A gcn method for power distribution network state consequence fast calculation

Abstract

The application provides a GCN method for power distribution network state consequence rapid calculation, comprising the following steps: generating label data of a power distribution network based on a sequential Monte Carlo simulation method; wherein the label data comprises a power distribution network operation state and corresponding load shedding amount; constructing a GCN-DNN proxy model; wherein the GCN-DNN proxy model comprises an upstream graph convolution network model and a downstream deep neural network model; training the GCN-DNN proxy model by using the label data to obtain a state consequence rapid calculation model; and inputting a power distribution network operation state to be evaluated into the state consequence rapid calculation model to obtain a load shedding amount prediction result. While ensuring the evaluation accuracy, the calculation efficiency is improved, and the problems of poor timeliness and weak adaptability in the power distribution network reliability evaluation are solved.

Description

Technical Field

[0001] This invention relates to the field of distribution network reliability assessment technology, and in particular to a GCN method for rapid calculation of distribution network state consequences. Background Technology

[0002] With the large-scale integration of renewable energy sources such as wind power and photovoltaics, the power distribution network is evolving towards higher penetration and greater complexity. This significantly increases the uncertainty and volatility of system operation, posing challenges to the reliability assessment of the power distribution network in terms of both solution efficiency and time cost.

[0003] Traditional reliability assessment methods can be divided into analytical methods and simulation methods. However, with the continuous evolution of distribution networks, both face the problem of solution efficiency. Analytical methods require detailed modeling of system components, which can easily lead to solution difficulties due to the curse of dimensionality in large-scale systems. Simulation methods, represented by Sequential Monte Carlo Simulation (SMCS), are more adaptable to large-scale distribution systems. Its solution process consists of four steps: component modeling, system state sampling, state consequence calculation, and reliability index calculation. However, state consequence analysis involves a large number of complex discrete quantities and nonlinear constraints, and its solution process is an NP-hard problem. This means that as the system size increases and the solution period increases, the solution efficiency of SMCS will increase exponentially, resulting in a convergence bottleneck and failing to meet the timeliness requirements of the assessment.

[0004] To address this, researchers have proposed a surrogate model approach based on deep learning (DL). This approach establishes a mapping between input states and output consequences, learning and replacing the original state-consequence analysis process. However, traditional Euclidean space methods also have some problems. Problem 1: Solution efficiency: Training relies on massive amounts of labeled samples, and these labels originate from the state-consequence analysis process. This still doesn't avoid the most time-consuming part of the SMCS method and cannot effectively handle scenarios with uncertain source-load distribution. Problem 2: Distribution drift: Existing DL methods are mainly trained using Euclidean space samples, assuming that the input distribution remains unchanged. However, in scenarios with highly uncertain source-load distribution in distribution networks, data drift is easily encountered during online operation, leading to a significant decrease in model accuracy and failing to meet the accuracy requirements for reliability assessment. Summary of the Invention

[0005] This invention provides a GCN method for rapid calculation of distribution network state consequences, in order to solve the problems of poor timeliness and weak adaptability in the existing technology of distribution network reliability assessment.

[0006] On one hand, this invention provides a GCN method for rapid calculation of state consequences in distribution networks, comprising: Tag data for the distribution network is generated based on the sequential Monte Carlo simulation method; wherein, the tag data includes the operating status of the distribution network and the corresponding load shedding amount; Construct a GCN-DNN proxy model; wherein the GCN-DNN proxy model includes an upstream graph convolutional network model and a downstream deep neural network model; The GCN-DNN proxy model is trained using the labeled data to obtain a fast calculation model for state consequences; The operating status of the distribution network to be evaluated is input into the fast calculation model of the state consequences to obtain the predicted load shedding amount.

[0007] Optionally, the generation of distribution network tag data based on the sequential Monte Carlo simulation method includes: Establish a repairable forced failure model for components to describe the operational probability characteristics of components in the distribution network; Based on the repairable forced failure model, the system state is sampled using the state duration sampling method to obtain the operating state of the distribution network. Optimal load shedding calculations are performed on the operating state of the power distribution network to obtain the corresponding load shedding amount; Tag data is generated based on the operating status of the distribution network and the corresponding load shedding amount.

[0008] Optionally, the trouble-free operating time of a component is expressed as: ; The fault repair time of a component is expressed as: ; The amount of load shearing is expressed as: ; in, Indicates the time between failures; Indicates the fault repair time; and All are random numbers distributed in the interval [0,1]. For the failure rate of components, The component repair rate; In running state; Represents the moment t Specific operating state The amount of load shedding generated by the system; For a moment t Running status s Next node Upper load resection value; For continuous variables, Represents state variables; and These are inequality constraints and equality constraints that describe the safe operation of the distribution network, respectively.

