Operation method and apparatus for digital twin system of power system, and device, medium and program product

Abstract

Disclosed in the embodiments of the present application are an operation method and apparatus for a digital twin system of a power system, and a device, a medium and a program product. The method comprises: on the basis of data collected in real time, determining Riemannian curvature approximations of a plurality of Riemannian manifolds in a high-dimensional feature space of a final convolutional layer of a data-driven model, so as to obtain an optimal Riemannian metric; using the optimal Riemannian metric to construct a geodesic tangent bundle based on the Riemannian manifolds; when the Riemannian manifolds are geodesically completed, determining that a digital twin system is a stable system; when the Riemannian manifolds are not geodesically completed, determining that the digital twin system is an unstable system; for the digital twin system which is a stable system, performing a deduction operation on the digital twin system; for the digital twin system which is an unstable system, performing a deduction operation on the digital twin system on the basis of a principle of least action, so as to obtain a deduction operation result; and converting the deduction operation result into a feature cluster of a low-dimensional feature space, thereby completing the operation of the digital twin system.

Description

Power system digital twin system operation method, device, equipment, medium and program product

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This disclosure is based on the Chinese patent application with application number 202311417646.5, application date October 30, 2023, and application name “New Power System Digital Twin System Operation Method, Device, Equipment and Medium”, and claims the priority of the Chinese patent application. The entire content of the Chinese patent application is hereby introduced into this disclosure as a reference. Technical Field

[0003] The present application relates to the field of power grid simulation operation, and specifically to a method, device, equipment, medium and program product for operating a digital twin system of a power system. Background Art

[0004] The new power system is a nonlinear dynamic system. With the integration of large-scale renewable energy and the re-electrification of the load side, a large number of power sources, loads, energy storage equipment, and other equipment with diverse characteristics are connected to the existing power system through power electronics interfaces, rapidly developing the power system toward a high proportion of renewable energy and power electronics. Compared with traditional power systems dominated by synchronous generators, the dynamic characteristics of the new power system have new and more complex dynamic characteristics. The goal of digital twins is to accurately predict and optimize complex dynamic characteristics by fitting various nonlinear relationships from data. Currently, existing digital twin operations use three-dimensional (3D) displays or mechanism formulas based on data acquisition, which cannot meet the operation and optimization requirements of data-driven models or hybrid models for multi-level systems.

[0005] Taking the simulation operation of traditional power grid equipment as an example, the modeling process mainly includes seven steps:

[0006] (1) Convert the power grid model into a mathematical model: Each part of the power grid model needs to be represented by a mathematical model. For example, the generator can be represented by rotor speed and potential angle, and the transmission line can be represented by parameters such as resistance, inductance and capacitance.

[0007] (2) Determine the simulation time step: The simulation system needs to divide the simulation time into several time steps, and perform a calculation within each time step. The length of the time step needs to be determined based on the calculation accuracy and efficiency required by the simulation system.

[0008] (3) Determine the initial conditions: The simulation system needs to determine the grid status at the beginning of the simulation, including parameters such as generator output power, voltage, current, and load.

[0009] (4) Calculating the dynamic response of the power grid: The simulation system calculates the dynamic response of the power grid at each time step based on the power grid model and initial conditions, including changes in parameters such as voltage, current, and power. During the calculation process, the simulation system needs to consider the mutual influence between various components in the power grid, as well as the impact of various disturbances and load changes on the power grid operation.

[0010] (5) Update the grid status: The simulation system updates the grid status based on the calculation results, including changes in parameters such as generator output power, voltage, current, and load.

[0011] (6) Check the simulation end conditions: The simulation system needs to check whether the simulation has reached the end conditions, for example, whether the simulation time has reached the preset time, whether the power grid is stable, etc.

[0012] (7) Output simulation results: The simulation system outputs simulation results, including the changing trends of the grid status and the changes in parameters such as voltage, current, and power of each component. The simulation results can be used to evaluate the stability, security, and reliability of the grid, as well as to make grid planning and operation decisions.

[0013] The main disadvantages of the above existing technologies are that they can only cover the data distribution of mechanism formulas, but cannot cover the actual sample distribution in reality, that is, they do not support the operation of digital twin systems represented by data-driven modeling and hybrid modeling.

[0014] Summary of the Invention

[0015] The purpose of this application is to provide a method, device, equipment, medium and program product for operating a digital twin system of a power system to overcome the defects of the existing technology. Through the method for operating a digital twin system of a power system provided in the embodiment of this application, the deduction and operation capability of the multi-scale digital twin system is realized.

[0016] To achieve the above objectives, this application adopts the following technical solutions:

[0017] In a first aspect, an embodiment of the present application provides a method for operating a digital twin system of a power system, the method comprising:

[0018] Based on real-time collected data, the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model is determined to obtain the optimal Riemannian metric;

[0019] Using the optimal Riemannian metric, we construct a geodesic tangent bundle based on the Riemannian manifold.

[0020] In the case that the Riemannian manifold is geodesically complete, determining that the digital twin system is a stable system;

[0021] In the case that the Riemannian manifold is geodesically incomplete, determining that the digital twin system is an unstable system;

[0022] For a digital twin system that is a stable system, performing deduction and operation on the digital twin system;

[0023] For a digital twin system that is an unstable system, the digital twin system is simulated and run based on the principle of least action to obtain a simulation result;

[0024] The deduction operation results are converted into feature clusters in a low-dimensional feature space to complete the operation of the digital twin system.

[0025] In some embodiments, determining the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on the real-time collected data to obtain the Riemannian metric includes:

[0026] Determine the Mahalanobis distance between two data points in the high-dimensional feature space of the last convolutional layer of the data-driven model;

[0027] The Mahalanobis distance is used to approximate the Riemann curvature, and the optimal Riemann metric is obtained by optimizing the objective function.

[0028] In some embodiments, the Mahalanobis distance is expressed as follows: d M (x k -x l )=(x k -x l ) T M(x k -x l )

[0029] Among them, x k and x l are two points in the high-dimensional feature space, M is a positive definite matrix, T represents the transpose, d M (x k -x l ) indicates that under the metric defined by the positive definite matrix M, the point x k and x l The Mahalanobis distance between

[0030] Perform Cholesky decomposition on the positive definite matrix M and obtain the following expression: M=W T W

[0031] Where W is a triangular matrix;

[0032] From this we get: d M (x k -x l )=((x k -x l ) T W T )W(xk -x l )=(W(x k -x l )) T (W(x k -x l ) =(Wx k -Wx l ) T (Wx k -Wx l ).

[0033] In some embodiments, the method of approximating the Riemann curvature using the Mahalanobis distance and obtaining the optimal Riemann metric by optimizing the objective function includes:

[0034] The Mahalanobis distance is used to express the approximation of Riemann curvature as follows:

[0035] Among them, x i 、x k and x j Represents a point in the high-dimensional feature space, d M (x i ,x k ),d M (x k ,x j ),d M (x i ,x j ) respectively indicate that under the current measurement, x i and x k 、x k and x j 、x i and x j The distance between them, |R ij | represents point x i 、x k and x j The absolute value of the Riemann curvature between ;

[0036] The objective function is expressed as:

[0037] Among them, M t represents the Riemannian metric matrix at the tth iteration, M t+1 represents the Riemannian metric matrix at the t+1th iteration, represents the change of the Riemann metric in two consecutive iterations, |R t | represents the absolute value of the Riemann curvature under the current metric, λ 1,t represents the regulating factor;

[0038] The specific process of optimizing the objective function is:

[0039] Sampling the feature tensor point set {x1, x2, ..., x n}, the feature tensor point set represents a set of data points in a high-dimensional feature space, each data point represents a feature tensor, and a neighborhood coefficient and a Euclidean metric E are preset; wherein n represents the number of feature tensors in the feature tensor point set;

[0040] Based on the neighborhood coefficient, find a set of minimum overlapping local neighborhoods as x n The nearest neighbor U i ;

[0041] Use the Euclidean metric E as the initial Riemann metric and set the initial value of the adjustment factor λ 1,1 ;

[0042] Use the following formula to update the adjustment factor λ 1,t Until convergence, the optimal Riemann metric is obtained;

[0043] Among them, η t is the learning rate; A ij =(x i -x j )(x i -x j ) -1 , represents the data point x i and x j The outer product of the distances between t represents the nearest neighbor U i The mean value of the interior Riemann curvature; tr represents the trace of the Riemann metric matrix.

