A method for measuring and analyzing the state of electric variables of a power distribution network

Abstract

The application relates to the field of measuring electric variables, and particularly relates to a power distribution network electric variable measurement and state analysis method, which comprises the following steps: obtaining current original values at each moment, voltage original values at each moment and power original values at each moment; calculating data matrices of each sub-section; calculating a decoupling characteristic matrix according to coupling components; constructing a state analysis model, training the state analysis model to obtain a trained state analysis model; collecting new power distribution network electric variables to obtain new current original values at each moment, new voltage original values at each moment and new power original values at each moment; inputting the processed new power distribution network electric variables into the trained state analysis model to obtain state probability vectors; and taking a state category corresponding to a maximum probability value as a state analysis result of the sub-section. The existing power distribution network electric variable measurement and state analysis method has the problem of low accuracy of state analysis of the power distribution network, and the method provided by the application has high accuracy of state analysis of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of measuring electrical variables, and more specifically to a method for measuring and analyzing the electrical variables of a distribution network. Background Technology

[0002] A distribution network refers to a power grid that receives electrical energy from the transmission and distribution network or regional power plants and distributes it locally or in stages according to voltage to various users through distribution facilities. During operation, the distribution network is affected by various factors such as load fluctuations, line switching, fault impacts, and electromagnetic transient disturbances, causing electrical variables such as current, voltage, and power to exhibit significant non-stationary characteristics.

[0003] To ensure the safe and stable operation of the distribution network and improve the efficiency of power supply for various users, it is necessary to measure the electrical variables (current and voltage) of the distribution network and analyze the operating status of the distribution network based on the measured electrical variables. The operating status includes normal state, short circuit fault, overvoltage, undervoltage, harmonic interference, transient oscillation, etc.

[0004] Existing methods for measuring and analyzing electrical variables in distribution networks typically employ fixed sampling rates, making them ill-suited to adapt to transient events and resulting in insufficient timeliness of data acquisition at critical moments, hindering the comprehensive capture of instantaneous changes. Furthermore, in analyzing electrical variables, firstly, the data processing methods lack specificity, often relying solely on simple filtering techniques for noise suppression, failing to effectively remove complex interference from distribution network signals and impacting the accuracy and reliability of electrical variable analysis. Secondly, conventional signal segmentation methods use fixed-length sliding windows, which cannot flexibly adapt to complex events in distribution networks, often failing to retain important electromagnetic transient information, leading to distorted feature extraction. Finally, current multivariate feature extraction methods often directly concatenate multiple electrical variables, ignoring their nonlinear coupling relationships, easily resulting in redundant features and reducing the performance and identification capabilities of the state analysis model. All these factors affect the performance of the final state analysis model, thereby impacting the accuracy of state analysis of the distribution network.

[0005] Therefore, existing methods for measuring electrical variables and analyzing the state of distribution networks have the problem of low accuracy in analyzing the state of distribution networks. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for measuring and analyzing the electrical variables of a distribution network with high accuracy in the state analysis of the distribution network.

[0007] To solve the above-mentioned technical problems, the present invention provides a method for measuring and analyzing the electrical variables of a distribution network, comprising:

[0008] S1. Calculate instantaneous power, and calculate the original values ​​of current, voltage, and power at each time point based on the power variable data of the power distribution network measured at the sampling time sequence.

[0009] S2. Calculate the joint current mutation index at each time moment, calculate the segment boundary set based on the joint current mutation index at each time moment, and divide the original current value, the original voltage value, and the original power value at each time moment into multiple sub-segments based on the boundary points of the segment boundary set. Calculate the data matrix of each sub-segment. The data matrix of each sub-segment includes the current sequence, the voltage sequence, and the power sequence of each sub-segment.

[0010] S3. Calculate the coupling components based on the current sequence, voltage sequence, and power sequence of each sub-segment, and calculate the decoupling characteristic matrix based on the coupling components;

[0011] S4. Construct a state analysis model and train the state analysis model to obtain the trained state analysis model;

[0012] S401. Calculate the dual-channel fusion feature matrix;

[0013] S402. Calculate the state probability vector and total loss function for each sub-segment;

[0014] S403. Based on the total loss function, repeat S401~S402 to train and iteratively optimize the state analysis model;

[0015] S5. Obtain new raw values ​​of current, voltage, and power at each time step by collecting new power variables from the distribution network in S1. After executing S2~S3, input them into the trained state analysis model to obtain the probability vector of each state. Take the state category corresponding to the maximum probability as the state analysis result of this sub-segment.

[0016] As a further improvement of the present invention: step S1 includes:

[0017] S101. To address the non-stationary characteristics of distribution network signals, a variable step size dynamic adjustment sampling interval method is adopted for sampling, and the sampling time sequence is calculated;

[0018] S102. Apply Kalman filtering to the sampled analog current signal and analog voltage signal at each time moment to reduce noise, and obtain the filtered current value and filtered voltage value at each time moment;

[0019] S103. Convert the filtered current value and filtered voltage value at each time moment into digital signals through a current quantization function to obtain the original current value and the original voltage value at each time moment.

[0020] S104. Calculate the original power value at each time point based on the original current value and the original voltage value at each time point.

[0021] Preferably, the sampling time sequence consists of n sampling times; the first... Each sampling time The calculation formula is:

[0022] ,

[0023] In the formula, This is a time index, which defaults to the current time point; For the first Each sampling time; For sampling point index, , This represents the total number of sampling points; For the first Each sampling time; For the first Each sampling interval is determined through adaptive dynamic adjustment.

[0024] No. sampling interval The calculation formula is:

[0025] ,

[0026] In the formula, The reference sampling interval; It is the L2 norm, also known as the Euclidean norm, and is used in... Represents the input object; specifically, the input object here refers to... ; for Simulated current signals are constantly measured using a current transformer. for The simulated voltage signal is constantly measured by a voltage transformer. For the first One sampling time; for Simulated current signals are constantly measured using a current transformer. for The simulated voltage signal is constantly measured by a voltage transformer. For the first Each sampling time.

