Prediction-Assisted State Estimation Method Based on Spatio-Temporal Graph Convolutional Neural Network

Abstract

The present invention relates to a prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network. A frequency-domain convolution method based on graph Fourier transform is adopted to construct a multi-layer graph convolutional neural network model for ultra-short-term state prediction of a power system, and the latest state of the system is accurately predicted when the power system is in a quasi-steady state. The present invention effectively improves the accuracy of state estimation and the reliability of data.

Description

Technical Field

[0001] The present invention relates to the technical field of power system dispatching automation, and particularly relates to a prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network. Background Art

[0002] State estimation is the most important method for real-time monitoring of a power system, and is one of the core functions of the Energy Management System (EMS) of a power grid dispatching control center, and is the data source for other network analysis applications, online security and stability analysis, etc. With the large-scale access of new energy and the widespread application of high-power power electronic devices, the randomness and volatility of modern power systems have been greatly enhanced, and the operation modes and dynamic characteristics of the power grid have become more and more complex and changeable. Traditional state estimation systems based on SCADA are difficult to meet the requirements of modern power grids for quickly and accurately obtaining states in terms of estimation accuracy, real-time performance, and calculation stability. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network to realize ultra-short-term state prediction of a power system and accurately predict the latest state of the system when the power system is in a quasi-steady state.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions:

[0005] A prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network, comprising the following steps:

[0006] Step S1: Construct a GCN network, train it based on historical power grid state data and network parameters, and initialize FASE using the WLS static state estimation method;

[0007] Step S2: Input the consecutive state estimation results before the current moment into the trained GCN network to obtain state prediction values;

[0008] Step S3: Calculate the standard innovation value based on the obtained state prediction values;

[0009] Step S4: Determine whether the maximum standard innovation value is greater than the threshold. If it is greater than the threshold, go to the next step; otherwise, it means that no bad data and system state mutations are detected, and directly go to step S7;

[0010] Step S5: Determine whether the innovation of the area is greater than the threshold: If so, it means that a mutation in the state of the power grid is detected and prediction-assisted state estimation cannot be used, and go to step S8; otherwise, it means that only suspicious measurements have occurred, and go to the next step;

[0011] Step S6: Replace the suspected bad data with the predicted value of the usage status to form a new measurement set;

[0012] Step S7: Perform state filtering to obtain the predicted auxiliary state estimation value, save the estimation result, and return to Step S2;

[0013] Step S8: Perform static state estimation calculation based on least squares in the complex domain, and save the estimation result.

[0014] Furthermore, the state estimation is performed using the WLS static state estimation method, specifically:

[0015] x k = x k-1 + w k

[0016]

[0017] where is the system state value at the previous moment of the system,, is the predicted value at the upcoming moment, z k is the measurement value at the latest moment, is the state estimation value at the latest moment, w k is the process noise that conforms to the normal distribution, respectively represent the state estimation values using the WLS and KF methods.

[0018] Furthermore, Step S2 is specifically:

[0019] Θ* G x = Θ(L)x = Θ(UΛU T )x = UΘ(Λ)U T x

[0020] In the formula, the operator symbol of the graph frequency domain convolution operation of the convolution kernel Θ and the graph data x is denoted as * G ; L is the Laplacian matrix of the graph, is the basis of the Fourier transform, and it is the matrix composed of the eigenvectors {u i} of L; L is a symmetric matrix, and Λ is the diagonal matrix composed of the eigenvalues {λ i} of L;

[0021] L = I n - D -1 / 2 WD -1 / 2 = UΛU T

[0022] U = (u 1 , u 2 , …, u n )

[0023]

[0024] In the formula, I n is the identity matrix, D is the degree matrix, which is a diagonal matrix, and each diagonal element of the matrix is the degree of the graph node. W is the weighted adjacency matrix of the graph;

[0025] T k (x) = 2xT k-1 (x) - T k-2 (x)

[0026] In the formula, T k represents that the Chebyshev polynomial is a series of orthogonal polynomial sequences defined recursively.