[0044] In some embodiments, constructing a geodesic tangent bundle based on a Riemannian manifold using an optimal Riemannian metric specifically includes the following steps:

[0045] Selecting a first point and a second point on a Riemannian manifold, and using the first point as a starting point of a geodesic and the second point as an end point of the geodesic;

[0046] Based on the starting point and end point of the geodesic, the geodesic equation is defined using the local Riemannian metric on the Riemannian manifold to represent the geodesic;

[0047] The tangent bundle used to study geodesics is defined as follows:

[0048] Where C is a high-dimensional Riemann manifold, TC is the tangent bundle on the high-dimensional Riemann manifold C, and for each point x in the high-dimensional Riemann manifold C, T x C is the tangent space of C at point x;

[0049] Define an affine connection connecting tangent spaces at adjacent points on a Riemannian manifold The affine connection It uses the Levi-Civita connection, which has the following properties:

[0050] 1) For any feature tensor X, Y in a high-dimensional feature space, Where [X,Y] is the Lie bracket of the feature tensor; It is the derivative along the feature tensor X, acting on the feature tensor Y; It is the derivative along the feature tensor Y, acting on the feature tensor X;

[0051] 2) For any feature tensor X, Y, Z, Where g is a function used to measure the distance between two vectors, X g (Y,Z) is the new characteristic tensor formed by affine connection and function; It is the derivative along the feature tensor X, acting on the feature tensor Z; yes The inner product of Z at a given point; It is Y and Inner product at a given point;

[0052] The derivative of the geodesic is expressed as the inner product of the affine connection and the geodesic. By using the affine connection to solve the geodesic equation, the shortest path connecting two points on the Riemann manifold is found.

[0053] In some embodiments, determining whether a Riemannian manifold is geodesically complete includes:

[0054] Obtaining the dimension, Riemannian metric, Riemannian manifold boundary, and ergodic threshold of the Riemannian manifold;

[0055] Taking any two points on the Riemannian manifold, obtaining a geodesic by solving the geodesic equation;

[0056] In the case where the geodesic between the two points is infinite, determining that the Riemannian manifold is geodesically incomplete;

[0057] Repeat the above process when the geodesic between the two points is finite;

[0058] When the number of repetitions is less than the traversal threshold, determining whether an intersection point between the geodesic and the boundary of the Riemann manifold can be obtained;

[0059] When an intersection point of the geodesic and the boundary of the Riemannian manifold can be obtained, determining that the Riemannian manifold is geodesically complete;

[0060] When the intersection point of the geodesic and the boundary of the Riemannian manifold cannot be obtained, it is determined that the Riemannian manifold is geodesically incomplete.

[0061] In some embodiments, the digital twin system is simulated and operated based on the principle of least action, including:

[0062] Determining the minimum action, minimum action threshold, and neighborhood parameters of the starting point of the digital twin system;

[0063] Taking the original feature tensor of the starting point as the root node, the original feature tensor is randomly moved to the neighborhood edge in four directions based on the neighborhood parameters of the starting point to obtain a new feature tensor;

[0064] Determining a difference between a physical quantity corresponding to the new eigentensor and a physical quantity corresponding to the original eigentensor;

[0065] When the difference is less than the minimum action threshold, the new feature tensor is used as a leaf node, and the difference is used as the value of the leaf node.

[0066] Repeat the above steps until the tree structure with all feature tensors as root nodes is completed;

[0067] For each of the tree structures, summing the values ​​of all leaf nodes of the tree structure;

[0068] The tree structure with the minimum sum is regarded as the non-geodesic shortest path;

[0069] The feature tensor is moved according to the non-geodesic shortest path as the running path of the digital twin system.

[0070] In some embodiments, converting the deduction operation results into feature clusters in a low-dimensional feature space includes:

[0071] Constructing a local homotopy relationship graph of the high-dimensional feature space that reflects the local topological structure of the data in each neighborhood of the high-dimensional feature space;

[0072] Connect all local homotopy graphs of high-dimensional feature space together to form a global homotopy graph of high-dimensional feature space that reflects the global topological structure of the data;

[0073] Project the high-dimensional feature space to the low-dimensional feature space through the kernel function for dimensionality reduction;

[0074] Constructing a local homotopy relationship graph of the low-dimensional feature space in each neighborhood of the low-dimensional feature space that reflects the local topological structure of the data;

[0075] Connect all local homotopy graphs of low-dimensional feature space together to form a global homotopy graph of low-dimensional feature space that reflects the global topological structure of the data;

[0076] Calculate the homotopy group and homology group of high-dimensional feature space based on the global homotopy relationship graph of high-dimensional feature space, and calculate the homotopy group and homology group of low-dimensional feature space based on the global homotopy relationship graph of low-dimensional feature space;

[0077] If the homotopy groups and homology groups of the high-dimensional feature space and the low-dimensional feature space are the same, the feature cluster after dimensionality reduction in the high-dimensional feature space is used as the operating state of the digital twin system, otherwise the operation fails.

[0078] In a second aspect, an embodiment of the present application provides a power system digital twin system operation device, the device comprising:

[0079] An optimal Riemannian metric acquisition module is configured to determine the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on real-time collected data to obtain the optimal Riemannian metric;

[0080] a judgment module configured to construct a geodesic tangent bundle based on a Riemannian manifold using the optimal Riemannian metric; determine that the digital twin system is a stable system if the Riemannian manifold is geodesically complete; and determine that the digital twin system is an unstable system if the Riemannian manifold is geodesically incomplete;

[0081] The deduction and operation module is configured to perform deduction and operation on the digital twin system for a stable system; and to perform deduction and operation on the digital twin system for an unstable system based on the principle of least action to obtain deduction and operation results;

[0082] A dimensionality reduction module is configured to convert the deduction operation results into feature clusters in a low-dimensional feature space to complete the operation of the power system digital twin system.

[0083] In a third aspect, an embodiment of the present application provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for operating the digital twin system of the power system are implemented.

[0084] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the power system digital twin system operation method.

[0085] In a fifth aspect, an embodiment of the present application provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the steps of the above-mentioned power system digital twin system operation method.

[0086] Compared with the existing technology, this application has the following beneficial technical effects:

[0087] This application can realize the deduction and operation capability of the multi-scale digital twin system through the power system digital twin system operation method, which is detailed as follows:

[0088] (1) Based on the Riemann curvature approximation in the high-dimensional feature space of digital twins, the problem of metric inconsistency in non-Euclidean space is solved.

[0089] (2) Based on the geodesic-based tangent bundle provided for the eigentensor in the Riemannian manifold, the problem of inconsistent coordinates during the translation of the eigentensor is solved.

[0090] (3) For the operating status of digital twin systems of different new power systems, this application proposes a geodesically complete deduction operation method based on Riemannian manifolds to reflect the operation of stable systems; and proposes a minimum action method based on non-geodesically completeness to reflect the operation of unstable systems (i.e., systems with state changes or disturbances), thereby solving the state evolution problem of digital twin systems.

[0091] (4) Based on the dimensionality reduction method of homology equivalence from high-dimensional feature space to low-dimensional feature space, the problem of inconsistent deduction in the dimensionality reduction process is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] The drawings in the specification are used to provide further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application.

[0093] FIG1 is a schematic diagram of a flow chart of a method for operating a digital twin system of a power system according to an embodiment of the present application;

[0094] FIG2 is a schematic diagram of the structure of an operating device of a power system digital twin system provided in an embodiment of the present application;

[0095] FIG3 is a schematic diagram of an approximation of Riemann curvature provided in an embodiment of the present application. DETAILED DESCRIPTION

[0096] The present application is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0097] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0098] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in a sequence other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0099] The operation of a digital twin model refers to the following: assuming that the set of digital twin models for each device is M = {M1+M2+…+Mn}, where M1, M2…Mn represent the digital twin models of each device and n is the number of devices. Let the high-dimensional state space of the digital twin system be S, where S = {Ω1Ω2…Ωn}, where Ω1, Ω2…Ωn are disjoint distributions of operational state samples, with Ω1 associated with M1, Ω2 associated with M2…Ωn associated with Mn. Let T be the input state space of the digital twin system. The operation of the digital twin system means that when it is provided with continuous input based on the input state space T, the operational data D belongs to the high-dimensional state space S. Traditional simulation operation, however, is based on mechanism formulas, and its state space is a proper subset of the high-dimensional state space S, unable to support state changes within the high-dimensional state space S.

