Reconstruction error and sensitivity analysis-based data-driven power flow model applicable boundary quantification method
By constructing a two-stage fully connected neural network model based on reconstruction error and sensitivity analysis, the accuracy degradation problem of data-driven power flow calculation models under distribution differences is solved, and the quantification and reliability assessment of the model's applicability boundary are realized, thereby improving the computational security and accuracy of the power system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-07
AI Technical Summary
Existing data-driven power flow calculation models may experience a sharp drop in accuracy when faced with distributional differences, making it impossible to accurately quantify the applicable boundaries of the model and resulting in unreliable output results.
A two-stage fully connected neural network model is constructed using a method based on reconstruction error and sensitivity analysis. By calculating the input reconstruction error and the output absolute error, a comprehensive loss function is established and the model is trained. Sensitivity analysis is then used to determine the reliability of the model's output features.
It achieves the quantification of the applicability boundary of the data-driven trend model, improves the safety and reliability of the model when facing samples with unknown distributions, can effectively identify and eliminate high-risk samples, and ensures computational accuracy.
Smart Images
Figure CN121809268A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power systems, and specifically relates to a method for quantizing the applicable boundary of a data-driven power flow model based on reconfiguration error and sensitivity analysis. Background Technology
[0002] With the large-scale grid connection of wind power, photovoltaics, and electric vehicles, the uncertainty of the power system has surged, necessitating high-frequency power flow calculations to assess the grid's operational status. Power flow calculation essentially involves solving high-dimensional nonlinear equations. High-frequency power flow calculations face the bottleneck of heavy computational burden. With the rapid development of artificial intelligence (AI) technology, data-driven methods offer a new approach to address this bottleneck: utilizing AI models to uncover the mapping relationship between power flow inputs and outputs, and directly mapping massive power flow calculation results through matrix operations during computation, avoiding iterative calculations. Currently, research has applied data-driven techniques to the field of power flow calculation, including support vector machines, radial basis function networks, fully connected neural networks, convolutional neural networks, and graph neural networks. Existing data-driven power flow calculation models generally suffer from the following problems in practical applications: the distribution of working samples inevitably differs from the distribution of training samples, potentially exceeding the generalization boundary of the AI model and leading to a sharp decline in computational accuracy. Using out-of-distribution detection methods to determine the applicability of data-driven models can avoid outputting unreliable results.
[0003] The core idea of reconstruction-based out-of-distribution detection methods is that data-driven models typically have high computational accuracy for in-distribution samples but low output accuracy for out-of-distribution samples. Therefore, the difference in reconstruction model performance can serve as an important indicator for discerning distribution differences. Methods for quantifying distribution differences based on reconstruction error are simple, intuitive, and highly adaptable; however, existing research has not yet established a mathematical relationship between reconstruction error and model output accuracy, making it impossible to accurately quantify the applicability boundaries of data-driven models.
[0004] In summary, there is an urgent need for a boundary quantization method for data-driven trend flow models to achieve boundary quantization between samples within and outside the distribution, which is of great significance for judging the reliability of model calculation results. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention proposes a data-driven power flow model applicability boundary quantification method based on reconstruction error and sensitivity analysis. This method includes:
[0006] S1: Obtain power data to construct the input feature vector for training;
[0007] S2: Input the input feature vector into the data-driven power flow calculation model for processing; the data-driven power flow calculation model includes a one-stage reconstruction model and a two-stage calculation model.
[0008] S3: Calculate the input reconstruction error and output absolute error based on the model processing results;
[0009] S4: Calculate the comprehensive loss function based on the input reconstruction error and the output absolute error, and train the data-driven power flow calculation model based on the comprehensive loss function;
[0010] S5: Input the input feature vector of the sample to be tested into the trained data-driven power flow calculation model, and calculate the sensitivity between the input reconstruction error and the output absolute error based on the model's weights and biases.
[0011] S6: Calculate the absolute output error of the test sample based on the sensitivity and the input reconstruction error of the test sample; determine the reliability of the model output features based on the absolute output error.