[0009] Optionally, the graph convolutional network model models the distribution network topology as an undirected graph; wherein the undirected graph uses distribution network nodes as the set of nodes and line connection relationships as the set of edges; An adjacency matrix is ​​constructed based on the undirected graph to describe the physical connection relationships between nodes.

[0010] Optionally, the graph convolutional network model calculates the degree matrix based on the adjacency matrix; Construct a symmetric normalized Laplace matrix based on the adjacency matrix and the degree matrix; Based on the Laplacian matrix, node information is updated through multi-layer graph convolution.

[0011] Optionally, the adjacency matrix elements are represented as follows: ; in, These are elements of the adjacency matrix; Represents a node With nodes There are physical wiring connections between them; Let it be the set of edges; The degree matrix includes: ; ; The Laplace matrix includes: ; in, It is a degree matrix; , , , where are the degrees of node 1, node 2, and node n, respectively; n is the total number of nodes; The degree matrix after adding self-loops; For n The identity matrix of n; It is a Laplace matrix; It is an adjacency matrix; The update of node information is represented as follows: ; in, Representing the Layer node information; Representing the Layer node information; f( ) represents the activation function; It is the first Layer weight matrix.

[0012] Optionally, training the GCN-DNN proxy model using the labeled data includes: An active learning strategy is adopted, based on a hybrid criterion of uncertainty sampling and diversity sampling, to iteratively update the pre-trained GCN-DNN surrogate model until the model's performance on the validation set meets the preset requirements; The diversity sampling is based on the deep feature representation of the samples in the feature space to calculate the similarity between samples, and the feature distance between samples is obtained according to the similarity. A diversity sampling subset is selected based on the feature distance. The uncertainty sampling is based on the mutual information score calculated by the entropy value of the sample prediction and the expected entropy value under the posterior distribution of the model parameters, and unlabeled samples are selected based on the mutual information score.

[0013] Optionally, the final sample set selected through active learning can be represented as follows: ; Similarity is expressed as: ; The feature distance is represented as: ; The diversity sampling subset is represented as: ; in, This is the final sample set selected through active learning; Represents a diversity sampling subset. Represents a subset of samples with uncertainties; For diversity sampling budget, Budget for uncertain sampling; Total sampling budget; For the sample and samples Similarity; These are unlabeled samples; For reference only; For the sample Deep feature representation; For the sample Deep feature representation; This is the bandwidth parameter, i.e., the Gaussian kernel width that controls the sensitivity of the kernel function; For the sample With sample Spatial feature distance; For diversity sampling subsets; A subset of candidate incremental samples; For unlabeled sample pools; This is the labeled sample pool.

[0014] Optionally, the uncertainty information of the sample is represented as: ; Uncertainty sampling subset is represented as: ; in, Representative sample x Uncertain information, Represents prediction entropy, which is characterized by the model's response to the output. y Total uncertainty; Represents the expected posterior entropy, expressed as the value of the model's performance on a given set of labeled samples. Under these conditions, model parameters In the posterior distribution The following sample x The average forecast uncertainty; This is a subset of candidate uncertain samples.

[0015] Optional, also includes: The probability of insufficient power supply and the annual expected insufficient power supply value are calculated based on the load shedding prediction results to achieve distribution network reliability assessment. The probability of insufficient power supply is expressed as: ; The expected annual power supply shortage value is expressed as: ; ; For load reduction scenario functions; Total system evaluation time; Indicates running status s The duration of the state; Represents the set of all system operating states during the total evaluation period; The probability of insufficient power supply; Annual expected power supply shortage value.

[0016] This invention provides a GCN method for rapid calculation of state consequences in distribution networks. It utilizes sequential Monte Carlo simulation to generate labeled data containing operating states and load shedding amounts, thus providing an accurate physical benchmark. A GCN-DNN surrogate model is constructed, consisting of an upstream Graph Convolutional Network (GCN) and a downstream Deep Neural Network (DNN). The GCN effectively overcomes the curse of dimensionality in large-scale systems through a full graph parameter sharing mechanism, while the DNN enhances nonlinear mapping capabilities. By training the labeled data, the GCN-DNN surrogate model learns the mapping relationship between input states and output consequences, replacing the traditional time-consuming physical calculation process. While ensuring assessment accuracy, this method improves computational efficiency and enhances the timeliness and adaptability of distribution network reliability assessment. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the GCN method for rapid calculation of distribution network state consequences provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the state consequence proxy model architecture based on GCN provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the IEEE-33 node topology provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the reliability evaluation index curve of EENS variance provided in the embodiments of the present invention; Figure 5 This is a schematic diagram of the reliability evaluation index curve of LOLP variance provided in the embodiments of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] Figure 1 This is a flowchart illustrating the GCN method for rapid calculation of distribution network state consequences provided in an embodiment of the present invention.