[0100] The following are definitions of the abbreviations and key terms mentioned in the embodiments of this application:

[0101] 1. Definition of Abbreviations

[0102] (1) Isomap algorithm: Isometric Feature Mapping, a type of manifold learning, used for nonlinear data dimensionality reduction;

[0103] (2) LLE algorithm: Locally linear embedding, a type of manifold learning, is a nonlinear dimensionality reduction algorithm that can better maintain the original manifold structure of the data after dimensionality reduction;

[0104] (3) Laplacian Eigenmaps: Laplacian Eigenmaps is a graph-based dimensionality reduction algorithm that moves related points (connected points in the graph) as close as possible in the reduced space, so that the original data structure can be maintained after dimensionality reduction.

[0105] 2. Definition of Key Terms

[0106] (1) Digital twin data-driven model: using artificial intelligence (AI) or other data mining algorithms to directly extract models from data;

[0107] (2) Digital twin hybrid model: data-driven model and mechanism model work together in series, parallel or hybrid mode to adapt to the operation and optimization requirements in different scenarios;

[0108] (3) Riemannian manifold: It is a differential manifold in which the tangent space of each point p defines a dot product, and the value changes smoothly with the point p. It allows the definition of arc length, angle, area, volume, curvature, function gradient and divergence of tensor field. According to the Nash embedding theorem, by restricting the dot product of R^n to the tangent space, each smooth submanifold of R^n can derive the Riemannian metric. The Riemannian manifold can be defined as a smooth manifold, in which there exists a smooth section of the positive definite quadratic of the tangent bundle. This smooth section generates a metric space;

[0109] (4) Riemann curvature: It is a tensor and an intrinsic quantity of a non-Euclidean manifold. It is also the standard way of expressing curvature in a Riemannian manifold. It can express the curvature of a torsion-free or torsion-free manifold with an affine connection. Riemann curvature is generally given by the Levi-Civita connection.

[0110] (5) Riemannian metric: a tensor representing structures such as distance, volume, and angle on a Riemannian manifold;

[0111] (6) Geodesic: represents the generalization of a straight line in a curved space, and is the local shortest path between two points on a Riemannian manifold;

[0112] (7) Tangent bundle: a tensor bundle representing the tangent spaces at each point in a differentiable manifold;

[0113] (8) Tangent bundle space: represents the non-intersecting union of tangent bundles;

[0114] (9) Geodesic completeness: The completeness of the geodesic tangent bundle means that there exists a geodesic between any two points on the manifold, and the movement of tensors along this geodesic is completely invariant;

[0115] (10) Digital twin multi-distributed state space: the complete set of the domain and range of all modelable features of the physical system. Historical operating data is a proper subset of the digital twin multi-distributed state space.

[0116] 1 , this embodiment provides a method for operating a power system digital twin system, comprising the following steps:

[0117] Step S101, based on the real-time collected data, the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model is calculated to obtain the optimal Riemannian metric.

[0118] Step S102: Use the optimal Riemannian metric to construct a geodesic tangent bundle based on the Riemannian manifold, and determine whether the Riemannian manifold is geodesically complete. If it is geodesically complete, the digital twin system is a stable system; otherwise, the digital twin system is an unstable system.

[0119] Step S103: For a stable system, a digital twin deduction based on geodesic completeness is used; for an unstable system, a digital twin deduction based on the principle of least action is used to obtain a deduction result.

[0120] Step S104: convert the simulation results into feature clusters in a low-dimensional space to complete the operation of the power system digital twin system.

[0121] An embodiment of the present application proposes a method for operating a digital twin system of a power system, which is used to realize the state evolution of a digital twin system at the device level, unit level or system level of the power system.

[0122] In the embodiment of the present application, the Riemann curvature approximation of the high-dimensional feature space of the convolution layer at the end of the data-driven modeling process and the corresponding geodesic tangent bundle are used to construct and implement the operation state evolution of a multi-level digital twin system based on geodesic completeness or minimum action: the first step is to calculate the Riemann curvature approximation of multiple Riemann manifolds in the high-dimensional feature space of the convolution layer at the end of the data-driven model based on real-time collected data to obtain the optimal Riemannian metric; the second step is to use the optimal Riemannian metric to construct a geodesic tangent bundle based on the Riemannian manifold and determine whether the Riemannian manifold is geodesically complete; the third step is to use a digital twin deduction operation based on geodesic completeness for a stable system, and a digital twin deduction operation based on the principle of minimum action for a system with state changes or disturbances. Finally, the deduction operation results are converted into feature clusters in a low-dimensional feature space based on a nonlinear dimensionality reduction method that preserves homology equivalence.

[0123] In some embodiments, the description is as follows:

[0124] Step 1: Calculate the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on real-time collected data to obtain the optimal Riemannian metric;

[0125] This step is a preprocessing step that aims to obtain basic information used to describe the high-dimensional feature space, including its geometric structure (Riemannian manifold) and its related metric information (Riemannian metric). By calculating the approximation of the Riemannian curvature, the optimal Riemannian metric can be obtained, which helps to more accurately capture the local structural information of the high-dimensional feature space.

[0126] Step 2: Use the optimal Riemannian metric to construct a geodesic tangent bundle based on the Riemannian manifold and determine whether the Riemannian manifold is geodesically complete. If it is geodesically complete, the digital twin system is stable; otherwise, the digital twin system is unstable.

[0127] This step further utilizes the optimal Riemannian metric obtained in step 1 to construct the geodesic tangent bundle of the Riemannian manifold. The tangent bundle is a more complex structure that can be used to describe the global properties of the Riemannian manifold. This step also involves determining whether the Riemannian manifold is geodesically complete, a result that has a significant impact on how the deduction is performed in subsequent steps.

[0128] Step 3: For stable systems, a digital twin simulation based on complete geodesy can be used. For unstable systems (i.e., systems with state changes or disturbances), a digital twin simulation based on the principle of least action can be used to obtain simulation results.

[0129] This step selects different deduction and execution methods for stable and unstable systems based on the judgment results in step 2. For stable systems, deduction and execution can be performed directly using the geodesic completeness of Riemannian manifolds; for systems with state changes or disturbances, deduction and execution are based on the principle of least action.

[0130] Step 4: Based on the nonlinear dimensionality reduction method of homotopy equivalence, the deduction results are converted into feature clusters in the low-dimensional feature space;

[0131] This step involves dimensionality reduction of the deduction results, converting the operational state of the high-dimensional feature space into feature clusters in the low-dimensional feature space. This employs a nonlinear dimensionality reduction method based on homotopy equivalence, which means that the topological structure (homotopy equivalence) of the original high-dimensional feature space is preserved during the dimensionality reduction process.

[0132] In general, the above steps are a process from concrete (collecting data, calculating the Riemannian metric) to abstract (constructing the geodesic tangent bundle, judging geodesic completeness), and then to concrete (selecting the deduction operation mode and performing dimensionality reduction). The purpose is to establish a model that can perform effective deduction in a complex high-dimensional feature space and effectively represent the deduction results in a low-dimensional feature space.

[0133] In step 1, we first introduce the Mahalanobis distance, a commonly used metric learning method. In this metric learning method, through singular value decomposition, it is found that when the rank of the triangular matrix W after singular value decomposition is less than the dimension of the high-dimensional feature space x, metric learning is equivalent to manifold learning. This is because such a matrix W can achieve linear shrinkage of the data, that is, dimensionality reduction, which lays the foundation for the subsequent Riemannian metric approximation.

[0134] Metric learning is a method for mapping data from one space to another, with the goal of making similar data points closer and dissimilar data points farther apart in the mapped space. This is done to better reflect the inherent structure and relationships of the data, facilitating subsequent tasks such as classification and clustering.