[0027] As a further improvement of the present invention: step S2 includes:

[0028] S201. Calculate the joint current abrupt change index at each time step;

[0029] S202. Calculate the set of segmented boundaries based on the joint current abrupt change index at each time point;

[0030] S203. Based on the boundary points of the segment boundary set, divide the original values ​​of current, voltage, and power at each time moment into sub-segments to obtain the data matrix of each sub-segment composed of the current sequence, voltage sequence, and power sequence.

[0031] Preferably, the joint current abrupt change index at each time point, i.e., the joint current abrupt change index at time t. The calculation formula is:

[0032] ,

[0033] In the formula, The standard deviation of the signal within the window; For local window width; From Time's up The definite integral at time step; The variable is the integral variable, representing the time index within the local time window; for The original value of the current at that moment; The average value of the signal within the window; The standard Gaussian kernel function; Frequency index; Minimum frequency; Maximum frequency; The short-time Fourier transform of the signal within the window at time t is at the t-th The power spectrum percentage at a given frequency point; It is a logarithmic function, with the default base being the natural constant.

[0034] As a further improvement of the present invention: step S3 includes:

[0035] S301. Based on the current sequence, voltage sequence, and power sequence of each sub-segment, calculate the current sequence tensor, voltage sequence tensor, and power-current physical relationship constraint tensor of each sub-segment to obtain the coupling components.

[0036] S302. Apply sparse constraints to the coupled tensor using Tucker decomposition to obtain the core tensor and the factor matrix representing the coupling relationship of variables, the time evolution mode and the physical constraint mode. Define the decoupling feature matrix based on the factor matrix.

[0037] As a further improvement of the present invention: step S401 includes:

[0038] S4011. Calculate the spectral convolution output features of each column of the decoupled feature matrix to obtain the spectral convolution output matrix;

[0039] S4012. Calculate the temporal convolution output features of each column of the decoupled feature matrix to obtain the temporal convolution output matrix;

[0040] S4013. Calculate a dual-channel fusion feature matrix with spatiotemporal joint representation capability based on the spectral convolution output matrix and the temporal convolution output matrix.

[0041] Preferably, the dual-channel fused feature matrix The calculation formula is:

[0042] ,

[0043] In the formula, For the fusion weight matrix; The output matrix is ​​the spectral convolution matrix; For splicing operations; This is the output matrix of the temporal convolution; For Hadamah accumulation; For the Softmax function; This is a pattern 3 factor matrix; For dimension A vector of all 1s.

[0044] As a further improvement of the present invention: step S402 includes:

[0045] S4021. Calculate the enhanced feature matrix of each sub-segment based on the dual-channel fusion feature matrix;

[0046] S4022. Calculate the physical constraint mode difference scalar between each sub-segment and its predecessor based on the enhanced feature matrix of each sub-segment;

[0047] S4023. Calculate the state probability vector of each sub-segment;

[0048] S4024. Calculate the total loss function based on the physical constraint modal difference scalar between each sub-segment and its predecessor, and the state probability vector of each sub-segment.

[0049] Preferably, the total loss function The calculation formula is:

[0050] ,

[0051] In the formula, k is the sub-segment index. ; This represents the total number of sub-segments; For the first The true state label of each sub-segment; The power sequence of the k-th sub-segment; For the first The state probability vector of each sub-segment; This is the scaling factor; For the first The physical constraint modal difference scalar between each sub-segment and the previous sub-segment.

[0052] The beneficial effects of the present invention are as follows: The method for measuring and analyzing the electrical variables of a distribution network provided by the present invention has high accuracy in analyzing the state of the distribution network.

[0053] First, S1's multi-rate adaptive sampling method can dynamically adjust the sampling rate to ensure that more data is collected when the distribution network signal changes drastically, thereby improving the sampling accuracy and time synchronization of the signal and overcoming the limitations of traditional fixed sampling rate in capturing transient events. By combining Kalman filtering for noise suppression, the signal-to-noise ratio of current and voltage measurement signals is significantly improved, effectively eliminating the influence of noise interference in traditional measurement methods and ensuring the accuracy of the data.

[0054] Furthermore, S2 employs a joint mutation index and an adaptive signal segmentation method. By combining local kurtosis with spectral entropy, it can accurately detect structural mutation points in the signal, avoiding feature loss or distortion that may occur with traditional equal-length segmentation methods.

[0055] Finally, S3 constructs a third-order coupling tensor with embedded power-current constraints in the decoupling of multivariable coupling features, and extracts decoupling features through Tucker decomposition, eliminating redundant coupling between current, voltage and power, and improving the identification capability of distribution network state analysis.

[0056] In summary, by optimizing the dataset used to train the state analysis model, optimizing the dataset preprocessing method, and optimizing the state analysis model itself, the performance of the state analysis model is improved, thereby making the state analysis model more accurate for the distribution network. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the principle of the present invention;

[0058] Figure 2 This is a graph of current data collected at fixed time intervals using a conventional fixed sampling method.

[0059] Figure 3 This is a graph of current data collected by the adaptive sampling method of this technology;

[0060] Figure 4 This is a diagram illustrating the original current signal.

[0061] Figure 5 A diagram illustrating the detection of combined mutation indicators;

[0062] Figure 6This is a comparison chart of the classification accuracy of different methods under various power grid conditions. Detailed Implementation

[0063] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0064] like Figure 1 As shown, the method for measuring and analyzing power distribution network variables provided by this invention includes:

[0065] S1. Calculate instantaneous power, and calculate the original values ​​of current, voltage, and power at each time point based on the power variable data of the power distribution network measured at the sampling time sequence.

[0066] Distribution network power variable data include analog current signals measured at various times by current transformers and analog voltage signals measured at various times by voltage transformers.