[0012] Preferably, the input feature vector and output feature vector are represented as follows:
[0013]
[0014] in, This represents the input feature vector. This indicates that active power is injected into node i. This indicates that reactive power is injected into node i.
[0015] Preferably, the process of calculating the input reconstruction error includes:
[0016] A one-stage reconstruction model is used to reconstruct the input feature vector to obtain the reconstructed input feature vector; the difference between the standardized reconstructed input feature vector and the original input feature vector is used as the input reconstruction error.
[0017] Preferably, the one-stage reconstruction model and the two-stage computation model constitute a two-stage fully connected neural model.
[0018] Furthermore, the process of calculating the absolute error of the output includes:
[0019] The reconstructed input feature vector is fed into the two-stage computation model for processing to obtain the output feature vector; the difference between the standardized output feature vector and the true value vector of the power flow sample is taken as the output absolute error.
[0020] Furthermore, the output feature vector is represented as:
[0021]
[0022] in, This represents the output feature vector. This represents the square of the voltage magnitude at node i. This represents the phase difference between the first and last nodes of line (i, j).
[0023] Preferably, the comprehensive loss function is expressed as follows:
[0024]
[0025] in, Indicates the overall loss. This represents the total number of training samples. This indicates the number of columns in the reconstruction error matrix. This indicates the number of columns in the absolute error matrix. Indicates the input reconstruction error. This indicates the output absolute error.
[0026] Preferably, the formula for calculating sensitivity is expressed as follows:
[0027]
[0028]
[0029] in, Indicates sensitivity. Indicates the input reconstruction error. This indicates the output absolute error. This represents the standardized output feature vector. This represents the standardized input feature vector. This represents the standardized reconstructed input feature vector; , This represents the weights and bias parameters of the first-stage reconstruction model; , This represents the weights and bias parameters of the two-stage computation model; This represents the functional mapping relationship between model weights and bias parameters.
[0030] Preferably, the process of judging the credibility of the model output features based on the output absolute error includes: judging whether the output absolute error is less than a preset absolute error threshold; if it is less, the credibility of the model output features is judged to be high; otherwise, the credibility of the model output features is judged to be low.
[0031] Furthermore, the preset absolute error threshold is set according to the allowable error range of the output parameters specified in the national standard.
[0032] The beneficial effects of this invention are as follows: Based on a fully connected neural network, this invention constructs a method for quantifying the applicability boundaries of power system data-driven power flow models through techniques such as reconstruction error and sensitivity analysis, avoiding unreliable output results. First, a two-stage network model combined sequential learning architecture is constructed to calculate the reconstruction error and absolute error separately. Then, based on the coupling relationship between the power flow input reconstruction error and the power flow output error, sensitivity analysis is used to quantify the boundaries of in-distribution and out-of-distribution samples. Compared with existing technologies, this invention can establish a data-driven model credibility evaluation mechanism based on physical mechanisms (sensitivity). By quantifying the sample applicability boundaries, high-risk samples that cause model failure can be effectively identified and eliminated when facing unknown samples with varying distributions, improving the safety and reliability of power system data-driven power flow calculations in practical applications. Attached Figure Description
[0033] Figure 1 This is a schematic diagram of the data-driven power flow trusted computing architecture based on reconstruction error in this invention;
[0034] Figure 2 The graph shows the trends of reconstruction error and absolute error changes with sample distribution differences in the test samples of the method of the present invention on the IEEE 118 system, as well as the trend of absolute error changes with reconstruction error.
[0035] Figure 3 This is a graph showing the trend of reconstruction error and absolute error of test samples of the IEEE118 system based on different models using the method of this invention. Detailed Implementation
[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0037] This invention proposes a boundary quantification method for data-driven power flow models based on reconstruction error and sensitivity analysis. The method includes the following:
[0038] like Figure 1 As shown, this invention constructs a data-driven power flow trusted computing architecture based on reconstruction error to realize boundary quantization of the data-driven power flow model. The implementation process of this architecture is as follows:
[0039] S1: Obtain power data to construct the input feature vector for training.
