A = ZᵀY, where Z is the matrix constructed by B and C through the Khatri-Rao product (the initial B and C are used for the first time, and the updated B and C are used during the iteration), I1 is the identity matrix, and Y is the matrix obtained by reorganizing the three-dimensional tensor X; the decomposition factor matrix of the target dimension is updated by the above formula, and when the difference between two consecutive iterations of the optimization objective function is less than a preset threshold (such as 10 -5 ), the iteration is considered to have converged.

[0036] Reorganizing a 3D tensor X into Y is accomplished by performing a mode-1 expansion X{(1)} on X. Similarly, when updating B, reorganizing a tensor X into Y is accomplished by performing a mode-2 expansion X{(2)} on X; and when updating C, reorganizing a tensor X into Y is accomplished by performing a mode-3 expansion X{(3)} on X.

[0037] Furthermore, a tensor index mapping method is used to extract the voltage sub-tensor from the measurement tensor.

[0038] In the specific implementation, in step S5.1, the complete measurement tensor T is reconstructed using the optimal decomposition factor matrices A1, B1, and C1. T is represented as the sum of R rank-1 tensors, that is, , where aᵣ, bᵣ, and cᵣ are the r-th columns of the A1, B1, and C1 matrices, respectively, and ◦ represents the outer product operation. Assuming that the index of the voltage measurement type in the third dimension is kᵥ, the voltage sub-tensor can be obtained through the slicing operation T(:,:,kᵥ).

[0039] Furthermore, the denormalization of the voltage sub-tensor based on the historical measurement data and the measurement tensor includes: Obtaining the maximum value and the minimum value of voltage measurement data in the historical measurement data by using a data distribution analysis method; The voltage sub-tensor is restored to a value between the maximum value and the minimum value of the voltage measurement data by a linear mapping method, so as to obtain an estimated value of the voltage state of the distribution network.

[0040] In specific implementation, the voltage measurement data in the historical measurement data is first statistically analyzed to extract its numerical distribution characteristics. Then, the maximum value Tmax and minimum value Tmin of the voltage measurement data are determined based on the extracted distribution characteristics. Then, through the inverse normalization transformation Treal = Tmin + T × (Tmax - Tmin), the estimated value of the normalized scale is converted back to the actual physical scale to obtain the final voltage state estimate.

[0041] During the preprocessing of historical measurement data, the 3σ principle is a statistically based outlier detection method. Its theoretical basis is that in a normal distribution, the probability of data falling within the interval (μ - 3σ, μ + 3σ) is 99.73%. Therefore, data points falling outside this interval are considered outliers. In practice, the historical data mean μ and standard deviation σ are first calculated for each measurement point and measurement type. Then, each data point is determined to fall within the interval (μ - 3σ, μ + 3σ). Data points identified as outliers are replaced with the average of the data from adjacent moments. This method effectively removes the influence of outliers while maintaining the temporal continuity of the data.

[0042] Normalization is the process of mapping data of different dimensions to a uniform interval. The commonly used Min-Max normalization can be expressed as: x' = (x - x min ) / (x max -x min ), where x min and x max are the minimum and maximum values ​​of the original data, respectively. Normalization can eliminate the dimensionality effect, making different types of measurement data comparable, which helps stabilize the subsequent tensor decomposition algorithm.

[0043] During the tensor construction phase, the mathematical expression of a three-dimensional tensor is X ∈ Rᴵˣᴶˣᴷ, where I, J, and K represent the sizes of the time dimension, node dimension, and measurement type dimension, respectively. Compared to traditional matrix data structures, three-dimensional tensors can simultaneously express the three-dimensional characteristics of data and preserve the multi-dimensional relationships between data. For example, for a system with 100 time points, 30 nodes, and 4 measurement types, a 100×30×4 three-dimensional tensor will be constructed. Each tensor element x ij k represents the data value of measurement type k at time point i and node j.