[0067] S101. To address the non-stationary characteristics of distribution network signals, a variable step size dynamic adjustment sampling interval method is adopted for sampling. When the signal changes drastically, the sampling rate is automatically increased, and when the signal is stable, the sampling rate is decreased to balance the data volume and resolution, and the sampling time sequence is calculated.

[0068] The sampling time sequence consists of n sampling times; the first... Each sampling time The calculation formula is:

[0069] ,

[0070] In the formula, This is a time index, which defaults to the current time point; For the first Each sampling time point is used to construct a sampling time sequence; For sampling point index, , This represents the total number of sampling points; For the first Each sampling time; For the first Each sampling interval is determined through adaptive dynamic adjustment.

[0071] No. sampling interval The calculation formula is:

[0072] ,

[0073] In the formula, The baseline sampling interval can be set to 0.001 seconds. This refers to the L2 norm, also known as the Euclidean norm. Represents the input object; specifically, the input object here refers to... ; for Simulates current signal at all times; for Simulate voltage signal at all times; For the first One sampling time; for Simulates current signal at all times; for Simulate voltage signal at all times; For the first Each sampling time;

[0074] S102. Apply Kalman filtering to the sampled analog current signal and analog voltage signal at each time moment to reduce noise, suppress measurement noise and interference, improve the signal-to-noise ratio, and obtain the filtered current value and filtered voltage value at each time moment.

[0075] Filter current value at any time The calculation formula is:

[0076] ,

[0077] In the formula, for The Kalman gain of the current at time step is calculated using the Kalman filtering algorithm; for Simulates current signal at all times; for Filter current value at any given time;

[0078] Filter voltage value at any time The calculation formula is:

[0079] ,

[0080] In the formula, for The Kalman gain of the voltage at time step is calculated using the Kalman filtering algorithm; for Simulate voltage signal at all times; for Filtered voltage value at any time.

[0081] S103. Convert the filtered current value and filtered voltage value at each time moment into digital signals through a current quantization function to obtain the original current value and the original voltage value at each time moment, so as to ensure that the current and voltage values ​​are aligned at the same time point.

[0082] The raw current value at time t represents the original value of the measured current. Current at any moment The calculation formula is:

[0083] ,

[0084] In the formula, This is a current quantization function that maps analog values ​​to digital values; for Filter current value at any given time;

[0085] Define the input of the current quantization function as ,but The calculation formula is:

[0086] ,

[0087] In the formula, This is a rounding function; This is the minimum value of the current, i.e., the lower limit of the quantization range. It is specifically set according to the measurement range of the current transformer or the minimum value of historical data, such as -1000A. This is the maximum value of the current, i.e., the upper limit of the quantization range. It is specifically set according to the measurement range of the current transformer or the maximum value of historical data, such as 1000A. The quantization bit depth is 16 by default. It is used to determine the number of bits for the digital value in analog-to-digital conversion, and determines the quantization resolution, i.e. the number of discrete levels that the digital value can be.

[0088] The raw voltage value at time is a representation of the raw voltage value obtained from the measurement. Original voltage value at time The calculation formula is:

[0089] ,

[0090] In the formula, This is a voltage quantization function that maps analog values ​​to digital values;

[0091] Define the input of the voltage quantization function as , The calculation formula is:

[0092] ,

[0093] In the formula, This is the minimum voltage value, i.e., the lower limit of the quantization range. It is specifically set according to the measurement range of the voltage transformer or the minimum value of historical data, such as -35kV. This is the maximum voltage value, i.e., the upper limit of the quantization range. It is specifically set according to the measurement range of the voltage transformer or the maximum value of historical data, such as 35kV.

[0094] S104. The original power values ​​at each moment are calculated using instantaneous power theory based on the original current and voltage values ​​at each moment;

[0095] The raw power value at time step represents the raw power value obtained from the measurement. raw power value at time The calculation formula is:

[0096] ,

[0097] In the formula, It is a cosine function; for The phase difference between the current and voltage at any given moment is calculated using the Hilbert transform.

[0098] Phase difference between current and voltage at any given moment The calculation formula is:

[0099] ,

[0100] In the formula, To obtain the phase angle; For Hilbert transform; It is a conjugate complex number;

[0101] Measurement of power variables in distribution networks is fundamental to state analysis. Conventional fixed sampling methods use fixed time intervals for data acquisition, maintaining the same sampling frequency regardless of whether the signal is in a stable or rapidly changing state, making it difficult to capture the details of transient events. In contrast, the adaptive sampling method proposed in this technology dynamically adjusts the sampling interval based on signal variation characteristics. It automatically increases the sampling density when current and voltage signals change drastically and appropriately decreases the sampling frequency when the signal is stable. Through multi-rate adaptive sampling combined with Kalman filtering noise reduction, it synchronously acquires current and voltage signals and calculates power values ​​based on instantaneous power theory, ensuring the accuracy and synchronization of the raw data. To verify the performance of the adaptive sampling method proposed in S1, it is compared with the conventional fixed sampling method, yielding... Figure 2 , Figure 3It can be observed that in regions where the signal waveform changes rapidly, the sampling point distribution of conventional fixed sampling methods is relatively sparse, which may not be able to fully capture the detailed features of transient events. However, the adaptive sampling method of this technology significantly increases the sampling point density in these key regions, forming a denser sampling distribution. The dynamic adjustment capability enables the adaptive sampling method of this technology to record abrupt changes and transient processes in the signal more accurately while ensuring data acquisition efficiency.

[0102] S2. Calculate the joint current mutation index at each time moment, calculate the segment boundary set based on the joint current mutation index at each time moment, and divide the original current value, the original voltage value, and the original power value at each time moment into multiple sub-segments based on the boundary points of the segment boundary set. Calculate the data matrix of each sub-segment. The data matrix of each sub-segment includes the current sequence, the voltage sequence, and the power sequence of each sub-segment.

