CN120470269A - Ground fault prediction method based on IP-GNN and federal learning - Google Patents
Ground fault prediction method based on IP-GNN and federal learningInfo
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Abstract
The invention discloses a ground fault prediction method based on IP-GNN and federal learning, which comprises the following steps of collecting power distribution network operation data, constructing a power distribution network dynamic topology model based on the power distribution network operation data, constructing a hybrid dimension topology space based on the power distribution network dynamic topology model, fusing dynamic graph convolution, a self-adaptive partition strategy and a multi-head attention mechanism to construct an improved partition graph neural network, combining the improved partition graph neural network with a privacy protection federal learning framework to construct a ground fault prediction model, inputting the hybrid dimension topology space into the ground fault prediction model to realize the prediction of the ground fault, and fusing the improved partition graph neural network with the privacy protection federal learning depth, so that not only is the cross-organization data collaborative modeling realized, but also the traditional balance bottleneck between the topology analysis efficiency and the data privacy protection is broken through.
Description
Technical Field
The invention relates to the technical field of power system fault diagnosis, in particular to a ground fault prediction method based on IP-GNN and federal learning.
Background
The power distribution network is used as a key component of a power system, and the safe and reliable operation of the power distribution network directly relates to the quality of power supply of users and the overall stability of the power grid. With the promotion of smart grid construction and the wide access of distributed energy sources, the topology structure of the power distribution network is increasingly complicated and dynamic, and the occurrence frequency and the hazard degree of the ground faults are continuously increased. Particularly, the high-resistance ground fault is difficult to accurately identify and position by the traditional detection method because the characteristics are not obvious. Meanwhile, the dispersibility and sensitivity of the power distribution network data bring new challenges to fault prediction. Although each power company has massive operation data, due to the consideration of business confidentiality and user privacy protection, direct sharing and centralized analysis of the data are difficult to realize, a data island effect is formed, and the performance improvement of a fault prediction model is severely restricted.
The existing research method has various limitations in the process of predicting and treating the ground fault of the large-scale power distribution network. The traditional fault detection method is difficult to accurately identify and position the high-resistance ground fault, and cannot meet the requirements of the complex dynamic power distribution network. The existing graph neural network algorithm has low efficiency when processing a large-scale topological structure, and is difficult to meet the real-time fault prediction requirement. The standard federal learning framework has the risk of data privacy disclosure, and can not effectively protect sensitive information. In addition, the existing method is difficult to simultaneously consider topology processing efficiency and privacy security, and lacks cooperative breakthrough.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a ground fault prediction method based on IP-GNN and federal learning, and aims to solve the problems in the background art.
In order to achieve the above purpose, the invention provides a ground fault prediction method based on IP-GNN and federal learning, which comprises the following steps:
Collecting power distribution network operation data, constructing a power distribution network dynamic topology model based on the power distribution network operation data, and constructing a mixed dimension topology space based on the power distribution network dynamic topology model;
the dynamic graph convolution, the self-adaptive partition strategy and the multi-head attention mechanism are fused to construct an improved partition graph neural network;
Combining the improved partition map neural network with a privacy protection federal learning framework to construct a ground fault prediction model;
and (3) inputting the mixed dimension topological space into a ground fault prediction model to realize the prediction of the ground fault.
Further, the specific process of constructing the improved partition map neural network by fusing the dynamic map convolution, the self-adaptive partition strategy and the multi-head attention mechanism is as follows:
The adaptive partition strategy is:
Dynamic network partitioning based on spectral clustering algorithm and sub-graph set definition ,Represent the firstA subgraph satisfyingAnd is also provided with,The union is represented by a representation of the union,Represent the firstThe number of sub-pictures is one,Represent the firstThe number of sub-pictures is one,The representation of the empty set is made,Representing the whole graph, which is composed of the union of all sub-graphs;
the subgraph is processed through dynamic graph convolution, a multi-head attention mechanism is introduced in the process, and the characteristic update formula of each attention head in the multi-head attention mechanism is expressed as follows:
;
in the formula, Is shown in the firstIn the attention header, graph nodesThe updated feature vector; Representing graph nodes Is a neighbor map node set; is shown in the first Graph node in each attention headOpposite graph nodeIs a weight of attention of (2); Represent the first A weight matrix of the individual attention heads; Representing graph nodes Is a feature vector of the input of the (a); Representing graph nodes Sum graph nodeIn the first placeSimilarity scores between feature representations in the individual attention headers; representing an exponential function; Representing graph nodes Sum graph nodeIn the first placeSimilarity scores between feature representations in the individual attention headers,Represent the firstThe query vectors in the individual attention headers,Representing graph nodesIs used to determine the input feature vector of (a),Representing vector stitching; Representation of Activating a function;
the improved partition map neural network is constructed by fusing the dynamic map convolution, the self-adaptive partition strategy and the multi-head attention mechanism, and is expressed as follows:
;
;
in the formula, Representation of improved partition map neural network inAn output feature matrix of the layer; Representing a splicing operation; Representing the number of attention heads; representing an activation function; Represent the first Graph node in each attention headOpposite graph nodeThe attention weight among the two is calculated through normalization of a softmax function; Represent the first A weight matrix of the individual attention heads; Represent the first An input feature matrix of the layer; Representing a subgraph aggregation function; representing a dynamic graph convolution; Represent the first A degree matrix of layers; Represent the first Adding an adjacent matrix after self-connection in a layer; Represent the first A trainable weight matrix of a layer; Representing a feature fusion operation.
