A fault prediction self-healing power distribution method

Abstract

The present application relates to the technical field of power system distribution network, and more particularly to a fault prediction self-healing power distribution method, which comprises the following steps: first, obtaining equivalent admittance and physical residual by controlled disturbance and synchronous phasor measurement, generating spectrum-topology co-embedded coordinates and innovation consistency index, and completing topology checking; then, fusing space evidence, time evidence and physical evidence, combining hazard rate evaluation to form control access strength value; performing bias search under the constraints of feasible domain prior, action shielding and control barrier, and obtaining self-healing operation sequence by power flow optimization with conditional value at risk as the target; finally, according to counterfactual energy margin shaping operation threshold, completing full sequence checking and generating execution package according to signal time sequence logic and satisfiability model theory, and realizing low misoperation, provable safety and rapid recovery.

Description

Technical Field

[0001] This invention relates to the field of power system distribution network technology, and in particular to a fault prediction and self-healing distribution method. Background Technology

[0002] The distribution network is experiencing simultaneous growth in distributed generation, electrification load, and power supply reliability assessment. Traditional "alarm-manual handling" or "passive tripping-post-reconfiguration" operating methods are insufficient to balance power outage losses, power quality, and protection coordination under complex network structures and uncertain output conditions. A proactive approach encompassing the entire process of "prediction-isolation-reconfiguration-release" is a key path to reducing power outage energy, shortening recovery time, and improving audit traceability. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a fault prediction and self-healing power distribution method. This invention actively obtains equivalent admittance and physical residual through observability, and combines spectral-topological co-embedding and innovation consistency to form a control admission strength value; it generates candidates under feasible domain priors and control barrier constraints, and obtains a self-healing operation sequence through conditional risk value power flow optimization; finally, it drives threshold shaping with counterfactual energy margin, and combines the release of temporal logic and satisfiability mode theory consistency proof summaries to reduce false trips and power outage energy.

[0004] A fault prediction and self-healing power distribution method includes the following steps:

[0005] A controlled disturbance is applied and the voltage and current response is obtained by synchronous phasor measurement. The equivalent admittance and physical residual are calculated based on the injection response relationship. The spectrum-topology co-embedding coordinates and innovation consistency index are generated. The topology verification is completed to obtain the verified topology state.

[0006] Suspicious clusters are identified on the spectral-topological co-embedding coordinates. Spatial, temporal, and physical evidence are fused together with hazard rate assessment to obtain control access strength values.

[0007] Based on the control access strength value, the conditional risk value confidence level and barrier advancement coefficient are set. Candidate atomic actions are screened by feasible region prior and action shielding. The search is carried out within the joint state space determined by the verified topology state under the constraint of the control barrier function. The power flow is optimized with the conditional risk value as the objective to obtain the self-healing operation sequence and calculate the counterfactual energy margin.

[0008] Based on the counterfactual energy margin and control access strength value, the upper voltage limit, lower voltage limit and upper current limit are dynamically tuned. The entire sequence consistency is checked based on the signal timing logic and satisfiability modulus theory, and an execution package is generated.

[0009] Preferably, a controlled disturbance is applied at the power supply side or the tie switch position, and the voltage and current responses aligned with the disturbance are obtained through synchronous phasor measurements; the equivalent admittance and physical residual calculated based on the injection response relationship are used to construct a weighted graph of the measurement points and generate spectrum-topology co-embedding coordinates through graph Laplace spectrum embedding; the innovation consistency index is obtained by graph domain coherence calculation of the innovation quantity of the linear prediction model of zero-sequence voltage or phase current; the topology verification generates a verified topology state based on the consistency of power direction and phase.

[0010] Preferably, a density-based clustering method is used to divide suspicious clusters on the spectral-topological co-embedding coordinates, and the clustering results are mapped to physical line segments to determine the target segments.

[0011] Preferably, spatial, temporal, and physical evidence are synthesized using the Durmst-Schafer evidence fusion method. The hazard rate assessment uses a semi-parametric hazard rate model to calculate the arrival probability and uses it as a priori weight to weight and correct the synthesized result. The control access strength value is determined by the weighted and corrected evidence belief measure.

[0012] Preferably, the conditional value at risk confidence level and the barrier advance coefficient are set in a monotonic correspondence with the control access strength value, and the conditional value at risk confidence level and the barrier advance coefficient are increased accordingly as the control access strength value increases.

[0013] Preferably, the feasible region prior is constructed by using a learning method with confidence coverage to build the outer envelope of the feasibility classifier. The output of the feasible region prior is three categories: feasible, uncertain, and infeasible. Candidate atomic actions corresponding to uncertain and infeasible are eliminated in the screening stage.

[0014] Preferably, the action shielding includes the following rules: prohibiting the formation of closed-loop connection without the support of relay protection, limiting the grid-connected phase angle difference to no more than the upper limit of the grid-connected phase angle difference, limiting the short-circuit current level to no more than the upper limit of the short-circuit current level, and prohibiting cross-level operation that crosses the time limit window of the superior protection.

[0015] Preferably, the search is performed in the joint state space where the verified topology has been determined using a random exploration tree algorithm. Candidate sequences are generated under the constraints of the control barrier function, and the sampling bias is set according to the spectral-topology co-embedding coordinates, and the path cost is shaped according to the innovation consistency index.

[0016] Preferably, the power flow optimization with conditional risk value as the objective is based on a linearized AC power flow model. The constraints include upper voltage limit, lower voltage limit, upper current limit, short-circuit current level, relay protection coordination and operation mode. The optimization outputs a self-healing operation sequence and generates a feasible domain proof document containing the voltage and current envelopes, short-circuit current level and relay protection coordination verification results. At the same time, the counterfactual energy margin is calculated based on the optimization duality sensitivity.

[0017] Preferably, the signal timing logic specifications include node voltage falling within the shaped upper and lower voltage limits, achieving the target load recovery rate within a preset time window, and prohibiting parallel operations without relay protection; the satisfiability modal theory encodes the relay protection logic, and performs a full-sequence consistency check on the short-circuit current level and topology connectivity; the execution package includes a self-healing operation sequence, a dynamic threshold plan, a signal timing logic check report, and a summary of the satisfiability modal theory consistency proof.

[0018] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0019] By jointly modeling controlled disturbances and synchronous phasor measurements, equivalent admittance and physical residuals, a high separability of precursors and a topologically consistent operational baseline were achieved. Through spectral-topology co-embedding coordinates and innovation consistency indices, evidence fusion and hazard rate assessment, control access strength values ​​were generated, achieving "intervention only upon evidence consistency" gating. By coupling feasible domain priors, action shielding and control barrier functions with random exploratory tree search, candidate generation and rapid convergence of process safety were achieved. Through power flow optimization targeting conditional at-risk value, the goals of tail risk suppression and intrinsic electrical feasibility satisfaction in uncertain scenarios were achieved. By counterfactual energy margin-driven operational threshold shaping, combined with signal timing logic and satisfiability modulo theory verification, provable safety before release and adaptive protection during runtime were achieved. By carrying threshold plans, robustness and proof summaries in execution packets, hierarchical execution and end-to-end audit traceability were achieved. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0021] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation.

[0022] like Figure 1 As shown, a fault prediction and self-healing power distribution method includes the following steps:

[0023] A controlled disturbance is applied and the voltage and current response is obtained by synchronous phasor measurement. The equivalent admittance and physical residual are calculated based on the injection response relationship. The spectrum-topology co-embedding coordinates and innovation consistency index are generated. The topology verification is completed to obtain the verified topology state.

[0024] This invention is used in fault prediction and self-healing distribution methods to build proactive observability capabilities. The aim is to transform previously indistinguishable fault precursors into measurable, comparable, and transferable evidence, forming an analytical baseline consistent with power flow and topology. Through controlled disturbance injection and synchronous phasor measurement, highly sensitive estimates of line equivalent parameters and network consistency are obtained under weak disturbance conditions, providing reliable input for subsequent evidence fusion and self-healing sequence synthesis.

[0025] Controlled disturbance injection is implemented on the power supply side or at the tie switch location. The disturbance waveform amplitude is limited and the frequency band avoids the device's resonant band. The synchronous phasor measurement device acquires the voltage and current responses within the disturbance window using a unified clock, with the timestamp strictly aligned with the disturbance trigger. To eliminate measurement bias, the short windows before and after the disturbance are first de-trending and calibrated for amplitude and phase, followed by frequency decimation to ensure a stable and comparable injection-response relationship.