[0103] S201. Calculate the joint current abrupt change index at each time step;

[0104] The kurtosis quantification time-domain abrupt change intensity of the signal within a local window and the spectral entropy quantification frequency-domain complexity based on the power spectrum ratio are weighted and fused through a sliding Gaussian window to form a current joint abrupt change index, thereby achieving comprehensive quantification of nonstationarity intensity.

[0105] The joint current abrupt change index at each time step, i.e., the joint current abrupt change index at time t, characterizes the nonstationarity of the signal in both the time and frequency domains. A larger value indicates a more pronounced abrupt change in the signal structure. The calculation formula is:

[0106] ,

[0107] In the formula, The standard deviation of the signal within the window represents local fluctuations and is obtained by calculating the standard deviation of the signal within the local window. The local window width is preferably set to 256 points, which is used to define the local calculation interval. From Time's up The definite integral at time step; for The original value of the current at that moment; The variable is the integral variable, representing the time index of the change within the local time window; The mean of the signal within the window represents the local benchmark and is obtained by calculating the mean of the signal within the local window. For standard Gaussian kernel function, Characterized by a standard Gaussian kernel function that weights the signals within a local window, centered at time t, with the weights varying accordingly. The decay occurs as time moves further away from time t; Frequency index; The minimum frequency can be set to 0.1Hz to cover low-frequency components; The maximum frequency can be set to 2kHz to cover high-frequency components; The short-time Fourier transform of the signal within the window at time t is at the t-th The power spectral density of a frequency point is calculated using a short-time Fourier transform and is used to quantize the frequency complexity of the signal. It is a logarithmic function, with the default base being the natural constant;

[0108] In the above formula, The term characterizes local kurtosis, quantifies the intensity of abrupt changes in the signal in the time domain, and is used to detect impulse or disturbance events. The term characterizes the local spectral entropy and quantifies the complexity of the signal in the frequency domain. It is used to detect spectral changes. The two complement each other to more comprehensively detect abrupt changes in non-stationary signals, avoid false detections by a single indicator, preserve the complete electromagnetic transient process, and improve segmentation accuracy.

[0109] The short-time Fourier transform of the signal within the window at time t is at the t Power spectral density at frequency points The calculation formula is:

[0110] ,

[0111] In the formula, for The short-time Fourier transform of the signal within the time window is at the 1st The power spectral density value at a frequency point is obtained by performing a short-time Fourier transform on the signal within a local window;

[0112] S202. Calculate the set of segmented boundaries based on the joint current mutation index at each time point to achieve adaptive boundary determination;

[0113] Multi-scale wavelet mode maxima detection is performed on the joint current abrupt change index at various time points. Extreme points with curvature exceeding a dynamic threshold are screened to determine the locations of signal structure abrupt changes, resulting in an adaptive set of segmented boundaries. This set contains all detected abrupt change points, corresponding to time points where signal characteristics undergo significant changes, and exhibits both adaptability and multi-scale characteristics. The calculation formula is:

[0114] ,

[0115] In the formula, The set of all time points that satisfy the conditions; The joint current mutation index at time t The second derivative with respect to time characterizes the curvature change of the joint mutation index. The curvature maxima correspond to mutation points, that is, the index changes drastically at the mutation points. This is the curvature threshold coefficient, which can be set to 0.15 to determine significant abrupt changes; For joint mutation index sequences The absolute maximum value, The joint mutation indicator sequence, i.e. A sequence that changes over time. The t-th element is .

[0116] S203. Based on the boundary points of the segment boundary set, divide the original values ​​of current, voltage, and power at each time moment into multiple sub-segments, calculate the data matrix of each sub-segment, and the data matrix of each sub-segment includes the current sequence, voltage sequence, and power sequence of each sub-segment.

[0117] The dimension of the data matrix for the kth sub-segment is... , For the first The length of each sub-segment, where each row corresponds to a time point, each column corresponds to an electrical variable, and each sub-segment corresponds to a continuous interval between signal structure abrupt changes; the data matrix of the k-th sub-segment. The calculation formula is:

[0118] ,

[0119] In the formula, This is the current sequence of the k-th sub-segment; This is the voltage sequence of the k-th sub-segment; Let k be the power sequence of the k-th sub-segment; k is the sub-segment index. ; This represents the total number of sub-segments;

[0120] Distribution network current, voltage, and power time-series data exhibit non-stationary characteristics, with transient disturbances and steady-state fluctuations intertwined. Conventional equal-length segmentation methods for signal segmentation analysis, by simply dividing the data at equal intervals based on time length, easily fragment a complete transient process into different sub-segments, compromising event integrity. Furthermore, fixed-length sliding windows cannot adapt to the duration of dynamic changes in events such as fault impacts and harmonic oscillations, leading to distorted feature extraction. S2 constructs a joint abrupt change index by fusing kurtosis and spectral entropy indices to dynamically detect abrupt changes in signal structure, achieving adaptive non-stationary signal segmentation while preserving the complete electromagnetic transient process. Figure 4 , Figure 5As shown, the joint mutation index curve used in S2 reflects the comprehensive change characteristics of the signal in the time and frequency domains. Regions with higher index values ​​correspond to time points when the signal characteristics change significantly. By detecting these mutation points, the segment boundaries are adaptively determined. The segment boundaries based on the mutation index can more accurately correspond to the actual location of the signal characteristic changes, ensuring the relative consistency of the signal characteristics within each sub-segment.

[0121] S3. Calculate the coupling components based on the current sequence, voltage sequence, and power sequence of each sub-segment, and calculate the decoupling characteristic matrix based on the coupling components;

[0122] S301. Based on the current sequence, voltage sequence, and power sequence of each sub-segment, calculate the current sequence tensor, voltage sequence tensor, and power-current physical relationship constraint tensor of each sub-segment to obtain the coupling components.

[0123] The coupling tensor of the k-th sub-segment represents the first... The physical coupling relationship of current, voltage and power in each segment is embedded with power-current constraints to eliminate redundancy and characterize the multivariable nonlinear physical relationship.

