Fault prediction self-healing power distribution method

Abstract

The invention relates to the technical field of a power distribution network of a power system, in particular to a fault prediction self-healing power distribution method, which comprises the following steps of: firstly, acquiring equivalent admittance and physical residual by controlled disturbance and synchronous phasor measurement, generating a spectrum-topology co-embedded coordinate and an innovation consistency index, and finishing topology check; fusing the space evidence, the time evidence and the physical evidence, and combining hazard rate evaluation to form a control admission intensity value; executing offset search under the constraint of feasible region prior, action shielding and control barrier, and performing power flow optimization by taking a condition in-danger value as a target to obtain a self-healing operation sequence; and finally, the operation threshold is shaped according to the anti-fact energy margin, complete sequence checking is completed according to the signal sequential logic and the satisfiability model theory, an execution packet is generated, low misoperation is achieved, and safety and rapid recovery can be proved.

Description

Technical Field

[0001] The present invention relates to the technical field of power system distribution network, and in particular to a fault prediction and self-healing power distribution method. Background Art

[0002] Distribution networks are undergoing a simultaneous surge in distributed generation, increasing electrified loads, and assessing power supply reliability. Traditional operational models of "alarm-manual resolution" or "passive tripping-post-reconfiguration" struggle to balance outage losses, power quality, and protection coordination under complex grid conditions and uncertain output conditions. Automating the entire "prediction-isolation-reconfiguration-release" process is key to reducing unpowered energy, shortening restoration time, and improving audit traceability. Summary of the Invention

[0003] In response to the many problems existing in the above-mentioned prior arts, the present invention provides a fault prediction and self-healing power distribution method. The present invention obtains equivalent admittance and physical residual through active observability, combines spectral-topological co-embedding with innovative consistency to form a control access strength value; generates candidates under the constraints of feasible domain prior and control barrier, and optimizes the self-healing operation sequence by conditional risk value flow; finally, drives threshold shaping with counterfactual energy margin, cooperates with temporal logic and satisfiability module theory consistency proof summary to reduce false operation and unpowered energy.

[0004] A fault prediction and self-healing power distribution method comprises the following steps: Apply controlled disturbances and use synchronized phasor measurements to obtain voltage and current responses. Calculate the equivalent admittance and physical residual based on the injection-response relationship, generate spectral-topological co-embedding coordinates and innovative consistency indicators, and complete the topology verification to obtain the verified topological state. Divide suspicious clusters on the spectral-topological co-embedding coordinates, integrate spatial evidence, temporal evidence and physical evidence, and combine them with hazard rate assessment to obtain the control access intensity value; The confidence level of the conditional VAR and the barrier propulsion coefficient are set according to the control access strength value. The candidate atomic actions are screened with the help of feasible domain prior and action shielding. The search is constrained by the control barrier function in the joint state space determined by the verified topological state. The power flow is optimized with the conditional VAR as the target, and the self-healing operation sequence is obtained and the counterfactual energy margin is calculated. Based on the counterfactual energy margin and the control access strength value, the voltage upper limit, voltage lower limit and current upper limit are dynamically adjusted, and the full sequence consistency is checked based on the signal timing logic and satisfiability module theory to generate an execution package.

[0005] Preferably, a controlled disturbance is applied at the power supply side or the tie switch position, and voltage and current responses aligned with the disturbance are obtained through synchronized phasor measurement; 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 calculating the graph domain coherence of the innovation quantity of the linear prediction model of the zero-sequence voltage or phase current; and the topology verification generates a verified topology state based on the power direction and phase consistency.

[0006] 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 sections to determine the target section.

[0007] Preferably, the fusion of spatial evidence, temporal evidence and physical evidence is synthesized using the Demster-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 perform weighted correction on the synthesis result, and the control access strength value is determined by the weighted corrected evidence belief measure.

[0008] Preferably, the setting of the confidence level of the conditional value at risk and the barrier advancement coefficient establishes a monotonic correspondence with the control access strength value, and as the control access strength value increases, the confidence level of the conditional value at risk is correspondingly increased and the barrier advancement coefficient is increased.

[0009] Preferably, the feasible domain prior uses a learning method with confidence coverage to construct an outer envelope of the feasibility classifier. The output of the feasible domain prior is divided into three categories: feasible, uncertain and infeasible. The candidate atomic actions corresponding to uncertain and infeasible are eliminated in the screening stage.

[0010] Preferably, the action shielding includes the following rules: prohibiting the formation of closed-loop merging without the support of relay protection, limiting the grid-connected phase angle difference to not exceed the upper limit of the grid-connected phase angle difference, limiting the short-circuit current level to not exceed the upper limit of the short-circuit current level, and prohibiting overstepping operations that cross the upper-level protection time limit window.

[0011] Preferably, a random exploration tree algorithm is used to search in the joint state space determined by the verified topological state, generate candidate sequences under the constraint of the control barrier function, set the sampling bias according to the spectral-topological co-embedding coordinates and shape the path cost according to the innovation consistency index.

[0012] Preferably, the power flow optimization with the conditional value at risk as the target is established based on the linearized AC power flow model. The constraints include the voltage upper limit, voltage lower limit, current upper limit, short-circuit current level, relay protection coordination and operation mode. The output self-healing operation sequence is optimized and a feasible domain certification document containing the voltage and current envelopes, short-circuit current level and relay protection coordination verification results is generated. At the same time, the counterfactual energy margin is calculated based on the optimization dual sensitivity.

[0013] Preferably, the signal timing logic specifications include the node voltage falling within the voltage upper limit and voltage lower limit interval after shaping, achieving the target load recovery rate within the preset time window, and prohibiting parallel operation without relay protection coordination; the satisfiability module theory encodes the relay protection logic, short-circuit current level and topological connectivity for full sequence consistency verification; the execution package includes the self-healing operation sequence, dynamic threshold plan, signal timing logic verification report and the summary of the satisfiability module theory consistency proof.

[0014] Compared with the prior art, the advantages and beneficial effects of the present invention are: Through the joint modeling of controlled disturbances and synchronized phasor measurements, equivalent admittance, and physical residuals, a highly separable precursor and topologically consistent operational baseline were achieved. Spectral-topological co-embedded coordinates, innovative consistency indicators, evidence fusion, and hazard rate assessment were used to generate control access strength values, enabling "intervention only when evidence is consistent" gating. Through a randomized exploration tree search coupled with feasible domain priors, action masking, and control barrier functions, candidate generation and rapid convergence for in-process safety were achieved. Through power flow optimization targeting the conditional value at risk, tail risk suppression and intrinsic satisfaction of electrical feasibility were achieved in uncertain scenarios. Pre-release provable safety and runtime adaptive protection were achieved through operational threshold shaping driven by counterfactual energy margins, combined with signal timing logic and satisfiability modulo theory verification. By carrying threshold plans, robustness metrics, and proof summaries in execution packages, hierarchical execution and full-link audit traceability were achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0016] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present disclosure. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present disclosure.

[0017] like Figure 1 As shown, a fault prediction self-healing power distribution method includes the following steps: Apply controlled disturbances and use synchronized phasor measurements to obtain voltage and current responses. Calculate the equivalent admittance and physical residual based on the injection-response relationship, generate spectral-topological co-embedding coordinates and innovative consistency indicators, and complete the topology verification to obtain the verified topological state. This invention establishes active observability within fault prediction and self-healing distribution methods. Its goal is to transform previously indistinguishable fault precursors into measurable, comparable, and transferable evidence, while also forming an analytical baseline consistent with power flow and topology. Through controlled disturbance injection and synchronized phasor measurements, highly sensitive estimates of line equivalent parameters and network consistency are obtained under weak disturbance conditions, providing trusted input for subsequent evidence fusion and self-healing sequence synthesis.

[0018] Controlled disturbance injection is implemented at the power supply or tie-breaker location. The disturbance waveform amplitude is limited, and the frequency band avoids the device's resonance band. A synchronized phasor measurement device acquires the voltage and current responses within the disturbance window using a unified clock, with the timestamps strictly aligned with the disturbance trigger. To eliminate measurement bias, the short windows before and after the disturbance are first detrended and amplitude-phase calibrated, followed by frequency extraction to ensure stable and comparable injection-response relationships.

