A power distribution network measurement data driven voltage sensitivity fitting method and system

Abstract

The application discloses a kind of distribution network measurement data driven voltage sensitivity fitting method and system, the method is first based on the injection power of certain operating state distribution network node, has measurement voltage and neighborhood characteristics to construct node input feature matrix, and input to variational autoencoder model, estimate the voltage of all network nodes;Subsequently, around the operating state, construct multiple groups of small power reference disturbance samples, and again utilize the model to generate corresponding voltage response;Finally, the power difference and voltage difference between each disturbance sample and reference state are calculated, to construct overdetermined equation group, least square method is used to fit voltage sensitivity matrix, and the fitting result is averaged to improve the estimation accuracy.The application can still achieve high-precision voltage estimation and voltage sensitivity fitting under the condition of lacking topological structure and line parameters, and sparse voltage measurement, and is suitable for state estimation, voltage management and operation optimization tasks in typical distribution network scenarios such as sparse voltage measurement and incomplete topological information.

Description

Technical Field

[0001] This invention relates to voltage sensitivity fitting technology, and in particular to a voltage sensitivity fitting method and system driven by distribution network measurement data. Background Technology

[0002] According to statistics from the National Energy Administration, my country's newly installed distributed photovoltaic (PV) capacity reached 118.18 million kilowatts in 2024, bringing the total installed capacity to 372 million kilowatts. More than 90% of this distributed PV capacity was connected to medium- and low-voltage distribution networks, accounting for 44% of the total installed PV capacity. This high proportion of distributed PV, especially in medium- and low-voltage distribution networks, has significantly altered the power flow distribution and voltage characteristics of traditional distribution networks. Under high penetration conditions, the supply-demand imbalance between power sources and loads has become increasingly prominent. Voltage overruns caused by power backfeeding have become a core challenge in the operation of medium- and low-voltage distribution networks, seriously threatening their safe and reliable operation.

[0003] To address the challenges of voltage management, voltage sensitivity analysis has been widely studied due to its efficiency and practicality. It can be used to identify voltage-dominant nodes, optimize the allocation of control resources, and provide a theoretical basis for reactive power compensation and distributed generation regulation. However, the calculation of voltage sensitivity usually relies on a complete physical power flow model. In practical applications, especially in rural distribution networks, traditional model methods are difficult to apply due to limitations such as unclear topology, missing line parameters, and insufficient deployment of voltage measurement equipment.

[0004] To overcome the aforementioned problems, some researchers have attempted to fit voltage sensitivity matrices using a data-driven approach, even when topological and parameter information is lacking and voltage measurement data for some nodes is incomplete. While this type of method possesses some fitting capability, it still faces the following technical bottlenecks in practical deployment:

[0005] 1) Insufficient feature representation ability: Traditional methods use node-level P / Q / U raw data as model input, ignoring the state, structural information and observability factors of neighboring nodes, which limits the generalization performance of the model;

[0006] 2) Inadequate handling of missing data: There is a lack of effective missing measurement modeling mechanism, and placeholder or masking operations are often used, which can easily lead to training bias and misleading inference;

[0007] 3) Sample construction does not fit the actual deployment scenario: The model is usually trained under the assumption of full measurement, which fails to take into account the dynamic changes of non-uniform measurement configuration in the real distribution network, resulting in unstable estimation accuracy of key nodes.

[0008] Therefore, there is an urgent need for a new voltage sensitivity estimation method that can take into account both node characteristic structure modeling and adapt to real measurement deployment conditions, so as to provide more accurate technical support for the operation optimization and voltage management of distribution networks. Summary of the Invention

[0009] Purpose of the invention: The purpose of this invention is to provide a voltage sensitivity fitting method and system driven by distribution network measurement data, which solves the problems of insufficient feature representation ability, insufficient processing of missing measurement data, and sample construction that does not fit the actual deployment scenario in the prior art.

[0010] Technical solution: The voltage sensitivity fitting method driven by power distribution network measurement data described in this invention includes the following steps:

[0011] Step 1: Obtain the injected power data, voltage data of the measured nodes, and node neighborhood features of the distribution network nodes under operating state j; construct the input sample feature vector matrix; input the input sample feature vector matrix into the trained variational autoencoder to obtain the overall network voltage estimation result under operating state j; the node neighborhood features include the average power and average voltage of the neighboring nodes of each distribution network node.

[0012] Step 2: Select G power reference disturbances of distribution network nodes under operating state j, G voltage data of measured nodes, and G sets of node neighborhood features to construct G sets of reference disturbance feature vector matrices. Input the reference disturbance feature vector matrices into the trained variational autoencoder to obtain the whole network voltage estimation results of G sets of reference disturbances under this operating state.

[0013] Step 3: Calculate the power difference between the injected power data and the power reference disturbance, calculate the voltage difference between the estimated voltage of the entire network and the estimated voltage of the reference disturbance, and use the least squares method to obtain the estimated values ​​of the voltage sensitivity matrix of group G based on the power difference and voltage difference.

[0014] Step 4: Calculate the mean of the estimated voltage sensitivity values ​​for group G to obtain the voltage sensitivity matrix.

