Power transmission line live-line state determination method and system based on sliding window regularization inversion and multi-window fusion

Abstract

The invention relates to a power transmission line live-line state determination method and system based on sliding window regularization inversion and multi-window fusion, and belongs to the technical field of power transmission line on-line monitoring. According to the method and the system, a non-contact three-dimensional electric field sensor is used for collecting space electric field signals, and the live-line state of the power transmission line is identified through a sliding window regularization inversion algorithm and a multi-window probability fusion model. According to the method, a Tikhonov regularization and multi-point augmentation strategy is adopted, so that the average inversion error is reduced by more than 50% compared with that of a traditional method under the working condition of containing 5% of random noise, and the jump problem under safe distance measurement is solved; abnormal interference in a track can be automatically recognized through a sliding window weight fusion mechanism, and it is ensured that accurate electrified state information can still be output when local data are damaged; meanwhile, discrimination confidence is introduced into the probabilistic determination model, frequent jump errors of a hard threshold value at boundary points are solved, and the acceptability of a diagnosis result is improved.

Description

Technical Field

[0001] This invention belongs to the field of online monitoring technology for power transmission lines, and relates to a method and system for determining the energized state of power transmission lines based on sliding window regularization inversion and multi-window fusion. Background Technology

[0002] In the context of intelligent power system inspection, non-contact monitoring using electric field sensors within a safe distance is a core method for determining the energized state of power lines. However, due to the strict electrical insulation safety distance between transmission lines and sensors, the spatial electric field signal attenuates significantly and overlaps in phase during long-distance propagation, resulting in extremely high spatial coupling of the excitation contributions formed by each phase conductor at the measuring point. Mathematically, this manifests as an extremely high condition number in the decoupling matrix, exhibiting significant numerical ill-conditioning. Under this ill-posed inversion structure, traditional pseudo-inverse algorithms amplify minute power frequency noise in the environment, sensor attitude disturbances, and system biases caused by model simplification (such as conductor sag and split conductor effects) by orders of magnitude. This directly leads to drastic random jumps or spurious fluctuations in the inverted source-side voltage, severely affecting the stability and usability of the inversion results, making it difficult to support reliable condition diagnosis at the industrial level.

[0003] On the other hand, the identification of the energized state of transmission lines is essentially a classification and decision-making problem, encompassing various dynamic conditions such as undervoltage, steady-state operation, and overvoltage. Traditional decision-making logic typically relies on the absolute amplitude of the inverted voltage and uses a fixed-ratio hard threshold as the switching criterion. However, in real-world complex electromagnetic fields and non-ideal measurement environments, relying solely on a single inverted value for hard threshold determination is highly prone to misjudgment in the threshold neighborhood; that is, even small amplitude drifts can cause frequent jumps in the identification result between different states. Furthermore, due to the lack of quantitative assessment of uncertainties during the measurement process, existing decision-making systems cannot provide maintenance personnel with reliable results, leading to a high risk of misjudgment or missed detection when handling boundary conditions (such as slight undervoltage caused by high-resistance grounding). Therefore, how to suppress the noise amplification effect in the inversion process through algorithmic innovation while ensuring physical isolation safety, and how to construct a probabilistic decision-making system that is compatible with measurement uncertainties and has fault-tolerant decision-making capabilities, are key bottlenecks that current online monitoring technology for transmission lines urgently needs to overcome.

[0004] For online monitoring of high-voltage transmission lines, existing technologies mainly rely on ground-based or near-field electromagnetic field sampling and numerical analysis. However, under the constraint of ensuring electrical safety distances, these traditional methods often exhibit common problems such as limited observation dimensions, poor algorithm robustness, and rigid decision-making strategies. They struggle to maintain stable identification accuracy under complex on-site electromagnetic environments. Their main shortcomings include:

[0005] 1) Limitations of static single-point measurement: Relying solely on the electric field information of a single spatial measurement point to establish a low-dimensional analytical matrix lacks spatial redundancy information support. The inversion results are easily affected by local electromagnetic interference or strong influence from a single abnormal sampling point, resulting in a serious lack of stability in the judgment.