[0040] Acquire power data and construct an input feature vector for training based on the power data. This input feature vector is represented as follows:
[0041]
[0042] in, This represents the input feature vector. This indicates that active power is injected into node i. This indicates that reactive power is injected into node i.
[0043] To eliminate the influence of differences in the dimensions of the input and output variables of the power flow and to ensure the convergence of the training model, the samples are usually standardized using z-score.
[0044] S2: Input the input feature vector into the data-driven power flow calculation model for processing; the data-driven power flow calculation model includes a one-stage reconstruction model and a two-stage calculation model.
[0045] In the data-driven power flow calculation model, the transfer function expression for the input feature vector is:
[0046]
[0047] in, The input feature vector is the standardized form. The standardized reconstructed input feature vector; The standardized output feature vector; For the first Layer input; For the first The predicted output of the layer, The first t layers are the number of network layers from the input vector to the reconstructed vector, and the (t+1)th to nth layers are the number of network layers from the reconstructed vector to the output vector. , For the first Layer and First Weight matrices and offset vectors between neurons in a layer; For the activation function, this invention selects the PReLU function. A fully trained model architecture can directly map the power flow input feature vector to obtain the power flow output feature vector. Then, by performing inverse normalization on the output vector, easily observable power flow calculation results can be obtained. The model's output feature vector is represented as:
[0048]
[0049] in, This represents the output feature vector. This represents the square of the voltage magnitude at node i. This represents the phase difference between the first and last nodes of line (i, j).
[0050] The data-driven power flow computation model is composed of two fully connected neural models: "input feature vector - reconstructed input feature vector" and "reconstructed input feature vector - output feature vector", which are named the one-stage reconstruction model and the two-stage computation model, respectively.
[0051] S3: Calculate the input reconstruction error and output absolute error based on the model processing results.
[0052] The input reconstruction error and the output absolute error are obtained in the following way:
[0053] A one-stage reconstruction model is used to reconstruct the input feature vector, resulting in a reconstructed input feature vector. The difference between the standardized reconstructed input feature vector and the original input feature vector is used as the input reconstruction error. The reconstructed input feature vector is then fed into a two-stage computation model for processing, yielding an output feature vector. The difference between the standardized output feature vector and the true value vector of the power flow samples is used as the output absolute error.
[0054] Therefore, the input reconstruction error and the output absolute error are expressed as:
[0055]
[0056] in, Input reconstruction error; To output the absolute error; This is the standardized truth vector of the power flow samples. This represents the standardized original input feature vector. This represents the standardized output feature vector. This represents the standardized reconstructed input feature vector.
[0057] S4: Calculate the comprehensive loss function based on the input reconstruction error and the output absolute error, and train the data-driven power flow calculation model based on the comprehensive loss function.
[0058] The overall loss function is expressed as:
[0059]
[0060] in, Indicates the overall loss. This represents the total number of training samples, i.e., the number of rows in the error matrix; This indicates the number of columns in the reconstruction error matrix. This indicates the number of columns in the absolute error matrix. Indicates the input reconstruction error. This indicates the output absolute error.
[0061] By training a data-driven power flow calculation model by minimizing the comprehensive loss function, the coupling relationship between network reconstruction error and absolute error in the two stages was established, laying the model foundation for subsequent quantitative research on the applicable boundary of the computing architecture.
[0062] S5: Input the input feature vector of the sample to be tested into the trained data-driven power flow calculation model, and calculate the sensitivity between the input reconstruction error and the output absolute error based on the model's weights and biases.
[0063] Based on the established coupling relationship, a sensitivity analysis is conducted between the input reconstruction error and the output absolute error. The sensitivity between the input reconstruction error and the output absolute error is expressed as:
[0064]
[0065] In the formula, It characterizes the sensitivity of the computational architecture to the absolute output error and the input reconstruction error; This characterizes the rate of change between the reconstructed vector and the input vector in the one-stage reconstruction model. It represents the rate of change between the output vector and the input vector of the computing architecture.
