Fault location method for distribution network based on exterior differential tensor and adaptive curvature optimization

Abstract

The application discloses a power distribution network fault positioning method based on an external differential tensor and adaptive curvature optimization, and comprises the following steps: calculating the energy integral centroid time of a transient traveling wave signal in a specified frequency band, generating a real external differential measurement tensor by performing an external differential operation; calculating the generalized topological divergence of the real external differential measurement tensor and a virtual measurement tensor in a probability space to obtain a non-convex objective function; establishing an isotropic decay spatial prior anchor field in the power grid topology space; taking the minimization of time information difference degree as the only target, reconstructing the continuous confidence surface of the physical cost in the reproducing kernel Hilbert space, constructing an evaluation strategy functional with a double manifold modulation mechanism, cyclically solving the evaluation strategy functional until a set convergence tolerance is reached, and extracting the topological coordinates corresponding to the global absolute minimum of the time information difference degree. The application can solve the problem of local optimization and realize low-cost and high-robust fault positioning.

Description

Technical Field

[0001] This invention relates to the field of power system fault diagnosis technology, and specifically to a method for fault location in distribution networks based on external differential tensors and adaptive curvature optimization. Background Technology

[0002] With the continuous integration of renewable energy into the grid, voltage source converter (VSC) technology, with its decoupled power control and immunity to commutation failure, has become the preferred solution for modern DC grids. However, the extremely low tolerance of power electronic devices to rapid fault currents and the lack of reliable fault location technology have become key bottlenecks restricting its development. Furthermore, the complex multi-branch topology of VSC-DC grids makes traditional transmission line fault location methods ineffective. When a permanent fault occurs in the system, accurate location is of great significance for reducing downtime, lowering maintenance costs, and accelerating grid recovery.

[0003] Existing traveling wave (TW) positioning methods rely on wavefront detection and expensive GPS synchronization, and the propagation speed in the transmission medium is difficult to estimate accurately. To overcome the shortcomings of traditional physical analysis, many studies have transformed fault location into an algorithm optimization problem. However, traditional intelligent optimization algorithms, such as particle swarm optimization (PSO) and genetic algorithm (GA), are prone to getting trapped in local optima in complex multimodal environments, affecting the convergence stability of the positioning results. Summary of the Invention

[0004] The purpose of this invention is to provide a fault location method for distribution networks based on external differential tensors and adaptive curvature optimization, so as to solve the problem that existing technologies are prone to getting trapped in local optima when facing complex multimodal environments, and to achieve low-cost and highly robust fault location.

[0005] A method for fault location in distribution networks based on external differential tensors and adaptive curvature optimization includes:

[0006] Step S1: Obtain the transient traveling wave signals collected by each measurement terminal when the fault occurs through the central computing server, map the transient traveling wave signals to a two-dimensional time-frequency space, calculate the energy integral centroid time of each transient traveling wave signal in the specified frequency band, convert the energy integral centroid time into the zero-order differential form on the topological manifold, and generate a true external differential measure tensor that eliminates translational common-mode interference by performing external differential operations.

[0007] Step S2: Set continuous virtual coordinates on the power grid topology manifold, combine nonlinear frequency-varying electromagnetic distribution parameters, deduce the theoretical centroid time of the virtual coordinates propagating to each measurement terminal, and apply external differential mapping to construct a virtual measure tensor. Then, adopt a regularized transmission cost mechanism to calculate the generalized topological divergence between the real external differential measure tensor and the virtual measure tensor in the probability space. Define the generalized topological divergence as the time information difference degree, and use it as the non-convex objective function for continuous domain optimization.

[0008] Step S3: The non-redundant components of the real external differential measure tensor are used as discrete observation state vectors and input into a multidimensional orthogonal subspace constructed based on historical mapping data for dimensionality reduction projection. Then, the posterior distribution expectation and cognitive divergence of the topological coordinates are analyzed through a random subspace probability aggregation mechanism. Based on this, an isotropic decaying spatial prior anchor field is established in the power grid topology space.

[0009] Step S4: With minimizing the temporal information difference as the sole objective, a continuous confidence surface of the physical cost is reconstructed in the regenerating kernel Hilbert space, thereby constructing an evaluation strategy functional with a dual manifold modulation mechanism. The first layer of the dual manifold modulation mechanism uses the spatial prior anchor field to apply probabilistic constraints to the search space. The second layer introduces an adaptive curvature damping factor based on the local curvature gradient of the objective function's evolution trajectory to dynamically limit the manifold transition step size. The evaluation strategy functional is solved iteratively until the set convergence tolerance is reached. The topological coordinates corresponding to the global absolute minimum of the temporal information difference are extracted as the fault location result.