[0019] The equivalent admittance estimation is based on the injection-response relationship. For the injection point and the affected measurement point, the voltage increment and current increment caused by the disturbance are defined, and the frequency domain equivalent admittance estimation is calculated as follows: ,in Injection point With measuring point In frequency The equivalent admittance estimate at is the current complex amplitude increment caused by injection, is the increase in the complex amplitude of the voltage caused by the injection. By comparing the equivalent admittance estimate with the historical baseline admittance, we can obtain the parameter deviation distribution, which can be used to indicate precursors such as insulation degradation, poor contact, and local heating.

[0020] The physical residual is used to check the consistency between the measurement and the network equation. Based on the linearized AC power flow model, a set of algebraic equations is constructed to evaluate the consistency of the power flow state vector at the current moment. The residual is defined as ,in For the moment The physical residual of is the coefficient matrix generated by the calibrated device parameters and topology, is the state vector composed of node voltage and branch power, is a constant vector consisting of the injected power and the control settings. When the physical residual exceeds the adaptive threshold, it indicates that there is a discrepancy between the current power flow and the network model, requiring a more frequent retest or entering the abnormal channel of evidence fusion.

[0021] Spectral-topological co-embedding coordinates are used to unify "electrical parameter changes," "topological adjacency," and "traveling wave and zero-sequence characteristics" into the same geometric space. The method flow is as follows: a node feature vector is composed of the equivalent real part of admittance, the equivalent imaginary part of admittance, the physical residual, and the zero-sequence quantity characteristics. A weighted graph is constructed in combination with the electrical distance. The first several eigenvectors of the graph Laplacian are calculated to obtain low-dimensional coordinates. Spectral-topological co-embedding coordinates are used in the present invention for two types of tasks: one is to perform density aggregation in the coordinate space to identify suspicious clusters and map them back to physical lines; the other is to serve as a basis for sampling bias and cost shaping in subsequent searches and optimizations, thereby reducing the search range and convergence time.

[0022] The innovation consistency index is used to characterize the degree of spatial coordination of time series precursors. Taking the short window sequence of zero-sequence voltage or phase current as the object, a linear prediction model is used to decompose the stable part and the innovation amount. The model is ,in is the time series sample of the measurement point, is the linear prediction coefficient, is the model order, The innovation sequence is represented by a generalized coherence statistic of the innovation sequences of adjacent measurement points, resulting in an innovation consistency index. This index is used to identify coordinated anomalies caused by early, weak-amplitude, and intermittent disturbances. The innovation consistency index provides temporal evidence for evidence fusion and, in subsequent search phases, rewards and penalties for path costs, encouraging earlier isolation of suspicious sections.

[0023] Topology verification uses phasor angle differences and power direction as constraints, combining equivalent admittance estimation with physical residuals to infer the consistency of switch states. This eliminates topology combinations that do not match the measurements, ultimately forming a verified topology state. This verified topology state serves a dual purpose in this invention: it serves as the sole topology input for physical residual calculation and power flow optimization, and it also serves as a boundary condition for action masking rules and control barrier functions, preventing merging or switching in unprotected ring networks.

[0024] Preferably, a controlled disturbance is applied at the power supply side or the tie switch position, and voltage and current responses aligned with the disturbance are obtained through synchronized phasor measurement; 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 calculating the graph domain coherence of the innovation quantity of the linear prediction model of the zero-sequence voltage or phase current; and the topology verification generates a verified topology state based on the power direction and phase consistency.

[0025] The present invention is aimed at the demand for active observability of fault prediction and self-healing power distribution. By applying low-amplitude controlled disturbances on the power supply side or at the tie-switch position, and using a synchronized phasor measurement device to collect voltage and current responses aligned with the disturbance, an "injection-response" link is constructed, so that the line equivalent parameters and network consistency can be identified with high sensitivity under weak disturbance conditions, thereby forming structured observation features, spectral-topological co-embedded coordinates, innovative consistency indicators and verified topological states, providing a unified baseline for subsequent evidence fusion and self-healing sequence synthesis.

[0026] Controlled disturbance injection uses an amplitude-limited, band-controlled waveform with unified trigger and measurement timestamps. To suppress measurement bias, detrending, amplitude-phase calibration, and windowing are performed within a short window before and after the disturbance. Complex amplitude increments are then extracted at the disturbance frequency to ensure stability and repeatability in subsequent ratio calculations.

[0027] The equivalent admittance estimation is based on the "injection-response" relationship, which converts the voltage increment and current increment caused by the disturbance into a ratio in the frequency domain. By comparing the equivalent admittance estimate with the historical baseline admittance, the parameter deviation distribution can be obtained to indicate fault precursors such as insulation degradation, poor contact, and local heating; the incremental definition makes the indicator more sensitive to slowly varying anomalies.

[0028] Physical residuals are used to verify the consistency of measurements with network equations. Algebraic constraints are constructed based on the 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 tide and the model, which should trigger re-measurement or enter the abnormal evidence channel; it is complementary to the equivalent admittance estimation, the former tends to model consistency, and the latter tends to parameter drift.

[0029] In order to unify the representation of "electrical parameter changes", "topological adjacency" and "zero-sequence characteristics", a weighted graph of measurement points is constructed and the graph Laplace spectrum is embedded to obtain the spectrum-topology co-embedding coordinates. For each measurement point, a feature vector consisting of the equivalent real part of admittance, the equivalent imaginary part of admittance, the physical residual and the zero-sequence quantity statistics is extracted, and the kernel weight is defined in combination with the electrical distance. ,in For measuring points With measuring point The similarity of For measuring points The eigenvector of is the weighted binorm, and are the kernel scale and distance attenuation parameters, is the electrical distance. The graph Laplacian is obtained from the weight matrix, and its first several eigenvectors are taken as low-dimensional coordinates. Spectral-topological co-embedding coordinates form "suspicious clusters" in the coordinate space, facilitating mapping back to the physical line location of anomaly areas. They also serve as a basis for sampling bias and cost shaping in self-healing sequence synthesis, narrowing the search domain.

[0030] The innovative consistency index is used to characterize the spatial coordination of time sequence precursors. A linear prediction model is established for the short window sequence of zero sequence voltage or phase current. The innovation sequences of adjacent measurement points are statistically correlated in the graph domain and aggregated at the node level into an innovation consistency index. This index can highlight the spatial synchronization of weak-amplitude, intermittent anomalies such as high-resistance grounding and intermittent arcing, and can be used as temporal evidence in evidence fusion. It also applies rewards and penalties to path costs during the sequence search phase, promoting the "early isolation, near splicing" strategy.

[0031] Topology verification uses phasor angle differences and power direction as criteria, combining equivalent admittance estimation with physical residuals to infer the consistency of switch states. Topology combinations that do not meet the consistency requirements of angle differences and power direction are eliminated to generate a verified topology state. This verified topology state is also used as the sole topology input for subsequent power flow optimization and as a boundary condition for action shielding, preventing merging or switching without relay protection coordination.

[0032] Example 1: A city ring network system completes controlled disturbance injection at the interconnecting switch, and the two end measurement points collect responses by synchronous phasor measurement devices. The data processing module completes detrending, amplitude and phase calibration, and frequency extraction within the disturbance window, and calculates the equivalent admittance estimate and physical residual. The imaginary part of the equivalent admittance of one branch increases and the real part decreases, and the physical residual peaks in the same time window. The equivalent admittance estimate, physical residual and zero-sequence quantity statistics are jointly constructed to construct a weighted graph of measurement points, and the corresponding nodes in the spectral-topological co-embedding coordinates form dense clusters; the graph domain coherence statistics are performed on the innovation sequence of the cluster neighborhood, and the innovation consistency index is significantly increased. Based on this, the topology verification excludes a segmented switch hypothesis that does not conform to the power direction, and outputs the verified topology state. Finally, the structured observation features, spectral-topological co-embedded coordinates, innovative consistency indicators and verified topological states are submitted to the evidence fusion module, which prioritizes isolation and reconstruction path searches in the corresponding physical segments, reducing the number of attempts and consistency checks in the self-healing sequence while ensuring that voltage and current constraints are not breached.