[0006] 2) Instability of the pseudo-inverse algorithm: The traditional Moore-Penrose pseudo-inverse method lacks the ability to suppress observation noise when dealing with high condition number (ill-conditioned) decoupling matrices. Under long-distance measurement conditions, weak measurement errors can be amplified by the algorithm, causing the output voltage estimate to deviate from the physical true value, or even produce unexplained negative values ​​or out-of-limit values.

[0007] 3) Rigid hard threshold decision logic: Existing technologies lack statistical modeling of measurement noise and model errors, and use fixed discrimination intervals. At the critical point of power transmission line state switching, frequent false alarms are easily generated due to signal disturbances, and it is impossible to output a confidence index that reflects the reliability of the current diagnostic results. Summary of the Invention

[0008] In view of this, and in view of the technical problems existing in the prior art, the purpose of the present invention is to provide a method and system for determining the energized state of transmission lines based on sliding window regularized inversion and multi-window fusion. The method and system use a non-contact three-dimensional electric field sensor to collect spatial electric field signals, and identify the energized state of transmission lines through a sliding window regularized inversion algorithm and a multi-window probabilistic fusion model.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion, the method specifically includes the following steps: S1. Establish a field-source coupling model based on a sliding window: Collect three-dimensional electric field data from multiple measuring points on the safe trajectory of the transmission line, construct a linear equation set between the electric field observation vector and the source-side voltage vector based on the principle of electric field superposition, and group the measuring points using a sliding window strategy to construct a local inversion unit. S2. Multi-window fusion Tikhonov regularized inversion solution: For the electric field observation data in each sliding window, the voltage estimate is solved by the Tikhonov regularized least squares method, and the weight of each window is calculated based on the window condition number and residual ratio. The inversion results of multiple windows are weighted and fused to obtain the final voltage estimate. S3. State probabilistic determination based on softmax mapping: The fused voltage estimate is normalized, the deviation of each state interval is calculated by the interval distance function, the state probability of each window is obtained by combining the softmax function, and the window weights are used for weighted fusion to output the final charged state and its confidence level.

[0010] Furthermore, in step S1, the transmission line consists of N conductors, and each phase conductor is represented by a straight line segment in space. This straight line segment is uniquely determined by two spatial coordinate points: the starting point and the ending point. A single sensor is used to move and sample along a predetermined safe trajectory to collect M sets of three-dimensional electric field vector data. The spatial redundancy information provided by the continuous sampling points is used to avoid instantaneous interference. The total electric field vector response at the measuring point is formed by the linear superposition of the electric field contributions formed by all conductors under unit voltage excitation.

[0011] Furthermore, step S1 specifically includes: S11, let the first j Under a unit voltage excitation, the first conductor... i Measurement points P i =( x i , y i , z i The electric field response vector generated at the measuring point under unit excitation is defined as: (twenty three) According to the principle of electric field integration, when the first... i The voltage across the conductor is a unit voltage. V i =1V, and when the voltage of other conductors is 0, the linear charge density is denoted as: The elements of the decoupling matrix in each direction are obtained: x The elements of the directional decoupling matrix are: (twenty four) y The elements of the directional decoupling matrix are: (25) z The elements of the directional decoupling matrix are: (26) S12. The electric field strength at the measuring point and the source-side voltage satisfy the following relationship: (27) Among them, coefficient Depending solely on the geometry of the conductor, its spatial location, and the coordinates of the measurement points,M The three-dimensional electric field data from each measurement point are summarized, and the following system of equations is established: (28) The matrix form is as follows: (29) Constructing a least-squares objective function based on the L2 norm (30) To make the objective function Minimize, let its gradient be about The gradient is zero: (31) After sorting, we can obtain: (32) In the formula, That is, a matrix Moore-Penrose generalized inverse matrix; S13. For each discrete point, a single-circuit line is a 3x3 square matrix, and a double-circuit line is a 3x6 underdetermined matrix. An augmented matrix needs to be constructed using continuous multi-point methods to transform the underdetermined system into a well-determined system. To achieve unified processing, a length of [missing information] is defined. L The sliding window (with adjacent measurement points along the path forming a local inversion unit), the first k A set of measurement points covered by a window { k , k +1,……., k + L -1}; Stack the electric field observations and decoupling matrices within the window row by row to obtain the windowed electric field quantity and the augmented decoupling matrix: (33) in n u =3 or n u =6; therefore, only 3 needs to be satisfied. L ≥ n u The window system can then be converted from under-determined to over-determined: single-circuit lines can take... L ≥1, for double-circuit lines, at least take L ≥2. The significance of this sliding window strategy lies in the fact that it retains the advantage of "enhancing stability with multi-point information" while avoiding the strong pull of local anomalies caused by stacking the entire path into a single large matrix at once, thus making it more suitable for statistical fusion of online engineering processing and subsequent state determination.