[0010] The distribution network fault location method based on external differential tensor and adaptive curvature optimization provided by the present invention has the following beneficial effects:

[0011] (1) This invention analyzes the posterior distribution expectation and cognitive divergence of topological coordinates through a random subspace probability aggregation mechanism. Based on this, an isotropic decaying spatial prior anchor field is established in the power grid topology space, which can cut off a large number of invalid blind search spaces. In addition, this invention introduces a regularized transmission cost mechanism to calculate the generalized topological divergence of the real external differential measure tensor and the virtual measure tensor in the probability space, thereby obtaining the non-convex objective function for continuous domain optimization. This mechanism can use the entropy regularization effect to force the non-convex search space full of rugged extrema to become stable, fundamentally solving the optimization dead end caused by the branching point of the tree network. With the adaptive curvature damping factor to dynamically limit the manifold transition step size, the optimization sequence can accurately reach the global optimum with an extremely smooth geodesic trajectory. The number of calculation iterations is effectively reduced compared with the traditional heuristic algorithm, and the absolute convergence stability of the positioning result under unknown and complex working conditions is guaranteed from the underlying algorithm logic level.

[0012] (2) This invention utilizes the energy integral centroid time instead of the traditional microscopic instantaneous wavefront detection. Even under extreme conditions such as low sampling rate or high transition resistance, this invention can still accurately locate the implicit physical extrema between discrete grids by relying on the super-resolution continuous reconstruction capability of the evaluation strategy functional constructed by the regenerative kernel Hilbert space (RKHS). When facing changes in the power grid structure, this invention does not require retraining; it only needs to update the graph theory adjacency matrix to adapt. This highly robust technical approach not only effectively reduces positioning errors but also avoids the stringent dependence on high-specification hardware, thus reducing costs. Attached Figure Description

[0013] Figure 1 A flowchart illustrating the fault location method for distribution networks based on external differential tensor and adaptive curvature optimization provided by this invention.

[0014] Figure 2 This is an example simulation model topology diagram. Detailed Implementation

[0015] To facilitate understanding of the present invention, a more complete description will be given below with reference to various embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0016] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0017] Please see Figure 1 The present invention provides a method for fault location in a distribution network based on external differential tensor and adaptive curvature optimization, comprising steps S1 to S4:

[0018] Step S1: Obtain the transient traveling wave signals collected by each measurement terminal when the fault occurs through the central computing server, map the transient traveling wave signals to a two-dimensional time-frequency space, calculate the energy integral centroid time of each transient traveling wave signal in the specified frequency band, convert the energy integral centroid time into the zero-order differential form on the topological manifold, and generate a true external differential measure tensor that eliminates translational common-mode interference by performing external differential operations.

[0019] The method of this invention relies on a hardware architecture consisting of distributed measurement terminals (such as edge computing gateways or micro PMUs) and a central computing server. When a fault occurs, each measurement terminal records transient voltage / current traveling wave data at a specific sampling rate and transmits the data slices back to the central computing server via industrial Ethernet, 5G, or a dedicated fiber optic network. After receiving the data, the CPU / GPU heterogeneous computing module inside the server executes the core computational logic of this invention.

[0020] For transient attenuation and dispersion problems caused by high impedance faults or long-distance transmission in practical engineering, this step expands the one-dimensional time-domain signal to a two-dimensional time-frequency space, extracts integral features with global noise resistance and smoothing characteristics, and removes the unknown initial fault time at the algebraic topology level.

[0021] To expand this one-dimensional time-domain signal into a two-dimensional time-frequency space, a scaling factor is introduced to adjust the bandwidth resolution. Translation factor used for positioning the time axis And select an appropriate time-frequency domain orthogonal basis.

[0022] Specifically, the present invention is set Each measurement terminal acquires the transient traveling wave signal collected by each measurement terminal at the time of the fault through the central computing server. During the process of mapping the transient traveling wave signal to a two-dimensional time-frequency space, the following equation is satisfied:

[0023]

[0024] in, For the first Transient traveling wave signals collected by a measurement terminal for The corresponding time-frequency coefficients, It is the complex conjugate of the mother wavelet function. For time, This represents the scaling factor used to adjust the bandwidth resolution. This represents the translation factor used to position the time axis. express The differential.