[0021] See Figure 1 The GCN method for rapid calculation of distribution network state consequences may include the following steps 101 to 104.

[0022] Step 101: Generate tag data for the distribution network based on the sequential Monte Carlo simulation method; wherein, the tag data includes the operating status of the distribution network and the corresponding load shedding amount.

[0023] Step 102: Construct the GCN-DNN surrogate model; wherein, the GCN-DNN surrogate model includes an upstream graph convolutional network model and a downstream deep neural network model.

[0024] Step 103: Train the GCN-DNN agent model using labeled data to obtain a fast calculation model for state consequences.

[0025] Step 104: Input the operating status of the distribution network to be evaluated into the state consequence rapid calculation model to obtain the load shedding prediction results.

[0026] In this embodiment, sequential Monte Carlo simulation is used to generate labeled data containing operating status and load shedding amounts, thereby providing an accurate physical benchmark. A GCN-DNN surrogate model is constructed, consisting of an upstream graph convolutional network (GCN) and a downstream deep neural network (DNN). The GCN effectively overcomes the dimensionality curse problem of large-scale systems through a full graph parameter sharing mechanism, while the DNN enhances the nonlinear mapping capability. By training with labeled data, the GCN-DNN surrogate model learns the mapping relationship between input states and output consequences, replacing the traditional time-consuming physical calculation process. While ensuring the accuracy of the assessment, the computational efficiency is improved, enhancing the timeliness and adaptability of distribution network reliability assessment.

[0027] In one embodiment of this specification, generating distribution network tag data based on the sequential Monte Carlo simulation method may include: Step 1: Establish a repairable forced failure model for components to describe the operational probability characteristics of components in the distribution network; The fault-free operating time of the component is expressed by formula (1). (1); The fault repair time of a component is expressed by formula (2): (2); Indicates the time between failures; Indicates the fault repair time; and All are random numbers distributed in the interval [0,1]. For the failure rate of components, The repair rate of the component is denoted by . Repeating the sampling process within a specified time yields the state transition sequence diagram for each component.

[0028] Step 2: Based on the repairable forced failure model, the system state is sampled using the state duration sampling method to obtain the operating state of the distribution network; Specifically, the state duration sampling method is adopted, which treats any change in the state of a component as a change in the state of the system, and the state duration is the time interval between adjacent system states.

[0029] Step 3: Under the condition of satisfying the safety constraints of the distribution network, perform optimal load reduction calculation for the operating state of the distribution network to obtain the corresponding load shedding amount; The load shearing amount is expressed as formula (3): (3); in, The running status can include source load, topology, and fault status; Represents the moment t Specific operating state Total load shelving generated by the system; For a moment t Running status Next node Upper load resection value; For continuous variables such as active power and power flow, This represents state variables such as switch actions; n is the total number of nodes. and These are the key inequalities and equality constraints that describe the safe operation of the distribution network.

[0030] Step 4: Generate tag data based on the operating status of the distribution network and the corresponding load shedding amount.

[0031] In this embodiment, the sampled distribution network operating status is used as the input sample, and the calculated load shedding amount is used as the label for the sample. Together, they constitute a complete labeled data sample pair. This embodiment can provide high-quality labeled samples for the subsequent training of the GCN-DNN surrogate model.

[0032] In one embodiment of this specification, after obtaining the predicted load shedding amount, the method may further include: The probability of insufficient power supply and the annual expected power supply shortage value are calculated based on the load shedding forecast results to achieve the reliability assessment of the distribution network.

[0033] The probability of insufficient power supply is expressed by formula (4); (4); The expected annual power supply shortage is expressed by formula (5). (5); (6); in, For load reduction scenario functions; Total system evaluation time; Indicates running status The duration of the state; Represents the set of all system operating states during the total evaluation period; The probability of insufficient power supply; Annual expected power supply shortage value.

[0034] In this embodiment, the probability of insufficient power supply and the annual expected power supply shortage value are calculated based on the load shedding prediction results, which enables a quantitative assessment of the power supply reliability of the distribution network. The probability of insufficient power supply reflects the possibility of load shedding in the system, and the annual expected power supply shortage value reflects the cumulative annual power supply shortage caused by the system due to faults.