[0012] Furthermore, step S2 specifically includes: S21. Considering noise and model error, Tikhonov regularized least squares is used to solve for the voltage estimate within each window. : (34) In the above formula, >0 is the regularization parameter. To balance the accuracy and stability of the solution, the L-curve method is used for adaptive determination. The optimal value, the inflection point of the L curve, represents the best balance between solution accuracy and stability; Equation (12) can be written in closed form as follows: (35) S22. The sliding window outputs a set of local inversion results that vary along the path. Considering that the ill-conditioned nature and observation quality of different windows are not consistent, it is necessary to measure the quality of the windowed results. For the ill-conditioned index of the matrix, the window augmentation matrix is ​​calculated. condition number This is used to measure the sensitivity of the window inversion to noise; Define the window residual ratio: (36) The window weights are constructed based on the degree to which the current window model interprets the observations. (37) in , >0 is used to adjust parameters, balancing ill-conditioned error and fitting error penalties; as the window slides along the path, and The weights will be recalculated. It also updates adaptively, a process that serves as a weight update mechanism; when the window satisfies... Too large or When the limit is exceeded, the weight is reduced to avoid low-quality windows misleading the final state determination; S23. After obtaining the inversion results and weights for each window, the weighted fusion yields the final voltage estimate: (38) in K The total number of windows is used to fuse the output, which in turn outputs the final voltage estimate. On the other hand, it retains the window weight distribution, which can serve as a source of confidence for subsequent state judgments.

[0013] Furthermore, step S3 specifically includes: S31. Map the fused voltage estimate to the per-unit space, let the first... k The inversion voltage vector of each sliding window is To eliminate the influence of voltage level differences, the corresponding per-unit voltage is defined as follows: The details are as follows: (39) in This corresponds to the number of phases in the line structure. This refers to the rated voltage value of the corresponding phase; S32. Divide the line into four energized states: undervoltage, normal voltage, and overvoltage, and denote them as sets. Each state is represented as an interval in the per-unit field. To avoid jump errors at interval boundaries caused by hard threshold determination, an interval distance function is introduced to characterize the deviation between the per-unit voltage and each state interval; for any per-unit voltage and state interval ,definition: (40) Therefore, when When a state falls within a certain state interval, its distance is zero; the farther it deviates from the interval, the larger the distance value, thus providing a continuous and differentiable metric basis for state determination; based on this, the distance is further calculated for the first state. k Components in each window j In state c m The discrimination score is defined as follows: (41) in Always greater than 0, used to adjust the smoothness of the probability distribution; the above scores are mapped to window-level state probabilities using the softmax function: (42) Thus, the first k Each window corresponds to a component j State probability vector (43) S33. Considering the significant differences in geometric information content and data consistency among different sliding windows, this invention utilizes the constructed window weights. Weighted fusion of window-level probabilities, and component j The probability of the fused state is defined as follows: (44) Finally, the state corresponding to the maximum fusion probability is obtained based on all windows. .

[0014] The present invention also provides a power transmission line energization status determination system based on sliding window regularization inversion and multi-window fusion, which adopts the method described above.

[0015] The beneficial effects of this invention are as follows: The method for determining the energized state of transmission lines described in this patent has the following advantages: 1) By adopting Tikhonov regularization and multi-point augmentation strategies, the average inversion error is reduced by more than 50% compared with traditional methods under the condition of 5% random noise, thus solving the problem of jump in safe distance measurement.

[0016] 2) The sliding window weight fusion mechanism can automatically identify abnormal interference in the trajectory, ensuring that accurate charged state information can still be output even when local data is damaged.