[0015] Furthermore, in step 2, based on the Euclidean distance calculation results, the power data of group G in the historical database that is most similar to the node injection power under operating state j is selected as the power reference disturbance, and the measured node voltage in group G of the historical database is taken as the voltage reference disturbance.

[0016] Further, in step 1, the i-th node in the input sample feature vector matrix is ​​constructed as follows:

[0017]

[0018] In step 2, the i-th node in the g-th group of reference perturbation eigenvector matrix is ​​constructed as follows:

[0019]

[0020] Among them, P i,jQ i,j U i,j These represent the active power, reactive power, and measured node voltage value of node i in operating state j, respectively; the unmeasured node voltage value is 0; m i This is a measurement mask; it is 1 if there is a voltage measurement, and 0 otherwise. i The degree of node connectivity; These represent the average active power, average reactive power, and average voltage of the adjacent nodes of node i in operating state j, respectively; n is the number of network nodes.

[0021] These represent the active power, reactive power, and measured node voltage value of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively. The measurement mask for the i-th node in the g-th group of reference perturbation eigenvector matrix; For node connectivity, These are the average active power, average reactive power, and average voltage of the adjacent nodes of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively.

[0022] Furthermore, during the training of the variational autoencoder, a weighted reconstruction error function based on node observability masks is adopted:

[0023]

[0024] in, Let m be the loss function; i is the voltage mask for the node; n is the number of nodes; The voltage value is the value of a real voltage measurement node; The voltage value generated by the decoder.

[0025] Furthermore, during the training process of the variational autoencoder, a hierarchical masking mechanism is used to construct training samples. Some key structural nodes remain in a measurement-free state in all training samples, while the remaining nodes are masked in a random manner in different training samples.

[0026] The voltage sensitivity fitting system driven by power distribution network measurement data according to the present invention includes:

[0027] The whole network voltage estimation module is used to acquire the injected power data, voltage data of the measured nodes, and node neighborhood features of the distribution network nodes under operating state j. It constructs an input sample feature vector matrix and inputs the input sample feature vector matrix into the trained variational autoencoder to obtain the whole network voltage estimation result under operating state j. The node neighborhood features include the average power and average voltage of the neighboring nodes of each distribution network node.

[0028] The whole-network voltage estimation module for reference disturbances is used to select G power reference disturbances of distribution network nodes under operating state j, G voltage data of measured nodes, and G sets of node neighborhood features to construct G sets of reference disturbance feature vector matrices. The reference disturbance feature vector matrices are then input into the trained variational autoencoder to obtain the whole-network voltage estimation results of G sets of reference disturbances under this operating state.

[0029] The voltage sensitivity matrix estimation module is used to calculate the power difference between the injected power data and the power reference disturbance, calculate the voltage difference between the voltage estimation result of the whole network and the voltage estimation result of the reference disturbance, and obtain the estimated values ​​of the voltage sensitivity matrix of group G by using the least squares method based on the power difference and voltage difference; calculate the mean of the estimated values ​​of the voltage sensitivity matrix of group G.

[0030] Furthermore, in the network voltage estimation module for the reference disturbance, the power data of group G in the historical database that is most similar to the node injection power under operating state j is selected as the power reference disturbance based on the Euclidean distance calculation results, and the measured node voltages in group G of the historical database are taken as the voltage reference disturbance.

[0031] Furthermore, in the whole-network voltage estimation module, the i-th node in the input sample feature vector matrix is ​​constructed as follows:

[0032]

[0033] In the network voltage estimation module for reference disturbances, the i-th node in the g-th group of reference disturbance eigenvector matrices is constructed as follows:

[0034]

[0035] Furthermore, during the training of the variational autoencoder, a weighted reconstruction error function based on node observability masks is adopted:

[0036]

[0037] in, Let m be the loss function; i is the voltage mask for the node; n is the number of nodes; The voltage value is the value of a real voltage measurement node; The voltage value generated for the decoder.

[0038] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the voltage sensitivity fitting method driven by power distribution network measurement data.

[0039] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the voltage sensitivity fitting method driven by power distribution network measurement data.

[0040] Beneficial effects: Compared with the prior art, the advantages of the present invention are: (1) In the case of a scenario where some voltage measurement data is missing, the present invention adopts a variational autoencoder to establish a model to obtain the voltage estimation result of the whole network in order to achieve accurate estimation of the voltage of the unmeasured node; at the same time, the present invention designs an input vector that includes node power, voltage measurement value and mask, connectivity and average features of neighboring nodes, and guides the model to explicitly distinguish between observable and unobservable nodes by multiplying the voltage measurement value with the mask; (2) In the training process of the variational autoencoder, the present invention adopts a weighted reconstruction error function based on the node observability mask, dynamically masks the missing measurement nodes in the loss calculation, and only performs mean square error measurement on nodes with real voltage labels, thereby suppressing false labels. (2) The noise interference on the back propagation path enhances the convergence and generalization performance of the variational autoencoder in scenarios with incomplete voltage measurements; (3) The present invention adopts a masking strategy of "partially fixed + partially random" to construct samples, and combines the weighted reconstruction loss function of the node observability mask to improve the estimation robustness and generalization ability of key nodes; (4) The present invention constructs an overdetermined set of equations based on multiple sets of disturbance samples, and uses the least squares method to fit the relationship between power disturbance and voltage change to obtain multiple sets of voltage sensitivity matrix estimation results. Finally, the arithmetic mean is taken to improve the accuracy of the final estimation result. Even under the condition of lack of line parameters and topology information, high-precision voltage estimation and sensitivity fitting can still be achieved, which is suitable for distribution network scenarios with sparse voltage measurements. Attached Figure Description

[0041] Figure 1 This is a flowchart of the voltage sensitivity fitting method of the present invention.