[0066] The sensitivity between the input reconstruction error and the output absolute error can be calculated based on the model's weights and biases:
[0067]
[0068] in, , This represents the weights and bias parameters of the first-stage reconstruction model; , This represents the weights and bias parameters of the two-stage computation model; This represents the functional mapping relationship between model weights and bias parameters.
[0069] After the model training is completed, the weights and bias parameters of the model in the two stages are extracted, and the rate of change is calculated. and The values of these parameters are readily obtainable. Therefore, the expression for calculating sensitivity shows that the sensitivity between the input reconstruction error and the output absolute error exists as a mathematical analytical expression expressed by the architecture's own parameters. Introducing reconstruction error not only quantifies distributional differences but also allows for the direct analysis of the absolute error of new samples without ground truth label data when dealing with new input samples from unknown distributions, based on the sensitivity relationship.
[0070] Specifically, a deep neural network that meets a given computational accuracy requirement is obtained based on the training sample distribution. After training, the weights and biases of the model are constant, and its weights and bias parameters represent linearly with respect to input and output data that are identically or approximately distributed. From the above equation, it can be seen that the weights and biases of the model itself represent... , and The parameters will also exhibit approximately linear variation. Furthermore, when constructing the input-output eigenvectors in this invention, the selected power flow variables, after simplified derivation using the power flow equations in polar coordinates, also exhibit an approximately linear relationship as shown in the following equation.
[0071]
[0072] In the formula, P i Q i For the injected active and reactive power of node i; g ij b ij Indicates the conductance and susceptance of line (i, j); v i v j θ represents the voltage magnitude at nodes i and j; ij K represents the phase difference between the first and last nodes of line (i, j); i This represents the set of branches connected to node i.
[0073] As can be seen from the above formula, v 2 With θ ij Treated as independent variables, since for a given power system g ij b ij The parameters are constant, therefore the node-injected active power P i Reactive power Q i With the square of the node voltage magnitude v 2 Phase angle difference θ between each line ij The relationship between them is approximately linear.
[0074] Therefore, a well-trained deep neural network with input-output feature vectors constructed based on the aforementioned power flow variables exhibits input-output characteristics similar to linear power flow equations, and can be considered approximately linear when dealing with data distributed similarly to the training samples. However, limited by the network's generalization ability, the architecture's error may grow exponentially as the distribution differences of the input samples increase. Therefore, for distribution samples within the model's applicable boundaries, the architecture of this invention can obtain output results with expected absolute errors meeting accuracy requirements; for distribution samples exceeding the applicable boundaries, the architecture's output results will be unreliable and should be discarded as high-risk samples.
[0075] S6: Calculate the absolute output error of the test sample based on the sensitivity and the input reconstruction error of the test sample; determine the reliability of the model output features based on the absolute output error.
[0076] Based on the sensitivity and the input reconstruction error of the sample under test, the absolute output error of the sample under test can be calculated in reverse by substituting them into the sensitivity formula.
[0077] Since reconstruction error and sensitivity analysis cannot directly determine the applicability of a model, it is necessary to rely on manual experience to set an absolute error threshold to quantify the applicability boundary of the model, thereby determining whether the absolute error meets the given computational accuracy requirements and ensuring the reliability of the output results of the computational architecture. Specifically: it is determined whether the output absolute error is less than a preset absolute error threshold. If it is less, the reliability of the model's output features is considered high; otherwise, the reliability of the model's output features is considered low. The preset absolute error threshold can be set according to the allowable error range of output parameters specified in national standards.
[0078] In summary, by using a large number of test samples with known distribution variations as input to the model architecture, this invention can effectively grasp the input-output sensitivity relationship of the trained architecture when faced with different input sample distributions. This involves quantifying and pre-defining the applicable boundaries of the model. When the model is actually applied online, it is used with new input samples of unknown distribution, based on known... The magnitude of the reconstruction error between the parameters and the actual sample It is easy to obtain the absolute error between the output result and the actual power flow truth value by inverse solving. By comparing the model's applicable boundaries with the required computational accuracy, the reliability of the model's output results for new input samples can be quickly determined.