[0035] In one embodiment of this specification, the graph convolutional network model models the distribution network topology as an undirected graph; wherein, the undirected graph has the distribution network nodes as the set of nodes and the line connection relationships as the set of edges; An adjacency matrix is ​​constructed based on an undirected graph to describe the physical connections between nodes.

[0036] The elements of the adjacency matrix are shown in formula (7): (7); in, These are elements of the adjacency matrix; Represents a node With nodes There are physical wiring connections between them; Let it be the set of edges.

[0037] In this embodiment, an identity matrix is ​​added to the adjacency matrix to preserve the node's own information. To preserve the node's own characteristic information, self-loops are typically introduced into the graph. .

[0038] In one embodiment of this specification, the graph convolutional network model calculates the degree matrix based on the adjacency matrix; Construct a symmetric normalized Laplace matrix based on the adjacency matrix and degree matrix; Based on the Laplacian matrix, node information is updated through multi-layer graph convolution.

[0039] The degree matrix is ​​shown in formulas (8) and (9) below, and the Laplace matrix is ​​shown in formula (10) below: (8); (9); (10); in, It is a degree matrix; , , , where are the degrees of node 1, node 2, and node n, respectively; n is the total number of nodes; The degree matrix after adding self-loops; For n The identity matrix of n; It is a Laplace matrix; It is an adjacency matrix; The node information is updated as shown in formula (11): (11); in, Representing the Layer node information; Representing the Layer node information; f( ) represents the activation function, which is usually ReLU. It is the first The weight matrix of the layer. The dimension of the weight matrix is ​​determined only by the feature dimension and is independent of the number of nodes. All nodes within each layer share the same convolutional kernel. Therefore, full graph sharing of parameters can be achieved, thereby enabling the model to adapt to changes in source loads.

[0040] In some other embodiments of this specification, the input matrix of the GCN-DNN proxy model is constructed by fusing multi-dimensional features; Multidimensional features may include: the active and reactive power of the node at time t; the photovoltaic output of the node at time t, etc.

[0041] The active power is shown in formula (12), the reactive power is shown in formula (13), the photovoltaic output is shown in formula (14), and the characteristic matrix of the 0th layer (input layer) of GCN at time t is shown in formula (15): (12); (13); (14); (15); and Representing time respectively t No. The active and reactive power of each node. and Representing nodes respectively Active and reactive loads on the surface and Representing time respectively t Active and reactive load rates are specified. t An integer between 0 and 23, representing different times of day. Representative moment t node Powering solar energy Representative moment t node The maximum active power output limit of photovoltaic power generation. It is a moment t Photovoltaic power generation capacity. To store the maximum discharge power, The initial energy storage capacity. This is the maximum amount of energy that can be stored. The status of tie switches is coded: the operation and connection status of tie switches on nodes are represented by numbers. A value of 1 indicates no tie switch, 2 indicates an open tie switch, and 3 indicates a closed tie switch during power transfer. For the GCN layer 0 (input layer) at time... t The feature matrix; For nodes At any moment t Fault indication bit; The fault indication position uses a node method to depict the fault section of the line; The expression that maps line faults to node faults is formula (16): (16).

[0042] in, For nodes exist t The fault indicator bit at any given time.

[0043] Specifically, the state consequence proxy model architecture based on GCN can be found in [reference needed]. Figure 2 An initial input matrix is ​​constructed using node data, source load data, and fault data. This matrix is ​​then processed by an upstream GCN for graph convolution and information aggregation to extract topological features. Finally, a downstream DNN performs nonlinear mapping to output the optimal load reduction value, thereby enabling rapid calculation of state consequences.

[0044] In one embodiment of this specification, training a GCN-DNN surrogate model using labeled data may include: An active learning strategy is adopted, based on a hybrid criterion of uncertainty sampling and diversity sampling, to iteratively update the pre-trained GCN-DNN surrogate model until the model's performance on the validation set meets the preset requirements; Among them, diversity sampling calculates the similarity between samples based on the deep feature representation of the samples in the feature space, obtains the feature distance between samples based on the similarity, and selects a diversity sampling subset based on the feature distance; Uncertainty sampling calculates mutual information scores based on the predicted entropy of the samples and the expected entropy under the posterior distribution of the model parameters, and selects unlabeled samples based on the mutual information scores.

[0045] In one embodiment of this specification, the final sample set selected through active learning is represented by formula (17): (17); Similarity is expressed by formula (18): (18); The feature distance is expressed as formula (19): (19); The diversity sampling subset is represented by formula (20): (20); in, This is the final sample set selected through active learning; Represents a diversity sampling subset. Represents a subset of uncertain samples; For diversity sampling budget, Budget for uncertain sampling; This is the total sampling budget. For the sample and samples Similarity; These are unlabeled samples; For reference only; For the sample Deep feature representation; For the sample Deep feature representation; This is the bandwidth parameter, i.e., the Gaussian kernel width that controls the sensitivity of the kernel function. For the sample With sample Spatial feature distance; For diversity sampling subsets; A subset of candidate incremental samples; Unlabeled sample pool; This is the labeled sample pool.