[0042] Figure 2 This is a power distribution network topology diagram according to an embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram illustrating the changes in the loss function value during the training process according to an embodiment of the present invention.

[0044] Figure 4 This is a thermogram of the theoretical active voltage sensitivity in an embodiment of the present invention.

[0045] Figure 5 This is a thermogram of the fitted active voltage sensitivity in an embodiment of the present invention.

[0046] Figure 6 This is a thermogram of the theoretical reactive voltage sensitivity in an embodiment of the present invention.

[0047] Figure 7This is a thermogram of the fitting reactive voltage sensitivity in an embodiment of the present invention. Detailed Implementation

[0048] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0049] like Figure 1 As shown, the voltage sensitivity fitting method driven by power distribution network measurement data includes the following steps.

[0050] S1. Construct encoder input features for a variational autoencoder using partial voltage data of nodes with measurements, load data of all nodes, and node neighborhood features. Construct an input feature vector for each node in the distribution network. The features include: active power, reactive power, voltage measurement value (0 if there is no measurement), measurement mask (1 if there is voltage measurement, otherwise 0), node connectivity (i.e., the number of neighboring nodes of the node), average active power of neighboring nodes, average reactive power of neighboring nodes, and average voltage of neighboring nodes (ignoring nodes without measurements).

[0051] To achieve accurate estimation of voltages at unmeasured nodes and adapt to training environments with missing and uncertain observational information, a variational autoencoder is chosen as the main modeling framework. Its advantages are:

[0052] 1) The encoder part of the variational autoencoder can extract latent variables from the input features of all network nodes to form a low-dimensional representation of the system's operating state, overcoming the problems of information redundancy and noise in the original high-dimensional input.

[0053] 2) The variational autoencoder is essentially a reconstruction model. It can reconstruct the voltage of the unmeasured node by means of the intrinsic structure of the samples in the latent space when the input is missing. This helps to achieve robust estimation in sparse measurement scenarios.

[0054] 3) Combining the mask-weighted reconstruction error design proposed in this invention, the variational autoencoder can flexibly adapt to the mechanism of calculating training loss only on some observation nodes, thereby improving the stability and convergence speed of the training process.

[0055] In summary, variational autoencoders are more suitable than traditional feedforward networks or generative adversarial networks for the distribution network voltage estimation and sensitivity fitting tasks with high-dimensional, sparse measurements and uncertain structural information, as addressed in this invention.

[0056] However, it is worth noting that although this invention uses a variational autoencoder as an example model for construction and training, the input feature design, masking mechanism and sample training strategy described are also applicable to other generative model structures with potential representation learning and reconstruction capabilities, such as graph neural networks and generative adversarial networks.

[0057] Specifically, the encoder input features of the variational autoencoder are:

[0058] The input feature vector of any node in a distribution network under a certain operating state j is defined as follows:

[0059]

[0060] After concatenating the features of all nodes in the network, an input sample matrix is ​​formed:

[0061]

[0062] In the formula, x i,j P is the feature vector of node i in state j; i,j Q represents the active power of node i in state j. i,j U represents the reactive power of node i in state j; i,j The voltage measurement value of node i in state j (0 if there is no measurement); m i This is a measurement mask; it is 1 if there is a voltage measurement, and 0 otherwise. i This represents the node's connectivity (i.e., the number of its neighboring nodes). Let be the average active power of the neighboring nodes of node i in state j; The average reactive power of the neighboring nodes of node i in state j; X is the average voltage of the adjacent nodes of node i in state j (ignoring nodes without measurement); j Let be the feature matrix of all nodes in the network at state j; n is the number of network nodes.

[0063] To avoid mistakenly treating the placeholder voltage 0 as the actual voltage during input, "U" is used. i,j ×m i,j The voltage input features are constructed in a way that allows for the creation of a feature representation structure with observation state awareness, explicitly encoding the observability information of each node, suppressing the interference of missing measurement nodes on the model parameter update process, and improving the stability and training effectiveness of the variational autoencoder under unstructured input conditions.

[0064] S2. The encoder part of the variational autoencoder outputs the mean vector and log-variance vector of the predicted latent variables.