[0026] The equivalent admittance estimation is based on the injection-response relationship. For the injection point and the affected measurement point, the voltage and current increments caused by the disturbance are defined, and the frequency domain equivalent admittance estimate is calculated using the following formula. ,in Injection point With measuring points In frequency Equivalent admittance estimation at the point, The increment of the complex amplitude of the injected current. This represents the voltage amplitude increment caused by the injection. By comparing the equivalent admittance estimate with the historical baseline admittance, the parameter deviation distribution can be obtained, which can be used to indicate precursors such as insulation degradation, poor contact, and localized heating.

[0027] Physical residuals are used to verify the consistency between measurements and network equations. Based on a linearized AC power flow model, a system of algebraic equations is constructed to evaluate the consistency of the power flow state vector at the current moment. The residuals are defined as follows: ,in For a moment The physical residuals The coefficient matrix is ​​generated from the verified equipment parameters and topology. The state vector consists of node voltages and branch powers. This is a constant vector composed of injected power and control settings. When the physical residual exceeds the adaptive threshold, it indicates an inconsistency between the current power flow and the network model, requiring the triggering of higher-density retesting or entry into the abnormal channel of evidence fusion.

[0028] Spectral-topological co-embedded coordinates are used to unify "electrical parameter variations," "topological adjacency relationships," and "traveling wave and zero-sequence characteristics" into a single geometric space. The method involves: constructing node feature vectors using the real part of equivalent admittance, the imaginary part of equivalent admittance, physical residuals, and zero-sequence characteristics; building a weighted graph by combining electrical distances; and calculating the first few feature vectors of the graph Laplace to obtain low-dimensional coordinates. In this invention, spectral-topological co-embedded coordinates are used for two types of tasks: first, to perform density clustering in the coordinate space to identify suspicious clusters and map them back to the physical circuit; and second, to serve as a basis for sampling bias and cost shaping in subsequent search and optimization, narrowing the search range and convergence time.

[0029] The innovation consistency index is used to characterize the degree of spatial coordination among time-series precursors. Taking short-window sequences of zero-sequence voltage or phase current as the object, a linear prediction model is used to decompose the stationary component and the innovation quantity. The model is as follows: ,in For time series samples of measurement points, The linear prediction coefficients are... The model order is... For innovative sequences, generalized coherence statistics are performed on innovative sequences from adjacent measuring points to obtain an innovation consistency index, which is used to identify cooperative anomalies caused by early, weak-amplitude, and intermittent perturbations. The innovation consistency index provides temporal evidence for evidence fusion and also rewards or penalizes path costs in subsequent search phases, encouraging earlier isolation of suspicious segments.

[0030] Topology verification uses phasor angle difference and power direction as constraints, and combines equivalent admittance estimation and physical residuals to make consistency inferences about switching states, eliminating topology combinations that do not match measurements, and finally forming a verified topology state. The verified topology state has a dual role in this invention: on the one hand, it serves as the sole topology input for physical residual calculation and power flow optimization; on the other hand, it serves as the boundary condition for action shielding rules and control barrier functions, preventing merging or switching in unprotected ring network states.

[0031] Preferably, a controlled disturbance is applied at the power supply side or the tie switch position, and the voltage and current responses aligned with the disturbance are obtained through synchronous phasor measurements; the equivalent admittance and physical residual calculated based on the injection response relationship are used to construct a weighted graph of the measurement points and generate spectrum-topology co-embedding coordinates through graph Laplace spectrum embedding; the innovation consistency index is obtained by graph domain coherence calculation of the innovation quantity of the linear prediction model of zero-sequence voltage or phase current; the topology verification generates a verified topology state based on the consistency of power direction and phase.

[0032] This invention addresses the need for proactive observability in fault prediction and self-healing power distribution. By applying low-amplitude controlled disturbances at the power supply side or tie switch location and collecting voltage and current responses aligned with the disturbances using a synchronous phasor measurement device, an "injection-response" link is constructed. This allows line equivalent parameters and network consistency to be identified with high sensitivity under weak disturbance conditions, thereby forming structured observation features, spectral-topology co-embedding coordinates, innovative consistency indicators, and verified topology states. This provides a unified baseline for subsequent evidence fusion and self-healing sequence synthesis.

[0033] Controlled disturbance injection employs waveforms with limited amplitude and controllable frequency band, with triggering and measurement timestamps synchronized. To suppress measurement bias, detrending, amplitude and phase calibration, and window function processing are first performed within a short window before and after the disturbance. Then, complex amplitude increments are extracted at the disturbance frequency to ensure the stability and repeatability of subsequent ratio calculations.

[0034] Equivalent admittance estimation is based on the "injection-response" relationship, and it converts the voltage increment and current increment caused by the disturbance into a frequency domain ratio. By comparing the equivalent admittance estimate with the historical baseline admittance, the parameter deviation distribution can be obtained, which can be used to indicate fault precursors such as insulation degradation, poor contact and local heating; the incremental definition makes this index more sensitive to slowly changing anomalies.

[0035] Physical residuals are used to verify the consistency between measurements and network equations. Algebraic constraints are constructed based on a linearized AC power flow model to evaluate the consistency of the current power flow state vector. When the physical residual exceeds the threshold, it indicates that there is an inconsistency between the current power flow and the model, and a retest should be triggered or an abnormal evidence channel should be entered; it is complementary to the equivalent admittance estimation, the former is biased towards model consistency, and the latter is biased towards parameter drift.

[0036] To unify the representation of "electrical parameter variation," "topological adjacency," and "zero-sequence characteristics," a weighted graph of measurement points is constructed and graph Laplace spectral embedding is performed to obtain spectral-topological co-embedded coordinates. For each measurement point, a feature vector is extracted, consisting of the real part of the equivalent admittance, the imaginary part of the equivalent admittance, the physical residual, and the zero-sequence statistic. Kernel weights are defined in conjunction with the electrical distance. ,in For measuring points With measuring points similarity, For measuring points eigenvectors, For weighted L2 norm, and For kernel scale and distance attenuation parameters, The distance is the electrical distance. The graph Laplacian is obtained from the weight matrix, and its first few eigenvectors are used as low-dimensional coordinates. The spectral-topological co-embedded coordinates form "suspicious clusters" in the coordinate space, facilitating mapping back to the physical line to locate abnormal areas; on the other hand, they serve as sampling bias and cost shaping criteria in self-healing sequence synthesis, narrowing the search solution domain.

[0037] The innovation consistency index is used to characterize the spatial coherence of timing precursors. A linear prediction model is established for short-window sequences of zero-sequence voltage or phase current. The innovative sequences of adjacent measuring points are statistically analyzed in the graph domain and summarized into an innovation consistency index at the node level. This index can highlight the spatial synchronicity of weak amplitude and intermittent anomalies such as high-resistance grounding and intermittent arcing, and be used as temporal evidence in evidence fusion. At the same time, it can apply rewards or penalties to path costs during the sequence search stage to promote the strategy of "early isolation and near splicing".

[0038] Topology verification uses phasor angle difference and power direction as criteria, and combines equivalent admittance estimation and physical residuals to infer the consistency of switching states. Topology combinations that do not meet the consistency requirements of angle difference and power direction are eliminated, generating verified topology states. Verified topology states are also used as the sole topology input for subsequent power flow optimization and as boundary conditions for action shielding, avoiding merging or switching in the absence of relay protection.

[0039] Example 1: In a city ring network system, a controlled disturbance injection is completed at the tie switch, and the responses at two end measurement points are collected by a synchronous phasor measurement device. The data processing module performs detrending, amplitude and phase calibration, and frequency extraction within the disturbance window, calculating the equivalent admittance estimate and physical residual. The imaginary part of the equivalent admittance of one branch increases while the real part decreases, and the physical residual shows a peak in the same time window. The equivalent admittance estimate, physical residual, and zero-sequence statistics are jointly used to construct a weighted graph of the measurement points. Corresponding nodes in the spectrum-topology co-embedded coordinates form dense clusters. Graph domain coherence statistics are performed on the innovation sequences in the neighborhood of this cluster, showing a significant increase in the innovation consistency index. Based on this, a piecewise switch assumption inconsistent with the power direction is eliminated during topology verification, and the verified topology state is output. Ultimately, the structured observation features, spectral-topology co-embedded coordinates, innovation consistency indicators, and verified topological states are submitted to the evidence fusion module. Isolation and reconstruction path searches are prioritized in the corresponding physical segments, reducing the number of attempts and consistency checks for the self-healing sequence, while ensuring that voltage and current constraints are not breached.

[0040] Suspicious clusters are identified on the spectral-topological co-embedding coordinates. Spatial, temporal, and physical evidence are fused together with hazard rate assessment to obtain control access strength values.

[0041] This invention uses spectral-topological co-embedded coordinates to spatiotemporally aggregate observational information, and generates a control access strength value through evidence fusion and hazard rate assessment, which serves as the sole gating quantity for self-healing sequence synthesis. The goal is to transform the spatial aggregation, temporal coordination, and physical consistency of precursors into a single scalar, ensuring that subsequent searches and optimizations are conducted only within segments proven "worth intervening in."