[0027]

[0028]

[0029] In the formula, θ k is the coefficient of the polynomial, K is the size of the convolution kernel, and the tilde on the matrix superscript represents normalization. It is the graph convolution calculation formula approximated by the Chebyshev polynomial

[0030]

[0031] The input and output of each spatio-temporal graph convolution module are both three-dimensional tensors. Let be the input of the l-th spatio-temporal graph convolution module; where are the convolution kernels of the upper and lower gated convolution network layers of the spatio-temporal graph convolution module respectively. Θ l is the spectral convolution kernel of frequency convolution, and ReLU is the commonly used rectified linear unit in neural networks, that is, the ramp function;

[0032] After obtaining the output through the spatio-temporal graph convolution module, it finally outputs the result through a temporal convolution layer and a fully connected layer; the last gated convolution layer is used to finally map the output of the last spatio-temporal graph convolution module to a single-step prediction value; obtain the final output Z from the entire deep learning neural network, and apply a linear transformation to the results on each channel to perform inverse normalization calculation to obtain the state prediction values of all nodes, where w is the weight vector and b is the bias

[0033]

[0034] In the formula, θ are all trainable parameters in the model; represents the state prediction value, x t+1 is the historical state estimation value.

[0035] Further, the specific steps of step S3 are as follows:

[0036] Covariance matrix of innovation:

[0037]

[0038]

[0039]

[0040] In the formula, v k+1 is the difference between the measurement value and the state prediction, that is, the innovation; is the measurement prediction value calculated according to the state prediction value; z k+1 is the measurement value, N k+1 , M k+1 , R k+1 are the innovation covariance matrix, the measurement covariance matrix, and the measurement error matrix.

[0041] Normalized innovation:

[0042]

[0043]

[0044] In the formula, it is assumed that the innovation load is a Gaussian distribution with zero mean.

[0045] Further, the specific steps of step S7 are as follows:

[0046] Step S71: Perform state filtering to obtain the predicted auxiliary state estimate value:

[0047]

[0048] In the formula, M is the covariance matrix of the predicted value. When the objective function is minimized, there is

[0049]

[0050] Let Substitute it into the above formula to solve, and the state estimate value at the latest moment can be obtained as shown in the following formula

[0051]

[0052] The above formula is further summarized in a recursive form. When the state prediction at the k + 1 moment and the measurement value z k+1 are obtained, the calculation method of the system state value is as shown in the following formula

[0053]

[0054]

[0055]

[0056] where K k+1 is the filtering gain matrix, and Σ k+1 is the estimated covariance matrix;

[0057] Using the measured value and the predicted value, a new state estimate value is obtained, and at the same time, the filtering gain matrix is updated

[0058] The covariance matrix of the predicted value is given by the following formula according to the Kalman filtering method

[0059]

[0060] Among them, the parameters F and G are obtained through online estimation using the parameter estimation method to complete the update of the covariance matrix of the predicted value.

[0061] The present invention has the following beneficial effects compared with the prior art:

[0062] The present invention obtains the spatio-temporal information characteristics of the power grid contained in a large amount of PMU measurement values through the GCN network, and applies them to the power system state prediction. And through the comprehensive analysis of the innovation of the predicted value, the possible bad data in the measurement value can be excluded, and the occurrence of the system state mutation can be identified, so as to complete the linear state estimation and improve the accuracy of the state estimation and the reliability of the data. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is the flowchart of the method of the present invention;

[0064] Figure 2 is the estimated value diagram of the amplitude and phase angle of the Beijiao Station obtained by the state estimation method assisted by GCN prediction in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0065] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] Please refer to Figure 1 , the present invention provides a prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network, including the following steps:

[0067] Step S1: Construct a GCN network, train it based on historical power grid state data and network parameters, and initialize the FASE using the WLS static state estimation method;

[0068] Step S2: Input the continuous state estimation results before the current moment into the trained GCN network to obtain state prediction values;

[0069] Step S3: Calculate the standard innovation value based on the obtained state prediction value;

[0070] Step S4: Determine whether the maximum standard innovation value is greater than the threshold. If it is greater than the threshold, proceed to the next step; otherwise, it indicates that no bad data or system state mutation is detected, and directly go to Step S7;

[0071] Step S5: Determine whether the innovation of the area is greater than the threshold: If so, it indicates that a mutation in the power grid state is detected, and predictive-aided state estimation cannot be used. Go to Step S8; otherwise, it indicates that only suspicious measurements have occurred, and proceed to the next step;

[0072] Step S6: Replace the suspicious bad data with the state prediction value to form a new measurement set;

[0073] Step S7: Perform state filtering to obtain the predictive-aided state estimation value, save the estimation result, and return to Step S2;

[0074] Step S8: Perform static state estimation calculation based on least squares in the complex domain, and save the estimation result.