[0025] Then, the energy integral centroid time of each transient traveling wave signal within a specified frequency band is calculated using the following formula:

[0026]

[0027] in, for In the characteristic frequency band set and integration time window Energy integral at the center of mass time within the space, express The differential, express The differential.

[0028] At the underlying level of engineering calculations, The energy integral centroid time of each measurement terminal is stored as a one-dimensional array. , , These are the energy integration centroid time of the transient traveling wave signal acquired by the first measurement terminal, and the second... The energy integral centroid time of the transient traveling wave signal acquired by a measurement terminal, and this one-dimensional array That is, the zeroth-order differential form on the manifold.

[0029] Then, the exterior differential operator is applied, which at the computer level manifests as a matrix traversal operation of subtracting array elements pairwise, generating a second-order inversely symmetric true exterior differential measure tensor. .

[0030] Then extract the true exterior differential measure tensor Non-redundant components This process rigorously isolates the translational common modulus, and the output difference tensor serves as the objective input for subsequent optimization.

[0031] Specifically, The expression is:

[0032]

[0033] in, For the first The transient traveling wave signal collected by each measurement terminal is located in the characteristic frequency band set. and integration time window The energy integral of the center of mass within the time, and .

[0034] Step S2: Set continuous virtual coordinates on the power grid topology manifold, combine nonlinear frequency-varying electromagnetic distribution parameters, deduce the theoretical centroid time of the virtual coordinates propagating to each measurement terminal, and apply external differential mapping to construct a virtual measure tensor. Then, adopt a regularized transmission cost mechanism to calculate the generalized topological divergence between the real external differential measure tensor and the virtual measure tensor in the probability space. Define the generalized topological divergence as the time information difference degree, and use it as the non-convex objective function for continuous domain optimization.

[0035] Traditional absolute value norm comparisons inevitably produce a large number of non-differentiable stagnation points (local minima) at topological bifurcation points in tree-like power grids with multiple branches. This step introduces the regularized transmission cost theory from measure theory to smooth the rugged physical distance space through measurement.

[0036] Suppose any continuous coordinates in the distribution network topology For a virtual state point, calculate its path along the topological graph to the _th ... The shortest physical distance of each measurement terminal Combining nonlinear frequency-varying distributed inductance and capacitor Analytical phase velocity And thus, the virtual state point is derived. Spread to the Theoretical centroid time of each measurement terminal .

[0037] Apply the exterior differential mapping operation to generate a virtual measure tensor. Virtual Measure Tensor The amount The expression is:

[0038]

[0039] in, propagation of virtual coordinates to the first The theoretical centroid time of a measurement terminal, propagation of virtual coordinates to the first The theoretical centroid time of a measurement terminal, These are virtual state points.

[0040] To overcome the multimodal trap, a regularized transmission cost mechanism is introduced, defining the temporal information difference degree. As the optimization objective in the continuous domain, its expression is:

[0041]

[0042]

[0043]

[0044] in, This indicates taking the minimum value. For logarithmic regularization, Where is the intensity constant. For point-to-point cost tensor elements, Denotes the joint probability measure space that satisfies the given marginal distribution constraints. and These represent the marginal distribution vectors before and after mapping, respectively. Indicates belonging to The joint transport mapping matrix, for The Middle line, number The mapping probability elements of the column, is the scale variance parameter of the Gaussian penalized kernel function, used to adjust the sensitivity to nonlinear penalty for measure differences.

[0045] In practice, The solution is obtained quickly using the Sinkhorn-Knopp matrix scaling alternating iterative algorithm, ensuring... It has strict continuous differentiability across the entire domain, thus resolving the dead-end optimization problem of tree topology.

[0046] Step S3: The non-redundant components of the real external differential measure tensor are used as discrete observation state vectors and input into a multidimensional orthogonal subspace constructed based on historical mapping data for dimensionality reduction projection. Then, the posterior distribution expectation and cognitive divergence of the topological coordinates are analyzed through a random subspace probability aggregation mechanism. Based on this, an isotropic decaying spatial prior anchor field is established in the power grid topology space.

[0047] This step establishes a distribution field based purely on the statistical regularity of the observed state, thereby significantly compressing the invalid search space of the objective function in step S4.

[0048] Specifically, pre-loaded into memory An independent orthogonal projection operator based on historical simulation. Targeting the discrete observation state vector extracted in real time. (by tensor) (The independent components are flattened to form the candidate coordinates), and each operator outputs candidate coordinates in its subspace.