[0033] Divide suspicious clusters on the spectral-topological co-embedding coordinates, integrate spatial evidence, temporal evidence and physical evidence, and combine them with hazard rate assessment to obtain the control access intensity value; This method uses spectral-topological co-embedded coordinates to perform spatiotemporal aggregation of observational information. Through evidence fusion and hazard rate assessment, it generates a control access intensity value, which serves as the sole gating variable for self-healing sequence synthesis. The goal is to transform the spatial aggregation, temporal coordination, and physical consistency of precursors into a single scalar, allowing subsequent search and optimization to be conducted only within segments proven "worthy of intervention."

[0034] The spectral-topological co-embedding coordinates are derived from the feature graph embedding in the previous step, reflecting the consistent geometric structure of electrical parameter changes and topological adjacencies. Using these coordinates as input, a density-based clustering algorithm is used to partition suspicious clusters in coordinate space. Cluster members are then mapped back to physical line segments to form a three-dimensional representation of candidate targets. Clustering serves only as a "spatial indicator" and does not directly trigger control; whether to initiate control is determined by a combination of evidence fusion and hazard rate.

[0035] Spatial, temporal, and physical evidence are all calculated at the cluster granularity. Spatial evidence is derived from a comprehensive score of the cluster's point density, the significance of equivalent admittance deviations, and the consistency of physical residuals, reflecting the specific anomaly. Temporal evidence uses the average and stability of the innovation consistency index obtained in the previous step within the cluster, reflecting whether anomalies occur synchronously at multiple measurement points. Physical evidence is derived from the proportion of physical residuals crossing thresholds within the cluster and the statistical significance of equivalent admittance deviations, reflecting whether anomalies are inconsistent with the network equations. These three types of evidence are then normalized and mapped into basic belief assignments. These are fed into the evidence fusion engine to output beliefs and likelihoods for "allow intervention," "do not intervene," and "uncertain."

[0036] Hazard rate assessment is used to provide prior weights and time window semantics for evidence fusion, using a semi-parametric hazard rate model. Given a feature vector based on the environment and asset status, the arrival rate and the probability of arrival within the future window are defined. , ,in is the fault arrival rate, For the moment The eigenvector of are model parameters, is the log-odds function, To evaluate the time window, is the arrival probability within the time window. The arrival probability participates in the weighted correction of the “allow intervention” belief, which is used to eliminate situations that appear to be abnormal in space but have low short-term risks from the control entrance.

[0037] Controlling the admission strength value compresses the fused interval belief into a single scalar for consistent calls across modules ,in To control the admission strength value, The belief of "allowing intervention" is lowered. is the upper bound of the possibility of “allowing intervention”, A larger control access strength value indicates more consistent evidence and a higher probability of arrival, which in turn increases the conservatism of the subsequent VAR and control barriers. When the control access strength value falls below the preset threshold, only warnings and retests are retained, and self-healing is not initiated.

[0038] Example 2: After a controlled disturbance and phasor acquisition were completed at the tie switch on a feeder in a city ring network, a high-density cluster of nodes appeared in a certain segment of the embedded coordinates. The equivalent admittance deviation within this cluster exhibited a coordinated increase in the imaginary part and decrease in the real part. The proportion of physical residuals crossing the threshold was high, indicating a consistent direction between spatial and physical evidence. The innovative consistency indicators of multiple adjacent measurement points within the same window increased simultaneously, forming temporal evidence. The hazard rate assessment used temperature, humidity, rainfall, and equipment age as feature vectors, calculating a high probability of arrival in the next few minutes. The evidence fusion output, indicating a high confidence and likelihood of "intervention allowed," resulted in a high control access strength value, according to the previous equation. Consequently, the system initiated self-healing sequence synthesis and prioritized isolation and reconstruction candidates in the physical segment corresponding to this cluster. This example demonstrates that, under weak disturbance and short-window measurement conditions, coordinate clustering combined with the constraints of three types of evidence can compress the three-dimensional "location-time-physical" information into a control access strength value, effectively avoiding the search and operation of irrelevant segments and improving the pass rate of subsequent consistency checks.

[0039] The cluster granularity is determined by the density threshold of the embedded coordinates and the minimum cluster size to balance positioning accuracy and robustness; evidence normalization uses robust quantile normalization to suppress isolated extreme values; belief mapping should be calibrated with labeled events during the training phase to ensure that the contribution of belief and possibility to the control access intensity value complies with the safety strategy; the hazard rate model is trained according to season and load scenario partitions to prevent the increase of spurious correlation; the threshold and trade-off coefficient of the control access intensity value are set according to the ratio of the false action cost to the missed action cost, and are periodically recalibrated based on audit records during the operation period.

[0040] Through the above design, the control access intensity value becomes a unified quantitative threshold throughout the prediction, decision-making and release links, realizing a verifiable transition from "seeing anomalies" to "worth intervention", and providing clear and stable entry conditions for subsequent conditional value-at-risk trend optimization and control barrier constraints.

[0041] 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 sections to determine the target section.

[0042] This method uses spectral-topological co-embedded coordinates as a spatial carrier to identify abnormal clusters within the coordinate space and rigorously map these clusters to physical line segments, resulting in target segments that can be directly used for self-healing decision-making. The core concept is to compress "electrical parameter changes," "topological adjacency," and "temporal precursor coordination" into geometric clusters, then restore them to a manageable physical range using network connectivity, achieving executable implementation from data features to the switch level.

[0043] The spectral-topological co-embedding coordinates are generated by the previous step, and the measurement points are recorded The coordinate vector of ( is the low-dimensional coordinate, For the coordinate dimension). To perform density-based clustering in the coordinate space, first calculate the kernel density score of each measurement point ,in For measuring points The density fraction of is the kernel scale parameter, is the Euclidean norm. The core points, boundary points and noise points are marked by density threshold and neighborhood connectivity relationship, and the cluster set is obtained through density reachability relationship. ( For the Clustering is a collection of measurement points in clusters. 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 of clusters to physical lines is achieved through topological indexing. Define the mapping The measuring point Corresponding to the physical node or line location ( is a one-to-one mapping from measurement points to physical locations). For each cluster , take its projection in the physical network , and solve the minimum connected subgraph on the distribution network topology cover All nodes and necessary edges of . In order to ensure operability, Further cutting is done according to the protection and operation mode boundaries, and only the continuous line segments that meet the relay protection coordination and operation mode constraints are retained as candidate physical segments. In order to determine the final target segment from multiple candidate physical segments, a cluster scoring function is constructed. ,in For the The rating of the clusters, is the average density fraction within the cluster, is the threshold-crossing ratio of the physical residual within the cluster (the definition of physical residual is given in the previous step), is the standardized significance of the equivalent admittance deviation within the cluster, is the weight. The candidate physical segment with the largest score is taken as the target segment and recorded as ( is the set of physical lines in the target section). This score combines "spatial clustering strength," "model consistency evidence," and "parameter shift evidence" into a sortable scalar, facilitating the connection with the subsequent calculation of control access strength values.

[0044] To enhance project usability, the mapping and pruning phase incorporates two constraints: a connectivity constraint requiring the target segment to be a singly connected subgraph; and a protection boundary constraint requiring the target segment to not cross closed-loop boundaries without relay protection coordination. If multiple candidate physical segments with similar scores overlap, the overlapping segments are merged and then reordered based on the merged scores. Clusters that only cover scattered measurement points and fail to form a connected subgraph are marked as "warning only" and fed back to the retest process.

[0045] The advantages of the above process in principle are: First, density clustering "sees" geometric highlights determined by multi-source features in the coordinate space, which can naturally filter out scattered noise and retain continuous anomalies along the line; second, topological mapping directly puts abstract coordinates on the physical line, ensuring that any subsequent actions have clear switching boundaries; third, the scoring function combines several types of orthogonal evidence into a sortable decision quantity, which not only reduces the subjectivity of manual thresholds, but also facilitates the connection with the control access intensity value to form a unified threshold.