[0065] The encoder structure design of the variational autoencoder is as follows:

[0066] The encoder consists of three fully connected layers, with the input layer connecting X. j Flattened into a one-dimensional vector with dimension D in (n×8), with two hidden layers, the dimension of hidden layer 1 is approximately The activation function is ReLU, and the hidden layer has approximately 2 dimensions. The activation function is ReLU, and the output layer consists of two parallel fully connected structures that predict the mean vector of the latent variables. With log-variance vector The total output dimension is 2k.

[0067] S3. The latent variables are transformed into a compressed state vector at the current time using the reparameterization technique, which serves as the decoder input of the variational autoencoder.

[0068] The specific steps for obtaining the decoder input of the variational autoencoder are as follows:

[0069] The encoder's output is not directly used as the decoder's input. Instead, it represents the probability distribution of a latent variable z. For each input sample x, the encoder network outputs the mean vector of the latent variable. With log-variance vector Thus, a conditional distribution is defined.

[0070]

[0071] To sample the latent variable z from this distribution while preserving the differentiability of the entire network, a reparameterization technique is used to represent the sampling process as follows:

[0072] z = μ + σ·ε, σ=exp(0.5·logσ 2 );

[0073] In the formula, μ and logσ 2 ε is the output of the encoder network; ε is a random vector that follows a standard normal distribution.

[0074] This transforms non-differentiable random sampling operations into differentiable ones, allowing the gradients of latent variables to propagate back to the encoder parameters, thus enabling end-to-end training. The final generated latent variables... This represents the compressed state vector of the system at the current moment, which serves as the input to the decoder.

[0075] S4. The decoder of the variational autoencoder is trained to compress the state vector and output the voltage data of all nodes.

[0076] The decoder structure design of the variational autoencoder is as follows:

[0077] The decoder consists of a three-layer fully connected network, with the input layer data being latent variables. There are two hidden layers, and the dimension of hidden layer 1 is approximately The activation function is ReLU, and the hidden layer has approximately 2 dimensions. The activation function is ReLU, and the output layer outputs all node voltage data.

[0078] S5. A weighted reconstruction error function based on node observability masking is adopted to dynamically mask missing measurement nodes in the loss calculation, and only perform mean square error measurement on nodes with real voltage tags, thereby suppressing the interference of pseudo-tag noise on the back propagation path and enhancing the convergence and generalization performance of the variational autoencoder in scenarios with incomplete voltage measurements.

[0079]

[0080] In the formula, Let m be the loss function; i is the voltage mask for the node; n is the number of nodes; The voltage value is the value of a real voltage measurement node; The voltage value generated for the decoder.

[0081] S6. A layered masking mechanism is adopted in the construction of training samples. Some key structural nodes remain in an unmeasured state in all training samples to enhance the model's generalization ability to unobservable regions. The remaining nodes are masked in different training samples in a random manner to simulate the dynamic uncertainty of measurement equipment deployment in actual operation, thereby constructing a training distribution that is more in line with the real scene and improving the robustness of the model and the stability of key node prediction.

[0082] S7. Using the least squares method in a data-driven manner, voltage sensitivity fitting that is independent of line parameters is obtained.

[0083] The specific steps for obtaining voltage sensitivity fitting using the least squares method are as follows:

[0084] Active / reactive voltage sensitivity can be approximated as:

[0085]

[0086] In the formula, S U-P S is the active voltage sensitivity matrix; U-Q ΔP is the reactive voltage sensitivity matrix; G and B are the real (conductance) and imaginary (susceptance) parts of the node admittance matrix, respectively, determined by the network topology; P and Q are the active and reactive power injected into the nodes. ΔP and ΔQ are the active / reactive power injection change vectors of the nodes, respectively; ΔU is the node voltage change vector.

[0087] Under a certain operating condition of the distribution network, several sets of small power variations are artificially generated. The corresponding voltages are obtained through a variational autoencoder voltage fitting model. Based on the relationship shown in the above formula, several sets of equations are obtained. By solving these overdetermined equations using the least squares method, the voltage sensitivity matrix under this operating condition can be obtained. The specific steps are as follows.

[0088] Step (1) involves acquiring power injection data, measured voltage data, and neighborhood features of distribution network nodes under a specific operating state j, and constructing node input features. The features of all network nodes are then concatenated to form an input sample feature vector matrix.

[0089]

[0090] In the formula, X j x is the input feature matrix of all nodes in running state j; n,j is the input feature vector for each node in running state j; n is the total number of nodes in the network; the matrix dimension is n×8.

[0091] Step (2) involves inputting the constructed input feature matrix into the trained variational autoencoder model, and then outputting the network voltage estimation result corresponding to the operating state through its decoder:

[0092] Y j =[U 1,j U 2,j ,...,U n,j ] T ;

[0093] In the formula, Y j Let be the voltages of the n nodes under operating condition j.

[0094] Step (3): Based on the Euclidean distance calculation results, select the G groups of power data in the historical database that are most similar to the node injection power under operating state j as the power reference perturbation, and construct the feature vector matrix of the G groups of reference perturbations. The feature vector of the i-th (i∈[1,n]) node of the g-th (g∈[1,G]) group of reference perturbations can be expressed as:

[0095]

[0096] In the formula, These are the active power, reactive power, and measured node voltage values ​​of the i-th node in the g-th reference disturbance group, respectively. Let be the measurement mask for the i-th node in the g-th group of reference perturbations; These are the average active power, average reactive power, and average voltage of the adjacent nodes of the i-th node in the g-th reference disturbance group, respectively.

