Method and system for estimating voltage of low-voltage power distribution network containing distributed photovoltaic

Abstract

The invention provides a distributed photovoltaic low-voltage distribution network voltage estimation method and system, and belongs to the field of distribution network voltage assessment, and the method comprises the steps: 1, inputting the voltage data, time information and space information measured by a measurement device into a learning supervision regression model, the learning supervised regression model maps voltage data measured by the measuring device to adjacent low-voltage power distribution network nodes through a random forest algorithm to obtain voltage data of the adjacent low-voltage power distribution network nodes; step 2, training the learning supervised regression model, and when a regression index is minimum, stopping training to obtain a trained learning supervised regression model; 3, performing voltage estimation on unmonitored nodes in the low-voltage power distribution network by using the trained learning supervision regression model; and based on the measurement data of the limited node, mapping the measurement data of the limited node to the adjacent node without the measurement device, and further carrying out voltage estimation on the unmonitored node in the low-voltage power distribution network containing the distributed photovoltaic.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network voltage evaluation, and in particular to a method for estimating the voltage of a low-voltage distribution network containing distributed photovoltaics. Background Art

[0002] With the large-scale access of distributed photovoltaics to the power grid, the voltage instability problem in low-voltage distribution areas is increasing. The intermittent and volatile nature of distributed photovoltaics has brought severe challenges to the voltage management of low-voltage distribution networks. Traditional voltage estimation methods have limitations in dealing with these challenges, especially in terms of real-time and adaptability. At the same time, the current monitoring and observation level of the power grid on the low-voltage distribution network is still relatively weak. How to gain insight into the voltage level of the entire low-voltage distribution network based on limited data is also a technical challenge. Therefore, it is urgent to develop a new low-voltage distribution network voltage estimation method to ensure accurate and rapid analysis of the impact of distributed photovoltaics on the voltage of the low-voltage distribution network, optimize the grid operating conditions, and ensure the quality of grid power supply.

[0003] In the prior art, the Chinese invention patent application with publication number CN117709526A, "A distribution network voltage prediction method based on long-term and short-term neural networks", screens and cleans a large amount of data based on the uncertainty of voltage changes under distributed power supply access and the difficulty in processing continuous massive data, and proposes a distribution network voltage prediction model of long-term and short-term neural networks with Bayesian optimization. The hyperparameters of the long-term and short-term neural networks are optimized by Bayes to improve the accuracy of distribution network voltage prediction. In this distribution network voltage prediction method, the distribution network measurement devices are sufficient, the distribution network voltage data is sufficient, and the focus is on predicting the voltage level of the large power grid in the future based on historical data. It is a data-sufficient time series prediction method. However, in the face of low-voltage distribution networks with weak monitoring and sparse data, this method cannot estimate the voltage of unmonitored nodes. Summary of the invention

[0004] The technical problem to be solved by the present invention is how to gain insight into the voltage level of the entire low-voltage distribution network based on limited data.

[0005] The present invention solves the above technical problems through the following technical solutions: a method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics, comprising the following steps:

[0006] Step 1: input the voltage data, time information, and spatial information measured by the measuring device into a learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to adjacent low-voltage distribution network nodes by a random forest algorithm to obtain voltage data of adjacent low-voltage distribution network nodes.

[0007] Step 2: Train the learning supervised regression model. When the regression index is the smallest, stop the training to obtain a trained learning supervised regression model.

[0008] Step 3: Use the trained learning supervised regression model to estimate the voltage of unmonitored nodes in the low-voltage distribution network.

[0009] The present invention takes into account the background of large-scale access of distributed photovoltaic to low-voltage distribution network. Photovoltaic is scatteredly connected to the low-voltage distribution network, which will not only affect the connected nodes, but also many nearby nodes, resulting in changes in the voltage level of each node of the entire low-voltage distribution network system. In the face of this situation, the traditional voltage estimation method cannot accurately estimate the voltage data of the unmonitored nodes, and considering the low coverage rate of the voltage monitoring device of the low-voltage distribution network, the monitoring device is only installed at a limited number of nodes in the low-voltage distribution network. For the low-voltage distribution network with weak monitoring and missing data samples, the present invention is a data-sparse voltage estimation method, based on the measurement data of limited nodes, by mapping the limited node measurement data to adjacent nodes without measurement devices, and then estimating the voltage of the unmonitored nodes in the low-voltage distribution network containing distributed photovoltaics, which can more realistically understand the voltage level of the low-voltage distribution network with sparse monitoring devices as a whole, more accurately grasp the voltage status of the low-voltage distribution network, improve the observability of the low-voltage distribution network, timely adjust and optimize the operation of the power grid, improve the stability and power supply quality of the power grid, and can replace or supplement smart meter data and pseudo-measurement values.