[0135] Mahalanobis distance is a commonly used metric learning method, which can be expressed as the following formula (1) under the conditions of symmetry, non-negativity, triangle inequality and identity: M (x k -x l )=(x k -x l ) T M(x k -x l ) formula (1);

[0136] Among them, x k and x l are two data points in the high-dimensional feature space, M is a positive definite matrix, and defines x k and x l The distance metric between them, T represents transposition, d M (x k -x l ) indicates that under the metric defined by the positive definite matrix M, the point x k and x l The Mahalanobis distance between

[0137] Perform Cholesky decomposition on the positive definite matrix M and obtain the following formula (2): M=W T W formula (2);

[0138] Cholesky decomposition is a method for decomposing a positive definite symmetric matrix into the product of a lower triangular matrix and its transpose. A primary use of this decomposition is to solve linear systems, often outperforming Gaussian elimination in terms of numerical stability and computational efficiency. For positive definite matrices, the Cholesky decomposition is numerically stable and generally more efficient than other methods.

[0139] Where W is a triangular matrix, from which we can get another formula (3) to express the Mahalanobis distance: M (x k -x l )=((x k -x l ) T W T )W(x k -x l )=(W(xk -x l )) T (W(x k -x l )= (Wx k -Wx l ) T (Wx k -Wx l ) formula (3);

[0140] At this point, if the rank (i.e., order) of the triangular matrix W is smaller than the dimension of the high-dimensional feature space, the data set can be linearly shrunk, that is, the purpose of better displaying the inherent structure of the high-dimensional feature space is achieved through dimensionality reduction. If a triangular matrix W with a rank smaller than the dimension of the high-dimensional feature space can be found, then the original high-dimensional feature space can be mapped to a lower-dimensional feature space through dimensionality reduction. This means that by finding a suitable triangular matrix W, the high-dimensional feature space can be reduced to a low-dimensional feature space that is more intuitive and easier to process, greatly reducing the complexity and computational complexity of processing high-dimensional data. Then, on this low-dimensional feature space, Riemann curvature can be more conveniently applied for approximation, because in low-dimensional feature space, concepts such as curvature are easier to understand and calculate.

[0141] The Riemannian metric is then approximated using Riemann curvature. Because the presence of Riemann curvature makes the Riemannian metric inequivalent to the Euclidean distance, exploiting Riemannian curvature is crucial for metrics in high-dimensional feature spaces. Because approximating the Riemannian curvature of discrete data is difficult, the Mahalanobis distance is proposed to approximate the Riemannian curvature. An objective function is proposed and, by optimizing the objective function, the optimal Riemannian metric is output. The approximation of the Riemannian curvature can be shown in Figure 3.

[0142] As can be seen from Figure 3, the existence of Riemann curvature causes the Riemann metric to be not equivalent to the Euclidean distance, so the mining of Riemann curvature is crucial for the measurement of high-dimensional feature spaces. Considering the difficulty of directly calculating the Riemann curvature, the Mahalanobis distance can be used to represent the approximation of the Riemann curvature; the formula for calculating the Riemann curvature approximation is shown in formula (4):

[0143] Among them, x i 、x k and x j represents a point in the high-dimensional feature space, |R ij | represents point x i 、x k and x j The absolute value of the Riemann curvature between M (x i ,x k ),d M (x k ,xj ),d M (x i ,x j ) respectively indicate that under the current measurement, x i and x k 、x k and x j 、x i and x j This formula is based on the assumption that within a local neighborhood, the data points on the Riemann manifold can be approximated as linear, so that the Riemann curvature can be approximated by the sum of the geodesic lengths minus the straight-line distance between the two points.

[0144] The objective function is expressed as formula (5):

[0145] The above formula is the optimization objective function, which is used to find the optimal Riemann metric. t is the Riemannian metric matrix at the tth iteration, which defines the distance metric between points in the high-dimensional feature space at a specific moment; M t+1 is the Riemann metric matrix at the t+1th iteration, which can be regarded as the matrix from M t The next metric matrix to be updated or evolved. Represents the change of the Riemann metric during the iteration process, which is used to measure the change or distance of the Riemann metric matrix between two consecutive iterations. t | represents the absolute value of the Riemann curvature under the current metric, λ 1,t is a regulating factor that balances the weights of metric change and Riemann curvature. The goal of the entire objective function is to find an optimal Riemannian metric that can both maintain the stability of the Riemannian metric as much as possible (i.e., avoid large changes in the Riemannian metric) and minimize the size of the Riemannian curvature (i.e., make the distribution of data points under the Riemannian metric closer to Euclidean space).

[0146] The specific optimization process is divided into the following four steps:

[0147] (1) Sampling the feature tensor point set {x1, x2, ..., x n The feature tensor point set represents a collection of data points in a high-dimensional feature space. Each data point represents a feature tensor. A neighborhood coefficient k (used to define the size of the local neighborhood) and a Euclidean metric E (representing the distance between defined points in Euclidean space) are preset. This step determines the dataset and parameters required for calculating the Riemannian metric. The feature tensor point set in the high-dimensional feature space is the dataset. The neighborhood coefficient k is used to determine the nearest neighbor of each point, and the Euclidean metric E is the initial Riemannian metric.

[0148] (2) Based on the neighborhood coefficient, find a set of minimum overlapping local neighborhoods as x nThe nearest neighbor U i ; This step is based on the neighborhood coefficient k to determine the nearest neighbors for each data point. The nearest neighbors of each data point are the k data points closest to it.

[0149] (3) Set the initial Riemann metric to L0 and the initial adjustment factor λ 1,1 ; This step is to set the initial value of the optimization process, where the initial Riemann metric L0 is usually set to the Euclidean metric E, λ 1,1 is the initial value of the adjustment factor, usually set to a small positive number.

[0150] (4) Update λ using the following formula (6): 1,t Until convergence:

[0151] Among them, η t is the learning rate, which is used to control the step size of each update, A ij =(x i -x j )(x i -x j ) -1 , represents the data point x i and x j The outer product of the distances between t represents the nearest neighbor U i The mean value of the internal Riemann curvature; tr represents the trace of the Riemann metric matrix (i.e., the sum of the diagonal elements).

[0152] This step is the core of the optimization process, by iteratively updating the adjustment factor λ 1,t , so that the objective function reaches the minimum value.

[0153] The formula is used to update λ 1,t ,λ 1,t It is the weight used to control the change of Riemann metric. The purpose of the update is to achieve a balance between Riemann curvature and Riemann metric change under certain conditions, so as to find the optimal Riemann metric.

[0154] In step 2, constructing a geodesic tangent bundle based on the Riemannian manifold and determining whether the Riemannian manifold is geodesically complete are key steps in enabling deductive operations on high-dimensional feature spaces. On the one hand, constructing the geodesic tangent bundle provides a structure describing the high-dimensional feature space, which provides a foundation for subsequent computation and understanding. On the other hand, determining the geodesic completeness of the Riemannian manifold ensures that this structure fully describes all possible states and dynamics of the high-dimensional feature space, which is a fundamental condition for deductive operations on high-dimensional feature spaces.

[0155] First, we construct a geodesic tangent bundle based on a Riemannian manifold. We select two points on the Riemannian manifold and define the geodesic equation using the local Riemannian metric tensor. Next, we define a tangent bundle on the Riemannian manifold, which is a frame of related high-dimensional tensors in a high-dimensional feature space. We then define a connection equation that preserves the Riemannian metric. Finally, by solving the connection equation and the geodesic equation, we obtain the parameters and path of the geodesic, completing the construction of the geodesic tangent bundle.

[0156] The construction of geodesic tangent bundle is divided into the following 5 steps:

[0157] (1) Select two points p and q on the Riemannian manifold C and use them as the starting and ending points of the geodesic. The choice of these two points is not restricted, but they must belong to the same Riemannian manifold to ensure that a geodesic can be defined between them based on the Riemannian metric. These two points are essentially the mapping of the two operating states of the digital twin system in the high-dimensional feature space;

[0158] (2) Based on the starting and ending points of the geodesic, the geodesic equation is defined using the local Riemannian metric on the Riemannian manifold. Here, the local Riemannian metric is a tensor field defined on the Riemannian manifold that describes the local distance measure between points on the Riemannian manifold;

[0159] (3) Define the tangent bundle for studying geodesics. Let C be a high-dimensional Riemannian manifold and TC be the tangent bundle on the high-dimensional Riemannian manifold C. For each point x in C, define T x C is the tangent space of C at point x, that is, T x C is the vector space composed of all tangent vectors at point x. TC is the vector space composed of all T x The tensor bundle formed by smoothly "gluing" C on C is formula (7): TC=∪ x∈C T x C Formula (7)

[0160] The tangent bundle can be used as a basis for related high-dimensional feature tensors in a high-dimensional feature space, providing a coordinate system for describing vectors or feature tensors at each point.