[0046] In this embodiment, the diverse sampling subset selected from the unlabeled sample pool can maximize the coverage of the feature space of the unlabeled samples, effectively reducing the structural redundancy of the training samples.

[0047] In one embodiment of this specification, the uncertainty information of the sample is expressed as formula (21): (twenty one); Uncertainty sampling subsets are represented by formula (22): (twenty two); in, Representative sample x Uncertain information, Represents prediction entropy, which is characterized by the model's response to the output. y The total uncertainty is such that a larger entropy value indicates greater uncertainty in the prediction. Represents the expected posterior entropy, expressed as the value of the model's performance on a given set of labeled samples. Under these conditions, model parameters In the posterior distribution The following sample x The average prediction uncertainty. The difference between the two is mutual information. The larger the mutual information value, the greater the discrepancy in the model parameters' predictions of the sample, and the greater the benefit of labeling the sample. Formula (22) means that after removing the selected diversity samples from the unlabeled pool, the subset with the largest mutual information score is selected as the uncertain sample. This is a subset of candidate uncertain samples.

[0048] In this embodiment, the selected uncertain samples can minimize the uncertainty of model parameters, thereby achieving the greatest improvement in model performance with the least amount of manual annotation cost.

[0049] In some other embodiments of this specification, the hidden layer connection relationship of the deep neural network model is set to 64 / 128 / 1, and the loss function is L1 Loss; the number of layers of the graph convolutional network model is set to 2, the number of hidden layers is set to 16, the activation function is ReLU, and residual connections are introduced between the graph convolutional layers.

[0050] In summary, the present invention has the following advantages: I. Adaptive Explanation of Source Load Changes: According to the above formula (11), during the forward propagation process, all nodes in each layer share the same convolution kernel. Therefore, full graph sharing of parameters can be achieved, thereby enabling the model to adapt to changes in source loads.

[0051] II. Explanation of high generalization in small samples: By combining GCN layers with DNNs, this algorithm design significantly accelerates model training and achieves rapid convergence. Although the introduction of GCN layers increases the number of input learning parameters, the counterintuitive fact is that multi-layered GCNs iteratively integrate node domain information, explicitly incorporate strong inductive biases of the power grid topology, and employ smoothing regularization algorithms to limit the model's fluctuation range, making the model more stable. The following systematic proof is provided from three aspects: convergence speed, model training time, and generalization ability with limited data.

[0052] (1) Convergence rate: The proof regarding the model's convergence speed is as follows, denoted as [dataset name]. ,in , The target value is the model output. The model parameters are The diagram structure symbols are the same as those in formulas (8)-(10), and the empirical risk function is defined as formula (23): (twenty three); in, For empirical risk functions; The number of samples; The sample number; For the first One input sample; For the first The target value for each sample. ( ) represents the loss function.

[0053] When a graphical prior is introduced, the objective function becomes formula (24): (twenty four): in, To introduce the objective function after graph regularization; Output a vector consisting of all nodes. It is a PSD (positive semi-definite matrix). Let be the regularization coefficient. Therefore, the above formula is rewritten as formula (25): (25); in, For empirical loss function, it is the average loss between the model's predictions and the true values ​​on the training set; This is a regularization term, a penalty term for model complexity, used to constrain model parameters or output.

[0054] Therefore, the gradient of formula (24) and the Hessian can be approximated by formulas (26) and (27): (26); (27); in, The gradient of the objective function; Let be the Hessian matrix of the objective function; The gradient of the experience loss; The Hessian matrix representing the experience loss; The gradient of the regularization term; is the Hessian matrix for the regularization term.