[0042] The spectral-topology co-embedding coordinates are derived from the feature map embedding in the previous step, reflecting the consistent geometric structure of electrical parameter variations and topological adjacencies. Using these coordinates as input, a density-based clustering algorithm is employed to divide the coordinate space into suspicious clusters, and cluster members are mapped back to physical line segments, forming a three-dimensional candidate target. Clustering serves only as a "spatial indicator" and does not directly trigger control; whether control is initiated is jointly determined by evidence fusion and hazard rate.

[0043] Spatial, temporal, and physical evidence are all calculated at the "cluster granularity." Spatial evidence comes from a comprehensive score of the cluster's point density, the significance of equivalent admittance bias, and the consistency of physical residuals, reflecting "which segment is more anomalous." Temporal evidence uses the average value and stability of the innovation consistency index obtained in the previous step within the cluster, reflecting "whether the anomaly occurs simultaneously at multiple measurement points." Physical evidence comes from the proportion of physical residuals exceeding the threshold and the statistical significance of equivalent admittance bias within the cluster, reflecting "whether the anomaly is inconsistent with the network equation." After interval normalization, the three types of evidence are mapped to basic belief assignments and enter the evidence fusion unit to output the beliefs and probabilities of "allowing intervention," "not intervening," and "uncertain."

[0044] Hazard rate assessment is used to provide prior weights and time window semantics for evidence fusion, employing a semi-parametric hazard rate model. Given a feature vector based on environmental and asset states, arrival rate and probability of arrival within a future window are defined. , ,in For fault arrival rate, For a moment eigenvectors, For model parameters, It is a logarithmic probability function. To evaluate the time window, This represents the probability of arrival within that time window. The probability of arrival is used to weight the "allow intervention" belief, in order to eliminate situations that "spatially appear abnormal but have low short-term risk" from the control entry point.

[0045] Controlling the admission strength value compresses the fused interval beliefs into a single scalar for consistent cross-module calls. ,in To control the access intensity value, As the lower bound of the belief that "intervention is permissible," This is the upper bound of the possibility of "permitting intervention". This is a weighted coefficient. The higher the control access strength value, the more consistent the evidence and the higher the probability of reaching it. The conservatism of subsequent conditions' risk value and control barriers is also increased. When the control access strength value is lower than the preset threshold, only alarms and retests are retained, and self-healing is not initiated.

[0046] Example 2: After the controllable disturbance and phasor acquisition are completed at the tie switch of a feeder in the urban ring network, a high-density cluster of nodes in a certain segment of the embedded coordinates appears. The equivalent admittance deviation within this cluster shows a coordinated change with an increase in the imaginary part and a decrease in the real part, and the proportion of physical residuals exceeding the threshold is relatively high, forming a consistent direction between spatial and physical evidence. The innovative consistency index of multiple neighboring measurement points within the same window increases synchronously, constituting temporal evidence. The hazard rate assessment uses temperature, humidity, rainfall, and equipment operating years as feature vectors to calculate a high probability of arrival in the next few minutes. The evidence fusion output shows that the belief and probability of "allowing intervention" are both in a high range, and the control access strength value obtained by the previous formula is in a high position. Based on this, the system enters the self-healing sequence synthesis and prioritizes the construction of isolation and reconstruction candidates in the physical segment corresponding to this cluster. This example shows that under weak disturbance and short window measurement conditions, through coordinate clustering and the joint constraint of three types of evidence, the three-dimensional information of "location-time-physical" can be compressed into a control access strength value, effectively avoiding the search and operation of irrelevant segments, while improving the pass rate of subsequent consistency verification.

[0047] Cluster granularity is determined by the density threshold of embedded coordinates and the minimum cluster size to balance positioning accuracy and robustness; evidence normalization uses robust quantile standardization to suppress isolated extreme values; belief mapping should be calibrated with labeled events during the training phase to ensure that the contribution of beliefs and probabilities to the control access strength value conforms to the safety strategy; the hazard rate model is trained in seasonal and load scenario partitions to prevent spurious correlation boosting; the threshold and trade-off coefficient of the control access strength value are set according to the ratio of false trigger cost to false trigger cost, and are periodically recalibrated based on audit records during operation.

[0048] Through the above design, the control access strength value becomes a unified quantitative threshold throughout the prediction, decision-making and release process, realizing a verifiable transition from "seeing an anomaly" to "worth intervening", and providing clear and stable entry conditions for subsequent conditional risk value trend optimization and control barrier constraints.

[0049] Preferably, a density-based clustering method is used to divide suspicious clusters on the spectral-topological co-embedding coordinates, and the clustering results are mapped to physical line segments to determine the target segments.

[0050] This invention uses spectral-topological co-embedded coordinates as a spatial carrier to detect anomalous clusters within the coordinate space. The clustering results are then rigorously mapped to physical line segments to obtain target segments that can be directly used for self-healing decisions. The core idea is to compress "electrical parameter changes," "topological adjacency," and "time precursor coordination" into geometric clusters, and then restore them to an operable physical range using network connectivity relationships, achieving an executable implementation from data characteristics to the switching layer.

[0051] The spectral-topological co-embedding coordinates are generated from the previous step, and the measurement points are recorded. The coordinate vector is ( Low-dimensional coordinates (For coordinate dimensions). Density-based clustering is performed in the coordinate space, first calculating the kernel density score for each measurement point. ,in For measuring points density fraction, For kernel scale parameters, The Euclidean norm is used. Core points, boundary points, and noise points are marked using density thresholds and neighborhood connectivity relationships, and cluster sets are obtained through density reachability relationships. ( For the first (A set of measurement points for each cluster). Density-based clustering can suppress isolated anomalies and adapt to non-convex shapes, which is particularly important for the geometry of "line-segment anomalies" in electrical networks. The mapping from clusters to physical lines is achieved through topological indexing. Defining the mapping... Measuring points Corresponding to physical node or line location ( (This is a one-to-one mapping from measurement points to physical locations). For each cluster... Take its projection in the physical network. And solve for the minimum connected subgraph on the distribution network topology. cover All nodes and required edges. To ensure operability, Further trimming based on protection and operation mode boundaries, only continuous line segments satisfying relay protection coordination and operation mode constraints are retained as candidate physical segments. To determine the final target segment from multiple candidate physical segments, a cluster scoring function is constructed. ,in For the first The rating of each cluster, This represents the average density fraction within the cluster. This represents the percentage of physical residuals that cross the threshold within the cluster (see the previous step for the definition of physical residuals). The standardized significance of the equivalent admittance bias within the cluster. The weight is used as the objective segment. The candidate physical segment with the highest score is selected as the objective segment, denoted as . ( (The set of physical routes in the target section). This score combines "spatial clustering intensity", "model consistency evidence", and "parameter offset evidence" into a sortable scalar, which facilitates the calculation of subsequent control access intensity values.

[0052] To enhance project usability, the mapping and trimming phase includes two constraints: connectivity constraints, requiring the target segment to be a simply connected subgraph; and protection boundary constraints, prohibiting the target segment from crossing closed-loop boundaries without relay protection coordination. If multiple candidate physical segments with similar and overlapping scores exist, the overlapping portions are merged first, and then reordered based on the merged scores. If a cluster only covers scattered measurement points and cannot form a connected subgraph, it is marked as "warning only" and sent back to the retesting process.

[0053] The advantages of the above process in principle are as follows: First, density clustering "sees" geometric salience determined by multiple source features in the coordinate space, which can naturally filter out scattered noise and retain continuous anomalies along the line; Second, topological mapping directly places abstract coordinates onto physical lines, ensuring that any subsequent actions have clear switching boundaries; Third, the scoring function synthesizes several types of orthogonal evidence into a sortable decision quantity, which reduces the subjectivity of manual thresholds and facilitates docking with control access strength values ​​to form a unified threshold.

[0054] Example 3: On a city ring network feeder, a high-density cluster consisting of 8 measuring points appears in the spectral-topology co-embedded coordinate system. The imaginary part of the equivalent admittance corresponding to this cluster increases overall, while the real part decreases overall, and the physical residual threshold crossing ratio is high. Mapping the cluster to the physical network, the minimum connected subgraph covers two adjacent branches and one sectionalizing switch. After trimming according to the protection and operation mode boundaries, two candidate physical sections are obtained. Calculating the scoring function, the first candidate has a higher average density and a larger physical residual threshold crossing ratio, and also a higher admittance deviation significance. The largest segment was identified as the target segment. The target segment is then passed to the control admission assessment module as the scope for priority isolation and reconstruction. Subsequent searches are only sampled and optimized within this scope, significantly reducing the number of candidate sequences and improving the pass rate of subsequent consistency checks.