[0161] (4) Define affine connection: Here we use the Levi-Civita connection, which is a tool that can describe parallel movement on a Riemannian manifold, that is, the corresponding digital twin system can be transformed from one state to another. The Levi-Civita connection satisfies the invariance of the Riemannian metric. Possess the following properties:

[0162] ① No torsion: For any feature tensor X, Y in a high-dimensional feature space, Where [X,Y] is the Lie bracket of the feature tensor; It is the derivative along the feature tensor X, acting on the feature tensor Y; It is the derivative along the feature tensor Y, acting on the feature tensor X;

[0163] ② Compatible metric: For any feature tensor X, Y, Z, Where g is a function used to measure the distance between two vectors, X g (Y,Z) is the new characteristic tensor formed by affine connection and function; It is the derivative along the feature tensor X, acting on the feature tensor Z; yes The inner product of Z at a given point; It is Y and Inner product at a given point.

[0164] Solving the geodesic equation: Expressing the derivative of a geodesic as the inner product of an affine connection and the geodesic, we use this affine connection to solve the geodesic equation and find the shortest path between two points on a Riemannian manifold. The geodesic equation is a second-order ordinary differential equation that describes how state changes correspond to forward motion along a geodesic line. The solution to the geodesic equation provides a specific motion path on the Riemannian manifold, as well as the tangent vector along that path.

[0165] Secondly, determining whether a Riemannian manifold is geodesically complete involves setting a traversal threshold, obtaining the dimension and metric of the Riemannian manifold, and then obtaining the boundary of the Riemannian manifold. Next, randomly selecting two points on the Riemannian manifold, solving the geodesic equation to obtain the geodesic, and determining whether the geodesic between the two points is finite. If so, repeating the above steps. Finally, if the geodesic intersects the boundary of the Riemannian manifold before the traversal threshold is reached, the Riemannian manifold is considered geodesically complete. The logical relationship is that by setting the traversal threshold, obtaining the boundary of the Riemannian manifold, solving the geodesic equation, and finally determining whether the geodesic intersects the boundary of the Riemannian manifold, one can determine whether the Riemannian manifold is geodesically complete.

[0166] Geodesic completeness is equivalent to the digital twin system being in a steady-state operation phase, that is, the digital twin system is a stable system. Otherwise, the digital twin system is an unstable system. The judgment of geodesic completeness is divided into the following four steps:

[0167] (1) Set the traversal threshold and obtain the dimension and Riemannian metric of the Riemannian manifold; this step sets a stopping condition and obtains the basic information required to determine geodesic completeness.

[0168] (2) Obtain the boundary of the Riemannian manifold, that is, clarify the topological structure of the Riemannian manifold, including the boundary and holes of the Riemannian manifold.

[0169] (3) Take any two points on the Riemannian manifold and obtain the geodesic by solving the geodesic equation. If the geodesic between the two points is infinite, the Riemannian manifold is geodesically incomplete. If the geodesic between the two points is finite, repeat the above steps, paying attention to whether the set traversal threshold is reached.

[0170] (4) If the intersection of the geodesic and the boundary of the Riemannian manifold is obtained before the threshold is traversed, then the Riemannian manifold is geodesically complete. Otherwise, the Riemannian manifold is geodesically incomplete.

[0171] In step 3, if the Riemannian manifold satisfies geodesic completeness, this means that any two points on the Riemannian manifold can be connected by a geodesic line. Therefore, the equivalent movement of the characteristic tensor can be completed based on this geodesic line (here the characteristic tensor is the mapping of the operating state of the digital twin system in the high-dimensional feature space). The equivalent movement here means that along this geodesic line, the characteristic tensor moves from one position to another while maintaining its intrinsic structure. If the Riemannian manifold does not satisfy geodesic completeness, it is necessary to complete the movement of the characteristic tensor based on the differential structure of the Riemannian manifold and the principle of minimum energy.

[0172] For a stable system, the current operating state is not significantly disturbed. In other words, the operating state of the digital twin system has not evolved towards a faulty state or a better state, but remains in a steady-state operation phase. In this case, an appropriate time interval can be set to accelerate the simulation operation of the digital twin system.

[0173] For unstable systems, it is necessary to find a path that minimizes the action of the digital twin system. This path is called a non-geodesic shortest path. The state of the digital twin system will transition according to this non-geodesic shortest path. Based on the principle of least action, such a non-geodesic shortest path can be found between any two points. Specifically, it includes the following seven steps:

[0174] (1) Define the minimum action of the digital twin system and set the minimum action threshold;

[0175] Action is a key concept in physics, representing a measure of the system dynamics under given initial and final states. Here, we first define the minimum action of the digital twin system and set a minimum action threshold. A valid path is considered to have been found only when the minimum action of the digital twin system is less than this threshold.

[0176] (2) Setting the neighborhood parameters of the starting point;

[0177] This step defines the scope of searching for valid paths, and the neighborhood parameter determines the range of points that are considered "close" in the high-dimensional feature space.

[0178] (3) Taking the original feature tensor of the starting point as the root node, the original feature tensor is randomly moved to the neighborhood edge in four directions based on the neighborhood parameters of the starting point to obtain a new feature tensor;

[0179] This step describes how to search for paths in a high-dimensional feature space, starting from an original root node (i.e., the original feature tensor), moving in four directions in the neighborhood, and using the points moved to the edge of the neighborhood as new feature tensors.

[0180] (4) Calculate the difference between the physical quantity represented by the new feature tensor and the physical quantity of the original feature tensor. If the difference is lower than the minimum action threshold, the new feature tensor group is used as a leaf node and the difference is used as the value of the leaf node. Otherwise, the new feature tensor is ignored.

[0181] (5) Repeat steps (3) and (4) until the tree structure with all feature tensors as root nodes is completed;

[0182] This step forms a tree structure in the high-dimensional feature space through repeated searching and testing, and each leaf node is a possible system state.

[0183] (6) Traverse all tree structures, sum the values ​​of all leaf nodes, and use the tree structure with the smallest sum as the non-geodesic shortest path;

[0184] This step evaluates and selects all possible paths, and selects the path that minimizes the sum of all node values ​​as the optimal path, that is, the non-geodesic shortest path.

[0185] (7) Move the feature tensor along the non-geodesic shortest path as the running path of the digital twin system.

[0186] For a digital twin system with a stable state change, it will re-enter a stable operation state after moving forward a finite number of steps along the non-geodesic shortest path. Otherwise, it means that the range of the disturbance increases and the digital twin system enters an unstable state. If the calculation results diverge in the above step (6), it can be considered that the digital twin system has crashed.

[0187] This method is very useful for digital twin systems that deal with steady-state changes. It can find a path that allows the digital twin system to re-enter a stable state within a finite number of steps. If such a path is not found, it means that the disturbance range of the digital twin system has increased and the digital twin system may enter an unstable state.

[0188] In step 4, the problem mainly focuses on how to reduce the dimensionality of the high-dimensional feature space. To address this problem, this application adopts a nonlinear dimensionality reduction method based on homology equivalence. This method first calculates the local and global homology relationship graphs, and then selects a kernel function to project the high-dimensional feature space into the low-dimensional feature space through the kernel function. Next, the homology groups and homology groups of the high-dimensional feature space and the low-dimensional feature space are calculated, and finally, based on the results of the first two steps, it is judged whether the high-dimensional feature space and the low-dimensional feature space are homology equivalent. The logical relationship is that if the high-dimensional feature space and the low-dimensional feature space are homology equivalent, then the output after dimensionality reduction can be used as the operating state of the digital twin system to achieve dimensionality reduction of the high-dimensional feature space.

[0189] The nonlinear dimensionality reduction method based on homotopy equivalence includes the following steps:

[0190] (1) Calculate the local homotopy relationship graph in high-dimensional feature space;

[0191] This step requires constructing a local homotopy graph within each neighborhood in the high-dimensional feature space. In the local homotopy graph, nodes represent data points. When two data points are in the same neighborhood, there is an edge between them. The local homotopy graph reflects the local topological structure of the data.

[0192] (2) Calculating the global homotopy graph of the high-dimensional feature space based on the local homotopy graph of the high-dimensional feature space;

[0193] The global homotopy graph of the high-dimensional feature space is constructed on the entire dataset, connecting all the local homotopy graphs of the high-dimensional feature space together to reflect the global topological structure of the data.