[0017] 3) The probabilistic judgment model introduces a discrimination confidence level, which solves the problem of frequent jump errors of hard thresholds at boundary points and improves the acceptability of diagnostic results.

[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 Diagram of a sensor decoupling model under a power transmission line; Figure 2 A schematic diagram illustrating the selection of regularization parameters for the L-curve method; Figure 3 This is a schematic diagram of sensor data acquisition. Figure 4 This is a flowchart illustrating the process of determining the energized state of a transmission line according to the present invention. Detailed Implementation

[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0021] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0022] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0023] The technical solution provided by this invention is a method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion. Figure 4 This is a flowchart illustrating the process of determining the energized state of a transmission line according to the present invention. The method specifically includes the following steps: S1. Establish a field-source coupling model based on a sliding window: Collect three-dimensional electric field data from multiple measuring points on the safe trajectory of the transmission line, construct a linear equation set between the electric field observation vector and the source-side voltage vector based on the principle of electric field superposition, and group the measuring points using a sliding window strategy to construct a local inversion unit. S2. Multi-window fusion Tikhonov regularized inversion solution: For the electric field observation data in each sliding window, the voltage estimate is solved by the Tikhonov regularized least squares method, and the weight of each window is calculated based on the window condition number and residual ratio. The inversion results of multiple windows are weighted and fused to obtain the final voltage estimate. S3. State Probabilistic Determination Based on Softmax Mapping: The fused voltage estimates are normalized, the deviation of each state interval is calculated using the interval distance function, the state probability of each window is obtained by combining the softmax function, and weighted fusion is performed using window weights to output the final charged state and its confidence level. The following is a detailed introduction to this plan: 1. Establish a field-source coupling model based on a sliding window. Routing power transmission lines N The system consists of several conductors, each represented in space by a straight line segment, uniquely determined by two spatial coordinate points: the starting point and the ending point. A single sensor is used to sample along a predetermined safety trajectory. M The system generates a set of three-dimensional electric field vector data, utilizing the spatial redundancy information provided by continuous sampling points to avoid transient interference. The total electric field vector response at the measurement point can be linearly superimposed from the electric field contributions generated by all conductors under unit voltage excitation. Figure 1 This is a diagram of a sensor decoupling model under a power transmission line. Figure 3 This is a schematic diagram of sensor data acquisition. Let the first... j Under a unit voltage excitation, the first conductor... i Measurement points P i =( x i , y i , z i The electric field response vector generated at the measuring point under unit excitation is defined as: (45) According to the principle of electric field integration, when the... i The voltage across the conductor is a unit voltage ( V i =1V), and when the voltage of other conductors is 0, the line charge density is denoted as: The elements of the decoupling matrix in each direction can be obtained.

[0024] x The elements of the directional decoupling matrix are: (46) y The elements of the directional decoupling matrix are: (47) z The elements of the directional decoupling matrix are: (48) The electric field strength at the measuring point and the source-side voltage satisfy the following relationship: (49) Among them, coefficient Depending solely on the geometry of the conductor, its spatial location, and the coordinates of the measurement points, M The summation of the three-dimensional electric field data from each measurement point allows us to establish the following system of equations: (50) The matrix form is as follows: (51) Constructing a least-squares objective function based on the L2 norm (52) To make the objective function Minimize, let its gradient be about The gradient is zero: (53) After sorting, we can obtain: (54) In the formula, That is, a matrix The Moore-Penrose generalized inverse matrix.

[0025] For each discrete point, a single-circuit line is a 3x3 square matrix, and a double-circuit line is a 3x6 underdetermined matrix. An augmented matrix needs to be constructed using continuous multi-point methods to transform the underdetermined system into a well-determined system. To achieve unified processing, a length of [missing information] is defined. L The sliding window (with adjacent measurement points along the path forming a local inversion unit), the first k A set of measurement points covered by a window { k , k +1,……., k + L -1}. Stacking the electric field observations and decoupling matrices within the window row by row yields the windowed electric field quantities and the augmented decoupling matrix: (55) in n u =3 or n u =6. Therefore, only 3 needs to be satisfied. L ≥ n u The window system can then be converted from under-determined to over-determined: single-circuit lines can take... L ≥1, for double-circuit lines, at least take L ≥2. The significance of this sliding window strategy lies in the fact that it retains the advantage of "enhancing stability with multi-point information" while avoiding the strong pull of local anomalies caused by stacking the entire path into a single large matrix at once, thus making it more suitable for statistical fusion of online engineering processing and subsequent state determination.