[0075] In this embodiment, preferably, the WLS static state estimation method is used for state estimation, which is specifically as follows:

[0076] x k = x k-1 + w k

[0077]

[0078] State prediction refers to using the system state value at the previous moment of the system (possibly also using the state values at earlier moments), and using a suitable state prediction method to predict the state value at the upcoming moment When the measurement value z at the latest moment k arrives, and the already obtained predicted value are jointly filtered to obtain the state estimation value at the latest moment where w k is the process noise that conforms to the normal distribution.

[0079] In this embodiment, preferably, the GCN state prediction based on spatio-temporal information fusion is specifically as follows:

[0080] Θ* G x = Θ(L)x = Θ(UΛU T )x = UΘ(Λ)U T x

[0081] In the formula, the operator symbol of the graph frequency domain convolution operation of the convolution kernel Θ and the graph data x is denoted as * G ; L is the Laplacian matrix of the graph, is the basis of the Fourier transform, which is a matrix composed of the eigenvectors {u i} of L. The Laplacian matrix of the graph is actually the degree matrix of the graph minus the adjacency matrix, so L is a symmetric matrix, and Λ is a diagonal matrix composed of the eigenvalues {λ i} of L.

[0082] L = I n - D -1 / 2 W D -1 / 2 = U Λ U T

[0083] U = (u 1 , u 2 , …, u n )

[0084]

[0085] In the formula, I n is the identity matrix, D is the degree matrix, which is a diagonal matrix, and each diagonal element of the matrix is the degree of the graph node. W is the weighted adjacency matrix of the graph.

[0086] T k (x) = 2 xT k-1 (x) - T k-2 (x)

[0087] In the formula, T k represents that the Chebyshev polynomial is a series of orthogonal polynomial sequences defined recursively.

[0088]

[0089]

[0090] In the formula, θ k is the coefficient of the polynomial, K is the size of the convolution kernel, and the tilde on the matrix superscript represents normalization. It is the graph convolution calculation formula approximated by the Chebyshev polynomial.

[0091]

[0092] The input and output of each spatio-temporal graph convolution module are both three-dimensional tensors. Let be the input of the l-th spatio-temporal graph convolution module. Among them are the convolution kernels of the upper and lower gated convolution network layers of the spatio-temporal graph convolution module respectively, and Θ lis the spectral convolution kernel of frequency convolution, and ReLU (Rectified Linear Unit) is a commonly used rectified linear unit in neural networks, that is, a ramp function.

[0093] After obtaining the output through multiple spatio-temporal graph convolution modules, the final output result is obtained through a temporal convolution layer and a fully connected layer. The final gated convolution layer is used to finally map the output of the last spatio-temporal graph convolution module to a single-step prediction value. Finally, the final output Z can be obtained from the entire deep learning neural network, and a linear transformation is applied to the results on each channel Inverse normalization calculation is performed to obtain the state prediction values of all nodes, where w is the weight vector and b is the bias.

[0094]

[0095] In the formula, θ are all trainable parameters in the model; represents the state prediction value, and x t+1 is the historical state estimation value.

[0096] Preferably, in this embodiment, the step S3 is specifically:

[0097] 1) Covariance matrix of innovation:

[0098]

[0099]

[0100]

[0101] In the formula, v k+1 is the difference between the measurement value and the state prediction, that is, innovation; is the measurement prediction value calculated according to the state prediction value.

[0102] 2) Normalized innovation:

[0103]

[0104]

[0105] In the formula, it is reasonably assumed that the innovation load is a Gaussian distribution with zero mean.