[0010] Preferably, the learning supervised regression model is obtained by training with training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

[0011] Preferably, the step 1 comprises:

[0012] 1.1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n;

[0013] 1.2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i The nonlinear function mapping and in separate bootstrap samples Independently generated above;

[0014] 1.3. Each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement, and the split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. When the feature subset q is equal to the total number of features p, the Bagging regression tree algorithm is used for splitting;

[0015] 1.4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes.

[0016] Preferably, the calculation formula for the final prediction result is:

[0017]

[0018] In formula (1), is the final prediction result, B is the number of regression trees, T b (x) is the prediction result of the bth regression tree.

[0019] Preferably, the regression index in step 2 includes root mean square error and mean absolute error, and the calculation formula of the root mean square error is:

[0020]

[0021] The formula for calculating the mean absolute error is:

[0022]

[0023] In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

[0024] The present invention also provides a voltage estimation system for a low-voltage distribution network including distributed photovoltaics, comprising:

[0025] A mapping module is used to input the voltage data, time information and spatial information measured by the measuring device into the learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to the adjacent low-voltage distribution network nodes by the random forest algorithm to obtain the voltage data of the adjacent low-voltage distribution network nodes;

[0026] The training module is used to train the learning supervised regression model. When the regression index is the smallest, the training is stopped to obtain the trained learning supervised regression model.

[0027] The voltage estimation module is used to estimate the voltage of unmonitored nodes in the low-voltage distribution network using the trained learning supervised regression model.

[0028] Preferably, the learning supervised regression model is obtained by training with training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

[0029] Preferably, the mapping module is also used for:

[0030] 1.1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n;

[0031] 1.2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i Nonlinear function mapping, and in a separate bootstrap sample ~T b Independently generated above;

[0032] 1.3. Each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement, and the split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. When the feature subset q is equal to the total number of features p, the Bagging regression tree algorithm is used for splitting;

[0033] 1.4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes.

[0034] Preferably, the calculation formula for the final prediction result is:

[0035]

[0036] In formula (1), is the final prediction result, B is the number of regression trees, T b (x) is the prediction result of the bth regression tree.

[0037] Preferably, the regression indicators in the training module include root mean square error and mean absolute error, and the calculation formula of the root mean square error is:

[0038]

[0039] The formula for calculating the mean absolute error is:

[0040]

[0041] In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

[0042] The advantages provided by the present invention are:

[0043] (1) The present invention takes into account the background of large-scale access of distributed photovoltaic to low-voltage distribution network. Photovoltaic is scatteredly connected to the low-voltage distribution network, which will not only affect the connected nodes, but also many nearby nodes, resulting in changes in the voltage level of each node of the entire low-voltage distribution network system. In the face of this situation, the traditional voltage estimation method cannot accurately estimate the voltage data of the unmonitored nodes. In addition, considering that the coverage rate of voltage monitoring devices in the low-voltage distribution network is not high, the monitoring devices are only installed at limited nodes in the low-voltage distribution network. For low-voltage distribution networks with weak monitoring and missing data samples, the present invention is a data-sparse voltage estimation method. Based on the measurement data of limited nodes, by mapping the limited node measurement data to adjacent nodes without measurement devices, the voltage of the unmonitored nodes in the low-voltage distribution network containing distributed photovoltaic is estimated. The voltage level of the low-voltage distribution network with sparse monitoring devices can be more realistically understood as a whole, the voltage status of the low-voltage distribution network can be more accurately grasped, the observability of the low-voltage distribution network can be improved, the grid operation can be adjusted and optimized in time, the stability and power supply quality of the grid can be improved, and the smart meter data and pseudo-measurement values ​​can be replaced or supplemented.

[0044] (2) When the feature subset q is equal to the entire input feature set p, the present invention uses the BRT algorithm to effectively control this complexity, reduce the risk of overfitting by integrating multiple models, and improve the accuracy of prediction.