Further, the improved partition map neural network is combined with a privacy protection federal learning framework, and the specific process for constructing the ground fault prediction model is as follows:
each regional node of the power distribution network is independently modeled and trained by utilizing the improved partition map neural network based on locally acquired power distribution network operation data, and a trained local model of each regional node is obtained;
the local model training process does not involve the operation data exchange of the locally acquired power distribution network, and only generates encryptable model parameters;
After the local model training is finished, the parameters of the local model are encrypted and then sent to a federal coordination center, and a model parameter encryption mode adopts a secure multiparty computing SMC and homomorphic encryption HE mechanism;
The federal coordination center performs differential privacy injection and weighted aggregation on the encrypted local model parameters to form a unified global prediction model, namely a ground fault prediction model, wherein the updating expression of the global prediction model is as follows:
;
in the formula, Representation ofGlobal predictive model parameters at that time; Represent the first The number of samples of the individual area nodes; Representing the number of regional nodes; representing a secure multiparty computing aggregate function; representing homomorphic encryption functions; representing a differential privacy noise injection operation; Represent the first Individual area nodes are atLocal model parameters at that time.
Further, the specific process of constructing the dynamic topology model of the power distribution network based on the power distribution network operation data comprises the following steps:
defining node voltage vectors for a three-phase unbalanced power system And branch current vectorEstablishing an electromagnetic field dynamic equation:
;
in the formula, Representing the magnetic field strength; representing current density; representing an electrical displacement; Representing time; representing the electric field strength; Representing the magnetic induction intensity; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A voltage vector of the phase; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A current vector of the phase; Representing a transpose; representing the partial guide symbol;
Taking the joule heat generated by the conductor skin effect and the proximity effect into consideration, constructing a thermal field diffusion equation:
;
in the formula, Representing the material density; represents the specific heat capacity; representing a temperature field distribution; Representing a gradient operator; Representing thermal conductivity; Indicating the conductivity of the material;
introducing a dynamic admittance tensor matrix:
;
in the formula, Representing a dynamic admittance tensor matrix under the synergistic effect of multiple physical fields; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; representing a temperature-frequency coupling factor matrix; Representing Hadamard product operation;
The dynamic admittance tensor matrix is degenerated into a ground fault characteristic equation:
;
in the formula, Determinant symbols representing a matrix; representing a characteristic value to be solved of a ground fault characteristic equation; Representing the identity matrix.
Further, a mixed dimension topological space is constructed based on a dynamic topological model of the power distribution network;
Collect verticesCorresponding node voltage vectorCollecting edgesCorresponding branch current vectorThe weight of the edge set of the connected physical connection elements is calculated byProviding, collecting the fieldCorresponding high-dimensional coupling characteristics including temperature field distributionFrequency ofThermal conductivityConductivity of materialTemperature-frequency coupling factor matrix。
Further, for the subareas containing sensitive operation data in the power distribution network, automatically identifying the sensitive level, and carrying out differential privacy enhancement by adopting a dynamic privacy budget allocation mechanism;
the dynamic regulation formula of the dynamic privacy budget allocation mechanism is expressed as:
;
in the formula, Representation allocation to the firstDynamic privacy budgets for sub-regions containing sensitive operational data; Represent the first A network complexity factor for a sub-region containing sensitive operational data; representing a total training round; representing a logarithmic function.
Further, the updated formula of the multi-head attention mechanism in the local model training phase is expressed as follows:
;
in the formula, Representation ofParameters of a multi-head attention mechanism in the local model; Represent the first Parameters of the individual attention heads; representing a loss function; representing the number of attention headers; Representing the learning rate.