[0194] (3) Select a kernel function, such as Isomap, LLE, or Laplacian Eigenmaps;

[0195] The kernel function is used to measure the similarity between data points. Different kernel functions provide different similarity measures. For example, Isomap is used to measure geodesic distance, LLE is used to maintain the relative position of data points in the neighborhood, and Laplacian Eigenmaps is used to measure the density of data points.

[0196] (4) Projecting the high-dimensional feature space to the low-dimensional feature space through the kernel function;

[0197] This step is actually a dimensionality reduction process, mapping the data in the high-dimensional feature space to the low-dimensional feature space through the kernel function.

[0198] (5) Constructing a local homotopy relationship graph in the low-dimensional feature space that reflects the local topological structure of the data in each neighborhood of the low-dimensional feature space;

[0199] (6) Connecting all local homotopy graphs of low-dimensional feature space together to form a global homotopy graph of low-dimensional feature space that reflects the global topological structure of the data;

[0200] (7) Calculating the homotopy groups of the high-dimensional feature space and the low-dimensional feature space based on the global homotopy relationship graph of the high-dimensional feature space and the global homotopy relationship graph of the low-dimensional feature space;

[0201] Homotopy groups are a concept in topology that can be used to measure the complexity of a topological space. This step computes the homotopy group of the original high-dimensional feature space and the reduced low-dimensional feature space. Homotopy groups are a tool for describing the invariance of a space under continuous deformations and can capture information about "holes" in the space. For example, in two-dimensional space, the homotopy group can describe the number of rings in the space, while in three-dimensional space, the homotopy group can describe the number of holes and rings in the space, and so on.

[0202] (8) Calculating the homology groups of the high-dimensional feature space and the low-dimensional feature space based on the global homotopy relationship graph of the high-dimensional feature space and the global homotopy relationship graph of the low-dimensional feature space;

[0203] Homology groups are also a concept in topology that can be used to measure another type of complexity in topological spaces. This step computes the homology groups of the original high-dimensional feature space and the reduced low-dimensional feature space. Homology groups are another tool for describing the invariance of a space under continuous deformations. They can also capture information about "holes" in the space, but they differ in that they describe a broader range. In mathematics, homology groups encompass not only information about homotopy groups but also other properties of a space, such as "shells," making them a powerful tool for studying topological spaces.

[0204] (9) Based on steps (7) and (8), determine whether the high-dimensional feature space and the low-dimensional feature space are homotopically equivalent;

[0205] If the homotopy and homology groups of the high-dimensional feature space and the low-dimensional feature space are the same, then we can determine that the high-dimensional feature space and the low-dimensional feature space are homotopically equivalent. Homotopy equivalent spaces are indistinguishable in terms of topological properties, so the feature clusters after dimensionality reduction in the high-dimensional feature space can be used as the operating status of the digital twin system.

[0206] Under the premise of homotopy equivalence between the high-dimensional feature space and the low-dimensional feature space, the reduced feature clusters can be used as the operating state of the digital twin system. The advantage of this nonlinear dimensionality reduction method based on homotopy equivalence is that it preserves the important topological properties of the original high-dimensional feature space, not just the distance or density information. This enables the reduced feature clusters to better reflect the structure and dynamic characteristics of the original digital twin system.

[0207] 2 , the present application provides a power system digital twin system operating device 200 , the power system digital twin system operating device 200 including:

[0208] The optimal Riemannian metric acquisition module 201 is configured to determine the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on the real-time collected data to obtain the optimal Riemannian metric;

[0209] The judgment module 202 is configured to construct a geodesic tangent bundle based on a Riemannian manifold using the optimal Riemannian metric; if the Riemannian manifold is geodesically complete, determine that the digital twin system is a stable system; if the Riemannian manifold is geodesically incomplete, determine that the digital twin system is an unstable system;

[0210] The deduction and operation module 203 is configured to perform deduction and operation on a digital twin system that is a stable system; and to perform deduction and operation on a digital twin system that is an unstable system based on the principle of least action to obtain a deduction and operation result;

[0211] The dimensionality reduction module 204 is configured to convert the deduction operation results into feature clusters in a low-dimensional feature space to complete the operation of the power system digital twin system.

[0212] In some embodiments, the optimal Riemannian metric acquisition module 201 is further configured to determine the Mahalanobis distance between two data points in the high-dimensional feature space of the last convolution layer of the data-driven model; use the Mahalanobis distance to approximate the Riemann curvature, and obtain the optimal Riemannian metric by optimizing the objective function.

[0213] In some embodiments, the optimal Riemannian metric acquisition module 201 is further configured to use Mahalanobis distance to represent the approximation of Riemannian curvature, as shown below:

[0214] Among them, x i 、x k and x j Represents a point in the high-dimensional feature space, d M (x i ,x k ),d M (x k ,x j ),d M (x i ,x j ) respectively indicate that under the current measurement, x i and x k 、x k and x j 、x i and xj The distance between them, |R ij | represents point x i 、x k and x j The absolute value of the Riemann curvature between ;

[0215] The objective function is expressed as:

[0216] Among them, M t represents the Riemannian metric matrix at the tth iteration, M t+1 represents the Riemannian metric matrix at the t+1th iteration, represents the change of the Riemann metric in two consecutive iterations, |R t | represents the absolute value of the Riemann curvature under the current metric, λ 1,t represents the regulating factor;

[0217] The process of optimizing the objective function is:

[0218] Sampling the feature tensor point set {x1, x2, ..., x n}, the feature tensor point set represents a set of data points in a high-dimensional feature space, each data point represents a feature tensor, and a neighborhood coefficient and a Euclidean metric E are preset; wherein n represents the number of feature tensors in the feature tensor point set;

[0219] Based on the neighborhood coefficient, find a set of minimum overlapping local neighborhoods as x n The nearest neighbor U i ;

[0220] Use the Euclidean metric E as the initial Riemann metric and set the initial value of the adjustment factor λ 1,1 ;

[0221] Use the following formula to update the adjustment factor λ 1,t Until convergence, the optimal Riemann metric is obtained;

[0222] Among them, η t is the learning rate; A ij =(x i -x j )(x i -x j ) -1 , represents the data point x i and x j The outer product of the distances between t represents the nearest neighbor U i The mean value of the interior Riemann curvature; tr represents the trace of the Riemann metric matrix.

[0223] In some embodiments, the determination module 202 is further configured to select a first point and a second point on a Riemannian manifold, and use the first point as the starting point of a geodesic line and the second point as the end point of the geodesic line;

[0224] Based on the starting point and the end point of the geodesic, a geodesic equation is defined using a local Riemannian metric on a Riemannian manifold to represent the geodesic;

[0225] The tangent bundle used to study geodesics is defined as follows:

[0226] Where C is a high-dimensional Riemann manifold, TC is the tangent bundle on the high-dimensional Riemann manifold C, and for each point x in the high-dimensional Riemann manifold C, T x C is the tangent space of C at point x;

[0227] Define an affine connection connecting tangent spaces at adjacent points on a Riemannian manifold The affine connection It uses the Levi-Civita connection, which has the following properties:

[0228] For any feature tensor X,Y in a high-dimensional feature space, Where [X,Y] is the Lie bracket of the feature tensor; It is the derivative along the feature tensor X, acting on the feature tensor Y; It is the derivative along the feature tensor Y, acting on the feature tensor X;

[0229] For any feature tensor X,Y,Z, Where g is a function used to measure the distance between two vectors, X g (Y,Z) is the new characteristic tensor formed by affine connection and function; It is the derivative along the feature tensor X, acting on the feature tensor Z; yes The inner product of Z at a given point; It is Y and Inner product at a given point;

[0230] The derivative of the geodesic is expressed as the inner product of the affine connection and the geodesic. By using the affine connection to solve the geodesic equation, the shortest path connecting two points on the Riemann manifold is found.