[0097] A set of eigenvector matrices for reference perturbation of all network nodes is as follows:

[0098]

[0099] Construct the eigenvector matrices of all G sets of reference perturbations, and input them sequentially into the variational autoencoder model to obtain the total network voltage of the G sets of reference perturbations:

[0100]

[0101] Step (4): After obtaining the total grid voltage of the reference disturbance G corresponding to operating state j, construct the active power, reactive power, and voltage difference vector between the reference disturbance G and operating state j:

[0102]

[0103] In the formula, ΔP i g Let be the difference in active power disturbance between node i and the g-th group of reference disturbances under operating state j. Let be the reactive power disturbance difference between node i and the g-th group of reference disturbances under operating state j. P represents the voltage difference between node i and the g-th reference disturbance under operating state j. i,j Q i,j Let U be the active power and reactive power of node i under operating state j; i,j Let be the voltage of node i under operating state j; The active power and reactive power of the reference disturbance in the i-th node and the g-th group are respectively taken from historical data; Let be the voltage of the i-th node in the g-th reference disturbance; n is the total number of nodes in the network.

[0104] Step (5) uses a set of reference disturbance samples under operating state j as an example to explain in detail the construction and calculation process of the voltage sensitivity matrix:

[0105] According to the definition of voltage sensitivity:

[0106]

[0107] In the formula, S U-P S is the active voltage sensitivity matrix; U-Q This is the reactive voltage sensitivity matrix.

[0108] in:

[0109]

[0110] In the formula, ΔP g ΔQ g , ΔU g These are the active, reactive, and voltage difference vectors of all network nodes in the operating state j and the reference disturbance set.

[0111] Additional settings:

[0112]

[0113] but:

[0114] D u =S·D p-q ;

[0115] At this point, it is necessary to find an optimal S such that S·D p-q The closest to D u That is, minimizing the error. Using the least squares method to solve for S, the objective is to minimize the following objective function:

[0116]

[0117] In the formula, ||·|| F The Frobenius norm (the square root of the sum of squares of the matrix elements) is represented by the objective function after expansion.

[0118]

[0119] Taking the derivative with respect to S and setting it to 0, we obtain the solution using the standard least squares method:

[0120] S T =(D p-q D p-q T ) -1 D p-q D u T ;

[0121] In the formula, S is the voltage sensitivity matrix obtained under the operating state j of the distribution network, which includes active power sensitivity and reactive power sensitivity.

[0122] Step (6): For the constructed G groups of power disturbance samples, the corresponding voltage sensitivity matrix can be estimated according to the above fitting process. Given that the disturbance amplitudes of each group are small, the obtained sensitivity matrices have good consistency under local linear approximation conditions. Therefore, their arithmetic mean can be taken to improve the accuracy of the final estimation result.

[0123]

[0124] In the formula, S avg This is the voltage sensitivity matrix obtained under the final operating state j of the distribution network.

[0125] To enable those skilled in the art to better understand the present invention, the following detailed description is provided in conjunction with specific embodiments.

[0126] Simulation analysis was performed based on the IEEE standard 33-node system. The network topology is shown below. Figure 2As shown. The effectiveness of the method is verified by hiding some node voltage measurement data. Due to the lack of actual operating data, simulated historical data covering various typical operating phases was first generated based on the IEEE 33-node standard test system for offline training of the variational autoencoder. The simulated data was generated by random power perturbation and photovoltaic injection changes, with 4000 sets of samples, of which the training set accounted for 80% of the total samples, the validation set accounted for 10%, and the test set accounted for 10%. Each set of input data includes 33 node features, and each node contains 8 feature information items: active power, reactive power, voltage measurement value (set to 0 if there is no measurement), voltage measurement mask (1 if there is measurement, 0 otherwise), node connectivity, average active power of adjacent nodes, average reactive power, and average voltage (ignoring nodes without measurement). A layered masking mechanism is used during the construction of training samples. In each training sample set, eight nodes are selected as unmeasured nodes. Four nodes are fixed (positions 2, 10, 18, and 30 in the network topology), and four nodes are randomly selected. These are used to construct the masked input and target output. This approach preserves the model's generalization ability while enhancing the learning ability of key nodes. The positions of the fixed unmeasured nodes in the network topology are shown below. Figure 2 .

[0127] After concatenating and expanding all node features, the input feature vector for each sample has a dimension of 264. The encoder employs a two-layer fully connected neural network (Multi-Layer Perceptron, MLP) structure. The first layer maps the 264-dimensional input to 128 dimensions using the ReLU activation function; the second layer further compresses the 128-dimensional features to 64 dimensions, also using the ReLU activation function. In the output layer, the encoder generates the mean vector and standard deviation vector of the latent variables, both with a dimension of 32, representing the distribution parameters of the latent space. Through reparameterization techniques, the latent variable vector z is sampled from this distribution for subsequent decoding.