Further, the method comprises the steps of,The non-linear relation is shown as follows:
;
in the formula, Indicating a reference temperatureConductivity under; Representing the temperature coefficient.
Further, the partition optimization objective function of the adaptive partition strategy is expressed as:
;
in the formula, Representing subgraphsComplement corresponding to selfThe size of the cut set between the two refers to the connectionAndThe cut set size is the number of edges in the set; Representing a first balancing factor for balancing AndWeights in between; Representing subgraphs Medium graph node setIs a variance of (2); Representing a second balancing factor for balancing AndWeights in between; Representing a sub-graph collection Is a function of the entropy of (a).
Furthermore, the improved partition map neural network adopts a layered training strategy, and local optimization is firstly carried out on the subgraph, then global parameter tuning is carried out, and the improved partition map neural network local loss function is obtainedThe definition is as follows:
;
in the formula, Representing the number of subgraphs; Representing subgraphs Is a real tag of (1); Representing subgraphs Is a predictive output of (2); representing the square of the Frobenius norm; representing a KL divergence regularization term; representing the trace of the matrix; Representing subgraphs Feature matrix of (a)Is a transpose of (2); representing a sub-graph laplace matrix; And Weight parameters of the balance items are represented; Representing subgraphs Is a predictive probability distribution of (2)Distribution with targetKL divergence between.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, the improved partition map neural network IP-GNN is deeply fused with the privacy protection federal learning framework PPFL, so that a prediction model for the power distribution network fault prediction task is constructed, the prediction model not only realizes cross-organization data collaborative modeling, but also breaks through the traditional balance bottleneck between topology analysis efficiency and data privacy protection.
(2) According to the invention, a multi-head attention mechanism is introduced into the graph neural network structure, and the high-order nonlinear association between graph nodes can be finely modeled, so that the characteristic distinction degree is improved by the mechanism, the detection accuracy of high-resistance ground faults is remarkably improved, the method is superior to the existing model, and the problem of blind spot of high-resistance ground fault detection is solved.
(3) The invention innovatively provides a differential privacy mechanism based on dynamic budget allocation, and is designed in cooperation with a secure multiparty computing protocol, noise is dynamically injected in the model parameter exchange and local model aggregation process, and the data privacy security of each participant is ensured.
Drawings
FIG. 1is a flow chart of the method of the present invention.
Detailed Description
As shown in FIG. 1, the invention provides a technical scheme that the ground fault prediction method based on IP-GNN and federal learning comprises the following steps:
Step S1, collecting operation data of a power distribution network, constructing a dynamic topology model of the power distribution network based on the operation data of the power distribution network, and constructing a mixed dimension topology space based on the dynamic topology model of the power distribution network;
Step S2, an improved partition map neural network (IP-GNN) is constructed by fusing dynamic map convolution, a self-adaptive partition strategy and a multi-head attention mechanism;
Step S3, combining the improved partition map neural network with a Privacy-preserving federal learning framework (Privacy-PRESERVING FEDERATED LEARNING, PPFL) to construct a ground fault prediction model (IP-GNN-PPFL);
and S4, inputting the mixed dimension topological space into a ground fault prediction model to realize the prediction of the ground fault.
The dynamic topology model of the power distribution network needs to construct a ubiquitous energy interaction model of electric, magnetic and thermal multi-field coupling, and breaks through the limitation of traditional single physical field analysis.
1. Constructing a dynamic topology model of the power distribution network based on the power distribution network operation data:
taking a three-phase unbalanced power system as a research object, and defining node voltage vectors of the three-phase unbalanced power system And branch current vectorEstablishing an electromagnetic field dynamic equation:
;
in the formula, Representing the magnetic field strength; representing current density; representing an electrical displacement; Representing time; representing the electric field strength; Representing the magnetic induction intensity; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A voltage vector of the phase; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A current vector of the phase; Representing a transpose; Representing the partial guide symbol.
Taking the joule heat generated by the conductor skin effect and the proximity effect into consideration, constructing a thermal field diffusion equation:
;
in the formula, Representing the material density; represents the specific heat capacity; representing a temperature field distribution; Representing a gradient operator; Representing thermal conductivity; Indicating the conductivity of the material.
Wherein, the The nonlinear relation with the temperature change can be expressed as:
;
in the formula, Indicating a reference temperatureConductivity under; Representing the temperature coefficient.