[0046] Example 3: On a city ring network feeder, a high-density cluster consisting of 8 measurement points appears in the spectral-topological co-embedding coordinates. The imaginary part of the equivalent admittance corresponding to this cluster increases as a whole, the real part decreases as a whole, and the physical residual exceeds the threshold ratio is high. The cluster is mapped to the physical network, and the minimum connected subgraph covers two adjacent branches and a segmented switch. After cutting according to the protection and operation mode boundaries, two candidate physical segments are obtained. The scoring function is calculated. The first candidate has a high average density and a larger physical residual exceeding the threshold ratio, and the admittance deviation significance is also higher, so The largest, identified as the target segment This target segment is then passed to the control access assessment module as the priority isolation and reconstruction range. Subsequent searches are only sampled and optimized within this range, significantly reducing the number of candidate sequences and improving the pass rate of subsequent consistency checks.

[0047] Through the above clustering-mapping-scoring link, the geometric information in the spectral-topological co-embedded coordinates is converted into physically operable target segments, which not only maintains consistency with electrical constraints but also provides a directly executable spatial entry for self-healing control, thus establishing a clear and verifiable connection between fault prediction and self-healing execution.

[0048] Preferably, the fusion of spatial evidence, temporal evidence and physical evidence is synthesized using the Demster-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 perform weighted correction on the synthesis result, and the control access strength value is determined by the weighted corrected evidence belief measure.

[0049] This method achieves spatiotemporal aggregation of observational information in spectral-topological co-embedded coordinates and employs Demster-Schafer evidence fusion and semi-parametric hazard rate assessment to generate control access strength values. The approach is to transform spatial, temporal, and physical evidence into weighted belief metrics and then use arrival probabilities to recalibrate beliefs within a time window, making the control access strength value the sole gating variable for entering the self-healing sequence synthesis.

[0050] Three types of evidence are constructed at the cluster level. Spatial evidence consists of the density score of the suspected cluster, the significance of the equivalent admittance deviation, and the consistency of the physical residual. Temporal evidence consists of the average and stability of the innovation consistency index within the cluster. Physical evidence consists of the threshold-crossing proportion of the physical residual and the statistical significance of the equivalent admittance deviation. After interval normalization, the three types of evidence are mapped into the basic belief distribution and enter the evidence fusion engine.

[0051] Demster-Schafer method , , and Assignment of basic beliefs to two sources; Assign basic beliefs to the fusion; is a subset of the framework set; The conflict coefficient is the conflict coefficient. Fusion is performed sequentially with two sources and then further integrated with the third source to obtain the lower bound of the belief and upper bound of the possibility of "allowing intervention". The conflict coefficient is used to suppress contradictory evidence and avoid forming a high belief with a single indicator. The hazard rate assessment provides the arrival probability within the time window and serves as a priori weight to weight the fusion result. , , For the moment Failure arrival rate; is the feature vector composed of the environment and asset status; is the model parameter vector; is the log-odds function; For the evaluation time window; To evaluate the arrival probability within the time window. The arrival probability is used to extrapolate clusters with low short-term risk and bring clusters with consistent evidence and high short-term risk to the front. Controlling the admission strength value compresses the weighted interval belief into a single scalar , To control the access intensity value, the value range is ; Set a lower bound for the belief that "intervention is allowed"; is the upper bound of the possibility of “allowing intervention”; is the weighting coefficient, and its value range is [0, 1].

[0052] When the control access strength value exceeds the threshold, the self-healing sequence synthesis is entered, and the risk value confidence level and control barrier advancement coefficient are monotonically tightened according to the control access strength value; when it is lower than the threshold, only alarms and retest instructions are issued.

[0053] Example 4: After the controlled disturbance and phasor acquisition are completed on a feeder line of the urban ring network, a high-density cluster consisting of multiple measurement points appears in the spectral-topological co-embedding coordinate. The equivalent admittance deviation in this cluster shows a coordinated change of increasing imaginary part and decreasing real part, the physical residual threshold crossing ratio is high, and the innovation consistency index increases synchronously in the neighborhood. After the three types of evidence are normalized, two-source fusion and three-source fusion are performed according to the above formula, and the lower bound of the belief and the upper bound of the possibility of "allowing intervention" are both at a high level. The hazard rate assessment uses temperature, humidity, rainfall and equipment service life to form a characteristic vector, and the probability of arrival in the next few minutes is calculated to be high. The control access intensity value calculated according to the above formula is at a high level, and the self-healing module then prioritizes the construction of isolation and reconstruction candidates in the target section corresponding to the cluster. The operation record shows that without expanding the scope of the power outage, the number of isolation steps and the number of consistency checks are reduced, and the conflicts before release are reduced.

[0054] The confidence level of the conditional VAR and the barrier propulsion coefficient are set according to the control access strength value. The candidate atomic actions are screened with the help of feasible domain prior and action shielding. The search is constrained by the control barrier function in the joint state space determined by the verified topological state. The power flow is optimized with the conditional VAR as the target, and the self-healing operation sequence is obtained and the counterfactual energy margin is calculated. The present invention converts the control access intensity value into risk scale and safety boundary, completes candidate atomic action screening, controlled search and power flow optimization under uncertainty in the verified topological state, outputs the self-healing operation sequence and provides the counterfactual energy margin for dynamic threshold setting and hierarchical execution before release.

[0055] Control the access strength value and establish a monotonic mapping with two types of core hyperparameters, so that risk and safety are tightened synchronously with the strength of evidence , , To control the admission strength value, is the confidence level of the conditional VaR, is the barrier propulsion coefficient, This mapping ensures that when there is sufficient evidence, the tail risk measurement is more conservative and the barrier is pushed more strongly; when there is insufficient evidence, the system maintains a relaxed setting and tends to warn and retest.

[0056] Candidate atomic actions are screened using a combination of feasible domain priors and action screening. The feasible domain prior constructs an outer envelope with confidence coverage based on historical power flow samples. The inputs are the atomic actions and local states, and the outputs are three values: feasible, uncertain, and infeasible. The latter two categories are directly eliminated during the screening phase. Action screening uses topological connectivity, relay protection coordination, grid phase angle difference, and short-circuit current levels as hard constraints. A prohibited transition set is compiled, and any actions that touch the prohibited transition set are excluded from the search.

[0057] The controlled search is performed in a joint state space consisting of the Cartesian product of the topological switching states and the linearized AC power flow solution. To ensure that the search process is always in a safe region where it can be advanced, a control barrier function is introduced, which defines the voltage, current and short-circuit current levels respectively. , , , To correspond to the safety margin, is the upper voltage limit, is the upper limit of current, is the upper limit of the short-circuit current level, is a real-time estimated value. Discrete advancement satisfies , For any barrier function, For the The joint state of the step, is the single-step action time scale, Given by the previous formula. This condition ensures that each step is within the propagable invariant set and excludes candidate paths that go beyond the limit boundary. On several candidate paths that pass the screening and barrier constraints, a power flow optimization with the conditional value at risk as the target is established to deal with the uncertainty of distributed power and load. , is an auxiliary variable, is the self-healing operation sequence, For scene collection, is the scene weight, is the expected unpowered energy in the scenario, is the positive operator, is the action cost weight, 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 operating mode consistency. The optimized output is a self-healing operation sequence that controls tail risks and meets electrical feasibility.

[0058] To measure the vulnerability of the plan to the next disturbance, the counterfactual energy margin is calculated for dynamic threshold shaping and backup sequence switching at the release layer. , For the The counterfactual energy margin of the step, is the motion disturbance, is the upper bound of the action amplitude, For the The dual vector of the step constraint, is the constraint function. The smaller the counterfactual energy margin, the greater the tightening of the pre-release threshold, and the priority of enabling the backup sequence.

[0059] Example 5. After evidence fusion, a certain ring network power supply area obtains a higher control access strength value. Based on this, the system simultaneously increases the confidence level of the conditional value at risk and the barrier advancement coefficient. The candidate atomic actions are first determined to be feasible by the feasible domain prior. The parallel closing that does not meet the relay protection coordination conditions is eliminated by the action shielding rule. In the joint state space, the search algorithm uses the density of the spectral-topological co-embedded coordinates as a sampling bias to generate several candidate paths under the control barrier function constraint. Subsequently, the power flow optimization with the conditional value at risk as the target is performed on these paths one by one to obtain a self-healing operation sequence, including the disconnection of the section switch, the closing of the tie switch, and the correction of the reactive power setting of the distributed power supply. The counterfactual energy margin of the sequence is calculated step by step, and 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 search and optimization converge quickly within a controlled security domain when the strength of evidence is high, and adaptive security reinforcement can be implemented based on counterfactual energy margins before release, thereby achieving isolation and reconstruction without expanding the scope of the power outage.