[0128] The decoder section also consists of two fully connected neural networks. First, the latent variables... The hidden representation is mapped to 64 dimensions, then expanded to 128 dimensions through a second layer, and finally output as a 33-dimensional vector, corresponding to the voltage estimate of all network nodes. The activation function of each hidden layer of the decoder is ReLU, and the output layer uses the Tanh activation function to ensure that the output voltage is in the range of [-1,1], and is linearly mapped to the per-unit value range of the actual voltage [0.95,1.05] in post-processing.

[0129] To prevent overfitting, a Dropout mechanism is introduced in the hidden layers of both the encoder and decoder, with a dropout ratio set to 0.3. During model training, the voltage estimation results output by the decoder are compared with the measured voltage data in the input. To avoid the model misidentifying voltage placeholder values ​​without measurement nodes as valid information during training, a voltage mask is used to guide the loss calculation, calculating the reconstruction error only at the measurement nodes. The total loss function is composed of a weighted average of the reconstruction error (mask mean square error) and the KL divergence of the latent variable distribution, achieving stable training and generalization capability of the model under conditions of incomplete voltage data.

[0130] Figure 3 The trend of the loss function during training is shown. This loss function is mask-weighted mean squared error (MSE), which calculates the error between the predicted and true values ​​only at nodes with actual voltage measurements, thus avoiding interference from nodes without measurements during the training process.

[0131] As can be seen from the figure, the model error decreased rapidly in the early stage of training (1–30 rounds), indicating that the model can quickly learn the basic structure of voltage distribution; in the middle and late stages (30–60 rounds), the loss gradually stabilized and the fluctuation amplitude decreased; after entering the later stage (60–100 rounds), the model converged and stabilized, the error remained at a low level, and no overfitting phenomenon occurred.

[0132] To verify the accuracy of the network voltage data generated by the variational autoencoder, this paper uses real voltage data from the test set as a reference and calculates two indicators: mean square error and mean absolute error (MAE) between the voltage data generated without measurement nodes and the real voltage data. The results are shown in Table 1.

[0133] Table 1. Error statistics of voltage generation at unmeasured nodes.

[0134]

[0135] As shown in the table above, the average absolute error of the generated voltage values ​​at the node level is 0.0225 pu, and the overall mean square error is 0.00259. Compared with the actual voltage data, the generated voltage distribution deviates to some extent from the actual value, but it is still within an acceptable range.

[0136] To verify the effectiveness of the proposed feature construction, masking mechanism, and training masking strategy in voltage estimation, five sets of comparative experiments were designed. While maintaining a consistent model structure, the core mechanisms were removed one by one, and the results are shown in Table 2.

[0137] Table 2 Comparative Experiments of Structural Improvements (Based on Variational Autoencoders)

[0138]

[0139] As shown in Table 2, after removing neighbor information and connectivity, the MSE increased from 0.00259 to 0.00413. This indicates that neighborhood features help guide the model to learn the local correlation of voltage between nodes and are an important source of information for improving fitting accuracy. If the original voltage values ​​are directly input without multiplying them with a mask to explicitly indicate observability, the model will have difficulty distinguishing between missing / real data sources, causing training misdirection (MSE increased from 0.00259 to 0.00375). After replacing the "partially fixed + partially random" strategy with a masking method that is only random or only fixed, the model overfits at some nodes, and the generalization ability at key nodes decreases, leading to an increase in error (MSE increased from 0.00259 to 0.00321). If the error is also calculated at nodes without measurement, spurious supervision signals are included in the gradient update, causing interference to the training process, and the error increases most significantly (MSE increased from 0.00259 to 0.00492), verifying the key role of the "weighted loss function" design in the stability of the model.

[0140] With identical feature inputs, masking mechanisms, training strategies, and loss function configurations, the performance differences of three different model structures in voltage estimation tasks were compared, and the results are shown in Table 3.

[0141] Table 3 Comparison of results using different models under the same structural conditions.

[0142]

[0143] As can be seen from the table, the voltage estimation method based on variational autoencoders outperforms the comparison methods in all metrics. Its MSE and MAE are significantly lower than the other two methods, demonstrating good estimation accuracy and stability.

[0144] The two sets of comparative experiments above demonstrate that the feature construction method, voltage × mask mechanism, training masking strategy, and mask-weighted reconstruction loss function proposed in this invention all play crucial roles in improving model performance. Isolating these mechanisms one by one significantly increases the error, validating their necessity and synergistic effectiveness. Under the same mechanism conditions, the variational autoencoder model exhibits stronger advantages in voltage estimation accuracy and stability compared to other mainstream structures.