[0124] No. The tensor dimension of the current sequence of each sub-segment is Storing current timing data, the first Current sequence tensor of each sub-segment The calculation formula is:

[0125] ;

[0126] No. The voltage sequence tensor dimension of each sub-segment is Store voltage timing data, the first Voltage sequence tensor of each segment The calculation formula is:

[0127] ;

[0128] No. The power-current physical relationship constraint tensor dimension of each segment is... Characterizing the physical constraints of the power-current relationship, the first Power-current physical relationship constraint tensor of each segment The calculation formula is:

[0129] ,

[0130] In the formula, For Hadamah accumulation; The current sequence of the kth sub-segment element-wise reciprocals;

[0131] The coupling tensor of the k-th sub-segment Dimensions , For the first The length of each segment, i.e., the number of time points; It corresponds to 3 modalities and 3 feature channels; among them, Corresponding Coupled Tensor The third dimension is the feature channel with an index of 1. Corresponding Coupled Tensor The third dimension has a feature channel index of 2. Corresponding Coupled Tensor The third dimension has a feature channel index of 3;

[0132] S302. Apply sparse constraints to the coupled tensor using Tucker decomposition to obtain the core tensor and the factor matrix representing the coupling relationship, time evolution mode, and physical constraint mode of the variables. Define the decoupling feature matrix based on the factor matrix.

[0133] The optimization function that minimizes the non-negativity constraint Tucker decomposition through an iterative process is expressed as:

[0134] ,

[0135] In the formula, This is the mode 1 factor matrix, with dimension 1. The solution is obtained through optimization algorithms, which characterize the coupling relationship between variables. It is calculated independently for each sub-segment, with the current sub-segment being the k-th sub-segment by default. This is a pattern 2 factor matrix with dimension 1. The time evolution pattern is obtained by optimizing the algorithm. It is calculated independently for each sub-segment, with the current sub-segment being the k-th sub-segment by default. This is a pattern 3 factor matrix with dimension 1. The solution is obtained through optimization algorithms, which characterize the physical constraint modes. Each sub-segment is calculated independently, with the current sub-segment being the k-th sub-segment by default. For about , and The minimization optimization problem is solved by calculating and optimizing the k-th sub-segment. It is the Frobenius norm; Let be the coupling tensor of the k-th sub-segment, with dimension . , characterizing the The physical coupling relationship of current, voltage and power in each segment is embedded with power-current constraints to eliminate redundancy; The core tensor, representing the latent dimensional relationships after decomposition, is obtained through optimization using the non-negativity-constrained Tucker decomposition algorithm. Initial values ​​are randomly generated, and iterative updates are performed to minimize the objective function, with dimensions of [dimensionality missing]. Calculations are performed independently for each sub-segment, with the current sub-segment being the k-th sub-segment by default. The rank of mode 1, with a default value of 8, represents the potential dimension of the variable coupling relationship; The rank of mode 2, with a default value of 8, represents the potential dimension of the time evolution mode; The rank of mode 3, with a default value of 3, represents the latent dimension of the physical constraint mode; The product of mode 1, i.e., the core tensor and Multiply along pattern 1; The product of mode 2, i.e., the core tensor and Multiply along pattern 2; For mode 3 product, i.e. and Multiply along pattern 3; This is the sparsity constraint coefficient, with a value of 0.01, used to control the sparsity of the factor matrix; For pattern index, Corresponding variable coupling, Corresponding to the evolution over time, Corresponding physical constraints; It is an L1 norm; For the first The factor matrix of each pattern is obtained by solving an optimization algorithm;

[0136] definition To decouple the characteristic matrix, due to the factor matrix Characterizing the time evolution pattern, therefore taking , dimension Each sub-segment is calculated independently, with the current sub-segment being the k-th sub-segment by default.

[0137] In practical implementation, by solving this optimization problem, we can obtain... and , , Factor matrix Feature representations that include a time dimension can effectively preserve information about the dynamic changes in signals and are suitable as input features for time-frequency feature extraction.

[0138] Strong nonlinear coupling exists between electrical variables. Directly concatenating these variables as inputs leads to feature redundancy, while conventional independent channel processing methods ignore physical constraints, thus reducing state identifiability. S3 constructs a third-order coupling tensor with embedded power and current physical constraints and applies a non-negative constraint Tucker decomposition to extract a decoupling feature matrix characterizing the coupling relationship and time evolution mode of variables, thereby eliminating redundant correlations between electrical variables.

[0139] S4. Construct a state analysis model and train the state analysis model to obtain the trained state analysis model;

[0140] S401. Calculate the dual-channel fusion feature matrix to construct the spectrum-time domain dual-channel feature extraction module;

[0141] S4011. Calculate the spectral convolution output features of each column of the decoupled feature matrix to obtain the spectral convolution output matrix;

[0142] The spectral convolution output feature of the j-th column feature, with dimension . The calculation is performed on the k-th sub-segment to characterize the adaptive frequency domain features, which can highlight the frequency domain patterns in signal abrupt change regions; the spectral convolution output features of the j-th column features. The calculation formula is:

[0143] ,

[0144] In the formula, To modify the activation function of the linear unit; This is the inverse Fourier transform, which converts the frequency domain signal back to the time domain; Fourier transform converts the time-domain signal to the frequency domain. For decoupling characteristic matrix The j-th column feature vector has dimension . The calculation is performed on the k-th sub-segment; This is an element-wise multiplication operation in the frequency domain; For complex spectral kernels, the dimension is The elements are complex numbers and are trainable parameters. Frequency domain features are adaptively learned through frequency domain convolution, and specific harmonic or transient frequency patterns of the distribution network are learned during training. Use the Sigmoid activation function; For the first The local spectral entropy vector of the column features, with dimension . It is used to modulate the convolution output, enhancing the sensitivity to complex frequency domain changes;