[0049] Then, based on the principle of probabilistic aggregation of random subspaces, global statistics are performed on the local features of the operator cluster to parse the posterior distribution expectation of the coordinate vector. Cognitive divergence with respect to divergent features This leads to the construction of a continuous spatial prior anchor field. .

[0050] Spatial a priori anchor field The expression is:

[0051]

[0052]

[0053]

[0054] in, For constrained gain scalar, For the posterior distribution expectation, For cognitive divergence, This represents the manifold geodesic distance between two points. This represents the total number of independent orthogonal projection operators in the historical mapping data. For the first An independent orthogonal projection operator.

[0055] When encountering rare distortion faults that cause operator projection discretization With a sudden increase, the anchor field automatically performs broad-based fault-tolerant decay to ensure that the physical search domain boundary is not forcibly truncated.

[0056] Step S4: With minimizing the temporal information difference as the sole objective, a continuous confidence surface of the physical cost is reconstructed in the regenerating kernel Hilbert space, thereby constructing an evaluation strategy functional with a dual manifold modulation mechanism. The first layer of the dual manifold modulation mechanism uses the spatial prior anchor field to apply probabilistic constraints to the search space. The second layer introduces an adaptive curvature damping factor based on the local curvature gradient of the objective function's evolution trajectory to dynamically limit the manifold transition step size. The evaluation strategy functional is solved iteratively until the set convergence tolerance is reached. The topological coordinates corresponding to the global absolute minimum of the temporal information difference are extracted as the fault location result.

[0057] In this step, convergence is achieved by fusing the boundary constraints provided in step S3 and the smoothness measure provided in step S2 with low computational overhead.

[0058] Specifically, will Mapping to the reproducing kernel Hilbert space (RKHS), the code implementation utilizes the kernel matrix inversion operation of Gaussian process regression (GPR) to calculate the predicted mean based on the known set of sampling points. Approximation variance .

[0059] This invention constructs an evaluation strategy functional. This drives subsequent sampling decisions. The core logic of this functional lies in quantizing the probability space through an integral operator. Contribution to positioning accuracy.

[0060] Specifically, the evaluation strategy functional The expression is:

[0061]

[0062] in, It is the minimum global underfimum divergence, which is the error benchmark of the best fault candidate position found up to the current iteration; For the integration variable, it maps The potential value that can be obtained; for The differential; This represents the local probability density equation based on the normal distribution, characterizing the probability of obtaining the target location while considering model uncertainty (variance). The probability distribution; To predict the mean, To approximate the variance.

[0063] The integral term is based on the improvement amount. In the positive improvement range By performing infinitesimal accumulation, the expected improvement of the current optimal solution is calculated. Finally, through the preconditions... Spatial modulation, This achieves a nonlinear coupling between physical priors and statistical improvements: on the one hand, it utilizes... This mechanism ensures that the optimization trajectory does not deviate from the high-probability physical region; on the other hand, it assigns greater weight to regions with high potential or high uncertainty through the integral term. This avoids the blind search defects of traditional algorithms, ensuring that the system can accurately locate the fault coordinates corresponding to the global absolute minimum with very few iterations.

[0064] To prevent the optimization sequence from crossing the real fault point in an environment with extremely low signal-to-noise ratio, this invention introduces an adaptive curvature damping control factor. Through a dynamic step size adjustment mechanism, its real-time strength is controlled by the local geometric features of the evolution trajectory.

[0065] Specifically, the expression for the adaptive curvature damping factor is:

[0066]

[0067] in, For the first Curvature damping factor at the next iteration is the damping response constant, used to define the system's feedback gain to changes in manifold curvature, which determines the sensitivity of the damping coefficient to changes in gradient. The ground state damping coefficient has the physical meaning of providing a basic search resistance, ensuring that the algorithm can still maintain a stable infinitesimal optimization step size in regions where gradients vanish or are flat, thereby effectively filtering out non-physical transitions caused by numerical noise. Indicates as of the date In each iteration, the historical optimal generation value reached by the evolutionary trajectory can be accurately captured by monitoring the evolution slope of the optimal value in real time, thus accurately capturing curvature mutations near the target point.

[0068] In the early stages of evolution ( The damping is relatively low, and the algorithm can take large steps to cross local stagnation points; as the virtual point approaches the real fault point ( abrupt changes in gradient curvature lead to It exhibits an exponential response, instantaneously applying extremely high transition resistance, forcing the iterative operator into a millimeter-scale pure local Taylor optimization mode.