[0055] Through the clustering-mapping-scoring link described above, the geometric information in the spectrum-topology co-embedded coordinates is transformed into physically operable target segments, which maintains consistency with electrical constraints and provides a directly executable spatial entry point for self-healing control, thereby establishing a clear and verifiable connection between fault prediction and self-healing execution.

[0056] Preferably, spatial, temporal, and physical evidence are synthesized using the Durmst-Schafer evidence fusion method. The hazard rate assessment uses a semi-parametric hazard rate model to calculate the arrival probability and uses it as a priori weight to weight and correct the synthesized result. The control access strength value is determined by the weighted and corrected evidence belief measure.

[0057] This invention achieves spatiotemporal aggregation of observational information in spectral-topological co-embedding coordinates, and jointly generates control access strength values ​​using Durmst-Schafer evidence fusion and semi-parametric hazard rate assessment. The idea is to transform spatial, temporal, and physical evidence into weighted belief measures, and then recalibrate the beliefs under a time window using arrival probabilities, making the control access strength value the sole gating variable for entering the synthesis of self-healing sequences.

[0058] Three types of evidence are constructed at the cluster granularity. Spatial evidence consists of the density fraction of suspicious clusters, the significance of equivalent admittance bias, and the consistency of physical residuals. Temporal evidence consists of the average value and stability of the innovation consistency index within the cluster. Physical evidence consists of the proportion of physical residuals exceeding the threshold and the statistical significance of equivalent admittance bias. After interval normalization, the three types of evidence are mapped to basic belief assignments and then enter the evidence fusion processor.

[0059] Evidence fusion employs the Durmst-Schafer method , , and Assignment of two fundamental beliefs; Assignment of basic beliefs after integration; A subset of the frame set; The conflict coefficient is used for fusion. Fusion proceeds sequentially from two sources, then continues with a third source, yielding a lower bound for the belief in "permissible intervention" and an upper bound for its likelihood. The conflict coefficient is used to suppress contradictory evidence, preventing a single indicator from forming a high belief. The hazard rate assessment provides the probability of arrival within a time window and serves as a priori weight to weight and correct the fusion results. , , For a moment Fault arrival rate; This is a feature vector composed of the environment and asset status; This is the model parameter vector; It is a logarithmic probability function; For the evaluation time window; To assess the probability of arrival within a time window, the probability of arrival is used to extrapolate clusters with low short-term risk and to prioritize clusters with consistent evidence and high short-term risk. Controlling the admission strength value compresses the weighted interval belief into a single scalar. , To control the access intensity value, the range of values ​​is: ; The lower bound of the belief that "intervention is permissible"; This is the upper bound of the probability of "permitting intervention"; This is a weighting factor, with a value range of [0, 1].

[0060] When the control access strength value exceeds the threshold, it enters the self-healing sequence synthesis and tightens the control access strength value monotonically at the risk value confidence level and the control barrier advancement coefficient; when it is below the threshold, only alarms and retest instructions are issued.

[0061] Example 4: After controlled disturbance and phasor acquisition were completed on a feeder of the urban ring network, a high-density cluster composed of multiple measurement points appeared in the spectral-topology co-embedded coordinate system. Within this cluster, the equivalent admittance bias exhibited a synergistic change of increasing imaginary part and decreasing real part, with a high proportion of physical residuals exceeding the threshold, and the innovation consistency index synchronously increasing in the neighborhood. After normalization of the three types of evidence, two-source fusion and three-source fusion were performed according to the aforementioned formula, resulting in high lower bounds for the belief of "allowing intervention" and upper bounds for probability. The hazard rate assessment used temperature, humidity, rainfall, and equipment service life to construct a feature vector, calculating a high probability of arrival in the next few minutes. The control access strength value calculated according to the above formula was high, and the self-healing module then prioritized constructing isolation and reconstruction candidates within the target section corresponding to this cluster. Operation records showed that, without expanding the power outage area, the number of isolation steps and consistency checks decreased, and pre-release conflicts were reduced.

[0062] Based on the control access strength value, the conditional risk value confidence level and barrier advancement coefficient are set. Candidate atomic actions are screened by feasible region prior and action shielding. The search is carried out within the joint state space determined by the verified topology state under the constraint of the control barrier function. The power flow is optimized with the conditional risk value as the objective to obtain the self-healing operation sequence and calculate the counterfactual energy margin.

[0063] This invention transforms the control access strength value into a risk scale and safety boundary, completes candidate atomic action screening, controlled search and power flow optimization under uncertainty in a verified topology state, outputs a self-healing operation sequence and provides a counterfactual energy margin for dynamic threshold tuning and hierarchical execution before release.

[0064] A monotonic mapping is established between the control access strength value and two types of core hyperparameters, so that risk and safety tighten in tandem with the strength of evidence. , , To control the access intensity value, Assuming a certain level of confidence in the value at risk, The barrier propulsion coefficient, This is a calibration constant. This mapping ensures that when there is sufficient evidence, the tail risk measurement is more conservative and the barrier advancement is stronger; when there is insufficient evidence, the system maintains a lenient setting and tends to issue warnings and conduct retests.

[0065] Candidate atomic actions are jointly screened using feasible region priors and action masking. The feasible region prior constructs an outer envelope with confidence coverage based on historical power flow samples. The inputs are atomic actions and local states, and the outputs are feasible, uncertain, and infeasible. The latter two categories are directly eliminated during the screening phase. Action masking uses topological connectivity, relay protection coordination, grid phase angle difference, and short-circuit current level as hard constraints to compile a prohibited transition set. Any action that violates this prohibited set is excluded from the search.

[0066] The controlled search is conducted within a joint state space, which consists of the Cartesian product of the topological switching states and the linearized AC power flow solution. To ensure that the search process remains within a propellable safe region, control barrier functions are introduced, defining voltage, current, and short-circuit current levels respectively. , , , To correspond to the safety margin, This is the upper limit of voltage. This is the upper limit of the current. This is the upper limit of the short-circuit current level. This is a real-time estimate. Discrete propulsion satisfies... , For any barrier function, For the first The joint state of the steps, For single-step action time scale, As given in the previous equation, this condition ensures that each step proceeds within the progressive invariant set, eliminating candidate paths that lead to boundary violations. On several candidate paths that have passed the screening and barrier constraints, a power flow optimization algorithm is established with conditional risk value as the objective, handling the uncertainties of distributed power sources and loads. , As an auxiliary variable, This is a self-healing operation sequence. For scene collection, As scene weight, For the desired unpowered energy in the scenario, For positive part operators, As a weight for action cost, Determined by the previous equation. Constraints include linearized power flow balance, upper and lower voltage limits, upper current limit, short-circuit current level, relay protection coordination, and consistency of operating modes. Optimize the output to achieve a self-healing operation sequence that controls tail risks and satisfies electrical feasibility.

[0067] To measure the vulnerability of the plan to subsequent perturbations, a counterfactual energy margin is calculated for use in dynamic threshold shaping of the release layer and backup sequence switching. , For the first The counterfactual energy margin of the step, For motion perturbation, This is the upper bound of the motion amplitude. For the first The dual vector of the step constraint, This is the constraint function. The smaller the counterfactual energy margin, the greater the tightening of the pre-release threshold, and the more likely the backup sequence will be used.

[0068] Example 5. After evidence fusion, a certain ring network power supply area obtained a high control access strength value. Based on this, the system simultaneously increased the conditional risk value confidence level and the barrier advancement coefficient. Candidate atomic actions are first determined to be feasible by prior judgment of the feasible region. Parallel closing actions that do not meet the relay protection coordination conditions are eliminated by action shielding rules. In the joint state space, the search algorithm uses the density of spectral-topology co-embedded coordinates as the sampling bias and generates several candidate paths under the constraints of the control barrier function. Subsequently, power flow optimization with conditional risk value as the objective is performed on each of these paths to obtain a self-healing operation sequence, including the disconnection of sectionalizing switches, the closing of tie switches, and the correction of reactive power settings of distributed generation. The counterfactual energy margin is calculated step by step for this sequence. The action corresponding to the minimum value is marked as a critical step. During the release phase, the voltage and current operating thresholds of this step are dynamically tightened, and a higher priority backup sequence is configured for it. This embodiment demonstrates that, under conditions of high evidence strength, search and optimization converge rapidly within a controlled security domain, and adaptive security hardening can be achieved based on counterfactual energy margin before release, thereby achieving isolation and reconstruction without expanding the scope of the power outage.

[0069] Preferably, the conditional value at risk confidence level and the barrier advance coefficient are set in a monotonic correspondence with the control access strength value, and the conditional value at risk confidence level and the barrier advance coefficient are increased accordingly as the control access strength value increases.