To characterize the impact of multi-physical field synergy on network topology, a dynamic admittance tensor matrix is introduced:
;
in the formula, Representing a dynamic admittance tensor matrix under the synergistic effect of multiple physical fields; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing a temperature-frequency coupling factor matrix for reflecting the temperature field distribution Sum frequencyDynamic influence on admittance characteristics; representing Hadamard product operation, i.e. multiplication of corresponding elements of the dynamic admittance tensor matrix one by one.
The dynamic admittance tensor matrix may be degenerated into the ground fault signature equation:
;
in the formula, Determinant symbols representing a matrix; representing a characteristic value to be solved of a ground fault characteristic equation; Representing the identity matrix.
EigenvaluesThe singular point of the (C) corresponds to the resonance state of the three-phase unbalanced power system, and the track evolution of the (C) can represent the network response characteristics under different ground fault modes.
2. Construction of hybrid dimension topology space based on dynamic topology model of power distribution networkWherein the vertex setMapping electrical nodes, edge setsDescribing physical connections, field setsEncoding multiple physical field coupling parameters.
The mixed dimension topological space can be used for fusing electric, magnetic, thermal and other multi-field information and is used for high-dimensional feature learning and complex ground fault feature modeling, so that the identification capacity and generalization performance of the model on hidden faults are remarkably improved.
Collect verticesCorresponding node voltage vectorCollecting edgesCorresponding branch current vectorThe weight of the edge set is determined by the physical connection elements (wires, transformers) connectedProviding, collecting the fieldCorresponding to high-dimensional coupling characteristics (temperature field distributionFrequency ofThermal conductivityConductivity of materialTemperature-frequency coupling factor matrix) For encoding multi-source heterogeneous information.
The hybrid dimension topological space is an input basis for modeling of the graph neural network, and dynamic behavior information in the electromagnetic thermal coupling process can be explicitly embedded into the graph structure, so that the perceptibility, abnormal recognition precision and spatial distribution robustness of the partition graph neural network to high-resistance ground faults are improved.
The improved partition map neural network (IP-GNN) mainly comprises a structural modeling and sub-graph partition mechanism, a fusion with federal learning and a privacy optimization training strategy. First, a core structure definition and partition optimization method for improving the partition map neural network is provided, and on the basis of the core structure definition and partition optimization method, the subsequent description further describes an integration mode of the partition map neural network and a privacy protection mechanism (such as PPFL, a multi-head attention mechanism, homomorphic encryption and the like).
The specific process of constructing the improved partition map neural network by fusing the dynamic map convolution, the self-adaptive partition strategy and the multi-head attention mechanism is as follows:
1. the self-adaptive partitioning strategy is to dynamically divide the network based on a spectral clustering algorithm and define a sub-graph set ,Represent the firstA subgraph satisfyingAnd is also provided with,The union is represented by a representation of the union,Represent the firstThe number of sub-pictures is one,Represent the firstThe number of sub-pictures is one,The representation of the empty set is made,Representing the entire graph, consisting of the union of all sub-graphs.
Wherein, the partition optimization objective function of the adaptive partition strategy is expressed as:
;
in the formula, Representing subgraphsComplement with it(Subtracting outObtained) cut set size, cut set refers to connectionAndThe cut set size is the number of edges in the set; Representing a first balancing factor for balancing AndWeights in between; Representing subgraphs Medium graph node setIs a variance of (2); Representing a second balancing factor for balancing AndWeights in between; Representing a sub-graph collection Is a function of the entropy of (a).
The subgraph is processed through dynamic graph convolution, a multi-head attention mechanism is introduced in the process, the capturing capability of complex relations among graph nodes is enhanced, and the characteristic updating formula of each attention head in the multi-head attention mechanism can be expressed as:
;
in the formula, Is shown in the firstIn the attention header, graph nodesThe updated feature vector; Representing graph nodes Is a neighbor map node set; is shown in the first Graph node in each attention headOpposite graph nodeIs a weight of attention of (2); Represent the first A weight matrix of the individual attention heads; Representing graph nodes Is a feature vector of the input of the (a); Representing graph nodes Sum graph nodeIn the first placeSimilarity scores between feature representations in the individual attention headers; representing an exponential function; Representing graph nodes Sum graph nodeIn the first placeSimilarity scores (attention scores) between the feature representations in the individual attention headers,Represent the firstThe query vectors in the individual attention headers,Representing graph nodesIs used to determine the input feature vector of (a),Representing vector stitching; Representation of The function is activated.