[0106] Preferably, in this embodiment, the step S7 is specifically:

[0107] 1) Perform state filtering to obtain the predicted auxiliary state estimation value:

[0108]

[0109] Where M is the covariance matrix of the predicted values, and when the objective function is minimized, there is

[0110]

[0111] Let Substitute it into the above formula to solve, and the state estimation value at the latest moment can be obtained, as shown in the following formula

[0112]

[0113] The above is the direct solution method of the estimated value, which does not require iterative calculation and has high computational stability and performance. The above formula can be further summarized in a recursive form. When the state prediction at time k + 1 and the measurement value z k+1 are obtained, the calculation method of the system state value is shown in the following formula

[0114]

[0115]

[0116]

[0117] where K k+1 is the filtering gain matrix, and Σ k+1 is the estimated covariance matrix. Using the measurement value and the predicted value, a new state estimation value is obtained, and at the same time, the filtering gain matrix is updated.

[0118] And the covariance matrix of the predicted values can be given by the following formula according to the Kalman filtering method

[0119]

[0120] The parameters F and G can be obtained through online estimation using the parameter estimation method to complete the update of the covariance matrix of the predicted values.

[0121] Example 1:

[0122] In this example, the widely used TensorFlow deep learning platform is adopted to implement the proposed power system prediction method based on the graph convolutional deep neural network, and its modeling and solution process is shown in Figure 1 as shown.

[0123] In order to further verify the effectiveness and accuracy of the prediction-assisted state estimation method on an actual large-scale power grid, the measured load data of China Southern Power Grid is used to conduct a simulation verification of the prediction-assisted state estimation algorithm in the case of the 500 kV transmission grid in Guangdong, China Southern Power Grid.

[0124] Similarly, first, power system state prediction based on the GCN method is performed, and the prediction results are compared with those of the VAR method and the Holt method. The voltage amplitude prediction results are shown in Table 1, and the phase angle prediction results are shown in Table 2.

[0125] Table 1 Simulation amplitude prediction results of state prediction for the Guangdong power grid case

[0126]

[0127] Table 2 Simulation phase angle prediction results of state prediction for the Guangdong power grid case

[0128]

[0129] As can be seen from the table, the state prediction method based on GCN is more accurate than the prediction results of the Holt two-parameter exponential smoothing method and the VAR method, and has a significant advantage in the prediction accuracy of the phase angle. At the same time, due to the acceleration strategy used in designing the GCN network, although the training process is relatively slow due to the large scale of the data used, only polynomial calculations are involved when using the neural network, and thanks to the use of GPUs and the rapid improvement of the existing neural network calculation efficiency, the calculation efficiency of the GCN state prediction proposed in this paper also reaches a relatively high level. In the embodiment of the present invention, the average calculation time for a single GCN state prediction is 4.68 ms, which can meet the requirements of wide-area real-time state perception.

[0130] After obtaining the system state prediction value, prediction-assisted state estimation is performed according to the proposed algorithm. The relevant indicators of the system state estimation results are summarized in Table 3.

[0131] Table 3 Comparison of prediction-assisted state estimation results

[0132]

[0133] In the embodiment of the present invention, the state estimation method based on GCN prediction assistance achieves better estimation results than other prediction-assisted state estimation methods and static state estimation methods. The estimated values of the amplitude and phase angle of the Beijiao substation are selected and plotted as Figure 2 shown.

[0134] For large-scale actual power grid simulation cases, as can be seen from the above tables and figures, state awareness based on GCN prediction assistance also achieves significantly better state estimation results than other prediction-assisted state estimation methods. At the same time, the estimation accuracy TVE is more than 50% higher than that of the least squares-based static state estimation method. From the estimated values of the phase angles, it can also be seen that the GCN prediction-assisted state estimation can also obtain good estimation results for the occurrence of small disturbances. Generally speaking, the prediction-assisted state estimation based on GCN can greatly reduce the error of PMU measurement values and accurately obtain the real-time state of the power grid.

[0135] The above are only the preferred embodiments of the present invention, and all equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope of the present invention.