[0060] Preferably, the setting of the confidence level of the conditional value at risk and the barrier advancement coefficient establishes a monotonic correspondence with the control access strength value, and as the control access strength value increases, the confidence level of the conditional value at risk is correspondingly increased and the barrier advancement coefficient is increased.

[0061] This method converts control access strength values ​​into risk scales and safety margins, allowing subsequent search and power flow optimization to proceed within a feasible domain consistent with the evidence. The core concept is to use a monotonic mapping to input control access strength values ​​into the conditional value-at-risk confidence level and barrier push coefficient. This allows for a more conservative tail risk metric and stricter safety push when the evidence is strong, while maintaining a relaxed setting and prioritizing early warning and retesting when the evidence is weak.

[0062] To establish a achievable monotonic relationship, a linear bounded mapping is used , , To control the admission strength value, is the confidence level of the conditional VaR, is the barrier propulsion coefficient, and is the confidence level baseline and gain, and The boost coefficient baseline and gain are used. Calibrate the constants through offline playback to ensure that the derived values ​​are within the feasible range and meet monotonicity. Clipping or smoothing is introduced as necessary to eliminate jumps.

[0063] Based on the above mapping, the previously defined conditional VAR objective function and barrier advancement condition directly use the updated confidence level and advancement coefficient. When the confidence level increases, the tail of the conditional VAR coverage becomes deeper, and the optimization will suppress the amplification of unpowered energy in adverse scenarios with a higher weight; when the advancement coefficient increases, the barrier margin shrinks faster, and the search will prioritize candidate paths away from the constraint boundary and eliminate action combinations that approach the limit. To maintain consistency throughout the entire process, candidate atomic actions enter the barrier constraint search and power flow optimization with conditional VAR objectives only after screening the feasible domain prior and action shielding. The optimized self-healing operation sequence is then used to calculate the counterfactual energy margin and enter the release phase.

[0064] The mapping implementation process consists of two parts: calibration and online adaptation. The calibration phase replays real operating conditions from recent years, selecting representative segments that cover seasonal, load, and distributed generation variations. A grid search or convex optimization algorithm is used to determine the constant set, ensuring that the tail indicator of unpowered energy is consistent with the operating alarm record under high control access strength values ​​and that the false operation probability satisfies the constraints under low control access strength values. The online phase monitors the minimum value of the counterfactual energy margin and the consistency check conflict count. 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 applied to the confidence level and boost coefficient.

[0065] To facilitate operational control and release verification, the above mappings and parameters are recorded in the execution metadata to facilitate post-audit and recalibration. At the same time, the minimum counterfactual energy margin and the corresponding step are marked in the plan for the release layer to dynamically tighten the threshold of this step and prioritize switching to the backup sequence.

[0066] Example 6. After evidence fusion, a ring network area obtained a control access strength value of 0.78. Linear mapping revealed a high confidence level for the conditional VAR and a high barrier propulsion coefficient. Candidate atomic actions were first screened through a priori feasible domain screening, and closed-loop merges without relay protection coordination were eliminated by action shielding. Controlled search generated multiple candidate paths within the joint state space. The barrier propulsion condition, due to its large propulsion coefficient, suppressed paths close to the voltage and current upper limits. Conditional VAR flow optimization was then performed with the updated confidence level to obtain a self-healing operation sequence, opening the section switches, closing the tie switches, and modifying the reactive power settings of the distributed generation (DGs). Counterfactual energy margins were calculated for each step, with the minimum value occurring at the tie closing step. Based on this, the release layer tightened the voltage and current operating thresholds for that step and assigned a higher priority to the backup sequence. This example demonstrates that when the evidence is strong, tail risks are fully suppressed, the search remains within the propulsion invariant set, and isolation and reconstruction are completed in a relatively small number of steps, while maintaining a consistent check pass rate.

[0067] Preferably, the feasible domain prior uses a learning method with confidence coverage to construct an outer envelope of the feasibility classifier. The output of the feasible domain prior is divided into three categories: feasible, uncertain and infeasible. The candidate atomic actions corresponding to uncertain and infeasible are eliminated in the screening stage.

[0068] This paper proposes a feasible domain prior to pre-screen candidate atomic actions with confidence coverage before entering controlled search and power flow optimization. The idea is to train a feasibility classifier using historical operation and simulation samples in the offline phase and calibrate the classifier's outer envelope using a learning method with confidence coverage in the online phase, ensuring that online decisions have controllable coverage errors. As a result, each candidate atomic action and its associated joint state summary are mapped into three output categories: feasible, uncertain, and infeasible. Uncertain and infeasible actions are directly eliminated during the screening phase, retaining only feasible ones for subsequent steps.

[0069] The construction of the feasible domain prior involves three steps: feature definition, classifier training, and confidence coverage calibration. In this paper, the features consist of a joint state summary and an action code. The joint state summary includes node voltage predictions, branch current predictions, short-circuit current level estimates, protection window numbers, and topological fingerprints. The action code describes the atomic action type and its location. The feasibility classifier outputs the boundary distance as the feasibility margin, with positive values ​​indicating a feasible side and negative values ​​indicating an infeasible side.

[0070] To obtain confidence coverage, an inconsistency score is introduced and a quantile threshold is determined on the calibration set. , represents a feature vector consisting of a joint state summary and action encoding; represents the feasibility margin of the classifier output; Indicates the marginal baseline of offline calibration; Indicates the inconsistency score. The inconsistency score set is calculated using an independent calibration set and its quantile threshold is taken. , represents the quantile threshold; Indicates coverage level; Represents the inconsistency score on the calibration set. The online decision rule is defined as follows: judged feasible; when Judged as uncertain; This rule corresponds to the outer envelope of the classifier decision boundary, and its coverage error is given by control.

[0071] To ensure consistency with electrical constraints, the feasible region prior training labels are not derived from a single empirical threshold. Instead, they are derived by solving constraints such as linearized AC power flow balance, upper and lower voltage limits, upper current limits, short-circuit current levels, and relay protection coordination in the sample space. This ensures that the learned margins of the classifier are consistent with the physically feasible region. The calibration phase covers seasonal variations, load levels, and distributed generation fluctuations to ensure that the quantile thresholds are stable under common operating conditions.

[0072] In online applications, the feature vector is first calculated for each candidate atomic action, along with the feasibility margin and inconsistency score. Three types of decisions are then output according to the aforementioned rules. Uncertain and infeasible decisions are eliminated during the screening phase to avoid controlled search; feasible decisions proceed to action screening and control barrier constraints. Due to the outer envelope property, the confidence coverage corresponding to the feasible decision is statistically valid, limiting the risk of false acceptance to a preset level. Compared to single-point thresholding methods, this method maintains coverage properties even in the presence of training errors and distribution drift.

[0073] The connection with subsequent modules is reflected in two key aspects. First, the higher the control access strength value, the system can select a higher coverage level and adjust the quantile threshold accordingly, aligning conservatism with the strength of evidence. Second, the three types of outputs from the feasible domain prior have direct flow semantics within the search and optimization module: feasible entry candidate generation, uncertainty triggering local retesting or feature augmentation, and infeasibility triggering action blocking statistical updates, which are used to modify the prohibited transition set.

[0074] Example 7. A feasibility classifier is trained in a certain ring network area based on historical data and simulation samples, and records covering four seasons and multiple load segments in the past year are 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 types of judgments based on this. Most actions close to the voltage upper limit and current upper limit boundaries are judged to be uncertain or infeasible and are directly eliminated. The remaining feasible actions enter the control barrier constraint search and power flow optimization with the conditional at-risk value as the target. The final self-healing operation sequence consists only of actions that were previously determined to be feasible, and the thresholds of key steps will be tightened according to the counterfactual energy margin before release. This embodiment shows that the feasible domain prior with confidence coverage can shrink the solution domain early and maintain a safe outer envelope consistent with the electrical constraints, so that subsequent searches and optimizations are carried out in a smaller feasible space, reducing the number of paths rejected by consistency checks during the release phase.