[0145] Time of the first Local spectral entropy vector of column features The calculation formula is:

[0146] ,

[0147] In the formula, Frequency index; For decoupling characteristic matrix The Column feature vector exist The short-time Fourier transform of the signal within the time window is at the 1st The power spectrum ratio at a frequency point is used to quantify the frequency complexity of the feature vector;

[0148] Decoupling feature matrix The Column feature vector exist The short-time Fourier transform of the signal within the time window is at the 1st Power spectral density at frequency points The calculation formula is:

[0149] ,

[0150] In the formula, For decoupling characteristic matrix The Column feature vector exist The short-time Fourier transform of the signal within the time window is at the 1st The power spectral density value at a frequency point is obtained by performing a short-time Fourier transform on the feature vector within a local window;

[0151] S4012. Calculate the temporal convolution output features of each column of the decoupled feature matrix to obtain the temporal convolution output matrix;

[0152] The time-domain convolution output feature of the j-th column features represents an adaptive time-domain feature, which can sensitively respond to the local rate of change of current and voltage; the time-domain convolution output feature of the j-th column features The calculation formula is:

[0153] ,

[0154] In the formula, This is the kernel offset; This defines the temporal radius of the convolution kernel, with a default value of 5, and defines the range of the convolution window. ; For the temporal convolution kernel at an offset of The weights at each point are trainable parameters that can be dynamically adjusted through learning to improve the capture of mutation features by responding to time series data. For decoupling characteristic matrix The j-th column eigenvector in The value at time; This is the sensitivity coefficient, which can be set to 5 to control the degree of sensitivity to changes in features; The characteristic difference characterizes the local rate of change;

[0155] Feature difference The calculation formula is:

[0156] ,

[0157] In the formula, For decoupling characteristic matrix The j-th column eigenvector in The value at time; For decoupling characteristic matrix The j-th column eigenvector in The value at any given moment.

[0158] S4013. Calculate a dual-channel fusion feature matrix with spatiotemporal joint representation capability based on the spectral convolution output matrix and the temporal convolution output matrix;

[0159] The dimension of the dual-channel fused feature matrix is It possesses spatiotemporal joint representation capabilities, fusing frequency domain and time domain features; dual-channel fused feature matrix. The calculation formula is:

[0160] ,

[0161] In the formula, To fuse the weight matrix, the dimension is , are trainable parameters that linearly transform the concatenated features to a low-dimensional space, reducing redundancy; The output matrix of the spectral convolution has dimensions of . The i-th column vector is the spectral convolution output feature of the j-th column feature. ; For splicing operations; The output matrix of the temporal convolution has a dimension of . The i-th column vector is the temporal convolution output feature of the j-th column feature. ; For the Softmax function; For dimension A vector of all 1s;

[0162] Decoupling features still lack frequency domain information. Conventional Fast Fourier Transform ignores time-frequency locality, while wavelet transform has fixed basis functions, making it difficult to adapt to diverse fault spectra. S401 overcomes this problem by performing frequency domain convolution with learnable spectral kernels and time domain convolution with feature differential modulation on the decoupling feature matrix in parallel, fusing them to generate dual-channel features with spatiotemporal joint representation capabilities.

[0163] S402. Calculate the state probability vector and total loss function for each sub-segment;

[0164] S4021. Calculate the enhanced feature matrix of each sub-segment based on the dual-channel fusion feature matrix;

[0165] The vector is obtained by multiplying the core tensor with the physical constraint mode, then linearly mapping the context weight matrix, modulating it with the Sigmoid function, and expanding the modulated vector to the same dimension as the two-channel feature matrix through the outer product operation. Then, the two-channel feature matrix is ​​enhanced by the Hadamard product to generate an enhanced feature matrix that can more effectively capture the key modes of state change.

[0166] No. The enhanced feature matrix of each sub-segment, with dimension [missing information]. Characterizing the spatiotemporal features modulated by physical constraints, it can more effectively capture key patterns of state changes; Enhanced feature matrix of each sub-segment The calculation formula is:

[0167] ,

[0168] In the formula, For dimension A vector of all 1s; This is the context weight matrix, with dimension 1. , are trainable parameters used to map the product vector of the core tensor and the physical constraint mode to the feature space; This is the outer product operation, used to copy a vector into a matrix; For vectorization operations;

[0169] S4022. Calculate the physical constraint mode difference scalar between each sub-segment and its predecessor based on the enhanced feature matrix of each sub-segment;

[0170] By calculating the Frobenius norm difference between the current sub-segment physical constraint mode and the previous sub-segment physical constraint mode, a physical constraint mode difference scalar is obtained, which is used to quantify the intensity of state changes between sub-segments.

[0171] No. The larger the value of the physical constraint modal difference scalar between the first sub-segment and the previous sub-segment, the more obvious the state abrupt change. scalar of physical constraint modal difference between each sub-segment and the previous sub-segment The calculation formula is:

[0172] ,

[0173] In the formula, This is the mode 3 factor matrix corresponding to the previous sub-segment, representing the physical constraint mode of the previous sub-segment. The current sub-segment is assumed to be the [number missing]th [segment missing]. Each segment;

[0174] S4023. Calculate the state probability vector of each sub-segment;

[0175] By using the current joint mutation index as attention weight, the enhanced feature matrix is ​​weighted and averaged over time points. Then, through the linear transformation of the classification weight matrix and the classification bias vector, the Softmax function is applied to obtain the state probability vector, thereby highlighting the importance of mutation points for state classification.