Claims

1. A prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network, characterized in that, it includes the following steps: Step S1: Construct a GCN network, train it based on historical power grid state data and network parameters, and initialize the FASE using the WLS static state estimation method; Step S2: Input the consecutive state estimation results before the current moment into the trained GCN network to obtain state prediction values; Step S3: Calculate the standard innovation value based on the obtained state prediction values; Step S4: Determine whether the maximum standard innovation value is greater than the threshold. If it is greater than the threshold, go to the next step; otherwise, it means that no bad data and system state mutations are detected, and directly go to Step S7; Step S5: Determine whether the innovation of the region is greater than the threshold: If so, it means that a mutation in the state of the power grid is detected, and prediction-assisted state estimation cannot be used. Go to Step S8. Otherwise, it means that only suspicious measurements have occurred, and go to the next step; Step S6: Replace the suspicious bad data with the state prediction value to form a new measurement set; Step S7: Perform state filtering to obtain the prediction-assisted state estimation value, save the estimation result, and return to Step S2; Step S8: Perform static state estimation calculation based on complex-domain least squares, and save the estimation result; The specific content of Step S2 is: In the formula, the operator symbol of the graph frequency domain convolution operation of the convolution kernel Θ and the graph data x is denoted as L is the Laplacian matrix of the graph, is the basis of the Fourier transform, and it is the matrix composed of the eigenvectors {u i} of L; L is a symmetric matrix, and Λ is a diagonal matrix composed of the eigenvalues {λ i} of L; L = I n -D -1 / 2 WD -1 / 2 = UΛU T U = (u 1 , u 2 , …, u n ) where I n is the identity matrix, D is the degree matrix, which is a diagonal matrix, and each diagonal element of the matrix is the degree of the graph node, and W is the weighted adjacency matrix of the graph; T k T(x) = 2xT k-1 T(x) - T k-2 T(x) where, T k represents a series of orthogonal polynomial sequences defined recursively as Chebyshev polynomials; where θ k is the coefficient of the polynomial, K is the size of the convolution kernel, and the tilde on the matrix superscript represents normalization. It is the graph convolution calculation formula approximated by the Chebyshev polynomial The input and output of each spatio-temporal graph convolution module are both three-dimensional tensors. Let be the input of the \(l\)-th spatio-temporal graph convolution module; where are the convolutional kernels of the upper and lower gated convolution network layers of the spatio-temporal graph convolution module respectively, and \(\Theta\) l is the spectral convolutional kernel of frequency convolution, and ReLU is the commonly used rectified linear unit in neural networks, that is, the ramp function; After obtaining the output through the spatio-temporal graph convolution module, the final output result is obtained through a temporal convolution layer and a fully connected layer; the final gated convolution layer is used to finally map the output of the last spatio-temporal graph convolution module to a single-step prediction value; the final output Z is obtained from the entire deep learning neural network, and a linear transformation is applied to the results on each channel Inverse normalization calculation is performed to obtain the state prediction values of all nodes, where w is the weight vector and b is the bias where θ represents all the trainable parameters in the model; x represents the predicted state value, and x t+1 is the estimated historical state value.

2. The prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network according to claim 1, characterized in that, the WLS static state estimation method is used for state estimation, specifically: x k = x k-1 + w k Among them, is the state estimation value at the latest moment, and w k is the process noise conforming to the normal distribution.

3. The prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network according to claim 1, characterized in that, the specific content of Step S3 is: Covariance matrix of the innovation: where, v k+1 is the difference between the measured value and the state prediction, i.e., the innovation; is the predicted measurement value calculated based on the state prediction value; Normalized innovation: In the formula, it is assumed that the innovation load is a Gaussian distribution with zero mean.

4. The prediction-assisted state estimation method based on a spatio-temporal graph convolutional neural network according to claim 1, characterized in that, the specific content of Step S7 is: Step S71: Perform state filtering to obtain the prediction-assisted state estimation value: In the formula, M is the covariance matrix of the prediction value. When the objective function is minimized, there is Let Substitute into the above formula to solve, and the state estimation value at the latest moment can be obtained as shown in the following formula The above equation is summarized in a recursive form. When the state prediction at time k+1 is obtained and the measurement value z k+1 are obtained, the calculation method of the system state value is shown as follows where K k+1 is the filtering gain matrix, and Σ k+1 is the estimated covariance matrix; Using the measurement value and the prediction value, a new state estimation value is obtained, and at the same time, the filtering gain matrix is updated The covariance matrix of the prediction value is given by the following formula according to the Kalman filtering method Among them, the parameters F and G are obtained through online estimation using the parameter estimation method to complete the update of the covariance matrix of the prediction value.

Images