[0045] (3) When the present invention trains the learning supervised regression model, the root mean square error (RMSE) indicator tends to impose a more severe penalty on larger prediction errors, while the mean absolute error (MAE) indicator does not give a large weight to larger errors compared to the root mean square error (RMSE). By evaluating the performance of the model through these two regression indicators, a learning supervised regression model with better prediction accuracy can be obtained, thereby improving the accuracy of the unmonitored node voltage prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A flow chart of a method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics provided in Embodiment 1 of the present invention;

[0047] Figure 2 A schematic diagram of a framework of a method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics provided in Embodiment 1 of the present invention;

[0048] Figure 3 It is the average RMSE and MAE indicator distribution diagram of each prediction model in Example 3, Case 1 of the present invention;

[0049] Figure 4 The prediction model performance under different potential monitoring node ratios of the prediction model in Example 1 of Example 3 of the present invention;

[0050] Figure 5 It is the average RMSE and MAE indicator distribution of each prediction model in Case 2 of Example 3 of the present invention. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the technical solution of the present invention is clearly and completely described below in combination with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] Example 1

[0053] like Figure 1 and Figure 2 As shown, this embodiment provides a method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics, comprising the following steps:

[0054] Step 1: input the voltage data, time information (timestamp t), and spatial information (node ​​coordinates X, Y) measured by the measuring device into the learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to the adjacent low-voltage distribution network nodes by the random forest algorithm to obtain the voltage data of the adjacent low-voltage distribution network nodes;

[0055] In step 1, the process of judging the amplitude of the voltage data measured by the measuring device is also included. When the amplitude of the voltage data is judged to be equal to 0, the data is excluded and the state of the measuring device is detected. The measuring device is usually a sensor.

[0056] The random forest algorithm represents a class of tree-based ensemble methods suitable for supervised classification and regression tasks, where the output is a categorical label in the case of classification and a continuous numeric value for regression problems.

[0057] The learning supervised regression model is trained by training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

[0058] The step one comprises:

[0059] 1.1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n,

[0060] 1.2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i Nonlinear function mapping, and in a separate bootstrap sample ~T b Independently generated.

[0061] 1.3. In order to avoid high correlation between regression trees, each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement. The split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. The quality of the split is measured by the mean square error criterion.

[0062] 1.4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes. The calculation formula for the final prediction result is:

[0063]

[0064] In formula (1), is the final prediction result, B is the number of regression trees, Tb (x) is the prediction result of the bth regression tree.

[0065] The optimal segmentation of the segmentation procedure in step 1.3 includes two methods: one is for the feature subset q, and the other is for the entire input feature set p. When all predictor variables are used as segmentation candidates at each node, the random forest algorithm is no longer used, but the Bagging Regression Tree (BRT) algorithm is used, which is the characteristic case when q=p.

[0066] Step 2: Train the learning supervised regression model. When the regression index is the smallest, stop the training to obtain a trained learning supervised regression model.

[0067] When training the learning supervised regression model, the input of the learning supervised regression model is the voltage data, time information, and spatial information measured by the measuring device, and the output is the voltage data of the adjacent low-voltage distribution network nodes. The voltage data of the adjacent low-voltage distribution network nodes are compared with the true value of the node voltage, and the root mean square error and the mean absolute error are calculated. When the root mean square error and the mean absolute error are both minimized, the training is stopped to obtain a trained learning supervised regression model.

[0068] The present invention uses two regression indicators, root mean square error and mean absolute error, to evaluate the performance of the learning supervised regression model. The calculation formula of the root mean square error is:

[0069]

[0070] The formula for calculating the mean absolute error is:

[0071]

[0072] In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

[0073] The RMSE metric tends to penalize larger prediction errors more severely, while the MAE metric does not weight larger errors as much as the RMSE. The lower the values ​​of these two metrics, the better the prediction model is likely to be.

[0074] When training the supervised regression model in step 2, the samples are divided into training samples and test samples, and the data percentages of the training samples and the test samples are directly determined by the percentages of the monitored and unmonitored nodes, respectively.

[0075] Step 3: Use the trained supervised learning regression model to estimate the voltage of unmonitored nodes in the low-voltage distribution network. The output of the supervised learning regression model is the voltage estimate of the i-th node.