[0026] 2. Multi-window fusion Tikhonov regularized inversion solution Considering noise and model error, Tikhonov regularized least squares is used to solve for the voltage estimate within each window. : (56) In the above formula, >0 is the regularization parameter. To strike a balance between the accuracy and stability of the solution, the L-curve method is used for adaptive determination. Optimal value, such as Figure 2 As shown, the inflection point of the L-curve represents the optimal balance between solution accuracy and stability.

[0027] The closed-form solution of equation (12) can be written as: (57) The sliding window outputs a set of locally inverted results that vary along the path. Considering that the ill-conditioned nature and observation quality of different windows are not consistent, it is necessary to measure the quality of the windowed results. For the ill-conditioned index of the matrix, the window augmentation matrix is ​​calculated. condition number This is used to measure the sensitivity of the window inversion to noise.

[0028] Define the window residual ratio: (58) The window weights are constructed based on the degree to which the current window model interprets the observations. (59) in , A value greater than 0 is used to adjust parameters, balancing the penalty for ill-conditioned error and fitting error. As the window slides along the path, and The weights will be recalculated. It also updates adaptively, a process that serves as a weight update mechanism. When the window satisfies... Too large or When the limit is exceeded, the weight is reduced to avoid low-quality windows misleading the final state determination.

[0029] After obtaining the inversion results and weights for each window, the weighted fusion yields the final voltage estimate: (60) in K The total number of windows is used to fuse the output, which in turn outputs the final voltage estimate. On the other hand, it retains the window weight distribution, which can serve as a source of confidence for subsequent state judgments.

[0030] 3. Probabilistic state determination based on softmax mapping The fused voltage estimate is mapped to the per-unit space, let the first... k The inversion voltage vector of each sliding window is To eliminate the influence of voltage level differences, the corresponding per-unit voltage is defined as follows: The details are as follows: (61) in This corresponds to the number of phases in the line structure. This refers to the rated voltage value of the corresponding phase.

[0031] The line is divided into four energized states: undervoltage, normal voltage, and overvoltage, denoted as set. Each state is represented as an interval in the per-unit field. To avoid jump errors at interval boundaries caused by hard thresholding, an interval distance function is introduced to characterize the deviation between the per-unit voltage and each state interval. For any per-unit voltage... and state interval ,definition (62) Therefore, when When a state falls within a certain state interval, its distance is zero; the further it deviates from the interval, the larger the distance value, thus providing a continuous and differentiable metric basis for state determination. Based on this, the [missing information]... k Components in each window j In state c m The discrimination score is defined as follows: (63) in Always greater than 0, used to adjust the smoothness of the probability distribution. The above scores are then mapped to window-level state probabilities using the softmax function: (64) Thus, the first k Each window corresponds to a component j State probability vector (65) Considering the significant differences in geometric information content and data consistency among different sliding windows, this paper utilizes the window weights constructed in Section 3.3.1. Weighted fusion of window-level probabilities. For the components... j The probability of the fused state is defined as follows: (66) Finally, the state corresponding to the maximum fusion probability is obtained based on all windows. .

[0032] Example: In this embodiment, a double-circuit AC overhead transmission line is used to verify the method of the present invention. The line adopts a double-circuit three-phase arrangement: taking a 110 kV line as an example, the heights of the three-phase conductors above ground are approximately 22.8 m, 19.0 m, and 15.0 m, respectively, and the vertical distances between phases are approximately 3.8 m and 4.0 m; the horizontal distance between the two circuits is approximately 6 m. For higher voltage levels (such as 220 kV) lines, the heights of the three-phase conductors above ground can be approximately 36.2 m, 29.8 m, and 23.0 m, the vertical distances between phases are approximately 6.4 m and 6.8 m, and the horizontal distance between the two circuits is approximately 10 m, while the process of the present invention remains consistent.