[0044] The missing marker matrix W ∈ Rᴵˣᴶˣᴷ has the same dimensional structure as the original tensor X, with element values ​​of 0 or 1, and is used to mark missing data in the original tensor. The missing marker matrix plays a key role in the tensor completion optimization process, ensuring that the optimization algorithm focuses only on the reconstruction error of known data and ignores the reconstruction error at the locations of missing data.

[0045] During the canonical multilinear factorization (CP factorization) stage, the CP factorization decomposes the three-dimensional tensor X into the sum of the outer products of three factor matrices: A∈Rᴵˣᴿ, B∈Rᴶˣᴿ, and C∈Rᴷˣᴿ. R is the rank of the factorization, representing the number of latent features. aᵣ, bᵣ, and cᵣ are the r-th column vectors of matrices A, B, and C, respectively. ◦ represents the vector outer product operation. CP factorization can be understood as projecting the original high-dimensional tensor data into a low-dimensional latent feature space, thereby capturing the main patterns in the data. CP factorization decomposes a three-dimensional tensor into the sum of R rank-1 tensors, each of which is the outer product of three vectors.

[0046] During the factor matrix initialization phase, a normal distribution random initialization method is used to provide a reasonable starting point for optimization. A normal distribution with a mean of 0 and a standard deviation of 0.1 produces initialization data with most values ​​concentrated in the interval [-0.3, 0.3]. This moderate initial value is conducive to stable convergence of the optimization algorithm. This avoids numerical instability caused by overly large initial values ​​or slow convergence caused by overly small initial values.

[0047] During the optimization objective function construction phase, the objective function consists of two parts: a reconstruction error term and a regularization term. The reconstruction error term = ‖W⊙(XT)‖F² measures the difference between the three-dimensional tensor and the measurement tensor at known data locations, and the Frobenius norm ‖·‖F² represents the square root of the sum of the squares of all elements in the tensor. The regularization term λ(‖A‖F² + ‖B‖F² + ‖C‖F²) controls the norm of the factor matrix to prevent model overfitting. λ is the regularization parameter, which is used to balance reconstruction error and model complexity.

[0048] The alternating least squares (ALS) algorithm is a commonly used CP decomposition optimization method. Its basic idea is to fix two factor matrices in each iteration, optimize the third factor matrix, and then repeat the process. This method transforms a nonlinear optimization problem into multiple linear least squares problems, greatly improving computational efficiency.

[0049] During the tensor reconstruction and voltage state estimation phase, the complete measurement tensor T is first reconstructed using the optimal decomposition factor matrix. Then, the voltage-related sub-tensors are extracted and denormalized to obtain the voltage state estimate at the actual physical scale. The denormalization process is the inverse of normalization. Example

[0050] See also Figure 1 The present invention also provides a distribution network model-free state estimation system based on canonical multilinear decomposition, comprising: The data preprocessing module is used to obtain historical measurement data of the distribution network and process the historical measurement data to obtain preprocessed measurement data; A tensor construction module is used to construct a three-dimensional tensor based on the preprocessed measurement data according to the time dimension, node dimension, and measurement type dimension, and generate a missing marker matrix with the same dimension as the three-dimensional tensor based on the three-dimensional tensor; A matrix initialization module is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension using a random number initialization method; Iterative optimization module, which is used to construct the objective function based on the three-dimensional tensor, the missing marker matrix and the initial decomposition factor matrix, and solve the objective function by alternating least squares method to obtain the optimal decomposition factor matrix in the time dimension, node dimension and measurement type dimension; A tensor reconstruction module is used to reconstruct the measurement tensor based on the optimal decomposition factor matrix of the time dimension, the node dimension, and the two-side type dimension, and extract the voltage sub-tensor from the measurement tensor; The state estimation module is used to perform denormalization on the voltage sub-tensor based on historical measurement data and the measurement tensor to obtain the voltage state estimation value of the distribution network.