[0075] Preferably, the action shielding includes the following rules: prohibiting the formation of closed-loop merging without the support of relay protection, limiting the grid-connected phase angle difference to not exceed the upper limit of the grid-connected phase angle difference, limiting the short-circuit current level to not exceed the upper limit of the short-circuit current level, and prohibiting overstepping operations that cross the upper-level protection time limit window.

[0076] Action screening 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 breaker closing, tap changer shifting, and distributed generation active and reactive power settings. Action screening is performed in a verified topology state. Each candidate atomic action is pre-measured and evaluated against its corresponding intended execution state, forming a set of inoperable actions. This ensures that subsequent path generation remains within the safe and feasible domain.

[0077] The protection coordination of closed-loop merging is the primary threshold. The coordination effectiveness is determined by the relay protection direction criterion, time limit coordination and backup coverage, which is recorded as , is a candidate atomic action, For the The joint state of the step, It is a binary value for relay protection coordination judgment. The value 1 indicates that the coordination is valid. The grid phase angle difference must be limited to suppress the active and reactive power impact at the moment of connection. The phase angle constraint is recorded as , is the phase angle difference between the two sides to be merged, is the upper limit of the phase angle difference, which is calibrated by the system operation procedures and can be tightened monotonically with the control access intensity value. The short-circuit current level must meet the equipment breaking capacity and busbar bearing capacity. The short-circuit constraint is recorded as , is the short-circuit current estimate under the fault assumption after operation, is the upper limit of the short-circuit current level, which is determined by the device capacity and operation strategy. Time coordination requires that the lower protection level should be activated before the upper protection level and a coordination margin should be left. The time coordination constraint is recorded as , The lower level protection period is For the superior protection time limit, To match the margin.

[0078] Action admission judgment is defined as , Action admission judgment, a value of 1 indicates that it is allowed to enter the search and optimization stage, and a value of 0 indicates that it is directly eliminated in the screening stage.

[0079] The above judgment process is linked to the control access strength value: when the control access strength value is high, the phase angle difference upper limit and the short-circuit current level upper limit are tightened according to the preset mapping, increasing the coordination margin and thus improving conservatism. When the control access strength value is low, the operating baseline is maintained, and early warning and retesting are favored. To avoid misjudgments caused by state drift, action shielding is re-evaluated before and after each step of candidate generation, search expansion, and optimization. It is used in conjunction with the feasible domain prior: uncertain and infeasible outputs in the three categories are directly eliminated without entering the action shield.

[0080] Example 8: Planned merging of a tie switch in an urban ring network. After candidate atomic actions are generated, the feasible domain prior is first used to perform three types of judgments, retaining only feasible actions for action screening. Under the proposed execution state, the predicted phase angle difference between the two sides of the grid is close to the upper limit of the phase angle difference, and the short-circuit current level is verified to be 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, the three constraints are triggered simultaneously, the action admission judgment is 0, and this direct merging is eliminated. The system first performs sectionalizing switch disconnection upstream of the target section to bring the predicted short-circuit current level and phase angle difference back into the safety zone. Then, based on the feasible conditions of the control barrier function, a candidate path is generated, including "disconnection-on-site reconstruction-tie merging". Then, power flow optimization is performed with the conditional at-risk value as the target. The final self-healing operation sequence is released, completing isolation and reconstruction while meeting protection coordination and electrical constraints, without any overstepping or merging shock.

[0081] Preferably, a random exploration tree algorithm is used to search in the joint state space determined by the verified topological state, generate candidate sequences under the constraint of the control barrier function, set the sampling bias according to the spectral-topological co-embedding coordinates and shape the path cost according to the innovation consistency index.

[0082] Based on a verified topological state, this method performs a randomized heuristic tree search within the joint "topology-power flow" state space. By controlling the barrier function, each expansion step is ensured to be within the propagable safety domain. Spectral-topological co-embedding coordinates and innovative consistency indicators are combined with shape sampling and path cost to generate candidate sequences for power flow optimization. The joint state is constructed from switch configurations and linearized AC power flow solutions. Atomic actions include sectionalizer disconnection, tie switch merging, tap changer shifting, and distributed generation power setting.

[0083] In order to introduce spatial orientation and temporal precursors into sampling, a bias is given to the sampling density of the joint state, so that the tree expands more concentratedly to the suspicious area and preferentially passes through nodes with significant temporal precursors. , Status Sampling density; The state is spectrally-topologically co-embedded into the target cluster distance; is a penalty function based on the innovation consistency index (the higher the innovation consistency, the smaller the value is, to encourage early arrival at the precursor area); and is the temperature parameter. This density makes the tree expansion "towards the suspicious and strong precursor" direction, shortening the candidate path convergence time. Each edge must satisfy the pushable constraint of the control barrier function before being added to the exploration tree to ensure that the search process does not go beyond the limit boundary. , A barrier function for a voltage safety margin, a current safety margin, or a short-circuit current level safety margin; and It is the joint state before and after expansion; is the time scale of a single-step action; is the barrier advancement coefficient (obtained by mapping the control access strength value). This condition ensures that each expansion leaves an "inward" margin to prevent the tree from wandering on the constraint boundary. In order to ensure that the candidate path takes into account both supply guarantee and early isolation, the path cost is defined as the weighted sum of tail power supply risk, action cost and time precursor guidance. , For path the price; Estimation of expected unpowered energy (based on online evaluation of fast power flow approximation); is the number of path action steps; In state The reward and penalty items are constructed by the innovation consistency index (the earlier the node passes through the precursor, the smaller the value); and This cost encourages candidate paths with “fewer actions, earlier isolation, and lower risk” to enter subsequent optimization.

[0084] The search process uses a random exploration tree with reconnection: starting from the current joint state, it samples the state space according to the aforementioned bias, selects the nearest neighbor state, and then advances the state using atomic actions. Edges that pass the barrier constraint are added to the tree, and an attempt is made to reconnect adjacent nodes to reduce the path cost. The search terminates when a number of candidate paths that meet the load recovery rate and connectivity constraints are obtained. The entire process is linked to the feasible domain prior and action shielding: only atomic actions that are judged "feasible" are included in the expansion, and actions that touch the prohibited transition set are not generated, avoiding the inefficient "generate first, then reject" approach.

[0085] Example 9. After evidence fusion, a feeder in a city ring network obtained a high control access strength value. Based on this, the system tightened the barrier advancement coefficient and set a smaller temperature parameter around the target cluster, concentrating the sampling density peak more closely. Starting from the current state, the search first generated sampling points in the high-density region of the spectral-topological co-embedding coordinates. Atomic actions near the upper voltage and current limits were eliminated using the feasible region prior. The edge advancement was then verified using the control barrier function. As the tree expanded, several paths reached the segmented switches covering the strong precursor region within just a few steps, and candidate sequences of "disconnection-in-place reconstruction-connection-merge" were successively generated. Path cost calculations showed that sequences with early isolation and fewer steps had the lowest cost and were output as the preferred candidates. Several backup candidates with slightly higher costs but covering different connection strategies were also generated for subsequent refinement in the conditional value-at-risk flow optimization. In this example, the total number of search nodes was significantly lower than in the unbiased case, and all candidates entering the optimization phase met the in-process safety constraints, resulting in a decrease in the number of conflicts in the pre-release consistency check.

[0086] Preferably, the power flow optimization with the conditional value at risk as the target is established based on the linearized AC power flow model. The constraints include the voltage upper limit, voltage lower limit, current upper limit, short-circuit current level, relay protection coordination and operation mode. The output self-healing operation sequence is optimized and a feasible domain certification document containing the voltage and current envelopes, short-circuit current level and relay protection coordination verification results is generated. At the same time, the counterfactual energy margin is calculated based on the optimization dual sensitivity.

[0087] The present invention takes "power flow optimization with conditional value at risk as the target" as the core of self-healing decision-making, unifies the tail power supply risk, action cost and electrical constraints into the same optimization framework, directly outputs the self-healing operation sequence, and generates feasible domain proof documents and counterfactual energy margin after the solution is completed, which are used for dynamic threshold shaping and hierarchical execution of the release layer.