[0055] remember about Jacobian matrix Approximately, we have formula (28): (28); Therefore, the Hessian can be written as formula (29): (29); in, It is a Jacobian matrix; The total Hessian matrix; The data item is the Hessian matrix; Represented as the Hessian contributed solely by formula (23), since L is a PSD, This improved the minimum eigenvalue of Hessian. This improves the condition number. In complex models such as DNN, It exhibits universal pathological characteristics, and has the smallest eigenvalue. Very close to 0, while the largest eigenvalue Since the condition number is relatively large, the addition of regularization will cause the overall condition number to decrease, as shown in the following formula (30): (30); Due to the function Satisfying the strong convexity and gradient Lipschitz continuity conditions in formulas (31) and (32): (31); (32); in, It is a strongly convex constant; It is the Lipschitz constant; Therefore, for gradient descent with a fixed step size (step size... When ), the iteration error satisfies formula (33): (33); in, For the first k The parameters for the next iteration; These are the initial values ​​for the model parameters at the start of training; is the Lipschitz constant; k is the number of iterations; To obtain an exact solution, the required precision must be achieved. Taking the logarithm of the above equation, we can obtain the number of iterations required, as shown in formula (34): (34); in, For the target accuracy; therefore, in When the value is large, formula (34) treats the numerator as a constant and the denominator as a constant, and the Taylor expansion can be transformed into formula (35): (35); The upper bound of the iteration can be approximated as: ,therefore A decrease in implies faster convergence.

[0056] In the frequency domain, graph convolution in GCN is equivalent to low-pass filtering, which makes the output smoother to local noise, thereby reducing the gradient variance in stochastic gradient descent. This allows for the use of a larger learning rate or a more stable descent path at the same learning rate, thus improving training speed in practice.

[0057] Rademacher complexity can be used to derive the probability bound of generalization error, that is, the performance of the algorithm on unseen test data. A smaller Rademacher complexity means that the model exhibits less fluctuation under random labels and has a stronger generalization ability. Rademacher complexity is defined by the following formula (36): (36); In the formula, Rademacher complexity; This represents a hypothesis class that contains all possible models. For expectation operators; Represented as training set Each sample The generated Rademacher variable has a value of either +1 or -1. `sup` indicates the function class... The operation of finding the supremum of all possible functions f represents finding the model that maximizes the performance under random labels within the hypothesis class. Graph constraint function class: Then the upper bound of the complexity is: (37); in, Empirical Rademacher complexity for constraint function classes. It is a constant. It is a constant. Represents the number of samples. The eigenvalue index; The eigenvalues ​​of the L-matrix represent the complexity of the graph structure; the larger the eigenvalue, the stronger the correlation between the graph nodes. For regularization parameters. The introduction of graph regularization leads to... Upper bound compared to DNN function classes without graph regularization Smaller, according to the generalization error formulas (38) and (38): (38); (39); in, This represents the generalization error of the unconstrained model. G represents the generalization error of the graph-constrained model; G is the generalization error, and Err is the training error. n The number of samples, subscript 0 It is represented as a DNN class, and the subscript s indicates the GCN+DNN structure. This represents the training error of the unconstrained model. The training error of the graph-constrained model; The time complexity is for functions without graph constraints; The complexity of the function class subject to graph constraints; This represents the number of training samples for the unconstrained model. This represents the number of training samples for the graph-constrained model. To achieve the same generalization error target... G The generalization error upper bound needs to be equal to G When complexity terms are equal, there must be a... n s <n Therefore, the number of samples required to achieve the same generalization error by introducing graph regularization is reduced. On the other hand, learning algorithms with smoothing regularization are generally more stable, thus providing better generalization bounds.

[0058] III. Analysis, Explanation, and Verification of the Consequences of Acceleration Deep learning algorithms can be trained offline and then reused online. They can directly infer results from the same input, making the whole process a linear one.

[0059] 3.1 Test Model and Data Generation This paper selects the IEEE-33 standard example as the experimental object. The SMCS method is used to sample a large number of scenarios, and the training set and validation set cover a variety of source and load scenarios, as detailed in the appendix.

[0060] To verify the superiority of the proposed GCN method, four experimental models were set up: M0: The traditional SMCS-based simulation method is used as a truth benchmark to measure the accuracy of the surrogate model.

[0061] M1: The AL-GCN method proposed in this paper serves as the core experimental object.

[0062] M2: A DNN method was used as a baseline for the Euclidean algorithm to verify the source-load adaptability of the proposed method.

[0063] M3: Contains only the GCN method, used to verify that the AL method proposed in this paper can reduce annotation.

[0064] The configuration of the above model algorithm is as follows: For the M1 method, all data are selected using AL, with 200 data points selected in each round for a total of 12 rounds.

[0065] Table 1 Proxy Model Parameter Configuration Table The input to the M2 method is the H matrix, which is expanded in one dimension except for the fault characterization column. The faulty line is directly represented as a 32-dimensional 0-1 feature.

[0066] Table 2 Algorithm Parameter Configuration Table All the models above are built on the PyTorch deep learning framework, and the hardware computing platform configuration is as follows: CPU: Intel Core i9-1300H; GPU: NVIDIA GeForce RTX-4060.