[0231] In some embodiments, the judgment module 202 is further configured to obtain the dimension, Riemannian metric, Riemannian manifold boundary and traversal threshold of the Riemannian manifold; take any two points on the Riemannian manifold and obtain the geodesic by solving the geodesic equation; when the geodesic between the two points is infinite, determine that the Riemannian manifold is geodesically incomplete; when the geodesic between the two points is finite, repeat the above process; when the number of repetitions is less than the traversal threshold, determine whether the intersection of the geodesic and the boundary of the Riemannian manifold can be obtained; when the intersection of the geodesic and the boundary of the Riemannian manifold can be obtained, determine that the Riemannian manifold is geodesically complete; when the intersection of the geodesic and the boundary of the Riemannian manifold cannot be obtained, determine that the Riemannian manifold is geodesically incomplete.

[0232] In some embodiments, the deduction operation module 203 is also configured to determine the minimum action, minimum action threshold and neighborhood parameters of the starting point of the digital twin system; take the original feature tensor of the starting point as the root node, and randomly move the original feature tensor to the neighborhood edge in four directions based on the neighborhood parameters of the starting point to obtain a new feature tensor; determine the difference between the physical quantity corresponding to the new feature tensor and the physical quantity corresponding to the original feature tensor; when the difference is less than the minimum action threshold, use the new feature tensor as a leaf node, and use the difference as the value of the leaf node, and repeat the above steps until a tree structure with all feature tensors as root nodes is completed; for each tree structure, sum the values ​​of all leaf nodes of the tree structure; use the tree structure with the smallest sum as the non-geodesic shortest path; move the feature tensor according to the non-geodesic shortest path as the operation path of the digital twin system.

[0233] In some embodiments, the dimensionality reduction module 204 is further configured to construct a local homotopy relationship graph of the high-dimensional feature space reflecting the local topological structure of the data in each neighborhood of the high-dimensional feature space; connect all the local homotopy relationship graphs of the high-dimensional feature space together to form a global homotopy relationship graph of the high-dimensional feature space reflecting the global topological structure of the data;

[0234] The high-dimensional feature space is projected to the low-dimensional feature space through a kernel function for dimensionality reduction; in each neighborhood of the low-dimensional feature space, a local homology relationship graph of the low-dimensional feature space is constructed to reflect the local topological structure of the data; all the local homology relationship graphs of the low-dimensional feature space are connected together to form a global homology relationship graph of the low-dimensional feature space that reflects the global topological structure of the data; based on the global homology relationship graph of the high-dimensional feature space, the homology group and homology group of the high-dimensional feature space are determined; based on the global homology relationship graph of the low-dimensional feature space, the homology group and homology group of the low-dimensional feature space are determined; when the homology group and homology group of the high-dimensional feature space and the low-dimensional feature space are the same, the feature cluster after dimensionality reduction of the high-dimensional feature space is used as the operating state of the digital twin system.

[0235] The description of the above device embodiment is similar to the description of the above method embodiment and has similar beneficial effects as the method embodiment. In some embodiments, the functions or modules included in the device provided in the embodiments of the present application can be used to perform the methods described in the above method embodiments. For technical details not disclosed in the device embodiments of the present application, please refer to the description of the method embodiments of the present application for understanding.

[0236] It should be noted that, in the embodiment of the present application, if the above-mentioned data processing method is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present application is essentially or the part that contributes to the relevant technology can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods of each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a magnetic disk or an optical disk. In this way, the embodiment of the present application is not limited to any specific hardware, software or firmware, or any combination of hardware, software and firmware.

[0237] An embodiment of the present application provides a computer device including a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor executes the program, some or all of the steps in the above method are implemented.

[0238] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements some or all of the steps in the above method. The computer-readable storage medium may be transient or non-transient.

[0239] An embodiment of the present application provides a computer program, including computer-readable code. When the computer-readable code runs in a computer device, a processor in the computer device executes some or all of the steps for implementing the above method.

[0240] The present application provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program. When the computer program is read and executed by a computer, some or all of the steps in the above method are implemented. The computer program product can be implemented in hardware, software, or a combination thereof. In some embodiments, the computer program product is embodied as a computer storage medium. In other embodiments, the computer program product is embodied as a software product, such as a software development kit (SDK).

[0241] It should be noted that the descriptions of the various embodiments above tend to emphasize the differences between the various embodiments, and their similarities or similarities can be referenced to each other. The descriptions of the above device, storage medium, computer program, and computer program product embodiments are similar to the descriptions of the above method embodiments and have similar beneficial effects as the method embodiments. For technical details not disclosed in the embodiments of the device, storage medium, computer program, and computer program product of this application, please refer to the description of the method embodiments of this application for understanding.

[0242] It should be noted that the description of the above storage medium and device embodiments is similar to the description of the above method embodiments and has similar beneficial effects as the method embodiments. For technical details not disclosed in the storage medium and device embodiments of this application, please refer to the description of the method embodiments of this application for understanding.

[0243] The processor may be at least one of an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a digital signal processing device (DSPD), a programmable logic device (PLD), a field programmable gate array (FPGA), a central processing unit (CPU), a controller, a microcontroller, and a microprocessor. It is understood that the electronic device that implements the functions of the processor may also be other electronic devices, which are not specifically limited in the embodiments of the present application.

[0244] The above-mentioned computer storage medium / memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic random access memory (FRAM), a flash memory (Flash Memory), a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM); it can also be various terminals including one or any combination of the above-mentioned memories, such as mobile phones, computers, tablet devices, personal digital assistants, etc.

[0245] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0246] The present application is described with reference to the flow chart and / or block diagram of the method, device (system), and computer program product according to the embodiment of the present application. It should be understood that each flow process and / or box in the flow chart and / or block diagram and the combination of the flow process and / or box in the flow chart and / or block diagram can be realized by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processing machine or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for realizing the function specified in one flow chart flow or multiple flows and / or one box or multiple boxes of the block diagram.

[0247] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a product including an instruction device that implements the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0248] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0249] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not intended to limit its scope of protection. Although the present application has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that after reading this application, those skilled in the art may still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention. Industrial Applicability

[0250] The embodiments of the present application provide a method, apparatus, equipment, medium and program product for operating a digital twin system of an electric power system. The method includes: based on real-time collected data, determining the Riemann curvature approximation of multiple Riemann manifolds in the high-dimensional feature space of the last layer of the convolution of a data-driven model to obtain the optimal Riemannian metric; using the optimal Riemannian metric to construct a geodesic tangent bundle based on the Riemannian manifold; when the Riemannian manifold is geodesically complete, determining that the digital twin system is a stable system; when the Riemannian manifold is geodesically incomplete, determining that the digital twin system is an unstable system; for a digital twin system that is a stable system, performing deduction and operation on the digital twin system; for a digital twin system that is an unstable system, performing deduction and operation on the digital twin system based on the principle of least action to obtain a deduction and operation result; converting the deduction and operation result into a feature cluster in a low-dimensional feature space to complete the operation of the digital twin system. In this way, the problem of metric inconsistency in non-Euclidean space is solved by approximating the Riemannian curvature in the high-dimensional feature space of digital twins; the problem of coordinate inconsistency during the translation of the feature tensor is solved by providing a geodesic-based tangent bundle for the feature tensor in the Riemannian manifold.

Claims

1. A method for operating a digital twin system of a power system, the method comprising: Based on real-time collected data, determine the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model to obtain the optimal Riemannian metric; Using the optimal Riemannian metric, constructing a geodesic tangent bundle based on a Riemannian manifold; In the case where the Riemann manifold is geodesically complete, determining that the digital twin system is a stable system; In the case where the Riemann manifold is geodesically incomplete, determining that the digital twin system is an unstable system; For a digital twin system that is a stable system, performing deduction and operation on the digital twin system; For a digital twin system that is an unstable system, the digital twin system is simulated and operated based on the principle of minimum action to obtain a simulation result; The deduction and operation results are converted into feature clusters in a low-dimensional feature space to complete the operation of the digital twin system.

2. The method for operating a digital twin system of a power system according to claim 1, wherein: The method of determining the Riemann curvature approximation of multiple Riemann manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on the real-time collected data to obtain the optimal Riemann metric includes: Determine the Mahalanobis distance between two data points in the high-dimensional feature space of the last convolution layer of the data-driven model; The Mahalanobis distance is used to approximate the Riemann curvature, and the optimal Riemann metric is obtained by optimizing the objective function.