[0145] After obtaining the overall network voltage estimate, the voltage sensitivity matrix, including the active power voltage sensitivity matrix and the reactive power voltage sensitivity matrix, is fitted using the least squares method. This matrix is ​​then compared with the actual network voltage sensitivity matrix. A set of test results is selected for presentation, showing the calculated active / reactive power voltage sensitivity matrix heatmap. The data for this set of data includes nodes 2, 6, 10, 14, 18, 22, 26, and 30 without measurement. In the graph, the value in the i-th row and j-th column represents the sensitivity of the voltage of the node corresponding to the i-th row to changes in the power of the node corresponding to the j-th column. Figure 4 Theoretical active voltage sensitivity thermogram, Figure 5 To fit the active voltage sensitivity thermogram, Figure 6 Theoretical reactive voltage sensitivity thermogram, Figure 7 To fit the reactive voltage sensitivity thermogram.

[0146] The active voltage sensitivity MSE of this set of fitted data is 0.00902% and MAE is 0.575%; the reactive voltage sensitivity MSE is 0.00367% and MAE is 0.287%.

[0147] The average values ​​of MSE and MAE were calculated for 400 test set data, and the results are shown in Table 3.

[0148] Table 4. Error statistics of voltage sensitivity fitting

[0149]

[0150] As shown in the table above, generating measurement-free node voltage data based on a variational autoencoder and fitting the voltage sensitivity matrix using the least squares method achieved good results. Although there is a certain deviation between the fitting results and the true values, the overall error is within an acceptable range, verifying the feasibility and application value of this method in practical voltage regulation control.

[0151] The voltage sensitivity fitting system driven by power distribution network measurement data according to the present invention includes:

[0152] The whole network voltage estimation module is used to acquire the injected power data, voltage data of the measured nodes, and node neighborhood features of the distribution network nodes under operating state j. It constructs an input sample feature vector matrix and inputs the input sample feature vector matrix into the trained variational autoencoder to obtain the whole network voltage estimation result under operating state j. The node neighborhood features include the average power and average voltage of the neighboring nodes of each distribution network node.

[0153] The whole-network voltage estimation module for reference disturbances is used to select G power reference disturbances of distribution network nodes under operating state j, G voltage data of measured nodes, and G sets of node neighborhood features to construct G sets of reference disturbance feature vector matrices. The reference disturbance feature vector matrices are then input into the trained variational autoencoder to obtain the whole-network voltage estimation results of G sets of reference disturbances under this operating state.

[0154] The voltage sensitivity matrix estimation module is used to calculate the power difference between the injected power data and the power reference disturbance, calculate the voltage difference between the voltage estimation result of the whole network and the voltage estimation result of the reference disturbance, and obtain the estimated values ​​of the voltage sensitivity matrix of group G by using the least squares method based on the power difference and voltage difference; calculate the mean of the estimated values ​​of the voltage sensitivity matrix of group G.

[0155] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the voltage sensitivity fitting method driven by power distribution network measurement data.

[0156] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the voltage sensitivity fitting method driven by power distribution network measurement data.

[0157] The computer-readable storage medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage devices, magnetic disk storage devices or other magnetic storage devices, flash memory or any other medium that can be used to store program code in the form of instructions or data structures and is accessible by a computer.

[0158] The processor is used to execute a computer program stored in memory to implement the various steps in the methods described in the above embodiments.

Claims

1. A voltage sensitivity fitting method driven by distribution network measurement data, characterized in that, Includes the following steps: Step 1: Obtain the injected power data, voltage data of the measured nodes, and node neighborhood features of the distribution network nodes under operating state j; construct the input sample feature vector matrix; input the input sample feature vector matrix into the trained variational autoencoder to obtain the overall network voltage estimation result under operating state j; the node neighborhood features include the average power and average voltage of the neighboring nodes of each distribution network node. Step 2: Select G power reference disturbances of distribution network nodes under operating state j, G voltage data of measured nodes, and G sets of node neighborhood features to construct G sets of reference disturbance feature vector matrices. Input the reference disturbance feature vector matrices into the trained variational autoencoder to obtain the whole network voltage estimation results of G sets of reference disturbances under this operating state. Step 3: Calculate the power difference between the injected power data and the power reference disturbance, calculate the voltage difference between the estimated voltage of the entire network and the estimated voltage of the reference disturbance, and use the least squares method to obtain the estimated value of the voltage sensitivity matrix of group G based on the power difference and voltage difference; wherein, calculating the power difference between the injected power data and the power reference disturbance includes calculating the difference between the injected power data of the distribution network node under operating state j and the power reference disturbance of group G; Step 4: Calculate the mean of the estimated voltage sensitivity values ​​for group G to obtain the voltage sensitivity matrix.

2. The voltage sensitivity fitting method driven by distribution network measurement data according to claim 1, characterized in that, In step 2, based on the Euclidean distance calculation results, the power data of group G in the historical database that is most similar to the node injection power under operating state j is selected as the power reference disturbance, and the measured node voltage in group G of the historical database is taken as the voltage reference disturbance.