[0076] The present invention takes into account the background of large-scale access of distributed photovoltaic to low-voltage distribution network. Photovoltaic is scatteredly connected to the low-voltage distribution network, which will not only affect the connected nodes, but also many nearby nodes, resulting in changes in the voltage level of each node of the entire low-voltage distribution network system. In the face of this situation, the traditional voltage estimation method cannot accurately estimate the voltage data of the unmonitored nodes, and considering the low coverage rate of the voltage monitoring device of the low-voltage distribution network, the monitoring device is only installed at a limited number of nodes in the low-voltage distribution network. For the low-voltage distribution network with weak monitoring and missing data samples, the present invention is a data-sparse voltage estimation method, based on the measurement data of limited nodes, by mapping the limited node measurement data to adjacent nodes without measurement devices, and then estimating the voltage of the unmonitored nodes in the low-voltage distribution network containing distributed photovoltaics, which can more realistically understand the voltage level of the low-voltage distribution network with sparse monitoring devices as a whole, more accurately grasp the voltage status of the low-voltage distribution network, improve the observability of the low-voltage distribution network, timely adjust and optimize the operation of the power grid, improve the stability and power supply quality of the power grid, and can replace or supplement smart meter data and pseudo-measurement values.

[0077] Example 2

[0078] This embodiment provides a voltage estimation system for a low-voltage distribution network including distributed photovoltaics, including:

[0079] A mapping module is used to input the voltage data, time information and spatial information measured by the measuring device into the learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to the adjacent low-voltage distribution network nodes by the random forest algorithm to obtain the voltage data of the adjacent low-voltage distribution network nodes;

[0080] The learning supervised regression model is trained by training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

[0081] The mapping module is also used to:

[0082] 1.1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n;

[0083] 1.2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i The nonlinear function mapping and in separate bootstrap samples Independently generated above;

[0084] 1.3. Each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement, and the split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. When the feature subset q is equal to the total number of features p, the Bagging regression tree algorithm is used for splitting;

[0085] 1.4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes. The calculation formula for the final prediction result is:

[0086]

[0087] In formula (1), is the final prediction result, B is the number of regression trees, T b (x) is the prediction result of the bth regression tree.

[0088] The training module is used to train the learning supervised regression model. When the regression index is the smallest, the training is stopped to obtain the trained learning supervised regression model. The regression indexes in the training module include the root mean square error and the mean absolute error. The calculation formula of the root mean square error is:

[0089]

[0090] The formula for calculating the mean absolute error is:

[0091]

[0092] In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

[0093] The voltage estimation module is used to estimate the voltage of unmonitored nodes in the low-voltage distribution network using the trained learning supervised regression model.

[0094] Example 3

[0095] This embodiment evaluates the applicability of the voltage estimation method of a low-voltage distribution network containing distributed photovoltaics in Embodiment 1 and the voltage estimation system of a low-voltage distribution network containing distributed photovoltaics in Embodiment 2 through specific case analysis.

[0096] Case 1: A case analysis is conducted on a feeder in the SMART-DS synthetic data set. When the residential rooftop photovoltaic is added, the voltage curve distribution of the low-voltage distribution station area will move to the right. Two low-voltage parts of the feeder are selected, 480V and 208V respectively, and the voltage amplitude is approximately in the range of 0.98-1.03 times the baseline value.

[0097] When distributed rooftop photovoltaics are not considered, the distribution of average indicators is as follows: Figure 3 As shown, each box plot corresponds to a regression model, and the traditional least squares linear regression is used as the baseline method. It can be seen from the figure that compared with the 208V case, the average RMSE and MAE of the tree model in the 480V case are 2.8-2.9 times higher. Figure 4 The average RMSE for different proportions of potential monitoring nodes in all random samples is shown. The tree model significantly outperforms the baseline model in all analyzed observability cases. When 50% or more of the voltage measurements are available, the RMSE of the best model drops to 1.8 10 in the case of a 208 V network. -3 and below.

[0098] Case 2: Table 1 summarizes the average performance indicators of all observability scenarios after adding rooftop photovoltaics in the distribution station area. It can be found that the average RMSE and MAE of the tree model in this case are 2.10 higher -4 and 0.13·10 -4 As with the case without considering rooftop PV, the distribution of average indicators is as follows Figure 5 As shown in Figure 2, it can be seen that the tree model is better than the baseline model, and the average voltage estimation value of the random forest algorithm is also better than that of the BRT algorithm.

[0099] Table 1

[0100]

[0101] In general, the voltage estimation method of the low-voltage distribution network containing distributed photovoltaics in the present invention can analyze the voltage level of the low-voltage distribution network with a high penetration rate of distributed photovoltaics based on limited data, solve the problem of insufficient monitoring and observation equipment for the low-voltage distribution network to a certain extent, and can accurately and quickly analyze the impact of distributed photovoltaics on the voltage of the low-voltage distribution network, ensuring the safe and stable operation of the distribution station area. At the same time, the method of the present invention also provides strong technical support for the further integration and utilization of distributed photovoltaics, which helps to promote energy transformation and the development of smart grids.