[0088] The goal of the optimization problem is to minimize the expected unpowered energy expressed by the conditional value at risk and superimpose the action cost. A scenario set is established to describe the uncertainty of distributed power and load, and the decision variables are time-ordered atomic action sequences. The objective function is denoted as , is an auxiliary variable; It is a self-healing operation sequence; For scene collection; is the scene weight; The expected unpowered energy in the scenario; is the positive operator; is the action cost weight; is the confidence level of the conditional VaR, obtained by the aforementioned control access intensity mapping.

[0089] The constraint system, based on linearized AC power flow, covers steady-state voltage, current, short-circuit current levels, relay protection coordination, and operating modes. First, linearized power flow balance is applied to ensure that node voltages, branch powers, and injected powers are consistent. Voltage upper and lower limits, as well as current upper limits, are then applied to each scenario at each time step to ensure thermal stability and power quality. Short-circuit current level constraints are calculated using an equivalent network to limit fault currents to the permissible values ​​for the equipment and busbars. Relay protection coordination and operating modes are encoded as mixed integer constraints using time-limited hierarchical, directional, and topological logic to ensure that any merging or switching falls within the permitted protection window and structural mode. Atomic action consistency constraints limit the occurrence of only one type of switching or setting change at a time step, and state transition equations are used to advance the topology and power flow from the current step to the next.

[0090] To avoid a buildup of solutions near the infeasible boundary, the process also inherits the control barrier constraints from the previous step. As long as candidate edges added to the exploration tree are retained, their corresponding linearized safety margins are incorporated into the optimization as simultaneous inequalities. This way, while the objective function aims to reduce tail risk, the solver no longer "trades costs for violations" but instead seeks optimization within the propagation invariant set.

[0091] After the solution results in a self-healing operation sequence, the system calculates the most unfavorable voltage and current envelopes for each step and scenario, and verifies the short-circuit current level and relay protection coordination item by item, generating a feasible region certification document. To facilitate rapid review by the release layer, the certification document provides three curves or intervals for each step: the voltage envelope range, the upper bound of the current envelope, and the estimated short-circuit current level. It also provides a consistency check for the step with the protection time limit and directionality.

[0092] To assess the vulnerability of the sequence to the next perturbation, the counterfactual energy margin is calculated , For the The counterfactual energy margin of the step, is the motion disturbance, is the upper bound of the action amplitude, For the The dual vector of the step constraint, is a constraint function. The smaller the counterfactual energy margin, the greater the sensitivity of the next step to limit violations. Based on this, the release layer implements stricter tightening of the voltage and current operating thresholds of the corresponding step and prioritizes the configuration of backup sequences.

[0093] The theoretical advantages of this approach lie in three key aspects. First, it explicitly incorporates uncertainty into the objective, directly constraining tail power supply risk rather than simply optimizing the mean. Second, it simultaneously satisfies steady-state electrical constraints, short-circuit verification, and protection coordination within a single solution framework, avoiding the iterative cycle of "finding a path only to be rejected." Third, the solution product includes demonstrable envelope and dual information, providing a traceable basis for formal verification before release, runtime monitoring, and fallback strategies.

[0094] Example 10. A feeder line in the urban ring network obtains a higher control access strength after evidence fusion, and the linear mapping obtains a higher confidence level of the conditional value at risk and a larger barrier advancement coefficient. The search phase outputs three candidate sequences: one is to reconstruct on-site after disconnection upstream of the target section, the second is to adjust the reactive power setting of the distributed power source first and then connect and combine, and the third is to connect and combine first and then disconnect. The three candidates are hot-started one by one to enter the flow optimization of the conditional value at risk target. The optimizer solves each candidate simultaneously in multiple scenarios, and after satisfying the linearized 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 domain certification document: the voltage envelope interval, current maximum value and short-circuit current level are given for each step, and a conclusion on consistency with the protection direction and time limit is attached. By calculating the counterfactual energy margin for the same sequence step by step, it was found that the margin for the interconnection and merging step was the smallest. Based on this, the release layer additionally tightened the voltage and current limits for this step and marked the "in-place reconstruction first" backup sequence as the preferred fallback path for this step. This example demonstrates that, given high evidence strength, the conditional value-at-risk target fully mitigates the risk of power failure in adverse scenarios. The coordination of control barriers and protection as hard constraints allows the sequence to directly enter pre-release verification. The counterfactual energy margin provides a clear safety margin indicator for key actions.

[0095] Based on the counterfactual energy margin and the control access strength value, the voltage upper limit, voltage lower limit and current upper limit are dynamically adjusted, and the full sequence consistency is checked based on the signal timing logic and satisfiability module theory to generate an execution package.

[0096] After the self-healing operation sequence is formed, this method dynamically shapes the operational threshold based on counterfactual energy margins and control access strength values. The entire sequence is then verified for consistency using signal timing logic and satisfiability modulo theory, ultimately generating an executable package that can be directly distributed. The goal is to prove "plan feasibility" as "execution safety" before release and to explicitly quantify the safety margins of key actions.

[0097] The operation threshold shaping adopts a linear tightening model to make the strength of evidence and fragility be reflected simultaneously at the threshold , , , and For the Step voltage upper limit and voltage lower limit, For the Step current upper limit, and are the upper and lower limits of the baseline voltage, is the upper limit of the baseline current, For the Step counterfactual energy margin, To control the admission strength value, is the shaping coefficient. After threshold shaping, the three sequences are smoothed to avoid threshold jumps caused by adjacent time steps.

[0098] Signal timing logic is used to perform time-domain verification of continuous quantity constraints. Core specifications include voltage range maintenance, target recovery achievement, and merging prohibition constraints: : , : , : , For the Step execution start time, is the observation window for this step, For the recovery time limit, is the target recovery ratio, is the voltage range after shaping. Calculate the robustness for each specification and take the minimum value of the entire sequence as the passing criterion.

[0099] Satisfiability modulo theory is used to verify the consistency of discrete and logical constraints throughout the entire sequence. Relay protection direction and time limit, upper bounds on short-circuit current levels, topological connectivity, and action mutual exclusion and order are encoded as satisfiability constraints. The entire self-healing operation sequence is solved at once, returning a "satisfiable" or "unsatisfiable" result. When unsatisfiability occurs, the conflicting step is located and an alternate sequence is triggered until the problem is resolved or reverted to reconstruction.

[0100] The execution package is generated in a unified format, including a self-healing action sequence, a step-by-step plan for upper and lower voltage and current operating thresholds, a report on the robustness of the sequential logic, a summary of the satisfiability proof, and alternative sequences and fallback paths for critical steps. All files are versioned and timestamped for easy audit and traceability.

[0101] Example 11. During the optimization phase, the urban ring network obtained a self-healing operation sequence of "disconnection - local reconstruction - interconnection and merging." Counterfactual energy margins indicated that the minimum value of the interconnection and merging step was lower than that of the other steps. Threshold shaping accordingly lowered the upper voltage limit, raised the lower voltage limit, and lowered the upper current limit for this step. Signal timing logic verification confirmed that the voltages of all steps remained within the shaping range within their respective observation windows, and target recovery was achieved within the set time limit. Satisfiability modulus theory verification also passed, with no short-circuit current level or protection time limit conflicts identified. Based on this, the system generated an execution package, marked the interconnection and merging step as a key monitoring step, and configured a backup sequence of "local reconstruction first, then delayed merging." The release process then began. The operational layer progressively issued the execution package and performed online comparisons of voltage and current within each step's observation window. If any deviations were detected, a fallback sequence was used. 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 release.

[0102] Preferably, the signal timing logic specifications include the node voltage falling within the voltage upper limit and voltage lower limit interval after shaping, achieving the target load recovery rate within the preset time window, and prohibiting parallel operation without relay protection coordination; the satisfiability module theory encodes the relay protection logic, short-circuit current level and topological connectivity for full sequence consistency verification; the execution package includes the self-healing operation sequence, dynamic threshold plan, signal timing logic verification report and the summary of the satisfiability module theory consistency proof.

[0103] After generating the self-healing operation sequence, the present invention constructs a two-layer verification framework before release: signal timing logic is used to perform time domain verification on continuous quantities, and satisfiability module theory is used to perform full sequence consistency verification on discrete and logical constraints. The operating threshold is dynamically shaped according to the counterfactual energy margin and the control access strength value, and finally a sendable execution package is formed.