[0067] 3.2 Evaluation Indicators 1) Classification task: For the classification task of whether a fault will cause a load reduction, the accuracy and F1 score are used for evaluation as shown in formula (40) and formula (41): (40); (41); For accuracy; The F1 score represents the number of samples where the model correctly predicted unreliable power supply, TN represents the number of samples where the model correctly predicted reliable power supply, FP represents the number of samples where the model misclassified as reliable power supply, and FN represents the number of samples where the model misclassified as unreliable power supply. A higher accuracy rate indicates a more accurate overall assessment of power supply reliability by the model.

[0068] 2) Regression task: For the regression task of load reduction forecasting, the mean absolute error (MAE) and the coefficient of determination R2 are used for evaluation, as shown in the following formulas (42) and (43): (42); (43) In the formula, R² ranges from 0 to 1, and the closer it is to 1, the better the model fits the current data. This represents the true value of the load shearing amount; This is the predicted value of the load shearing amount.

[0069] 3.3 Algorithm Performance Analysis 1) Superior algorithm efficiency This section uses the M1-M3 model to compare and analyze the model performance under different sample input conditions, verifying that the proposed method can quickly obtain a high-performance surrogate model in a short time, meeting the requirements for rapid reliability assessment.

[0070] Table 3 Algorithm Performance Comparison Table As shown in Table 3, the proposed method achieves a goodness of fit of 98.85% by selecting 1000 high-information-density samples using the AL mechanism. It achieves the training results of traditional DNN algorithms with only 1 / 10 of the data volume, using lightweight annotation to achieve high generalization performance of the surrogate model and enabling rapid reliability assessment. Furthermore, based on the performance of M2 and M3 under the same sample in Table 3, GCN itself possesses a certain degree of high generalization ability with small samples.

[0071] Table 4 Comparison of Algorithm Sample Generation Time As shown in the table above, the GCN method can achieve a significant reduction in training time compared to DNN. Although the method in this paper does not have an advantage in training time, the extremely low number of training samples can save a lot of training resources and the time spent in the sample generation stage is extremely low, so the overall time consumption is advantageous.

[0072] 2) Reliability assessment accuracy analysis To verify that the proposed method can achieve reliability assessment, an IEEE-33 node network structure was designed as follows: Figure 3 As shown, this includes nodes 1 to 33. Nodes 4, 9, 15, 22, 26, and 33 are equipped with 0.5, 1, 1, 1, 0.5, and 1 MW of photovoltaic power, respectively. Nodes 7, 16, 24, and 29 are equipped with 1, 0.5, 0.5, and 1 MW of energy storage, respectively. The upper limit of the energy storage state is... 0.8, the initial charge is any decimal place between 0.5 and 1.

[0073] Simulation results are as follows Figure 4 and Figure 5 As shown, the method of this invention achieves excellent generalization ability with a small number of samples. The LOLP curve completely overlaps with the actual model, with an error rate of 0%, demonstrating high-precision classification ability. The EENS curves are basically consistent with the actual physical model method, and the EENS variance is less than 1e-2, exhibiting superior regression prediction performance.

[0074] 3) Efficiency analysis of reliability assessment In the state consequence analysis stage, the time consumption of the traditional SMCS method increases exponentially with the increase of sample size, as shown in Table 5 below. The method in this paper maintains linear growth throughout, with an efficiency improvement of more than 134 times, enabling rapid evaluation.

[0075] Table 5. Comparison of state consequence analysis time under different sample sizes The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units.

[0076] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A GCN method for rapid calculation of state consequences in distribution networks, characterized in that, include: Tag data for the distribution network is generated based on the sequential Monte Carlo simulation method; wherein, the tag data includes the operating status of the distribution network and the corresponding load shedding amount; Construct a GCN-DNN proxy model; wherein the GCN-DNN proxy model includes an upstream graph convolutional network model and a downstream deep neural network model; The GCN-DNN proxy model is trained using the labeled data to obtain a fast calculation model for state consequences; The operating status of the distribution network to be evaluated is input into the fast calculation model of the state consequences to obtain the predicted load shedding amount.

2. The GCN method for rapid calculation of state consequences in distribution networks according to claim 1, characterized in that, The tag data for the distribution network generated based on the sequential Monte Carlo simulation method includes: Establish a repairable forced failure model for components to describe the operational probability characteristics of components in the distribution network; Based on the repairable forced failure model, the system state is sampled using the state duration sampling method to obtain the operating state of the distribution network. Optimal load shedding calculations are performed on the operating state of the power distribution network to obtain the corresponding load shedding amount; Tag data is generated based on the operating status of the distribution network and the corresponding load shedding amount.