3. The voltage sensitivity fitting method driven by distribution network measurement data according to claim 1, characterized in that, In step 1, the i-th node in the input sample feature vector matrix is ​​constructed as follows: ； In step 2, the i-th node in the g-th group of reference perturbation eigenvector matrix is ​​constructed as follows: ； in, , , These represent the active power, reactive power, and voltage value of node i in operating state j, respectively; the voltage value of node i with measurement is 0. This is the measurement mask for node i in running state j. It is 1 if there is a voltage measurement, and 0 otherwise. Let i be the node connectivity of node i in running state j; , , These represent the average active power, average reactive power, and average voltage of the adjacent nodes of node i in operating state j, respectively; n is the number of network nodes. , , These represent the active power, reactive power, and measured node voltage value of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively. The measurement mask for the i-th node in the g-th group of reference perturbation eigenvector matrix; Let be the node connectivity of the i-th node in the g-th group of reference perturbation eigenvector matrices. , , These are the average active power, average reactive power, and average voltage of the adjacent nodes of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively.

4. The voltage sensitivity fitting method driven by distribution network measurement data according to claim 1, characterized in that, During the training of the variational autoencoder, a weighted reconstruction error function based on node observability masks is used: ； in, The loss function; Let n be the measurement mask for node i; n is the number of network nodes. The voltage value is the value of a real voltage measurement node; The voltage value generated for the decoder.

5. The voltage sensitivity fitting method driven by distribution network measurement data according to claim 1, characterized in that, During the training process of the variational autoencoder, a hierarchical masking mechanism is used to construct training samples. Some key structural nodes remain in a measurement-free state in all training samples, while the remaining nodes are masked in a random manner in different training samples.

6. A voltage sensitivity fitting system driven by distribution network measurement data, characterized in that, include: The whole network voltage estimation module is used to acquire the injected power data, voltage data of the measured nodes, and node neighborhood features of the distribution network nodes under operating state j. It constructs an input sample feature vector matrix and inputs the input sample feature vector matrix into the trained variational autoencoder to obtain the whole network voltage estimation result under operating state j. The node neighborhood features include the average power and average voltage of the neighboring nodes of each distribution network node. The whole-network voltage estimation module for reference disturbances is used to select G power reference disturbances of distribution network nodes under operating state j, G voltage data of measured nodes, and G sets of node neighborhood features to construct G sets of reference disturbance feature vector matrices. The reference disturbance feature vector matrices are then input into the trained variational autoencoder to obtain the whole-network voltage estimation results of G sets of reference disturbances under this operating state. The voltage sensitivity matrix estimation module is used to calculate the power difference between the injected power data of the whole network and the power reference disturbance, calculate the voltage difference between the voltage estimation result of the whole network and the voltage estimation result of the reference disturbance, and obtain the estimated value of the voltage sensitivity matrix G by using the least squares method based on the power difference and voltage difference. The mean of the voltage sensitivity estimates for group G is calculated to obtain the voltage sensitivity matrix; among them, the calculation of the power difference between the injected power data of the whole network and the power reference disturbance includes calculating the difference between the injected power data of the distribution network node and the power reference disturbance of group G under operating state j.

7. The voltage sensitivity fitting system driven by distribution network measurement data according to claim 6, characterized in that, In the network voltage estimation module for the reference disturbance, the power data of group G in the historical database that is most similar to the node injection power under operating state j is selected as the power reference disturbance based on the Euclidean distance calculation results, and the measured node voltages in group G of the historical database are taken as the voltage reference disturbance.

8. The voltage sensitivity fitting system driven by distribution network measurement data according to claim 6, characterized in that, In the whole network voltage estimation module, the i-th node in the input sample feature vector matrix is ​​constructed as follows: ； In the network voltage estimation module for reference disturbances, the i-th node in the g-th group of reference disturbance eigenvector matrices is constructed as follows: ； in, , , These represent the active power, reactive power, and voltage value of node i in operating state j, respectively; the voltage value of node i with measurement is 0. This is the measurement mask for node i in running state j. It is 1 if there is a voltage measurement, and 0 otherwise. Let i be the node connectivity of node i in running state j; , , These represent the average active power, average reactive power, and average voltage of the adjacent nodes of node i in operating state j, respectively; n is the number of network nodes. , , These represent the active power, reactive power, and measured node voltage value of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively. The measurement mask for the i-th node in the g-th group of reference perturbation eigenvector matrix; Let be the node connectivity of the i-th node in the g-th group of reference perturbation eigenvector matrices. , , These are the average active power, average reactive power, and average voltage of the adjacent nodes of the i-th node in the g-th group of reference disturbance eigenvector matrix, respectively.

9. The voltage sensitivity fitting system driven by distribution network measurement data according to claim 6, characterized in that, During the training of the variational autoencoder, a weighted reconstruction error function based on node observability masks is used: ； in, The loss function; Let n be the measurement mask for node i; n is the number of network nodes. The voltage value is the value of a real voltage measurement node; The voltage value generated for the decoder.

10. The voltage sensitivity fitting system driven by distribution network measurement data according to claim 6, characterized in that, During the training process of the variational autoencoder, a hierarchical masking mechanism is used to construct training samples. Some key structural nodes remain in a measurement-free state in all training samples, while the remaining nodes are masked in a random manner in different training samples.

11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the voltage sensitivity fitting method driven by distribution network measurement data according to any one of claims 1-5.

12. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the voltage sensitivity fitting method driven by power distribution network measurement data according to any one of claims 1-5.

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