The improved partition map neural network (IP-GNN) is constructed by fusing dynamic map convolution, adaptive partition strategy and multi-headed attention mechanism, and can be expressed as:
;
;
in the formula, Representation of improved partition map neural network inAn output feature matrix of the layer; Representing a splicing operation; Representing the number of attention heads; representing an activation function; Represent the first Graph node in each attention headOpposite graph nodeThe attention weight among the two is calculated through normalization of a softmax function; Represent the first A weight matrix of the individual attention heads; Represent the first An input feature matrix of the layer; Representing a subgraph aggregation function; representing a dynamic graph convolution; Represent the first A degree matrix of the layer for normalizing the adjacency matrix; Represent the first Adding an adjacent matrix after self-connection in a layer; Represent the first A trainable weight matrix of a layer; Representing a feature fusion operation.
The improved partition map neural network (IP-GNN) adopts a layered training strategy, performs local optimization on a subgraph, and then performs global parameter tuning, and improves the local loss function of the partition map neural network (IP-GNN)The definition is as follows:
;
in the formula, Representing the number of subgraphs; Representing subgraphs Is a real tag of (1); Representing subgraphs Is a predictive output of (2); representing the square of the Frobenius norm; representing a KL divergence regularization term; representing the trace of the matrix; Representing subgraphs Feature matrix of (a)Is a transpose of (2); representing a sub-graph laplace matrix; And All of which represent weight parameters of the balance term,For adjusting the effect of the KL divergence regularization term,For adjusting the influence of trace regularization terms; Representing subgraphs Is a predictive probability distribution of (2)Distribution with targetThe Kullback-Leibler (KL) divergence between the two is used to measure the similarity between the distributions.
In order to achieve the dual goals of 'multi-region collaborative modeling' and 'Privacy security protection' in fault prediction, the invention deeply fuses an improved partition map neural network (IP-GNN) with Privacy protection federation (Privacy-PRESERVING FEDERATED LEARNING, PPFL) to construct a ground fault prediction model.
Specific:
1. local model training and structure definition.
Based on locally acquired power distribution network operation data, each regional node (such as a transformer substation, a power supply station, a power grid subsystem and the like) of the power distribution network is independently modeled and trained by using an improved partition map neural network (IP-GNN), and a trained local model of each regional node is obtained. Each regional node has an independent data set (including node information, edge weight, topological structure, operation time sequence and the like), and performs graph learning in a manner of sub-graph division, self-adaptive partition strategy, multi-head attention mechanism and the like to construct a local model with regional feature perception capability.
The local model training process does not involve the exchange of original data (collected power distribution network operation data), only generates encryptable model parameters (such as graph convolution weight, attention head parameters and the like), and lays a foundation for the subsequent federal aggregation.
2. Model parameter encryption and differential privacy protection.
After the training of the local model is finished, all regional nodes do not upload the original data, but encrypt the parameters of the local model and send the encrypted parameters to the federal coordination center. The model parameter encryption mode adopts a Secure Multiparty Computing (SMC) and Homomorphic Encryption (HE) mechanism, so that the security of sensitive information in transmission and processing is ensured.
And for the subareas containing sensitive operation data in the power distribution network, automatically identifying the sensitive level of the subareas, and carrying out differential privacy enhancement by adopting a dynamic privacy budget allocation mechanism.
The dynamic regulation formula of the dynamic privacy budget allocation mechanism is expressed as follows:
;
in the formula, Representation allocation to the firstDynamic privacy budgets for sub-regions containing sensitive operational data; Represent the first A network complexity factor for a sub-region containing sensitive operational data; representing a total training round; representing a logarithmic function.
Among the subregions containing sensitive operational data include, but are not limited to:
User side critical load areas (e.g., industrial loads, medical devices, etc.);
distributed energy dense access areas (e.g., photovoltaic, energy storage);
high frequency interaction areas (e.g., edge computation nodes);
An operation and maintenance mark is a device domain of 'sensitive' or 'secret';
Low sparsity of graph structure or high risk subgraph with obvious node characteristics, etc.
3. And (5) aggregating the weighted model and updating the global parameters.
The federal coordination center performs differential privacy injection and weighted aggregation on the encrypted local model parameters to form a unified global prediction model (ground fault prediction model (IP-GNN-PPFL)), and the update expression of the global prediction model is as follows:
;
in the formula, Representation ofGlobal predictive model parameters at that time; Represent the first The number of samples of the individual area nodes; Representing the number of regional nodes; the method comprises the steps of representing a secure multiparty computing aggregation function, and aggregating encrypted local model parameters of nodes in each region on the premise of protecting privacy of the nodes in each region; The homomorphic encryption function is used for encrypting local model parameters and ensuring the safety of data in the transmission and aggregation processes; representing a differential privacy noise injection operation; Represent the first Individual area nodes are atLocal model parameters at that time.