[0070] This invention transforms the control access strength value into a risk scale and safety boundary, enabling subsequent search and flow optimization to be performed within a feasible domain consistent with the evidence. The core idea is to use a monotonic mapping to input the control access strength value into the conditional risk value confidence level and barrier advancement coefficient, thereby employing a more conservative tail risk measurement and a stricter safety advancement when the evidence is strong, and maintaining a lenient setting and prioritizing early warning and retesting when the evidence is weak.

[0071] To establish an implementable monotonic relation, a linear bounded mapping is used. , , To control the access intensity value, Assuming a certain level of confidence in the value at risk, The barrier propulsion coefficient, and For confidence level baseline and gain, and To establish the baseline and gain of the advancement coefficients, constants are calibrated offline to ensure the derived values ​​remain within the feasible range and satisfy monotonicity. Pruning or smoothing is introduced as necessary to eliminate jumps.

[0072] Based on the above mapping, the previously defined conditional value-at-risk objective function and barrier advancement conditions directly utilize the updated confidence level and advancement coefficient. As the confidence level increases, the tail of the conditional value-at-risk coverage deepens, and the optimization will suppress the amplification of unpowered energy in adverse scenarios with higher weight. As the advancement coefficient increases, the barrier margin shrinks faster, and the search will prioritize retaining candidate paths far from the constraint boundary while eliminating action combinations approaching the limit. To maintain consistency throughout the process, candidate atomic actions are only entered into the barrier constraint search and power flow optimization with the conditional value-at-risk objective after feasible region prior and action masking screening. The self-healing operation sequence obtained from the optimization is then used to calculate the counterfactual energy margin and enter the release phase.

[0073] The mapping process comprises two parts: calibration and online adaptive operation. In the calibration phase, representative segments covering seasonal, load, and distributed power source variations are selected using real-world operating conditions from recent years. A set of constants is determined through grid search or convex optimization to ensure consistency between the tail indicators of unpowered energy and operational alarm records under high control threshold strength conditions, and to satisfy constraints on the probability of false tripping under low control threshold strength conditions. In the online phase, the minimum counterfactual energy margin is monitored, and the consistency check conflict count is checked. If deviations occur, the gain is adjusted in small steps while maintaining monotonicity and boundary conditions. To avoid jitter, first-order low-pass smoothing is used for the confidence level and the advancement coefficient.

[0074] To facilitate operational control and release verification, the above mappings and parameters are recorded in the execution metadata for easy post-auditing and recalibration. At the same time, the minimum counterfactual energy margin and the corresponding steps are marked in the plan for dynamic tightening of the threshold for this step and priority switching of the backup sequence at the release layer.

[0075] Example 6. After evidence fusion, the control access strength value for a certain ring network area is 0.78. Linear mapping yields a high confidence level for the conditional risk value and a high barrier advancement coefficient. Candidate atomic actions are first screened a priori through the feasible region, and closed-loop merging without relay protection is eliminated by action shielding. Controlled search generates multiple candidate paths in the joint state space. The barrier advancement condition, due to its large advancement coefficient, suppresses paths approaching the voltage and current upper limits. Subsequently, conditional risk value power flow optimization is performed with the updated confidence level, resulting in a self-healing operation sequence. This sequence disconnects sectionalizing switches, closes tie switches, and corrects the reactive power settings of distributed power sources. Counterfactual energy margin is calculated for each step; the minimum value occurs in the tie closing step. Based on this, the publishing layer further tightens the voltage and current operating thresholds for that step and assigns higher priority to the backup sequence. This example demonstrates that when the evidence is strong, tail risk is effectively suppressed, and the search remains within the advanceable invariant set throughout. Isolation and reconstruction are completed in fewer steps while maintaining a consistent pass rate.

[0076] Preferably, the feasible region prior is constructed by using a learning method with confidence coverage to build the outer envelope of the feasibility classifier. The output of the feasible region prior is three categories: feasible, uncertain, and infeasible. Candidate atomic actions corresponding to uncertain and infeasible are eliminated in the screening stage.

[0077] This invention proposes a feasible domain prior for pre-screening candidate atomic actions with confidence coverage before entering controlled search and power flow optimization. The idea is to train a feasibility classifier offline using historical running and simulation samples, and then calibrate the classifier's envelope online using a learning method with confidence coverage, ensuring controllable coverage error in online decision-making. Thus, each candidate atomic action and its associated joint state summary are mapped to three output categories: feasible, uncertain, and infeasible. Uncertain and infeasible actions are directly eliminated during the screening stage, retaining only feasible actions for subsequent steps.

[0078] The construction of feasible region priors includes three stages: feature definition, classifier training, and confidence coverage calibration. In this invention, features consist of a joint state summary and action codes. The joint state summary includes node voltage predictions, branch current predictions, short-circuit current level estimates, protection window numbers, and topological fingerprints. Action codes describe the types of atomic actions and their locations. The boundary distance output by the feasibility classifier serves as the feasibility margin; positive values ​​indicate a feasible side, and negative values ​​indicate an infeasible side.

[0079] To obtain confidence coverage, inconsistency scores are introduced and quantile thresholds are determined on the calibration set. Definitions are provided. , This represents a feature vector composed of a joint state summary and an action code; This represents the feasibility margin of the classifier output; This represents the offline calibrated marginal baseline; This represents the set of inconsistent scores. The set of inconsistent scores is calculated using the independent calibration set, and its quantile threshold is taken. , Indicates the quantile threshold; Indicates the coverage level; This represents the inconsistency score on the calibration set. Therefore, the online decision rule is defined as: when… Deemed feasible; when Determined as uncertain; when This rule is deemed infeasible. The rule applies to the outer envelope of the classifier's decision boundary, and its coverage error is determined by… control.

[0080] To ensure consistency with electrical constraints, the prior training labels for the feasible region are not derived from a single empirical threshold, but rather obtained by solving for each constraint in the sample space, including linearized AC power flow balance, upper and lower voltage limits, upper current limits, short-circuit current levels, and relay protection coordination. This ensures that the margin learned by the classifier aligns with the physical feasible region. The calibration phase covers seasonal variations, load levels, and distributed power source fluctuations to ensure the quantile threshold remains stable under common operating conditions.

[0081] In online applications, for each candidate atomic action, a feature vector is first calculated to obtain the feasibility margin and inconsistency score. Then, three categories of judgments are output according to the aforementioned rules. Uncertain and infeasible actions are eliminated during the screening stage to avoid entering the controlled search; feasible actions are then subject to action masking and control barrier constraints. Due to the outer envelope property, the confidence coverage corresponding to the feasible judgment is statistically valid, thus limiting the risk of false acceptance to a preset level. Compared with the single-point threshold method, this method can maintain the coverage property even when training errors and distribution drift exist.

[0082] The connection with subsequent modules is reflected in two aspects. First, the higher the control admission strength value, the higher the coverage level the system can select and adjust the quantile threshold accordingly, so that conservatism and evidence strength are consistent. Second, the three types of outputs of the feasible region prior have direct flow semantics within the search and optimization module: feasible entry candidate generation, uncertainty can trigger local retesting or feature augmentation, and infeasibility triggers action masking statistical updates, which are used to correct the prohibited transition set.

[0083] Example 7. A feasibility classifier for a certain ring network area is trained using historical data and simulation samples, with records covering all four seasons and multiple load segments over the past year used as a calibration set. During operation, a batch of candidate atomic actions are generated near a certain connection area. The system forms a feature vector for each action, calculates the feasibility margin and inconsistency score, and gives three categories of judgments accordingly. Most actions close to the upper limits of voltage and current are judged as uncertain or infeasible and are directly eliminated. The remaining feasible actions enter the control barrier constraint search and power flow optimization with conditional risk value as the objective. The final self-healing operation sequence consists only of actions previously judged as feasible, and the critical step thresholds are tightened based on counterfactual energy margin before release. This example shows that a feasible domain prior with confidence coverage can shrink the solution domain early and maintain a safe envelope consistent with electrical constraints, allowing subsequent search and optimization to be carried out in a smaller feasible space, reducing the number of paths rejected by consistency checks at the release stage.

[0084] Preferably, the action shielding includes the following rules: prohibiting the formation of closed-loop connection without the support of relay protection, limiting the grid-connected phase angle difference to no more than the upper limit of the grid-connected phase angle difference, limiting the short-circuit current level to no more than the upper limit of the short-circuit current level, and prohibiting cross-level operation that crosses the time limit window of the superior protection.