[0102] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics, characterized in that: The following steps are involved: Step 1: input the voltage data, time information, and spatial information measured by the measuring device into a learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to adjacent low-voltage distribution network nodes by a random forest algorithm to obtain voltage data of adjacent low-voltage distribution network nodes. Step 2: Train the learning supervised regression model. When the regression index is the smallest, stop the training to obtain a trained learning supervised regression model. Step 3: Use the trained learning supervised regression model to estimate the voltage of unmonitored nodes in the low-voltage distribution network.

2. The method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics according to claim 1 is characterized in that: The learning supervised regression model is trained by training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

3. The method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics according to claim 2 is characterized in that: The step one comprises: 1.

1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n; 1.

2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i The nonlinear function mapping and in separate bootstrap samples Independently generated above; 1.

3. Each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement, and the split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. When the feature subset q is equal to the total number of features p, the Bagging regression tree algorithm is used for splitting; 1.

4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes.

4. The method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics according to claim 3 is characterized in that: The calculation formula for the final prediction result is: In formula (1), is the final prediction result, B is the number of regression trees, T b (x) is the prediction result of the bth regression tree.

5. The method for estimating voltage of a low-voltage distribution network containing distributed photovoltaics according to claim 1, characterized in that: The regression indicators in step 2 include root mean square error and mean absolute error. The calculation formula of root mean square error is: The formula for calculating the mean absolute error is: In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

6. A voltage estimation system for a low-voltage distribution network containing distributed photovoltaics, characterized in that: include: A mapping module is used to input the voltage data, time information and spatial information measured by the measuring device into the learning supervised regression model. The learning supervised regression model maps the voltage data measured by the measuring device to the adjacent low-voltage distribution network nodes by the random forest algorithm to obtain the voltage data of the adjacent low-voltage distribution network nodes; The training module is used to train the learning supervised regression model. When the regression index is the smallest, the training is stopped to obtain the trained learning supervised regression model. The voltage estimation module is used to estimate the voltage of unmonitored nodes in the low-voltage distribution network using the trained learning supervised regression model.

7. The voltage estimation system for a low-voltage distribution network containing distributed photovoltaics according to claim 6 is characterized in that: The learning supervised regression model is trained by training samples T, and the training samples T include n pairs of output variables y i and the p-dimensional input vector x i , x i ∈R p ,y i ∈R, i=1,...,n.

8. The voltage estimation system for a low-voltage distribution network containing distributed photovoltaics according to claim 7 is characterized in that: The mapping module is also used to: 1.

1. Randomly extract from the training sample T with replacement and create B∈N bootstrap samples through the Bagging algorithm Each bootstrap sample size is n; 1.

2. Construct multiple regression trees T b , each regression tree T b Construct from the input vector x i to the output variable y i The nonlinear function mapping and in separate bootstrap samples Independently generated above; 1.

3. Each time a split decision is made, q feature subsets are randomly selected from the total number of p features without replacement, and the split procedure is performed based on the best split node candidate in the q feature subsets to split the node into two sub-nodes. When the feature subset q is equal to the total number of features p, the Bagging regression tree algorithm is used for splitting; 1.

4. Repeat recursively for each node independently, where each regression tree T b grow to the maximum extent possible without pruning, by b The prediction results are averaged to obtain the final prediction result, that is, the voltage data of adjacent low-voltage distribution network nodes.

9. The voltage estimation system for a low-voltage distribution network containing distributed photovoltaics according to claim 8, characterized in that: The calculation formula for the final prediction result is: In formula (1), is the final prediction result, B is the number of regression trees, T b (x) is the prediction result of the bth regression tree.

10. The voltage estimation system for a low-voltage distribution network containing distributed photovoltaics according to claim 6, characterized in that: The regression indicators in the training module include root mean square error and mean absolute error. The calculation formula of the root mean square error is: The formula for calculating the mean absolute error is: In formulas (2) and (3), RMSE is the root mean square error, MAE is the mean absolute error, and y i is the true value of the voltage at the ith node, is the predicted value of the voltage of the ith node, that is, the voltage data of the adjacent low-voltage distribution network node obtained in step 1.

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