Aiming at a few samples or a highly sensitive area, a threshold homomorphic encryption scheme is adopted, so that the original model can not be inverted by any party less than a preset threshold, and the model is prevented from being attacked reversely.
4. Global predictive model performance assessment and convergence guarantees.
After multiple rounds of iterative training, the constructed global prediction model has global generalization capability, and the prediction error meets the following convergence characteristics:
;
in the formula, Represent the firstGlobal prediction model parameters after the round training; Representing the optimal global predictive model parameters, and C representing a constant.
The update formula of the multi-head attention mechanism in the local model training stage is as follows:
;
in the formula, Representation ofParameters of a multi-head attention mechanism in the local model; Represent the first Parameters of the individual attention heads; representing a loss function; representing the number of attention headers; Representing the learning rate.
The mechanism ensures that the model still has stable learning ability and structural self-adaptability when fusing knowledge of a plurality of regional nodes.
The invention also designs a set of model structure optimization schemes based on the ground fault prediction model, which comprises the following steps:
1. defining partition optimization objective function for sub-graph partitioning strategy for guiding graph structure by comprehensively considering four types of structure characteristics :
;
In the formula,Representing sub-graph scale equality; The entropy value of the dividing result is expressed and used for measuring uncertainty and uniformity of sub-graph division; the modularity of the diagram division is represented and used for measuring the tightness degree inside the subgraph and the separation degree between the subgraphs; The community structure consistency index of the dynamic admittance matrix; 、、、 All represent balancing factors for adjusting the importance of each structural goal.
2. An improved dynamic graph convolution is constructed based on a circuit equation to enhance the extraction capability of time-frequency coupling characteristics, and a gating mechanism and a memory unit are introduced into the improved dynamic graph convolution, so that nonlinear and dynamic response in the fault propagation process can be effectively simulated, and the method is expressed as follows:
;
in the formula, Convolving the dynamic graph to represent improvementAn output feature matrix of the layer; the representation gating circulation unit is used for simulating the transient evolution process of the fault characteristics; representing an adjacency matrix of the graph for describing connection relationships between nodes in the graph; improved dynamic graph convolution An output feature matrix of the layer; and represents a bias term for adjusting the output of the model.
3. The improved dynamic graph convolution is integrated with a space-time perception multi-head attention mechanism, so that modeling capability of a model on a high-order nonlinear interaction relation between nodes is improved, and the integrated space-time perception multi-head attention mechanism is expressed as:
;
in the formula, Representing graph nodes in an mth attention headerSum graph nodeAn attention score between; Representing an attention mechanism function for calculating a similarity between the query vector and the key vector; Representing graph nodes in an mth attention header Is a query vector of (1); Representing graph nodes For capturing spatial location information of the graph nodes; Representing graph nodes For capturing time position information of the graph nodes; Representing graph nodes in an mth attention header Is a key vector of (a).
4. The method comprises the steps of designing a local model parameter aggregation rule for integrating encryption and information evaluation, realizing collaborative optimization among nodes in each region in a local model training stage, and guaranteeing data privacy safety, wherein the local model parameter aggregation rule can be expressed as:
;
in the formula, Representation ofGlobal predictive model parameters at that time; Represent the first The weight coefficient of each regional node; representing homomorphic encryption functions; Represent the first Individual area nodes are atLocal model parameters at that time; Representing the calculated first based on Fisher information matrix The parameter confidence degree of each regional node is used for dynamic weighted aggregation; Represent the first Parameter confidence of individual region nodes.
5. In the process of local model parameter exchange and final aggregation of each round of models, a dynamic differential privacy mechanism is introduced for further improving the privacy protection level:
;
in the formula, Representing the weight update items processed by the dynamic differential privacy mechanism; representing local model parameters; Mean 0 variance Is a gaussian noise of (c).
6. Design a self-adaptive dynamic privacy budget allocation mechanism by combining Fisher information matrix eigenvalues:
;
in the formula, Representation allocation to the firstDynamic privacy budgets for sub-regions containing sensitive operational data; A function representing a maximum eigenvalue mapping of the Fisher information matrix to privacy budget values; Represent the first Sub-region Fisher information matrix containing sensitive operation dataIs the maximum eigenvalue of (c).
The mechanism ensures that the noise intensity is dynamically regulated under the sensitivity degree of nodes in different areas, and the efficient utilization of privacy resources is realized.