[0085] Action masking is used to exclude candidate atomic actions that are incompatible with electrical safety before entering controlled search and power flow optimization. Atomic actions include sectionalizer disconnection, tie switch closing, tap changer adjustment, and active and reactive power settings of distributed generation. Action masking is performed under the verified topology state, predicting and judging each candidate atomic action and its corresponding intended execution state to form a set of inactive actions, ensuring that subsequent path generation always remains within the advanceable safety domain.

[0086] Closed-loop protection coordination is the primary threshold. The effectiveness of coordination is determined by relay protection direction criteria, time-delay coordination, and backup coverage, denoted as... , For candidate atomic actions, For the first The joint state of the steps, This is a binary quantity used for relay protection coordination determination; a value of 1 indicates effective coordination. The phase angle difference during grid connection must be limited to suppress active and reactive power surges at the moment of connection. The phase angle constraint is denoted as... , To simulate the phase angle difference between the two sides, This is the upper limit of the phase angle difference, calibrated by the system operating procedures and monotonically tightened with the control threshold strength value. The short-circuit current level must meet the equipment breaking capacity and the busbar bearing capacity. The short-circuit constraint is denoted as... , This is for estimating the short-circuit current under the fault assumption after the action. This represents the upper limit of the short-circuit current level, determined by the device's capacity and operating strategy. Time-coordination requires that lower-level protection operates before higher-level protection, with a coordination margin. The time-coordination constraint is denoted as... , For the protection time limit of the lower level, For the protection time limit of the superior, To accommodate the margin.

[0087] Action admission determination is defined as , For action admission criteria, a value of 1 indicates that the search and optimization are allowed, while a value of 0 indicates that the action is directly rejected during the filtering stage.

[0088] The above judgment process is linked to the control threshold value: when the control threshold value is high, the upper limit of phase angle difference and the upper limit of short-circuit current level are tightened according to the preset mapping, and the margin is increased, thereby improving conservatism; when the control threshold value is low, the operating baseline is maintained and warnings and retests are preferred. To avoid misjudgments caused by state drift, action masking is re-judged before and after each step of candidate generation, search expansion and optimization, and is used in conjunction with feasible region priors: uncertainties and infeasibility in the three types of outputs do not need to enter action masking and are directly excluded.

[0089] Example 8: A planned merging of a tie switch in a city ring network. After candidate atomic actions are generated, the feasible domain prior is first invoked for three types of judgment, retaining only feasible actions to enter the action shield. Under the proposed execution state, the predicted phase angle difference on both sides of the grid is close to the upper limit of the phase angle difference, and the short-circuit current level check is near the upper limit. The protection coordination judgment shows that the time difference between the upper and lower levels is insufficient to meet the coordination margin. As a result, all three constraints are triggered simultaneously, the action admission judgment is 0, and the direct merging is rejected. The system is changed to first perform the segment switch disconnection upstream of the target section, so that the expected short-circuit current level and phase angle difference return to the safety zone, and then generate a candidate path containing "disconnection-local reconfiguration-ticket merging" according to the advanceable conditions of the control barrier function, and then enter the power flow optimization with the conditional risk value as the objective. The final self-healing operation sequence completes isolation and reconfiguration under the premise of satisfying protection coordination and electrical constraints, without any overstepping actions or merging impacts.

[0090] Preferably, the search is performed in the joint state space where the verified topology has been determined using a random exploration tree algorithm. Candidate sequences are generated under the constraints of the control barrier function, and the sampling bias is set according to the spectral-topology co-embedding coordinates, and the path cost is shaped according to the innovation consistency index.

[0091] This invention performs a random exploratory tree search within the "topology-power flow" joint state space under a verified topology state. A control barrier function ensures that each expansion step is within a propellable safety region. Furthermore, it uses spectral-topology co-embedded coordinates and innovation consistency indices to jointly shape sampling and path costs, generating candidate sequences for power flow optimization. The joint state consists of switch configurations and linearized AC power flow solutions. Atomic actions include segmented switch disconnection, tie switch merging, tap changer adjustment, and distributed power supply setting.

[0092] To incorporate spatial orientation and temporal precursors into the sampling, a bias is assigned to the sampling density of the joint state, causing the tree to expand more concentratedly towards suspicious regions and prioritize traversing nodes with significant temporal precursors. , For state The sampling density; State in spectral-topological co-embedding coordinates into the target cluster The distance; This is a penalty function based on the innovation consistency index (the higher the innovation consistency, the smaller the value, to encourage early arrival in the precursor region). and This is a temperature parameter. This density concentrates the tree's expansion "towards suspicious and strong precursors," shortening the convergence time of candidate paths. Each edge must satisfy the propagation constraint of the control barrier function before being added to the exploration tree, ensuring that the search process does not reach the boundary. , It is a barrier function for voltage safety margin, current safety margin, or short-circuit current level safety margin; and To expand the joint state before and after; The time scale is for a single-step action; The barrier advancement coefficient (mapped from the control access strength value) ensures that each expansion has an "inward" margin, preventing the tree from wandering along the constraint boundary. To balance supply assurance and early isolation in candidate paths, the path cost is defined as a weighted sum of tail power supply risk, action overhead, and time-precursor guidance. , For path The cost; Estimate the expected unsupplied energy (based on a fast power flow approximation online assessment); This represents the number of steps in the path action; In the state The reward and penalty items are constructed based on the innovation consistency index (the earlier the node with strong precursors is passed, the smaller the value). and The weight is used to determine the optimal path. This cost encourages candidate paths that are "less reactive, earlier isolated, and lower risk" to be included in subsequent optimization.

[0093] The search process employs a randomized exploration tree with reconnection: starting from the current joint state, sampling is performed in the state space according to the aforementioned bias, and the nearest neighbor state is selected before state advancement is carried out using atomic actions; edges that pass through barrier constraints are added to the tree, and attempts are made to reconnect neighboring nodes to reduce path costs; the process terminates when several candidate paths satisfying the load recovery rate and connectivity constraints are accumulated. The entire process is linked with feasible region priors and action shielding: only atomic actions that are deemed "feasible" participate in the expansion, and actions that touch the prohibited transition set are not generated, avoiding the inefficient "generate first, then reject" approach.

[0094] Example 9. A feeder in an urban ring network obtains a high control access strength value after evidence fusion. Based on this, the system tightens the barrier advancement coefficient and sets a smaller temperature parameter around the target cluster to concentrate the sampling density peak. The search starts from the current state, first generating sampling points in the high-density region of spectral-topological co-embedded coordinates, using feasible region priors to eliminate atomic actions close to the upper voltage and upper current limits, and then verifying the advancement of the edges according to the control barrier function. As the tree expands, several paths reach the segmented switch covering the strong precursor region in just a few steps, and sequentially provide candidate sequences of "segmentation-in-situ reconstruction-connection merging". Path cost calculation shows that the sequence with early isolation and fewer steps has the lowest cost and is selected as the preferred candidate output; at the same time, several backup candidates with slightly higher costs but covering different connection strategies are generated for subsequent conditional value flow optimization to refine each one. In this example, the total number of search nodes is significantly lower than in the no-bias case, and all candidates entering the optimization stage have met the in-process safety constraints, thus reducing the number of conflicts in the consistency check before release.

[0095] Preferably, the power flow optimization with conditional risk value as the objective is based on a linearized AC power flow model. The constraints include upper voltage limit, lower voltage limit, upper current limit, short-circuit current level, relay protection coordination and operation mode. The optimization outputs a self-healing operation sequence and generates a feasible domain proof document containing the voltage and current envelopes, short-circuit current level and relay protection coordination verification results. At the same time, the counterfactual energy margin is calculated based on the optimization duality sensitivity.

[0096] This invention takes "power flow optimization with conditional risk value as the target" as the core of self-healing decision-making, unifies tail power supply risk, action cost and electrical constraints into the same optimization framework, directly outputs the self-healing operation sequence, and generates a feasible domain proof document and counterfactual energy margin after the solution is completed, which are used for dynamic threshold shaping and hierarchical execution of the release layer.

[0097] The objective of the optimization problem is to minimize the expected unpowered energy expressed in the conditional risk value formulation, with added action costs. A set of scenarios is established to describe the uncertainties of distributed power sources and loads, and the decision variables are time-ordered sequences of atomic actions. The objective function is denoted as... , As an auxiliary variable; This is a self-healing operation sequence; A collection of scenes; As scene weight; The expected unpowered energy in the scenario; For positive part operators; Weights for action costs; The conditional risk value confidence level is obtained by mapping the aforementioned control access strength.