3. The method for operating a digital twin system of a power system according to claim 2, wherein: The Mahalanobis distance is expressed as follows: M (x k -x l )=(x k -x l ) T M(x k -x l ) Among them, x k and x l are two points in the high-dimensional feature space, M is a positive definite matrix, T represents transposition, d M (x k -x l ) means that under the metric defined by the positive definite matrix M, the point x k and x l The Mahalanobis distance between Perform Cholesky decomposition on the positive definite matrix M and obtain the following expression: M=W T W Where W is a triangular matrix; From this we get: d M (x k -x l )=((x k -x l ) T W T )W(x k -x l )=(W(x k -x l )) T (W(x k -x l )= (Wx k -Wx l ) T (Wx k -Wx l )。 4. The method for operating a digital twin system of a power system according to claim 3, wherein: The method of using the Mahalanobis distance to approximate the Riemann curvature and obtaining the optimal Riemann metric by optimizing the objective function includes: The Mahalanobis distance is used to express the approximation of Riemann curvature as follows: Among them, x i 、x k and x j represents a point in the high-dimensional feature space, d M (x i ,x k ), d M (x k ,x j ), d M (x i ,x j ) respectively represent that under the current measurement, x i and x k 、x k and x j 、x i and x j The distance between |R ij | represents point x i 、x k and x j The absolute value of the Riemann curvature between ; The objective function is expressed as: Among them, M t represents the Riemann metric matrix at the tth iteration, M t+1 represents the Riemann metric matrix at the t+1th iteration, represents the change of the Riemann metric in two consecutive iterations, |R t | represents the absolute value of the Riemann curvature under the current metric, λ 1,t represents the regulating factor; The process of optimizing the objective function is: Sampling the feature tensor point set {x1, x2, ..., x n }, the feature tensor point set represents a set of data points in a high-dimensional feature space, each data point represents a feature tensor, and a neighborhood coefficient and a Euclidean metric E are preset; wherein n represents the number of feature tensors in the feature tensor point set; Based on the neighborhood coefficient, find a set of minimal overlapping local neighborhoods as x n The nearest neighbor U i ; Use the Euclidean metric E as the initial Riemann metric and set the initial value of the adjustment factor λ 1,1 ; Update the adjustment factor λ using the following formula 1,t Until convergence, the optimal Riemann metric is obtained; Among them, η t is the learning rate; A ij =(x i -x j )(x i -x j ) -1 , represents the data point x i and x j The outer product of the distances between t represents the nearest neighbor U i The mean value of the internal Riemann curvature; tr represents the trace of the Riemann metric matrix.

5. The method for operating a digital twin system of a power system according to any one of claims 1 to 4, wherein: The method of constructing a geodesic tangent bundle based on a Riemannian manifold by using the optimal Riemannian metric includes: Selecting a first point and a second point on a Riemann manifold, and using the first point as a starting point of a geodesic, and using the second point as an end point of the geodesic; Based on the starting point and the end point of the geodesic, a geodesic equation is defined using a local Riemannian metric on a Riemannian manifold to represent the geodesic; The definition of the tangent bundle used to study geodesics is as follows: Where C is a high-dimensional Riemann manifold, TC is the tangent bundle on the high-dimensional Riemann manifold C, and for each point x in the high-dimensional Riemann manifold C, T x C is the tangent space of C at point x; Define an affine connection for connecting tangent spaces at neighboring points on a Riemann manifold The affine connection It uses the Levi-Civita connection, which has the following properties: For any feature tensor X,Y in a high-dimensional feature space, Where [X,Y] is the Lie bracket of the feature tensor; It is the derivative along the feature tensor X, acting on the feature tensor Y; It is the derivative along the feature tensor Y, acting on the feature tensor X; For any feature tensor X,Y,Z, Where g is a function used to measure the distance between two vectors, X g (Y,Z) is the new characteristic tensor formed by affine connection and function; It is the derivative along the feature tensor X, acting on the feature tensor Z; yes The inner product of and Z at a given point; is Y and Inner product at a given point; The derivative of the geodesic is expressed as the inner product of the affine connection and the geodesic. By using the affine connection to solve the geodesic equation, the shortest path connecting two points on the Riemann manifold is found.

6. The method for operating a digital twin system of a power system according to claim 5, wherein: Determining whether the Riemann manifold is geodesically complete includes: Obtaining the dimension, Riemannian metric, Riemannian manifold boundary and ergodic threshold of the Riemannian manifold; Take any two points on the Riemann manifold and obtain the geodesic by solving the geodesic equation; In the case where the geodesic between the two points is infinite, determining that the Riemann manifold is geodesically incomplete; Repeat the above process when the geodesic line between the two points is finite; When the number of repetitions is less than the traversal threshold, determining whether an intersection point between the geodesic and the boundary of the Riemann manifold can be obtained; In the case where the intersection of the geodesic and the boundary of the Riemann manifold can be obtained, determining that the Riemann manifold is geodesically complete; When the intersection point of the geodesic and the boundary of the Riemann manifold cannot be obtained, it is determined that the Riemann manifold is geodesically incomplete.

7. The method for operating a digital twin system of a power system according to claim 5 or 6, wherein: The digital twin system is simulated and operated based on the principle of least action, including: Determining the minimum action, minimum action threshold, and neighborhood parameters of the starting point of the digital twin system; Taking the original feature tensor of the starting point as the root node, randomly moving the original feature tensor to the neighborhood edge in four directions based on the neighborhood parameter of the starting point to obtain a new feature tensor; Determine the difference between the physical quantity corresponding to the new feature tensor and the physical quantity corresponding to the original feature tensor; When the difference is less than the minimum action threshold, the new feature tensor is used as a leaf node, and the difference is used as the value of the leaf node. Repeat the above steps until the tree structure with all feature tensors as root nodes is completed; For each of the tree structures, summing the values ​​of all leaf nodes of the tree structure; The tree structure with the smallest sum is regarded as the non-geodesic shortest path; The feature tensor is moved according to the non-geodesic shortest path as the operation path of the digital twin system.

8. The method for operating a digital twin system of a power system according to claim 7, wherein: The step of converting the deduction operation result into a feature cluster in a low-dimensional feature space comprises: In each neighborhood of the high-dimensional feature space, a local homotopy relationship graph of the high-dimensional feature space is constructed to reflect the local topological structure of the data; Connecting all the local homotopy relationship graphs of the high-dimensional feature space together to form a global homotopy relationship graph of the high-dimensional feature space that reflects the global topological structure of the data; Projecting the high-dimensional feature space to a low-dimensional feature space by using a kernel function for dimensionality reduction; In each neighborhood of the low-dimensional feature space, a local homotopy relationship graph of the low-dimensional feature space is constructed to reflect the local topological structure of the data; Connecting all the local homotopy relationship graphs of the low-dimensional feature space together to form a global homotopy relationship graph of the low-dimensional feature space that reflects the global topological structure of the data; Based on the global homotopy relationship graph of high-dimensional feature space, the homotopy group and homology group of high-dimensional feature space are determined; Based on the global homotopy relationship graph of the low-dimensional feature space, the homotopy group and homology group of the low-dimensional feature space are determined; When the homotopy groups and homology groups of the high-dimensional feature space and the low-dimensional feature space are the same, the feature cluster after dimensionality reduction in the high-dimensional feature space is used as the operating state of the digital twin system.

9. A power system digital twin system operation device, the device comprising: An optimal Riemannian metric acquisition module is configured to determine the Riemannian curvature approximation of multiple Riemannian manifolds in the high-dimensional feature space of the last convolution layer of the data-driven model based on real-time collected data to obtain the optimal Riemannian metric; A judgment module is configured to construct a geodesic tangent bundle based on a Riemann manifold using the optimal Riemann metric; when the Riemann manifold is geodesically complete, determine that the digital twin system is a stable system; when the Riemann manifold is geodesically incomplete, determine that the digital twin system is an unstable system; The simulation operation module is configured to perform a simulation on the digital twin system for the digital twin system that is a stable system. Deduction and operation: For a digital twin system that is an unstable system, the digital twin system is deduced and operated based on the principle of minimum action to obtain a deduction and operation result; The dimensionality reduction module is configured to convert the deduction operation results into feature clusters in a low-dimensional feature space to complete the operation of the power system digital twin system.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method for operating a digital twin system of a power system as described in any one of claims 1 to 8 are implemented.

11. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for operating a digital twin system of a power system as described in any one of claims 1 to 8.

12. A computer program product, comprising a computer program or instructions, which, when executed by a processor, implements the steps of the method for operating a digital twin system of a power system as described in any one of claims 1 to 8.

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