7. Constructing a joint optimization objective function integrating task performance, model consistency and privacy protection:
;
In the formula,A loss function representing a ground fault prediction; represents Kullback-Leibler divergence (KL divergence) for measuring ground fault prediction model real data distribution And output distributionKL divergence between; representing ground fault prediction model inputs And output ofMutual information between the two is used for privacy constraint; All represent loss weight coefficients.
The objective function optimizes the performance of the model, simultaneously considers the consistency and privacy constraint of the model, and realizes the dynamic balance among the three.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (10)
1. The ground fault prediction method based on the IP-GNN and the federal learning is characterized by comprising the steps of collecting power distribution network operation data, constructing a power distribution network dynamic topology model based on the power distribution network operation data, constructing a mixed dimension topology space based on the power distribution network dynamic topology model, constructing an improved partition map neural network by fusing dynamic map convolution, a self-adaptive partition strategy and a multi-head attention mechanism, constructing a ground fault prediction model by combining the improved partition map neural network with a privacy protection federal learning framework, and inputting the mixed dimension topology space into the ground fault prediction model to realize the prediction of the ground fault.
2. The ground fault prediction method based on IP-GNN and federal learning of claim 1, wherein the specific process of constructing the improved partition map neural network by fusing dynamic map convolution, self-adaptive partition strategy and multi-head attention mechanism is as follows:
The adaptive partition strategy is:
Dynamic network partitioning based on spectral clustering algorithm and sub-graph set definition ,Represent the firstA subgraph satisfyingAnd is also provided with,The union is represented by a representation of the union,Represent the firstThe number of sub-pictures is one,Represent the firstThe number of sub-pictures is one,The representation of the empty set is made,Representing the whole graph, which is composed of the union of all sub-graphs;
the subgraph is processed through dynamic graph convolution, a multi-head attention mechanism is introduced in the process, and the characteristic update formula of each attention head in the multi-head attention mechanism is expressed as follows:
in the formula, Is shown in the firstIn the attention header, graph nodesThe updated feature vector; Representing graph nodes Is a neighbor map node set; is shown in the first Graph node in each attention headOpposite graph nodeIs a weight of attention of (2); Represent the first A weight matrix of the individual attention heads; Representing graph nodes Is a feature vector of the input of the (a); Representing graph nodes Sum graph nodeIn the first placeSimilarity scores between feature representations in the individual attention headers; representing an exponential function; Representing graph nodes Sum graph nodeIn the first placeSimilarity scores between feature representations in the individual attention headers,Represent the firstThe query vectors in the individual attention headers,The transpose is represented by the number,Representing graph nodesIs used to determine the input feature vector of (a),Representing vector stitching; Representation of Activating a function;
the improved partition map neural network is constructed by fusing the dynamic map convolution, the self-adaptive partition strategy and the multi-head attention mechanism, and is expressed as follows:
;
in the formula, Representation of improved partition map neural network inAn output feature matrix of the layer; Representing a splicing operation; Representing the number of attention heads; representing an activation function; Represent the first Graph node in each attention headOpposite graph nodeThe attention weight among the two is calculated through normalization of a softmax function; Represent the first A weight matrix of the individual attention heads; Represent the first An input feature matrix of the layer; Representing a subgraph aggregation function; representing a dynamic graph convolution; Represent the first A degree matrix of layers; Represent the first Adding an adjacent matrix after self-connection in a layer; Represent the first A trainable weight matrix of a layer; Representing a feature fusion operation.
3. The ground fault prediction method based on IP-GNN and federal learning of claim 2, wherein the specific process of combining the improved partition map neural network with the privacy protection federal learning framework to construct the ground fault prediction model is as follows:
each regional node of the power distribution network is independently modeled and trained by utilizing the improved partition map neural network based on locally acquired power distribution network operation data, and a trained local model of each regional node is obtained;
the local model training process does not involve the operation data exchange of the locally acquired power distribution network, and only generates encryptable model parameters;
After the local model training is finished, the parameters of the local model are encrypted and then sent to a federal coordination center, and a model parameter encryption mode adopts a secure multiparty computing SMC and homomorphic encryption HE mechanism;
The federal coordination center performs differential privacy injection and weighted aggregation on the encrypted local model parameters to form a unified global prediction model, namely a ground fault prediction model, wherein the updating expression of the global prediction model is as follows:
in the formula, Representation ofGlobal predictive model parameters at that time; Represent the first The number of samples of the individual area nodes; Representing the number of regional nodes; representing a secure multiparty computing aggregate function; representing homomorphic encryption functions; representing a differential privacy noise injection operation; Represent the first Individual area nodes are atLocal model parameters at that time.