[0069] Solve by loop The manifold extrema are used to determine the next sampling coordinates until the set convergence tolerance is reached. Extraction makes... The topological coordinates that reach the global strict minimum value are used to achieve high-precision physical positioning.

[0070] To rigorously verify the effectiveness of this invention, extreme pathological tests were conducted in a complex multi-branch four-terminal DC distribution network (VSC-DC) built based on PSCAD. The simulation model topology is shown below. Figure 2 As shown, Figure 2 In the diagram, A, B, C, and D are measurement terminals deployed at key nodes of the power distribution network; , , , These represent the transmission line segments of the corresponding branches. Under harsh operating conditions, with a transition resistance >2000Ω and the monitoring terminal hardware sampling rate degraded to an extremely demanding 50kHz, the positioning results using the method provided by this invention are shown in Table 1.

[0071] Table 1

[0072]

[0073] As can be seen from Table 1, the method provided by this invention can accurately identify faulty line sections at different locations in an active power distribution network, achieve precise distance measurement of the fault point, and provide the corresponding wave velocity estimation range. The positioning error is controlled within 150 meters, indicating that the method has high positioning accuracy and small distance measurement deviation.

[0074] The present invention was compared and analyzed with traditional particle swarm optimization (PSO) and genetic algorithm (GA) under the same working conditions. The comparison results are shown in Table 2.

[0075] Table 2

[0076]

[0077] As can be seen from Table 2, traditional particle swarm optimization (PSO) and genetic algorithm (GA) are trapped in local optima due to non-convex topology, and the positioning error is higher than 700m. However, the present invention can escape the multimodal trap, control the positioning error within 150m, and the normalized positioning deviation is smaller. Moreover, the number of computation iterations of the present invention is significantly reduced compared with traditional heuristic methods, demonstrating extremely high engineering practical value and computational cost economy.

[0078] In summary, the above-mentioned method for fault location in distribution networks based on external differential tensors and adaptive curvature optimization has the following beneficial effects:

[0079] (1) This invention analyzes the posterior distribution expectation and cognitive divergence of topological coordinates through a random subspace probability aggregation mechanism. Based on this, an isotropic decaying spatial prior anchor field is established in the power grid topology space, which can cut off a large number of invalid blind search spaces. In addition, this invention introduces a regularized transmission cost mechanism to calculate the generalized topological divergence of the real external differential measure tensor and the virtual measure tensor in the probability space, thereby obtaining the non-convex objective function for continuous domain optimization. This mechanism can use the entropy regularization effect to force the non-convex search space full of rugged extrema to become stable, fundamentally solving the optimization dead end caused by the branching point of the tree network. With the adaptive curvature damping factor to dynamically limit the manifold transition step size, the optimization sequence can accurately reach the global optimum with an extremely smooth geodesic trajectory. The number of calculation iterations is effectively reduced compared with the traditional heuristic algorithm, and the absolute convergence stability of the positioning result under unknown and complex working conditions is guaranteed from the underlying algorithm logic level.

[0080] (2) This invention utilizes the energy integral centroid time instead of the traditional microscopic instantaneous wavefront detection. Even under extreme conditions such as low sampling rate or high transition resistance, this invention can still accurately locate the implicit physical extrema between discrete grids by relying on the super-resolution continuous reconstruction capability of the evaluation strategy functional constructed by the regenerative kernel Hilbert space (RKHS). When facing changes in the power grid structure, this invention does not require retraining; it only needs to update the graph theory adjacency matrix to adapt. This highly robust technical approach not only effectively reduces positioning errors but also avoids the stringent dependence on high-specification hardware, thus reducing costs.