[0176] No. The state probability vector of each sub-segment has a dimension of . , characterizing the The state classification results of each sub-segment; the first The state probability vector of each sub-segment The calculation formula is:

[0177] ,

[0178] In the formula, This is the classification weight matrix, with dimension 1. , are trainable parameters used to linearly map the weighted averaged enhanced features to the state class space. This represents the number of status categories. By default, it includes six categories: normal state, short circuit fault, overvoltage, undervoltage, harmonic interference, and transient oscillation. In actual implementation, it must correspond to the number of categories and category names that are pre-marked by the user. For the first In each sub-segment The attention weight at time step is such that the larger the value, the more significant the change at that time step, representing the importance of the time step to the state classification. For the first Enhanced feature matrix of each sub-segment exist The row vector at time t, i.e. All feature values ​​at time , dimension ; This is the classification bias vector, with dimension . , are trainable parameters;

[0179] No. In each sub-segment Attention weight at any moment The calculation formula is:

[0180] ,

[0181] In the formula, for The instantaneous current combined abrupt change index; The current joint abrupt change index at time s; To distinguish it from the time index t;

[0182] S4024. Calculate the total loss function based on the physical constraint modal difference scalar between each sub-segment and its predecessor, and the state probability vector of each sub-segment;

[0183] The total loss function is calculated by combining classification cross-entropy loss and state transition constraint loss. The state transition constraint loss is obtained by exponentially weighting the L2 norm of the state probability vectors of adjacent sub-segments with the state transition features. The total loss function aims to ensure that the state analysis model accurately classifies states while conforming to the physical laws of state transitions. The calculation formula is:

[0184] ,

[0185] In the formula, For the first The true state labels of each sub-segment are one-hot vectors with dimensions of . These are data labels that have been pre-labeled by humans; The weight of the state transition constraint loss is a hyperparameter that can be set to 0.1. It serves as the weight hyperparameter for the state transition constraint loss and controls the strength of the smoothness constraint. For the first The state probability vector of each sub-segment has a dimension of . ; This is a scaling factor, a hyperparameter that can be set to 1.0, used to adjust the effect of physical constraint modal differences on smoothness loss;

[0186] Distribution network state analysis requires accurate identification of operating states. However, there are temporal correlations between states. Direct independent classification ignores the physical laws governing state transitions, which can easily lead to inconsistent classification results. Conventional methods only use classification losses and do not consider the smoothness of the state sequence, thus reducing the identifiability of states. S402 enhances dual-channel features by utilizing physical constraint modes to quantify the intensity of state changes between sub-segments. It also combines abrupt change indices for weighted classification and introduces state transition constraints through a joint loss function to ensure that the state classification results simultaneously satisfy accuracy and temporal consistency.

[0187] S403. Based on the total loss function, repeat S401~S402 to train and iteratively optimize the state analysis model;

[0188] Training continues until the stopping condition is met: training is terminated when the validation set loss does not decrease for 20 consecutive rounds, or the total number of iterations reaches the preset upper limit of 1000 rounds, and the parameters of the state analysis model with the best performance on the validation set are saved.

[0189] S5. Calculate the new original values ​​of current, voltage, and power at each time step using the new power distribution network variable data collected in S1. After executing S2~S3, input the data into the trained state analysis model to obtain the probability vector of each state. Take the state category corresponding to the maximum probability as the state analysis result of that sub-segment.

[0190] The classification accuracy of this method under various power grid conditions was compared with that of other methods under various power grid conditions, as shown in Table 1. Figure 6 As shown in Table 1, Figure 6 As shown, the classification accuracy of this technical method is the highest under various power grid conditions, and the average accuracy is also relatively advanced. Even under power grid conditions where other methods perform poorly, it can still achieve an accuracy of over 85%, proving the excellent performance of this technical method.

[0191] Table 1. Comparison of classification accuracy of different methods under various power grid conditions.

[0192]

[0193] To verify the performance improvement of our proposed method compared to the optimal benchmark method (here referring to machine learning), we compared the accuracy of our proposed method with that of the optimal benchmark method in different scenarios, as shown in Table 2. The overall average accuracy of our proposed method is higher because of the collaborative optimization throughout the entire process, from measurement, segmentation, decoupling to modeling, which systematically improves the state identification capability. The accuracy in steady-state scenarios (normal state) is higher because multi-rate sampling and Kalman filtering provide steady-state data with a higher signal-to-noise ratio, laying a more accurate foundation for classification. The accuracy improvement in transient and fault scenarios is significant because the joint mutation index segmentation ensures the integrity of transient events, and dual-channel feature extraction effectively captures the time-frequency local features of faults. The most significant accuracy improvement is in complex disturbance scenarios (harmonics, oscillations) because coupling tensor decoupling eliminates redundancy between variables, and state transition constraint loss makes the model's learning of continuous disturbance patterns more consistent with physical laws.

[0194] Table 2 Performance Improvement Analysis of This Technical Method Compared to the Optimal Benchmark Method

[0195]

[0196] Table 3 compares the misclassification rates of the optimal benchmark method (100% accuracy) and the proposed method under various power grid conditions. As shown in Table 3, the proposed method has a lower misclassification rate under normal conditions because high-precision measurement reduces false triggering, and feature decoupling avoids misclassifying normal fluctuations as abnormalities. Under short-circuit conditions, the proposed method has a lower misclassification rate because adaptive sampling fully captures fault spikes, and dual-channel features enhance the identification of abrupt change modes. Under harmonic interference, the proposed method has a lower misclassification rate because the spectral entropy index and learnable spectral kernel convolution are specifically optimized to separate complex frequency domain modes. Under transient oscillations, the proposed method has a lower misclassification rate because state transition constraints effectively smooth state jumps during oscillations, reducing isolated misclassification points.

[0197] Table 3. Effect of this technical method on reducing the misjudgment rate under various power grid conditions.