4. A ground fault prediction method based on IP-GNN and federal learning as claimed in claim 3, wherein:
The specific process for constructing the dynamic topology model of the power distribution network based on the power distribution network operation data comprises the following steps:
defining node voltage vectors for a three-phase unbalanced power system And branch current vectorEstablishing an electromagnetic field dynamic equation:
in the formula, Representing the magnetic field strength; representing current density; representing an electrical displacement; Representing time; representing the electric field strength; Representing the magnetic induction intensity; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A voltage vector of the phase; respectively represent three-phase unbalanced power system Phase(s),Phase(s),A current vector of the phase; representing the partial guide symbol;
Taking the joule heat generated by the conductor skin effect and the proximity effect into consideration, constructing a thermal field diffusion equation:
in the formula, Representing the material density; represents the specific heat capacity; representing a temperature field distribution; Representing a gradient operator; Representing thermal conductivity; Indicating the conductivity of the material;
introducing a dynamic admittance tensor matrix:
in the formula, Representing a dynamic admittance tensor matrix under the synergistic effect of multiple physical fields; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Phase nodeAdmittance between phase nodes; Representing three-phase unbalanced power system Self admittance of phase nodes; representing a temperature-frequency coupling factor matrix; Representing Hadamard product operation;
The dynamic admittance tensor matrix is degenerated into a ground fault characteristic equation:
in the formula, Determinant symbols representing a matrix; representing a characteristic value to be solved of a ground fault characteristic equation; Representing the identity matrix.
5. The ground fault prediction method based on IP-GNN and federal learning of claim 4, wherein the method is characterized by constructing a hybrid dimension topology space based on a dynamic topology model of the power distribution network;
Collect verticesCorresponding node voltage vectorCollecting edgesCorresponding branch current vectorThe weight of the edge set of the connected physical connection elements is calculated byProviding, collecting the fieldCorresponding high-dimensional coupling characteristics including temperature field distributionFrequency ofThermal conductivityConductivity of materialTemperature-frequency coupling factor matrix。
6. The ground fault prediction method based on IP-GNN and federal learning of claim 5, wherein for sub-regions containing sensitive operational data in the distribution network, identifying sensitivity levels and employing a dynamic privacy budget allocation mechanism for differential privacy enhancement;
the dynamic regulation formula of the dynamic privacy budget allocation mechanism is expressed as:
in the formula, Representation allocation to the firstDynamic privacy budgets for sub-regions containing sensitive operational data; Represent the first A network complexity factor for a sub-region containing sensitive operational data; representing a total training round; representing a logarithmic function.
7. The method for predicting a ground fault based on IP-GNN and federal learning of claim 6, wherein the updated formula for the multi-headed attention mechanism during the local model training phase is expressed as:
in the formula, Representation ofParameters of a multi-head attention mechanism in the local model; Represent the first Parameters of the individual attention heads; representing a loss function; representing the number of attention headers; Representing the learning rate.
8. The ground fault prediction method based on IP-GNN and federal learning of claim 7, wherein: The non-linear relation is shown as follows:
in the formula, Indicating a reference temperatureConductivity under; Representing the temperature coefficient.
9. The method for predicting the ground fault based on IP-GNN and federal learning of claim 8, wherein the partition optimization objective function of the adaptive partition strategy is expressed as:
in the formula, Representing subgraphsComplement corresponding to selfThe size of the cut set between the two refers to the connectionAndThe cut set size is the number of edges in the set; Representing a first balancing factor for balancing AndWeights in between; Representing subgraphs Medium graph node setIs a variance of (2); Representing a second balancing factor for balancing AndWeights in between; Representing a sub-graph collection Is a function of the entropy of (a).
10. The ground fault prediction method based on IP-GNN and federal learning of claim 9, wherein the improved partition map neural network adopts a layered training strategy to perform local optimization on a subgraph and global parameter tuning, and the improved partition map neural network local loss functionThe definition is as follows:
;
in the formula, Representing the number of subgraphs; Representing subgraphs Is a real tag of (1); Representing subgraphs Is a predictive output of (2); representing the square of the Frobenius norm; representing a KL divergence regularization term; representing the trace of the matrix; Representing subgraphs Feature matrix of (a)Is a transpose of (2); representing a sub-graph laplace matrix; And Weight parameters of the balance items are represented; Representing subgraphs Is a predictive probability distribution of (2)Distribution with targetKL divergence between.
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