[0098] The constraint system uses linearized AC power flow as its framework, covering steady-state voltage, current, short-circuit current levels, relay protection coordination, and operating modes. First, linearized power flow balancing is applied to ensure that node voltage, branch power, and injected power are consistent. Then, upper and lower voltage limits and upper current limits are applied to each scenario at each time step to guarantee thermal stability and power quality. Short-circuit current level constraints are obtained by calculating the fault current through an equivalent network, limiting it to within the allowable values ​​for equipment and buses. Relay protection coordination and operating modes are encoded into mixed integer constraints through time-limited hierarchical, directional, and topological logic coding, ensuring that any merging or switching falls within the allowed protection window and structural mode. Atomic action consistency constraints limit the occurrence of only one type of switching or setting change at the same time step, and state transition equations propagate the topology and power flow from the current step to the next.

[0099] To avoid solution accumulation near infeasible boundaries, the control barrier constraints from the previous step are inherited during the process. As long as the candidate edges added to the exploration tree are retained, their corresponding linearization safety margins are substituted into the optimization as simultaneous inequalities. In this way, while the objective function pursues the reduction of tail risk, the solver no longer "trades for violations at a cost," but instead seeks optimization within the progressive invariant set.

[0100] After the solution provides the self-healing operation sequence, the system calculates the most unfavorable envelopes of voltage and current for each step and scenario, and verifies the coordination between the short-circuit current level and relay protection item by item, forming a feasibility domain proof document. To facilitate rapid review at the release level, the proof document provides three curves or intervals for each step: the voltage envelope range, the upper limit of the current envelope, and the short-circuit current level estimate, and provides a consistency judgment between this step and the protection time limit and directionality.

[0101] To assess the vulnerability of the sequence to the next perturbation, the counterfactual energy margin is calculated. , For the first The counterfactual energy margin of the step, For motion perturbation, This is the upper bound of the motion amplitude. For the first The dual vector of the step constraint, This is the constraint function. The smaller the counterfactual energy margin, the more sensitive the next step is to exceeding the limit. Based on this, the publishing layer implements stricter tightening of the voltage and current operating thresholds for the corresponding step and prioritizes the allocation of backup sequences.

[0102] The advantages of this method in principle are reflected in three points. First, it explicitly incorporates uncertainty into the objective, directly constraining the tail power supply risk, rather than simply optimizing the mean. Second, it simultaneously satisfies steady-state electrical constraints, short-circuit checks, and protection coordination within a single solution framework, avoiding the iterative process of "finding a path first and then rejecting it." Third, the solution product inherently contains verifiable envelope and dual information, making the formal verification before release, runtime monitoring, and rollback strategies traceable.

[0103] Example 10. After evidence fusion, a feeder in the urban ring network achieves a high control access strength, and linear mapping yields a high conditional risk value confidence level and a large barrier advancement coefficient. During the search phase, three candidate sequences are output: one is to disconnect upstream of the target section and reconfigure locally; the second is to adjust the reactive power settings of distributed power sources before interconnection and reconnection; and the third is to interconnection and reconnection before disconnection. These three candidates are then hot-started one by one to enter the power flow optimization for the conditional risk value objective. The optimizer solves each candidate simultaneously under multiple scenarios, satisfying linearized power flow balance, steady-state envelope, short-circuit and protection coordination constraints. The sequence with the minimum expected unpowered energy at the tail and the fewest action steps is selected as the final self-healing operation sequence. The system then generates a feasible region proof document: providing the voltage envelope range, maximum current value, and short-circuit current level for each step, along with a conclusion consistent with the protection direction and time limit. By progressively calculating the counterfactual energy margin for the same sequence, it was found that the margin was smallest in the connection and merging step. Based on this, the release layer further tightened the upper limits of voltage and current for this step and marked the "local reconfiguration priority" backup sequence as the preferred fallback path for this step. This embodiment shows that, under conditions of high evidence strength, the conditional risk value objective effectively suppresses the risk of no power supply in adverse scenarios. The combination of control barriers and protection as hard constraints allows the sequence to directly enter the pre-release verification, while the counterfactual energy margin provides a clear safety margin indicator for critical actions.

[0104] Based on the counterfactual energy margin and control access strength value, the upper voltage limit, lower voltage limit and upper current limit are dynamically tuned. The entire sequence consistency is checked based on the signal timing logic and satisfiability modulus theory, and an execution package is generated.

[0105] This invention, after the self-healing operation sequence is formed, dynamically shapes the operating threshold based on counterfactual energy margin and control access strength value, and performs consistency verification of the entire sequence using signal timing logic and satisfiability modulus theory, ultimately generating an execution package that can be directly deployed. The goal is to prove "plan feasibility" as "execution safety" before release and to explicitly quantify the safety margin of critical actions.

[0106] The threshold shaping process employs a linear tightening model, ensuring that the strength and fragility of evidence are reflected simultaneously at the threshold. , , , and For the first Step voltage upper limit and voltage lower limit, For the first Step current limit and The upper and lower limits of the baseline voltage. The upper limit of the baseline current, For the first Counterfactual energy margin, To control the access intensity value, The value is the shaping coefficient. After threshold shaping, the three sequences are smoothed by first order to avoid threshold jumps caused by adjacent time steps.

[0107] Signal timing logic is used to perform time-domain verification of continuous quantity constraints. Core specifications include voltage range hold, target recovery achievement, and non-parallel constraints. : , : , : , For the first Step execution start time, This is the observation window for this step. To restore the time limit, To achieve the target recovery rate, This represents the voltage range after shaping. Robustness is calculated for each specification, and the minimum value across the entire sequence is used as the pass criterion.

[0108] Satisfiability model theory is used to perform full-sequence consistency checks on discrete and logical constraints. Relay protection direction and time limits, upper bounds of short-circuit current levels, topological connectivity, mutual exclusion of actions, and order are encoded as satisfiability constraints. The entire self-healing operation sequence is solved at once, returning "satisfiable" or "unsatisfiable." When an unsatisfiable constraint occurs, the conflicting step is located and a backup sequence replacement is triggered until the process passes or refactoring is initiated.

[0109] The execution package is generated in a standardized format and includes a self-healing operation sequence, a step-by-step plan of upper and lower voltage limits and upper current limits for operation, a timing logic robustness report, a satisfiability proof summary, and alternative sequences and fallback paths for critical steps. All files are accompanied by version numbers and timestamps for auditing and traceability.

[0110] Example 11. During the optimization phase, the urban ring network obtains a self-healing operation sequence of "disconnection-on-site reconfiguration-connection and merging". Counterfactual energy margin shows that the minimum value of the connection and merging step is lower than that of other steps. Based on this, threshold shaping adjusts the upper voltage limit, lower voltage limit, and upper current limit of this step. Signal timing logic verification shows that the voltage remains within the shaping range for all steps within their respective observation windows, and the target recovery is achieved within the set time limit; satisfiability mode theory verification also passes, and no short-circuit current level or protection time limit conflict is found. Based on this, the system generates an execution package, marking the connection and merging step as a key monitoring step and configuring a backup sequence "on-site reconfiguration first, then delayed merging". Subsequently, the deployment process begins, with the runtime layer progressively deploying according to the execution package and comparing the voltage and current online within each observation window. If a deviation occurs, the system rolls back according to the preset backup sequence. This example demonstrates that threshold shaping and dual verification can improve the safety margin of critical actions without increasing the number of action steps and prevent potential conflicts before deployment.

[0111] Preferably, the signal timing logic specifications include node voltage falling within the shaped upper and lower voltage limits, achieving the target load recovery rate within a preset time window, and prohibiting parallel operations without relay protection; the satisfiability modal theory encodes the relay protection logic, and performs a full-sequence consistency check on the short-circuit current level and topology connectivity; the execution package includes a self-healing operation sequence, a dynamic threshold plan, a signal timing logic check report, and a summary of the satisfiability modal theory consistency proof.

[0112] After generating the self-healing operation sequence, this invention constructs a two-layer verification framework before release: continuous quantities are verified in the time domain using signal timing logic, discrete and logical constraints are verified for full sequence consistency using satisfiability modulus theory, and the running threshold is dynamically shaped based on counterfactual energy margin and control access strength value, ultimately forming a deployable execution package.

[0113] The signal timing logic is based on the core specifications of "voltage range hold," "target recovery achieved," and "prohibition of parallel operation without relay protection." The robustness of voltage range hold is defined as follows: , This represents the minimum robustness maintained within the voltage range; The first self-healing operation sequence represents the... step; This indicates the observation window for this step; The time function representing the node voltage magnitude; , This represents the lower and upper voltage limits for this step after shaping. The robustness of achieving target recovery is defined as... , This indicates the robustness of achieving the goal; Indicates the recovery timeframe; This indicates the percentage of the target load that has been restored; This indicates the target recovery ratio. Parallel operations without relay protection coordination are prohibited and expressed as "never occurring," with robustness equal to the minimum safe distance of the parallel operation's disabled predicate. The timing logic of the entire sequence is determined by taking the minimum of three terms based on a criterion. , Indicates the overall robustness of sequential logic; This indicates the robustness of the parallel connection specification. If Then the continuous time domain specification is satisfied overall.