[0051] See also Figure 2 The present invention has been simulated and tested on an IEEE 34-node three-phase unbalanced distribution system. The IEEE 34-node three-phase unbalanced distribution network system has a total of 34 three-phase nodes, but the system is a three-phase unbalanced system, and the number of phases to be considered should be the number of three-phase unbalanced nodes. Excluding the missing phase nodes, the system has a total of 86 three-phase unbalanced nodes, so the node dimension of the constructed tensor is 86. The distribution system includes Advanced Metering Infrastructure (AMI) measurement and Supervisory Control and Data Acquisition (SCADA) measurement. AMI measurement provides node voltage amplitude measurement of load nodes, active power injection measurement of load nodes, and reactive power injection measurement of load nodes, while SCADA measurement provides node voltage amplitude measurement of non-load nodes. The active power injection and reactive power injection of non-load nodes use virtual loads and are always 0, so the measurement type dimension of the constructed data tensor is 3. When constructing the tensor, we use measurement data from 24 hours a day. The sampling interval for SCADA measurement is 5 minutes, and the sampling interval for AMI measurement is 15 minutes. Therefore, there are a total of 288 sampling moments, and the time dimension is 288. The detailed measurement configuration of the IEEE34 node is shown in Table 1.

[0052] Table 1 IEEE34 node measurement configuration Measurement type Measuring point AMI measurement node voltage amplitude 5-6,8-9,11,13,24-28,30-33,35,36-38,40,45-54,57,58-59,61-76,78-79,83-86 AMI measurement node injection power 5-6,8-9,11,13,24-28,30-33,35,36-38,40,45-54,57,58-59,61-76,78-79,83-86 SCADA measurement node voltage amplitude 4,7,10,12,14-23,29,34,39,41-44,55,56,60,75,77,80-82 The sampling moments at which both SCADA and AMI measurements can be collected are called synchronous sampling moments, while the sampling moments at which only SCADA measurements can be collected are called asynchronous sampling moments.

[0053] First, at the synchronous sampling moment, the AMI data and SCADA data configured in the system can be uploaded to the state estimation system. At this time, the main function of the distribution network model-free state estimation method based on the tensor algorithm proposed in the present invention is filtering, reducing the noise in the measurement data, and obtaining a result as close to the true value as possible. During the test, the rank value R of the data tensor is set to 1. Simulation calculations are performed on 288 sampling moments in a day, and then the results of 96 synchronous sampling moments are counted. At the same time, the estimation results of the WLS algorithm are added for comparison. The MAE of the voltage amplitude is as follows: Figure 3 As shown in the figure, the blue line, orange line, and yellow bar graph represent the MAEs of measurement noise, WLS estimates, and tensor algorithm estimates, respectively. As can be seen from the figure, the MAEs of the WLS and tensor algorithm estimates are both lower than the MAE of measurement noise, indicating that both WLS and the tensor algorithm have good noise filtering capabilities. The yellow bar graph representing the MAE of the tensor algorithm estimate is essentially below the orange line representing the MAE of the WLS estimate, indicating that the tensor algorithm has better estimation results than the WLS. To further quantitatively analyze the model-free state estimation method for distribution networks based on the tensor algorithm proposed in this chapter, the specific MAE values ​​of the voltage amplitude for measurement noise, WLS, and the tensor algorithm are given in Table 2. The data in Table 2 show that both the WLS and tensor algorithms can reduce measurement noise and obtain estimates that are closer to the true value, but the tensor algorithm's estimation accuracy is 38.36% higher than that of the WLS. This shows that the distribution network model-free state estimation method based on CP decomposition proposed in this invention can obtain high-precision state estimation values ​​at the synchronous sampling time even when the network topology and parameters are unknown, and its effect is even better than the traditional WLS algorithm based on network topology and parameters.