[0079] Simulation verification of the present invention:
[0080] 1. Data Analysis and Processing
[0081] This invention uses the IEEE 118-bus system for testing. Due to the complexity of power grid operation, this invention employs a power flow calculation model to generate simulated data. The optimization objective of the data-driven power flow model is to ensure the model's reliability under unknown sample conditions. It is assumed that the load curve follows a normal distribution, with the standard deviation set to 10% of the expected value. Then, multiple sets of out-of-distribution test samples with different mean values from the training sample distribution are generated through random sampling using a normal distribution. The mean value of each set of test samples varies stepwise according to a given growth rate. Both the obtained training and test samples are standardized and preprocessed, and the dataset is split. The model is then trained, using a fully connected neural network model. The dimensions of the input and output feature vectors correspond to the number of nodes and branches in the node system, and each hidden layer has 200 neurons. For the trained data-driven power flow reliable calculation architecture, the power flow calculation performance is tested using identically distributed test samples, and the sensitivity relationship between reconstruction error and absolute error is analyzed using out-of-distribution test samples. Figure 2 As shown, the trends of the reconstruction error and absolute error of the test sample with the sample distribution difference are obtained, as well as the trend of the absolute error with the reconstruction error.
[0082] 2. Model and indicator settings
[0083] To verify the correctness of the theoretical analysis of the proposed method and the applicability of the trusted computing framework to common models, the relationship between reconstruction error and absolute error of in-distribution and out-of-distribution test samples in simulation experiments was analyzed. For the IEEE 118 system, ridge regression, radial basis function (RBF), convolutional neural network (CNN), and fully connected neural network (DNN) models were selected to construct the computational architecture. The comparison results of the changing trends of reconstruction error and absolute error of the test samples are shown below. Figure 3 As shown.
[0084] Simulation comparisons show that although the magnitudes of errors vary depending on the chosen model used to construct the proposed computational architecture, similar trends in reconstruction error and absolute error are consistently observed. Simulation results verify the applicability of the proposed architecture to different types of network models. Among these, the computational architecture based on a fully connected deep neural network exhibits the smallest reconstruction error (within the range of 0-6) and the smallest absolute error (within the range of 0-35), demonstrating the best performance. This is because, compared to other types of networks, DNN networks, composed of multiple layers of stacked neurons, possess strong nonlinear feature extraction capabilities, giving them an advantage in mining power flow data features from power systems.
[0085] 3. Validation of the method effectiveness
[0086] To illustrate the effectiveness of the proposed method in quantifying the applicable boundaries of in-distribution and out-of-distribution samples under a data-driven flow model, 20,000 identically distributed samples with the same mean were generated, including 10,000 training samples and 10,000 test samples. Nine groups of out-of-distribution test samples following a normal distribution were generated with a growth rate of 3% of the distribution mean, each group containing 2,000 samples, for a total of 38,000 samples.
[0087] The table below compares the performance of the reconstruction-based detection method proposed in this invention with several other out-of-distribution detection methods. It is worth noting that the backbone network structures, data processing methods, and detection principles used by various out-of-distribution detection methods are not entirely the same. Therefore, the analysis in this invention only compares the detection metrics of different detection methods on the same power flow dataset.
[0088] Table 1 Test Performance Comparison Table
[0089]
[0090] This invention selects three of the most commonly used evaluation metrics for out-of-distribution detection: AUROC, AUPR, and FPR95. The performance of the error-based method presented in this invention is compared with that of the classification-based ODIN method, the density-based KDE method, and the distance-based RMD method. As shown in the table, the AUROC and AUPR metrics of the proposed method are very close to 1, indicating that for power flow datasets, the architecture constructed by this invention has a very low probability of misidentification when identifying out-of-distribution samples, significantly outperforming other methods. The FPR95 metric represents the probability of a normal sample being misclassified as an out-of-distribution sample when more than 95% of out-of-distribution samples are identified. The comparison of the data in the table also shows that this invention, by introducing reconstruction error, has a very low probability of misclassifying in-distribution samples. Therefore, in a data-driven power flow computation reliability architecture, the reconstruction-based method adopted in this invention performs better in identifying sample distribution categories, providing a good foundation for quantifying the applicability boundaries of the model. The effectiveness of the proposed method is verified in experiments using data from the IEEE 118-node system. The trained data-driven power flow model with applicable boundary quantization method can be applied to high-dimensional complex power grid systems. For new samples with unknown distributions caused by uncertainties such as the access of new energy sources, the model can also provide reliable results of the power grid voltage state, providing a reference for relevant personnel before taking protective measures.