[0198]

Claims

1. A method for measuring and analyzing the electrical variables of a distribution network, characterized in that, include: S1. Calculate instantaneous power, and calculate the original values ​​of current, voltage, and power at each time point based on the power variable data of the power distribution network measured at the sampling time sequence. S2. Calculate the joint current mutation index at each time moment, calculate the segment boundary set based on the joint current mutation index at each time moment, and divide the original current value, the original voltage value, and the original power value at each time moment into multiple sub-segments based on the boundary points of the segment boundary set. Calculate the data matrix of each sub-segment. The data matrix of each sub-segment includes the current sequence, the voltage sequence, and the power sequence of each sub-segment. S201. Calculate the joint current abrupt change index at each time step; The joint current abrupt change index at each time point, i.e., the joint current abrupt change index at time t. The calculation formula is: ， In the formula, This is a time index, which defaults to the current time point; The standard deviation of the signal within the window; For local window width; From Time's up The definite integral at time step; The variable is the integral variable, representing the time index within the local time window; for The original value of the current at that moment; The average value of the signal within the window; The standard Gaussian kernel function; Frequency index; Minimum frequency; Maximum frequency; The short-time Fourier transform of the signal within the window at time t is at the t-th The power spectrum percentage at a given frequency point; It is a logarithmic function, with the default base being the natural constant; S202. Calculate the set of segmented boundaries based on the joint current abrupt change index at each time point; S203. Based on the boundary points of the segment boundary set, divide the original values ​​of current, voltage, and power at each time moment into sub-segments to obtain the data matrix of each sub-segment composed of the current sequence, voltage sequence, and power sequence; S3. Calculate the coupling components based on the current sequence, voltage sequence, and power sequence of each sub-segment, and calculate the decoupling characteristic matrix based on the coupling components; S4. Construct a state analysis model and train the state analysis model to obtain the trained state analysis model; S401. Calculate the dual-channel fusion feature matrix; S402. Calculate the state probability vector and total loss function for each sub-segment; S403. Based on the total loss function, repeat S401~S402 to train and iteratively optimize the state analysis model; S5. Obtain new raw values ​​of current, voltage, and power at each time step by collecting new power variables from the distribution network in S1. After executing S2~S3, input them into the trained state analysis model to obtain the probability vector of each state. Take the state category corresponding to the maximum probability as the state analysis result of this sub-segment.

2. The method for measuring and analyzing power distribution network variables according to claim 1, characterized in that, The steps in S1 include: S101. To address the non-stationary characteristics of distribution network signals, a variable step size dynamic adjustment sampling interval method is adopted for sampling, and the sampling time sequence is calculated; S102. Apply Kalman filtering to the sampled analog current signal and analog voltage signal at each time moment to reduce noise, and obtain the filtered current value and filtered voltage value at each time moment; S103. Convert the filtered current value and filtered voltage value at each time moment into digital signals through a current quantization function to obtain the original current value and the original voltage value at each time moment. S104. Calculate the original power value at each time point based on the original current value and the original voltage value at each time point.

3. The method for measuring and analyzing power distribution network variables according to claim 2, characterized in that, The sampling time sequence consists of n sampling times; the first... Each sampling time The calculation formula is: ， In the formula, For the first Each sampling time; For sampling point index, , This represents the total number of sampling points; For the first Each sampling time; For the first Each sampling interval is determined through adaptive dynamic adjustment. No. sampling interval The calculation formula is: ， In the formula, The reference sampling interval; It is the L2 norm, also known as the Euclidean norm, and is used in... Represents the input object; specifically, the input object here refers to... ; for Simulated current signals are constantly measured using a current transformer. for The simulated voltage signal is constantly measured by a voltage transformer. For the first One sampling time; for Simulated current signals are constantly measured using a current transformer. for The simulated voltage signal is constantly measured by a voltage transformer. For the first Each sampling time.

4. The method for measuring and analyzing the electrical variables of a distribution network according to claim 1, characterized in that, The steps in S3 include: S301. Based on the current sequence, voltage sequence, and power sequence of each sub-segment, calculate the current sequence tensor, voltage sequence tensor, and power-current physical relationship constraint tensor of each sub-segment to obtain the coupling components. S302. Apply sparse constraints to the coupled tensor using Tucker decomposition to obtain the core tensor and the factor matrix representing the coupling relationship of variables, the time evolution mode and the physical constraint mode. Define the decoupling feature matrix based on the factor matrix.

5. The method for measuring and analyzing power distribution network variables according to claim 1, characterized in that, The steps in S401 include: S4011. Calculate the spectral convolution output features of each column of the decoupled feature matrix to obtain the spectral convolution output matrix; S4012. Calculate the temporal convolution output features of each column of the decoupled feature matrix to obtain the temporal convolution output matrix; S4013. Calculate a dual-channel fusion feature matrix with spatiotemporal joint representation capability based on the spectral convolution output matrix and the temporal convolution output matrix.

6. The method for measuring and analyzing power distribution network variables according to claim 5, characterized in that, The dual-channel fusion feature matrix The calculation formula is: ， In the formula, For the fusion weight matrix; The output matrix is ​​the spectral convolution matrix; For splicing operations; This is the output matrix of the temporal convolution; For Hadamah accumulation; For the Softmax function; This is a pattern 3 factor matrix; For dimension A vector of all 1s.

7. The method for measuring and analyzing the electrical variables of a distribution network according to claim 1, characterized in that, The steps in S402 include: S4021. Calculate the enhanced feature matrix of each sub-segment based on the dual-channel fusion feature matrix; S4022. Calculate the physical constraint mode difference scalar between each sub-segment and its predecessor based on the enhanced feature matrix of each sub-segment; S4023. Calculate the state probability vector of each sub-segment; S4024. Calculate the total loss function based on the physical constraint modal difference scalar between each sub-segment and its predecessor, and the state probability vector of each sub-segment.

8. The method for measuring and analyzing the electrical variables of a distribution network according to claim 7, characterized in that, The total loss function The calculation formula is: ， In the formula, k is the sub-segment index. ; This represents the total number of sub-segments; For the first The true state label of each sub-segment; The power sequence of the k-th sub-segment; The loss weights are used for state transition constraints; For the first The state probability vector of each sub-segment; This is the scaling factor; For the first The physical constraint modal difference scalar between each sub-segment and the previous sub-segment.

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