Claims

1. A power distribution network fault location method based on external differential tensor and adaptive curvature optimization, characterized in that, include: Step S1: Obtain the transient traveling wave signals collected by each measurement terminal when the fault occurs through the central computing server, map the transient traveling wave signals to a two-dimensional time-frequency space, calculate the energy integral centroid time of each transient traveling wave signal in the specified frequency band, convert the energy integral centroid time into the zero-order differential form on the topological manifold, and generate a true external differential measure tensor that eliminates translational common-mode interference by performing external differential operations. Step S2: Set continuous virtual coordinates on the power grid topology manifold, combine nonlinear frequency-varying electromagnetic distribution parameters, deduce the theoretical centroid time of the virtual coordinates propagating to each measurement terminal, and apply external differential mapping to construct a virtual measure tensor. Then, adopt a regularized transmission cost mechanism to calculate the generalized topological divergence between the real external differential measure tensor and the virtual measure tensor in the probability space. Define the generalized topological divergence as the time information difference degree, and use it as the non-convex objective function for continuous domain optimization. Step S3: The non-redundant components of the real external differential measure tensor are used as discrete observation state vectors and input into a multidimensional orthogonal subspace constructed based on historical mapping data for dimensionality reduction projection. Then, the posterior distribution expectation and cognitive divergence of the topological coordinates are analyzed through a random subspace probability aggregation mechanism. Based on this, an isotropic decaying spatial prior anchor field is established in the power grid topology space. Step S4: With minimizing the temporal information difference as the sole objective, a continuous confidence surface of the physical cost is reconstructed in the regenerating kernel Hilbert space, thereby constructing an evaluation strategy functional with a dual manifold modulation mechanism. The first layer of the dual manifold modulation mechanism uses the spatial prior anchor field to apply probabilistic constraints to the search space. The second layer introduces an adaptive curvature damping factor based on the local curvature gradient of the objective function's evolution trajectory to dynamically limit the manifold transition step size. The evaluation strategy functional is solved iteratively until the set convergence tolerance is reached. The topological coordinates corresponding to the global absolute minimum of the temporal information difference are extracted as the fault location result. In step S2, the time information difference degree The expression is: in, This indicates taking the minimum value. For logarithmic regularization, Where is the intensity constant. For point-to-point cost tensor elements, Denotes the joint probability measure space that satisfies the given marginal distribution constraints. and These represent the marginal distribution vectors before and after mapping, respectively. Indicates belonging to The joint transport mapping matrix, for The Middle line, number The mapping probability elements of the column, Let be the scaling variance parameter of the Gaussian penalty kernel function. For the true exterior differential measure tensor Non-redundant components, For virtual measure tensor The amount; In step S3, the spatial prior anchor field The expression is: in, For constrained gain scalar, For the posterior distribution expectation, For cognitive divergence, This represents the manifold geodesic distance between two points. This represents the total number of independent orthogonal projection operators in the historical mapping data. For the first An independent orthogonal projection operator These are virtual state points; In step S4, the policy functional is evaluated. The expression is: in, To minimize the global lower bound divergence, For integration variables, for The differential, This represents the local probability density equation based on the normal distribution. To predict the mean, To approximate the variance.

2. The distribution network fault location method based on external differential tensor and adaptive curvature optimization according to claim 1, characterized in that, In step S1, the transient traveling wave signals collected by each measurement terminal at the time of the fault are obtained through the central computing server. During the process of mapping the transient traveling wave signals to the two-dimensional time-frequency space, the following equation is satisfied: in, For the first Transient traveling wave signals collected by a measurement terminal for The corresponding time-frequency coefficients, It is the complex conjugate of the mother wavelet function. For time, This represents the scaling factor used to adjust the bandwidth resolution. This represents the translation factor used to position the time axis. express The differential.

3. The distribution network fault location method based on external differential tensor and adaptive curvature optimization according to claim 2, characterized in that, In step S1, the energy integration centroid time of each transient traveling wave signal within a specified frequency band is calculated using the following formula: in, for In the characteristic frequency band set and integration time window Energy integral at the center of mass time within the space, express The differential, express The differential.

4. The distribution network fault location method based on external differential tensor and adaptive curvature optimization according to claim 3, characterized in that, In step S1, the true external differential measure tensor Non-redundant components Calculate using the following formula: in, For the first The transient traveling wave signal collected by each measurement terminal is located in the characteristic frequency band set. and integration time window The energy integral of the center of mass within the time, and .

5. The distribution network fault location method based on external differential tensor and adaptive curvature optimization according to claim 4, characterized in that, In step S2, the virtual measure tensor The amount The expression is: in, propagation of virtual coordinates to the first The theoretical centroid time of a measurement terminal, propagation of virtual coordinates to the first The theoretical centroid time of each measurement terminal.

6. The distribution network fault location method based on external differential tensor and adaptive curvature optimization according to claim 5, characterized in that, In step S4, the expression for the adaptive curvature damping factor is: in, For the first Curvature damping factor at the next iteration Let be the damping response constant. The ground-state damping coefficient, Indicates as of the date The next iteration represents the historical optimal generation value reached by the evolutionary trajectory.

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