3. The GCN method for rapid calculation of state consequences in distribution networks according to claim 2, characterized in that, The trouble-free operating time of a component is expressed as: ； The fault repair time of a component is expressed as: ； The amount of load shearing is expressed as: ； in, Indicates the time between failures; Indicates the fault repair time; and All are random numbers distributed in the interval [0,1]. For the failure rate of components, The component repair rate; s In running state; Represents the moment t Specific operating state s The amount of load shedding generated by the system; For a moment t Running status s Next node Upper load resection value; For continuous variables, Represents state variables; and These are inequality constraints and equality constraints that describe the safe operation of the distribution network, respectively.

4. The GCN method for rapid calculation of state consequences in distribution networks according to claim 1, characterized in that, The graph convolutional network model models the distribution network topology as an undirected graph; wherein, the undirected graph has the distribution network nodes as the node set and the line connection relationships as the edge set; An adjacency matrix is ​​constructed based on the undirected graph to describe the physical connection relationships between nodes.

5. The GCN method for rapid calculation of state consequences in distribution networks according to claim 4, characterized in that, The graph convolutional network model calculates the degree matrix based on the adjacency matrix; Construct a symmetric normalized Laplace matrix based on the adjacency matrix and the degree matrix; Based on the Laplacian matrix, node information is updated through multi-layer graph convolution.

6. The GCN method for rapid calculation of state consequences in distribution networks according to claim 5, characterized in that, The elements of the adjacency matrix are represented as: ； in, These are elements of the adjacency matrix; Represents a node With nodes There are physical wiring connections between them; Let it be the set of edges; The degree matrix includes: ； ； The Laplace matrix includes: ； in, It is a degree matrix; , , , where are the degrees of node 1, node 2, and node n, respectively; n is the total number of nodes; The degree matrix after adding self-loops; For n The identity matrix of n; It is a Laplace matrix; It is an adjacency matrix; The update of node information is represented as follows: ； in, Representing the Layer node information; Representing the Layer node information; f( ) represents the activation function; It is the first Layer weight matrix.

7. The GCN method for rapid calculation of state consequences in distribution networks according to claim 1, characterized in that, The step of training the GCN-DNN proxy model using the labeled data includes: An active learning strategy is adopted, based on a hybrid criterion of uncertainty sampling and diversity sampling, to iteratively update the pre-trained GCN-DNN surrogate model until the model's performance on the validation set meets the preset requirements; The diversity sampling process calculates the similarity between samples based on the deep feature representation of the samples in the feature space, obtains the feature distance between samples based on the similarity, and selects a diversity sampling subset based on the feature distance. The uncertainty sampling is based on the mutual information score calculated by the entropy value of the sample prediction and the expected entropy value under the posterior distribution of the model parameters, and unlabeled samples are selected based on the mutual information score.

8. The GCN method for rapid calculation of state consequences in distribution networks according to claim 7, characterized in that, The final sample set selected through active learning is represented as follows: ； Similarity is expressed as: ； The feature distance is represented as: ； The diversity sampling subset is represented as: ； in, This is the final sample set selected through active learning; Represents a diversity sampling subset. Represents a subset of samples with uncertainties; For diversity sampling budget, Budget for uncertain sampling; Total sampling budget; For the sample and samples Similarity; These are unlabeled samples; For reference only; For the sample Deep feature representation; For the sample Deep feature representation; This is the bandwidth parameter, i.e., the Gaussian kernel width that controls the sensitivity of the kernel function; For the sample With sample Spatial feature distance; For diversity sampling subsets; A subset of candidate incremental samples; Unlabeled sample pool; This is the labeled sample pool.

9. The GCN method for rapid calculation of state consequences in distribution networks according to claim 8, characterized in that, The uncertainty information of the sample is represented as follows: ； Uncertainty sampling subset is represented as: ； in, Representative sample x Uncertain information, Represents prediction entropy, which is characterized by the model's response to the output. y Total uncertainty; Represents the expected posterior entropy, expressed as the value of the model's performance on a given set of labeled samples. Under these conditions, model parameters In the posterior distribution The following sample x The average forecast uncertainty; This is a subset of candidate uncertain samples.

10. The GCN method for rapid calculation of state consequences in distribution networks according to claim 1, characterized in that, Also includes: The probability of insufficient power supply and the annual expected insufficient power supply value are calculated based on the load shedding prediction results to achieve distribution network reliability assessment. The probability of insufficient power supply is expressed as: ； The expected annual power supply shortage value is expressed as: ； ； For load reduction scenario functions; Total system evaluation time; Indicates running status s The duration of the state; Represents the set of all system operating states during the total evaluation period; This represents the probability of insufficient power supply. Annual expected power supply shortage value.

Images