[0054] Table 2 Test results of synchronous sampling time MAE(pu) Tensor Algorithms 0.000678 WLS 0.001100 Measurement noise 0.004100 Then, at the asynchronous sampling moment, only SCADA measurements can be uploaded to the state estimation system. At this time, the method proposed in the present invention has two functions: one is to filter the SCADA measurements in the tensor to obtain a more accurate estimate, and the filtered estimate is called the filtered value. The other is to complete the missing data in the tensor to obtain an estimate of the uncollected data, and the completed estimate is called the completed value. It can be found from Table 3 that at the asynchronous sampling point, the MAE of the filtered value is the smallest, which can be closer to the true value, and the accuracy of the filtered value can reach 10 -4 The WLS results in Table 2 are calculated under the condition that both SCADA measurements and AMI measurements are uploaded, and their accuracy is only 10 -3 level, and the accuracy of the filter value at the asynchronous sampling moment can reach 10 -4The levels are calculated under the condition of only SCADA measurements, which shows that the method proposed in this invention has a good filtering effect on existing measurements, and its filtering ability is better than that of traditional WLS based on physical topology. Even at the asynchronous sampling moment with insufficient redundancy, the filtering ability of the method proposed in this chapter is better than that of traditional WLS based on physical topology. The MAE of the completion values ​​in Table 3 can reach 0.0010pu respectively. The MAE of traditional WLS based on physical topology and redundant measurement in Table 2 is 0.0011pu respectively. This shows that the accuracy of this method for completing the missing data in the tensor that has not been collected is almost equivalent to the accuracy of traditional WLS based on physical topology and redundant measurement.

[0055] Table 3 MAE of voltage amplitude of filtered and complemented values MAE(pu) Filter value 0.000869 Completion value 0.001000 Measurement noise 0.004100 Finally, for multi-source measurement systems, intermittent loss of measurement often occurs due to the different channels and sampling intervals for uploading measurement data from different measurement sources. Intermittent loss of measurement will lead to a reduction in measurement redundancy, which in turn will cause a reduction in the calculation accuracy of the traditional WLS algorithm, and in severe cases, even lead to non-convergence of the calculation. In order to test the effectiveness of the proposed tensor-based distribution network model-free state estimation method when intermittent loss of measurement occurs, 10%, 15% and 20% intermittent loss of SCADA measurement and AMI measurement are set at a certain synchronous sampling moment. The test results are shown in Figure 2. Figure 4 shown.

[0056] For a multi-source measurement system, since different measurement sources upload measurement data through different channels and sampling intervals, the horizontal axis in the figure represents the percentage of missing measurements, and the vertical axis shows the change in the MAE of the voltage amplitude estimates using the Tensor algorithm and the WLS algorithm as the percentage of missing measurements changes. The blue bar graph represents the MAE of the voltage amplitude estimates using the Tensor algorithm, and the orange bar graph represents the MAE of the voltage amplitude estimates using the WLS algorithm. Observing the changes in the bar graphs, we can see that as the percentage of missing measurements increases, the MAE of the voltage amplitude estimates using the WLS algorithm increases, indicating that the accuracy of the voltage amplitude estimates using the WLS algorithm decreases. Table 2 shows that when there are no missing measurements, the MAE of the voltage amplitude estimates using the WLS algorithm is 0.0011 pu. When the percentage of missing measurement data reaches 20%, the MAE of the voltage amplitude estimates using the WLS algorithm increases to 0.002956 pu, a nearly threefold improvement. When the percentage of missing measurement data is only 10%, the MAE of the voltage amplitude estimates using the WLS algorithm increases to 0.001958 pu, also a nearly twofold improvement. In the example, when there are no missing measurements, the tensor algorithm's voltage amplitude MAE is 0.000678 pu. When the missing measurement ratio reaches 20%, the tensor algorithm's voltage amplitude MAE is 0.001161, and when the missing measurement ratio reaches 10%, the MAE is 0.001040. This shows that in the IEEE 34-node three-phase unbalanced distribution network system, although the tensor algorithm's estimation accuracy decreases somewhat when a large amount of missing measurement data is present, it does not decrease as much as the WLS algorithm. Furthermore, the tensor algorithm's estimation accuracy remains similar as the missing measurement ratio increases from 10% to 20%. This demonstrates that the tensor algorithm maintains sufficiently high estimation accuracy even when missing measurements occur, meeting the system's operational computing requirements.