[0033] A single three-dimensional electric field sensor, while maintaining a safe distance, is used to acquire electric field vector data at multiple measurement points along the line corridor. An augmented equation system is constructed from the measurement point data using a sliding window approach. Within each window, regularized least squares inversion is employed to obtain the window voltage estimate. Weighting is then applied based on window ill-conditioning and residual consistency to perform multi-window weighted fusion, yielding a combined voltage estimate for each phase. To enable executable determination of the energized state, the combined voltage estimates are... With rated phase voltage U n A comparison was made. Based on the characteristics of the operating voltage amplitude, the state set was divided into four categories: undervoltage, normal, and overvoltage. Determined as depressurization c 1; when Determined as undervoltage c 2; when Judged as normal c 3; when It was determined to be an overvoltage. c 4. Construct a discrimination score and obtain the state probability through softmax. As shown in Table 1, in the double-circuit line operation, when only voltage disturbances (0%, 30%, 70%, 100%, 120%) are applied to phase A1, the system's judgment result for phase A1 shows a monotonic state transition consistent with the voltage level: gradually transitioning from undervoltage (0%) to undervoltage (30%, 70%), judged as normal near the rated voltage (100%), and judged as overvoltage after the voltage rises (120%); and the probability output corresponding to each state maintains a high degree of dominance (phase A1 shows the target state probability dominance under different operating conditions). At the same time, the other five phases are consistently judged as normal under the above-mentioned operating conditions, with the probability concentrated in the high range and only fluctuating slightly.

[0034] Table 1 Summary Table of Double-Circuit Status Judgment Tab1 Summary Table of Double-Trip Status Judgments

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for determining the energized state of transmission lines based on sliding window regularized inversion and multi-window fusion, characterized in that, The method specifically includes the following steps: S1. Establish a field-source coupling model based on a sliding window: Collect three-dimensional electric field data from multiple measuring points on the safe trajectory of the transmission line, construct a linear equation set between the electric field observation vector and the source-side voltage vector based on the principle of electric field superposition, and group the measuring points using a sliding window strategy to construct a local inversion unit. S2. Multi-window fusion Tikhonov regularized inversion solution: For the electric field observation data in each sliding window, the voltage estimate is solved by the Tikhonov regularized least squares method, and the weight of each window is calculated based on the window condition number and residual ratio. The inversion results of multiple windows are weighted and fused to obtain the final voltage estimate. S3. State probabilistic determination based on softmax mapping: The fused voltage estimate is normalized, the deviation of each state interval is calculated by the interval distance function, the state probability of each window is obtained by combining the softmax function, and the window weights are used for weighted fusion to output the final charged state and its confidence level.

2. The method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion according to claim 1, characterized in that, In step S1, the transmission line consists of N conductors, and each phase conductor is represented by a straight line segment in space. This straight line segment is uniquely determined by two spatial coordinate points: the starting point and the ending point. A single sensor is used to move and sample along a predetermined safety trajectory to collect M sets of three-dimensional electric field vector data. The spatial redundancy information provided by the continuous sampling points is used to avoid instantaneous interference. The total electric field vector response at the measuring point is a linear superposition of the electric field contributions generated by all conductors under unit voltage excitation.