[0104] The core specifications of signal timing logic are “voltage range maintenance”, “target recovery achievement” and “parallel operation without relay protection coordination”. The robustness of voltage range maintenance is defined as , Indicates the minimum robustness of voltage interval maintenance; Indicates the first step; Indicates the observation window of this step; represents the time function of the node voltage amplitude; 、 Represents the voltage lower limit and voltage upper limit of this step after shaping. The robustness of target recovery is defined as , Indicates the robustness of target recovery; Indicates the recovery time limit; Indicates the proportion of restored load to target load; Represents the target recovery ratio. The prohibition of parallel operation without relay protection coordination is expressed in the form of "never happening", and its robustness is the minimum safety distance of the parallel prohibition predicate. The temporal logic of the full sequence takes the minimum value of the three items through the judgment , Indicates the overall robustness of sequential logic; Indicates the robustness of the parallel prohibition specification. , then the continuous quantity time domain specifications are met as a whole.

[0105] Satisfiability modular theory uses first-order logic and integer constraints to express relay protection logic, short-circuit current level and topological connectivity, forming a full sequence consistency formula , "" represents the conjunction of satisfiability modulo-theoretic constraints; "Directional consistency" indicates that the relay protection direction criterion is consistent with the power flow direction; "Time limit coordination" indicates that the lower-level protection operates earlier than the upper-level protection and meets the coordination margin; "Short-circuit upper limit" indicates that the fault current does not exceed the upper limit; "Topological connectivity" indicates that the load group and the power node are connected; "Action mutual exclusion" indicates that only one atomic action is allowed in the same step. If the solution returns "satisfiable", it is considered logically and structurally consistent. If it returns "unsatisfiable", the conflicting step is located and replaced with an alternative sequence.

[0106] Threshold shaping uses the counterfactual energy margin and control access strength as independent variables, linearly tightening the upper, lower, and upper voltage limits at each step. This creates a linkage relationship where "stronger evidence, greater vulnerability, and stricter thresholds" is applied. To prevent threshold jumps, first-order smoothing is applied to the three threshold sequences on the time axis. The shaped thresholds are directly validated in sequential logic, ensuring greater safety redundancy for critical actions within the observation window.

[0107] The execution package is issued and audited to the operation layer and contains four parts. First, the self-healing operation sequence, which lists the atomic actions, target devices and expected timing in chronological order. Second, the dynamic threshold plan, which gives the operating thresholds of the voltage upper limit, voltage lower limit and current upper limit for each step, and also includes the source of the shaping coefficient and the key step identification. Third, the signal timing logic verification report, which gives 、 、 and The numerical curve of and the step where the minimum value is located. Fourth, the summary of the consistency proof of satisfiability modulo theory is given. The satisfiable conclusion, conflicting clauses (if any), and the replacement sequence number. The execution packet carries a version number and timestamp to support backtracking and recalibration.

[0108] Example 12. The self-healing sequence for a feeder in a city ring network is "disconnection - local reconfiguration - interconnection and merging." Counterfactual energy margins indicate that the minimum value of the interconnection and merging step is lower than that of the other steps. Dynamic threshold planning accordingly adjusts the upper voltage limit, lower voltage limit, and upper current limit for this step. The robustness of the sequential logic is calculated under the shaping threshold. The minimum robustness of the voltage interval occurs at the interconnection and merging step, and its value remains positive. The target recovery is achieved within the set time limit, resulting in a positive robustness. Parallel operation without relay protection coordination is prohibited and not triggered within the entire sequence. Satisfiability modulus theory solves the entire sequence for "consistent direction, time limit coordination, short-circuit upper limit, topological connectivity, and mutually exclusive actions," concluding that it is satisfiable. Based on this, the system generates an execution package, marks the interconnection and merging step as a key monitoring step, and configures a backup sequence of "local reconfiguration first, then delayed merging." The operation layer issues the execution package step by step, performing online verification of voltage and current within the observation window. If a deviation trend is detected, a fallback is performed according to the preset backup sequence. This embodiment shows that the double-layer verification of temporal logic and satisfiability modulo theory can improve the release success rate without increasing the number of action steps, and form a preemptive protection for key actions with dynamic thresholds.

[0109] The above are merely embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should be included within the scope of the claims of the present application.

Claims

1. A fault prediction self-healing power distribution method, characterized in that: The following steps are involved: Apply controlled disturbances and use synchronized phasor measurements to obtain voltage and current responses. Calculate the equivalent admittance and physical residual based on the injection-response relationship, generate spectral-topological co-embedding coordinates and innovative consistency indicators, and complete the topology verification to obtain the verified topological state. Divide suspicious clusters on the spectral-topological co-embedding coordinates, integrate spatial evidence, temporal evidence and physical evidence, and combine them with hazard rate assessment to obtain the control access intensity value; The confidence level of the conditional VAR and the barrier propulsion coefficient are set according to the control access strength value. The candidate atomic actions are screened with the help of feasible domain prior and action shielding. The search is constrained by the control barrier function in the joint state space determined by the verified topological state. The power flow is optimized with the conditional VAR as the target, and the self-healing operation sequence is obtained and the counterfactual energy margin is calculated. Based on the counterfactual energy margin and the control access strength value, the voltage upper limit, voltage lower limit and current upper limit are dynamically adjusted, and the full sequence consistency is checked based on the signal timing logic and satisfiability module theory to generate an execution package.

2. The method according to claim 1, characterized in that A controlled disturbance is applied at the power supply side or tie-breaker position, and synchronized phasor measurements are used to obtain voltage and current responses aligned with the disturbance. The equivalent admittance and physical residual calculated based on the injection-response relationship are used to construct a weighted graph of measurement points, and the graph is embedded in the Laplace spectrum to generate a spectral-topological co-embedding coordinate. The innovation consistency index is obtained by calculating the graph domain coherence of the innovation quantity of the linear prediction model of zero-sequence voltage or phase current; the topology verification generates the verified topology state based on the power direction and phase consistency.

3. The method according to claim 1, characterized in that 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.

4. The method according to claim 1, wherein The Demster-Schafer evidence fusion method is used to synthesize spatial evidence, temporal evidence and physical evidence. The hazard rate assessment uses a semi-parametric hazard rate model to calculate the arrival probability and use it as a priori weight to weight the synthesis result. The control access strength value is determined by the weighted and corrected evidence belief measure.

5. The method according to claim 1, wherein A monotonic correspondence is established between the setting of the confidence level of the conditional value at risk and the barrier advancement coefficient and the control access intensity value. As the control access intensity value increases, the confidence level of the conditional value at risk and the barrier advancement coefficient are increased accordingly.

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

7. The method according to claim 1, characterized in that Action shielding includes the following rules: it is prohibited to form a closed-loop connection without the support of relay protection, the grid-connected phase angle difference is limited to not exceed the upper limit of the grid-connected phase angle difference, the short-circuit current level is limited to not exceed the upper limit of the short-circuit current level, and it is prohibited to cross the upper-level protection time limit window.

8. The method according to claim 1, characterized in that A random exploration tree algorithm is used to search in the joint state space determined by the verified topological state, and candidate sequences are generated under the constraint of a control barrier function. The sampling bias is set according to the spectral-topological co-embedding coordinates and the path cost is shaped according to the innovation consistency index.

9. The method according to claim 1, characterized in that The power flow optimization with the conditional value at risk as the target is established based on a linearized AC power flow model. The constraints include the voltage upper limit, voltage lower limit, current upper limit, short-circuit current level, relay protection coordination and operation mode. The output self-healing operation sequence is optimized and a feasible domain certification document containing the voltage and current envelopes, short-circuit current level and relay protection coordination verification results is generated. At the same time, the counterfactual energy margin is calculated based on the optimization dual sensitivity.

10. The method according to claim 1, characterized in that Signal timing logic specifications include ensuring that node voltages fall within the upper and lower voltage limits after shaping, achieving the target load recovery rate within a preset time window, and prohibiting parallel operation without relay protection coordination; the satisfiability modulus theory encodes relay protection logic, short-circuit current levels, and topological connectivity for full-sequence consistency verification; the execution package includes a self-healing operation sequence, a dynamic threshold plan, a signal timing logic verification report, and a summary of the satisfiability modulus theory consistency proof.

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