[0091] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A boundary quantization method for data-driven power flow models based on reconstruction error and sensitivity analysis, characterized in that, include: S1: Obtain power data to construct the input feature vector for training; S2: Input the input feature vector into the data-driven power flow calculation model for processing; the data-driven power flow calculation model includes a one-stage reconstruction model and a two-stage calculation model. S3: Calculate the input reconstruction error and output absolute error based on the model processing results; S4: Calculate the comprehensive loss function based on the input reconstruction error and the output absolute error, and train the data-driven power flow calculation model based on the comprehensive loss function; S5: Input the input feature vector of the sample to be tested into the trained data-driven power flow calculation model, and calculate the sensitivity between the input reconstruction error and the output absolute error based on the model's weights and biases. S6: Calculate the absolute output error of the test sample based on the sensitivity and the input reconstruction error of the test sample; determine the reliability of the model output features based on the absolute output error.
2. The data-driven power flow model applicability boundary quantization method based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The input feature vector and the output feature vector are represented as follows: ； in, This represents the input feature vector. This indicates that active power is injected into node i. This indicates that reactive power is injected into node i.
3. The data-driven power flow model applicability boundary quantization method based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The one-stage reconstruction model and the two-stage computation model constitute a two-stage fully connected neural model.
4. The boundary quantization method for a data-driven power flow model based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The process of calculating the input reconstruction error includes: A one-stage reconstruction model is used to reconstruct the input feature vector to obtain the reconstructed input feature vector; the difference between the standardized reconstructed input feature vector and the original input feature vector is used as the input reconstruction error.
5. The boundary quantization method for a data-driven power flow model based on reconstruction error and sensitivity analysis according to claim 4, characterized in that, The process of calculating the absolute error of the output includes: The reconstructed input feature vector is fed into the two-stage computation model for processing to obtain the output feature vector; the difference between the standardized output feature vector and the true value vector of the power flow sample is taken as the output absolute error.
6. The boundary quantization method for a data-driven power flow model based on reconstruction error and sensitivity analysis according to claim 5, characterized in that, The output feature vector is represented as: ； in, This represents the output feature vector. This represents the square of the voltage magnitude at node i. This represents the phase difference between the first and last nodes of line (i, j).
7. The data-driven power flow model applicability boundary quantization method based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The comprehensive loss function is expressed as follows: ； in, Indicates the overall loss. This represents the total number of training samples. This indicates the number of columns in the reconstruction error matrix. This indicates the number of columns in the absolute error matrix. Indicates the input reconstruction error. This indicates the output absolute error.
8. The data-driven power flow model applicability boundary quantization method based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The formula for calculating sensitivity is expressed as: ； ； in, Indicates sensitivity. Indicates the input reconstruction error. This indicates the output absolute error. This represents the standardized output feature vector. This represents the standardized input feature vector. This represents the standardized reconstructed input feature vector; , This represents the weights and bias parameters of the first-stage reconstruction model; , This represents the weights and bias parameters of the two-stage computation model; This represents the functional mapping relationship between model weights and bias parameters.
9. The boundary quantization method for a data-driven power flow model based on reconstruction error and sensitivity analysis according to claim 1, characterized in that, The process of judging the credibility of the model output features based on the output absolute error includes: judging whether the output absolute error is less than the preset absolute error threshold. If it is less, the credibility of the model output features is judged to be high; otherwise, the credibility of the model output features is judged to be low.
10. The data-driven power flow model applicability boundary quantization method based on reconstruction error and sensitivity analysis according to claim 9, characterized in that, The preset absolute error threshold is set according to the allowable error range of the output parameters specified in the national standard.