[0114] Satisfiability modular theory uses first-order logic and integer constraints to describe relay protection logic, short-circuit current levels, and topological connectivity, forming a fully consistent formula. , This indicates the conjunction of the satisfiability model theoretical constraints; "Direction Consistency" means that the relay protection direction criterion is consistent with the power flow direction; "Time Coordination" means that the lower-level protection action time is earlier than the upper-level protection and meets the coordination margin; "Short Circuit Limit" means that the fault current does not exceed the upper limit; "Topological Connectivity" means that the load cluster and the power supply node are connected; "Action Mutual Exclusion" means that only one atomic action is allowed in the same step. When the solution returns "Satisfiable", it is considered that the logic and structure are consistent; when it returns "Unsatisfiable", the conflicting step is located and replaced with a spare sequence.

[0115] Threshold shaping uses counterfactual energy margin and control access strength as independent variables to linearly tighten the upper voltage limit, lower voltage limit, and upper current limit at each step, forming a linkage relationship of "the stronger the evidence, the greater the vulnerability, and the stricter the threshold." To avoid threshold jumps, first-order smoothing is applied to the three threshold sequences on the time axis. The shaped thresholds are directly used for timing logic verification, giving critical actions higher safety redundancy within the observation window.

[0116] The execution package is distributed and audited at the runtime layer and consists of four parts. First, a self-healing operation sequence, listing atomic actions, target devices, and expected timings in chronological order. Second, a dynamic threshold plan, providing operational thresholds for each step, including upper, lower, and upper voltage limits, along with the source of the shaping coefficients and critical step identifiers. Third, a signal timing logic verification report, providing... , , and The numerical curve and the step where the minimum value is located. Fourth, a summary of the proof of consistency between the satisfiability modulo theory is given. The satisfiable conclusions, conflicting clauses (if any), and alternative sequence numbers for replacement are included. The execution package includes a version number and timestamp to support backtracking and recalibration.

[0117] Example 12. The self-healing operation sequence of a feeder in the urban ring network is "disconnection-on-site reconfiguration-connection merging". Counterfactual energy margin shows that the minimum value of the connection merging step is lower than that of other steps. Based on this, the dynamic threshold plan adjusts the upper limit of voltage, the lower limit of voltage, and the upper limit of current for this step. The timing logic robustness is calculated under the shaping threshold. The minimum robustness of the voltage range occurs in the connection merging step, and its value is still positive. The target recovery is achieved within the set time limit, and the robustness is positive. Parallel operations without relay protection coordination are prohibited and are not triggered in the entire sequence. Satisfiability mode theory is used to solve the entire sequence for "direction consistency, timing coordination, short circuit upper limit, topology connectivity, and mutual exclusion of actions", and the conclusion is that it is satisfiable. The system generates an execution package accordingly and marks the connection merging step as a key monitoring step, configuring a backup sequence of "on-site reconfiguration first, then postpone merging". The operation layer issues the execution package step by step, and the voltage and current are confirmed online in the observation window. If a deviation trend is detected, the system rolls back according to the preset backup sequence. This embodiment demonstrates that the dual-layer verification of timing logic and satisfiability model theory can improve the release success rate without increasing the number of action steps, and form a forward protection for critical actions with dynamic thresholds.

[0118] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for failure prediction self-healing power distribution, characterized in that, The method comprises the following steps: The controlled disturbance is applied and the voltage and current responses are obtained by synchronous phasor measurement, the equivalent admittance and physical residual are calculated according to the injection response relationship, the spectrum-topology co-embedding coordinates and innovation consistency index are generated, and the topology is checked to obtain the checked topology state; the innovation consistency index is obtained by calculating the domain coherence of the linear prediction model innovation quantity of the zero sequence voltage or phase current; In the spectrum-topology co-embedded coordinates, suspicious clusters are divided, space evidence, time evidence and physical evidence are fused, and a control access intensity value is obtained by combining hazard rate evaluation; the control access intensity value is used to compress the fused interval belief into a single scalar, which is used for cross-module consistent calling wherein is a control access intensity value, is a belief lower bound of allowed intervention, is a possibility upper bound of allowed intervention, is a trade-off coefficient; The control admission intensity value is set according to a conditional value-at-risk confidence level and a barrier advance coefficient, wherein the control admission intensity value and the conditional value-at-risk confidence level and the barrier advance coefficient establish a monotonic mapping, so that the risk and the safety are simultaneously tightened with the evidence intensity , , is a control admission intensity value, is a conditional value-at-risk confidence level, is a barrier advance coefficient, is a calibration constant; With the help of feasible region priori and action screening, candidate atomic actions are filtered, and the search is constrained by the control barrier function in the joint state space determined by the checked topology state, and the conditional value at risk is taken as the target to optimize the power flow, and the self-healing operation sequence is obtained and the counterfactual energy margin is calculated; wherein the promotion meets , is any control barrier function, is the joint state of the first step, is the joint state of the first step, is the single-step action time scale; The counterfactual energy margin is used for release layer dynamic threshold shaping and backup sequence switching , is the first step counterfactual energy margin, is the action perturbation, is the action amplitude upper bound, is the first step dual vector of constraints, is the constraint function; The voltage upper limit value, the voltage lower limit value and the current upper limit value are dynamically adjusted according to the counterfactual energy margin and the control admission strength value, and the full sequence consistency is checked according to the signal time sequence logic and the satisfiability model theory to generate an execution package.

2. The method of claim 1, wherein, The controlled disturbance is applied at the power supply side or the tie switch position, and the voltage and current responses aligned with the disturbance are obtained by synchronous phasor measurement; the equivalent admittance and physical residual calculated according to the injection response relationship are used to construct a weighted graph of the measurement point and generate spectrum-topology co-embedding coordinates through graph Laplacian spectrum embedding; The topology checking generates a checked topology state according to the power direction and phase consistency.

3. The method of claim 1, wherein, The suspicious clusters are divided on the spectrum-topology co-embedding coordinates using a density-based clustering method, and the clustering results are mapped to physical line segments to determine the target segment.

4. The method of claim 1, wherein, The spatial evidence, temporal evidence and physical evidence are synthesized using the Dempster-Shafer evidence fusion method, the hazard rate is evaluated using a semi-parametric hazard rate model to calculate the arrival probability and weight the correction result as a prior weight, and the control admission strength value is determined by the evidence belief measure after the weighted correction.

5. The method of claim 1, wherein, The conditional value at risk confidence level and the barrier advancing coefficient are set to establish a monotonic corresponding relationship with the control admission strength value, and the conditional value at risk confidence level is increased and the barrier advancing coefficient is increased accordingly as the control admission strength value increases.

6. The method of claim 1, wherein, The feasible region prior uses a learning method with confidence coverage to construct the outer envelope of the feasibility classifier, and the output of the feasible region prior is three categories of feasible, uncertain and infeasible, wherein the candidate atomic actions corresponding to the uncertain and infeasible are excluded in the screening stage.

7. The method of claim 1, wherein, The action shielding includes the following rules: it is prohibited to form a closed loop without relay protection cooperation support, the grid connection phase angle difference is limited to be not more than the upper limit of the grid connection phase angle difference, the short-circuit current level is limited to be not more than the upper limit of the short-circuit current level, and it is prohibited to cross the time window of the upper-level protection.

8. The method of claim 1, wherein, The search is performed in the joint state space determined by the checked topology state using a random exploration tree algorithm, a candidate sequence is generated under the constraint of the control barrier function, and a sampling bias is set according to the spectrum-topology co-embedding coordinates and the path cost is shaped according to the innovation consistency index.

9. The method of claim 1, wherein, The conditional value at risk is taken as the target of the power flow optimization, which is based on a linearized alternating current power flow model, and the constraints include voltage upper limit, voltage lower limit, current upper limit, short-circuit current level, relay protection cooperation and operation mode, the optimization output is a self-healing operation sequence, and a feasible region proof file containing voltage and current envelope, short-circuit current level and relay protection cooperation checking result is generated, and the counterfactual energy margin is calculated according to the optimization dual sensitivity.

10. The method of claim 1, wherein, The signal timing logic specification includes that the node voltage falls into the shaped voltage upper limit and voltage lower limit interval, reaches the target load recovery rate within a preset time window, and prohibits parallel operation without relay protection cooperation; the satisfiability model theory encodes the relay protection logic, the short-circuit current level, and the topology connectivity for full sequence consistency checking; the execution package includes a self-healing operation sequence, a dynamic threshold plan, a signal timing logic checking report, and a satisfiability model consistency proof abstract.

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