3. The method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion according to claim 2, characterized in that, Step S1 specifically includes: S11, let the first j Under a unit voltage excitation, the first conductor... i Measurement points P i =( x i , y i , z i The electric field response vector generated at the measuring point under unit excitation is defined as: (1) According to the principle of electric field integration, when the first... i The voltage across the conductor is a unit voltage. V i =1V, and when the voltage of other conductors is 0, the linear charge density is denoted as: The elements of the decoupling matrix in each direction are obtained: x The elements of the directional decoupling matrix are: (2) y The elements of the directional decoupling matrix are: (3) z The elements of the directional decoupling matrix are: (4) in, For the first i Spatial coordinate vectors of each measuring point For the first j The parameters on the conductor segment are t The source point coordinate vector; S12, Electric field strength at the measuring point With source-side voltage The following relationship must be satisfied: (5) Among them, coefficient Depending solely on the geometry of the conductor, its spatial location, and the coordinates of the measurement points, M The three-dimensional electric field data from each measurement point are summarized, and the following system of equations is established: (6) The matrix form is as follows: (7) Constructing a least-squares objective function based on the L2 norm (8) To make the objective function Minimize, let its gradient be about The gradient is zero: (9) After sorting, we can obtain: (10) In the formula, That is, a matrix Moore-Penrose generalized inverse matrix; S13. For each discrete point, a single-circuit line is a 3x3 square matrix, and a double-circuit line is a 3x6 underdetermined matrix. An augmented matrix needs to be constructed using continuous multi-point methods to transform the underdetermined system into a well-posed system; the length is defined as... L The sliding window, the first k A set of measurement points covered by a window { k , k +1,……., k + L -1}; Stack the electric field observations and decoupling matrices within the window row by row to obtain the windowed electric field quantity and the augmented decoupling matrix: (11) in n u =3 or n u =6; therefore, only 3 needs to be satisfied. L ≥ n u The window system can then be converted from under-determined to over-determined: single-circuit lines can take... L ≥1, for double-circuit lines, at least take L ≥2.

4. The method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion according to claim 3, characterized in that, Step S2 specifically includes: S21. Solve for voltage estimates using Tikhonov regularized least squares within each window. : (12) In the above formula, >0 is the regularization parameter. To balance the accuracy and stability of the solution, the L-curve method is used for adaptive determination. The optimal value, the inflection point of the L curve, represents the best balance between solution accuracy and stability; Equation (12) can be written in closed form as follows: (13) S22. The sliding window outputs a set of local inversion results that vary along the path. ; Calculate the window augmentation matrix condition number This is used to measure the sensitivity of the window inversion to noise; Define the window residual ratio: (14) The window weights are constructed based on the degree to which the current window model interprets the observations. (15) in , >0 is used to adjust parameters, balancing ill-conditioned error and fitting error penalties; as the window slides along the path, and The weights will be recalculated. It also updates adaptively, a process that serves as a weight update mechanism; when the window satisfies... Too large or When the limit is exceeded, the weight is reduced to avoid low-quality windows misleading the final state determination; S23. After obtaining the inversion results and weights for each window, the weighted fusion yields the final voltage estimate: (16) in K The total number of windows is used to fuse the output, which in turn outputs the final voltage estimate. On the other hand, it retains the window weight distribution, which can serve as a source of confidence for subsequent state judgments.

5. The method for determining the energized state of transmission lines based on sliding window regularization inversion and multi-window fusion according to claim 4, characterized in that, Step S3 specifically includes: S31. Map the fused voltage estimate to the per-unit space, let the first... k The inversion voltage vector of each sliding window is To eliminate the influence of voltage level differences, the corresponding per-unit voltage is defined as follows: The details are as follows: (17) in This corresponds to the number of phases in the line structure. This refers to the rated voltage value of the corresponding phase; S32. Divide the line into four energized states: undervoltage, normal voltage, and overvoltage, and denote them as sets. Each state is represented as an interval in the per-unit field. To avoid jump errors at interval boundaries caused by hard threshold determination, an interval distance function is introduced to characterize the deviation between the per-unit voltage and each state interval; for any per-unit voltage and state interval ,definition: (18) when When a state falls within a certain state interval, its distance is zero; the farther it deviates from the interval, the larger the distance value, thus providing a continuous and differentiable metric basis for state determination; based on this, the distance is further calculated for the first state. k Components in each window j In state c m The discrimination score is defined as follows: (19) in Always greater than 0, used to adjust the smoothness of the probability distribution; the above scores are mapped to window-level state probabilities using the softmax function: (20) Thus, the first k Each window corresponds to a component j State probability vector (21) S33. Utilizing the constructed window weights Weighted fusion of window-level probabilities, and component j The probability of the fused state is defined as follows: (22) Finally, the state corresponding to the maximum fusion probability is obtained based on all windows. .

6. A system for determining the energized state of transmission lines based on sliding window regularized inversion and multi-window fusion, characterized in that, The system employs the method described in any one of claims 1 to 5.

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 5.

Images