[0057] Each functional module of the system of the present invention corresponds to each step of the aforementioned method. In specific implementation, a Python-based tensor computing library (such as TensorLy or NumPy) can be used to build a system prototype. The data preprocessing module is responsible for outlier detection and processing, data normalization, and other functions; the tensor construction module is responsible for the creation and management of three-dimensional data structures; the matrix initialization module is responsible for parameter setting and initialization of CP decomposition; the iterative optimization module implements the ALS algorithm and convergence control; the tensor reconstruction module completes data completion and state extraction; and the state estimation module performs denormalization and outputs results.

[0058] The system can also include a visualization module and a performance evaluation module to visually display state estimation results and evaluate estimation accuracy. The system can be deployed on a server in a distribution network monitoring center, receiving real-time measurement data and providing an estimate of the current system state, providing data support for distribution network operation decisions.

[0059] The present disclosure also provides a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program executes the steps of the method for model-free state estimation of a distribution network based on canonical multilinear decomposition described in the above method embodiment. The storage medium may be a volatile or non-volatile computer-readable storage medium.

[0060] In addition, an embodiment of the present disclosure also provides a computer program product, which stores a computer program. When the computer program is run by a processor, it executes the steps of the distribution network model-free state estimation method based on canonical multilinear decomposition provided by any of the above embodiments of the present disclosure. For details, please refer to the above method embodiments, which will not be repeated here.

[0061] The computer program product may be implemented in hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is embodied as a computer storage medium, which may be a volatile or non-volatile computer-readable storage medium. In another alternative embodiment, the computer program product is embodied as a software product, such as a software development kit (SDK).

[0062] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment and devices can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. In the several embodiments provided in the present disclosure, it should be understood that the disclosed equipment, devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0063] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0064] In addition, each functional unit in each embodiment of the present disclosure may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0065] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that is executable by a processor. Based on this understanding, the technical solution of the present disclosure, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present disclosure. The aforementioned storage medium includes: various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0066] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present disclosure, which are used to illustrate the technical solutions of the present disclosure, rather than to limit them. The scope of protection of the present disclosure is not limited thereto. Although the present disclosure has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-mentioned embodiments within the technical scope disclosed in the present disclosure, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should be included in the scope of protection of the present disclosure. Therefore, the scope of protection of the present disclosure should be based on the scope of protection of the claims.

Claims

1. A distribution network model-free state estimation method based on canonical multilinear decomposition, characterized in that: include: Obtain historical measurement data of the distribution network, and process the historical measurement data to obtain pre-processed measurement data; Based on the preprocessed measurement data, a three-dimensional tensor is constructed according to the time dimension, node dimension, and measurement type dimension, and a missing marker matrix with the same dimension as the three-dimensional tensor is generated based on the three-dimensional tensor; The random number initialization method is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension; The objective function is constructed based on the three-dimensional tensor, the missing marker matrix and the initialization decomposition factor matrix. The objective function is solved by the alternating least squares method to obtain the optimal decomposition factor matrix of the time dimension, the node dimension and the measurement type dimension. The optimal decomposition factor matrix based on the time dimension, node dimension and measurement type dimension is reconstructed to obtain the measurement tensor, and the voltage sub-tensor is extracted from the measurement tensor; The voltage sub-tensor is denormalized based on historical measurement data and measurement tensor to obtain the voltage state estimation value of the distribution network.

2. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The processing of the historical measurement data to obtain pre-processed measurement data includes: Identify abnormal data in historical measurement data through 3σ data processing method; Replace the abnormal data with the average value of the normal historical measurement data at the adjacent two moments of the abnormal data to obtain the measurement data after the abnormal value is processed; The measured data after outlier processing is normalized to obtain preprocessed measured data.

3. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The method of constructing a three-dimensional tensor based on the pre-processed measurement data according to the time dimension, the node dimension, and the measurement type dimension includes: Divide the preprocessed measurement data into time series to obtain time dimension data; Map the pre-processed measurement data to the monitoring point position to obtain node dimension data; Classifying the voltage amplitude, phase angle, active power, and reactive power in the preprocessed measurement data to obtain measurement type dimension data; The three-dimensional tensor is constructed by combining the time dimension data, the node dimension data and the measurement type dimension data.

4. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The generating of a missing marker matrix having the same dimension as the three-dimensional tensor based on the three-dimensional tensor includes: Identifying known measurement data locations and missing measurement data locations in a three-dimensional tensor; A binary mapping method is used to assign a value of 1 to the position of the known measurement data and a value of 0 to the position of the missing measurement data, thereby constructing the missing marker matrix.

5. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The objective function is constructed based on the three-dimensional tensor, the missing marker matrix and the initialization decomposition factor matrix, including: Obtaining a reconstruction error term based on the missing marker matrix and the initialization decomposition factor matrix; Obtaining a regularization term based on the norm calculation of the initialized decomposition factor matrix; The objective function is obtained based on the reconstruction error term and the regularization term.

6. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 5, characterized in that: The reconstruction error term is ‖W⊙(XT)‖F², where ‖•‖F represents the square root of the sum of the squares of all elements in the tensor, and T is the tensor reconstructed by the initialization factorization matrix. The calculation formula is, , aᵣ, bᵣ, cᵣ are the rth columns of the initialization decomposition factor matrices A, B, and C of the time dimension, node dimension, and measurement type dimension, respectively. ⊙ represents the Hadamard product; The regularization term is λ(‖A‖F 2 +‖B‖F 2 +‖C‖F 2 ), where λ is the regularization parameter; The objective function is expressed as f(A, B, C), and: f(A,B,C) = ‖W⊙(XT)‖F² + λ(‖A‖F²+‖B‖F²+‖C‖F²).

7. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The extracting the voltage sub-tensor from the measurement tensor includes: extracting the voltage sub-tensor from the measurement tensor using a tensor index mapping method.

8. The distribution network model-free state estimation method based on canonical multilinear decomposition according to claim 1, characterized in that: The denormalization of the voltage sub-tensor based on the historical measurement data and the measurement tensor includes: Obtaining a maximum value of voltage measurement data and a minimum value of voltage measurement data in the measurement data by using a data distribution analysis method; The voltage sub-tensor is restored to a value between the maximum value and the minimum value of the voltage measurement data by a linear mapping method, so as to obtain an estimated value of the voltage state of the distribution network.

9. A distribution network model-free state estimation system based on canonical multilinear decomposition, characterized in that: include: The data preprocessing module is used to obtain historical measurement data of the distribution network and process the historical measurement data to obtain preprocessed measurement data; A tensor construction module is used to construct a three-dimensional tensor based on the preprocessed measurement data according to the time dimension, node dimension, and measurement type dimension, and generate a missing marker matrix with the same dimension as the three-dimensional tensor based on the three-dimensional tensor; A matrix initialization module is used to obtain the initialization decomposition factor matrix of the time dimension, node dimension and measurement type dimension using a random number initialization method; Iterative optimization module, which is used to construct the objective function based on the three-dimensional tensor, the missing marker matrix and the initial decomposition factor matrix, and solve the objective function by alternating least squares method to obtain the optimal decomposition factor matrix in the time dimension, node dimension and measurement type dimension; A tensor reconstruction module is used to reconstruct the measurement tensor based on the optimal decomposition factor matrix of the time dimension, the node dimension, and the two-side type dimension, and extract the voltage sub-tensor from the measurement tensor; The state estimation module is used to perform denormalization on the voltage sub-tensor based on historical measurement data and the measurement tensor to obtain the voltage state estimation value of the distribution network.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the distribution network model-free state estimation method based on canonical multilinear decomposition as described in any one of claims 1 to 8 are implemented.

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