A Probability Prediction Method for Dynamic Thermal Rating of Transmission Lines Based on BILSTM-MDN

Abstract

The present invention provides a method for dynamically predicting the thermal rating probability of a transmission line based on BILSTM-MDN, belonging to the field of evaluating the operating state of power system lines. First, the ambient data around the transmission line and the DTR sequence data are normalized, and their autocorrelation coefficients are calculated. Secondly, the data are used to generate sliding window features and labels according to the common input length, and the sliding window data set is generated by rolling, and the training set and the prediction set are divided. Thirdly, a BILSTM-MDN neural network is built. After setting the hyperparameters, the training set is input for learning, and the hyperparameters are adjusted until the error reaches the minimum. Finally, the prediction accuracy of the model is evaluated through the prediction set, and the final prediction result and prediction error are obtained. In the present invention, the pre-network of MDN is replaced by BILSTM, combining the ability of BILSTM to extract temporal features and the ability of MDN to output probability density, so as to accurately predict the probability of DTR and reduce the influence of human factors between links.

Description

Technical Field

[0001] The present invention belongs to the field of power system line operation state evaluation, and evaluates the dynamic thermal rating of transmission lines through the combination of power big data and neural networks, and relates to a time-series probability prediction method combining BILSTM and MDN. Background Art

[0002] Under the background of carbon peaking and carbon neutrality proposed in 2020, a large number of new energy sources are connected to the power grid, making the proportion of new energy in the power system increase significantly. The power system with a high proportion of new energy has significantly higher requirements for aspects such as the consumption capacity of new energy, the optimal dispatching capacity of the power system, and the resource allocation capacity. And using the thermal rating to evaluate the line operation state of the power system is a basic way to evaluate the line transmission capacity. Under this condition, it is necessary to improve the line transmission capacity according to the dynamic thermal rating.

[0003] At the current stage, power workers adopt a conservative method represented by the static thermal rating (STR) for the thermal stability condition limitation of overhead transmission lines. That is, STR is calculated under the assumption that relatively unfavorable meteorological conditions (high ambient temperature, low wind speed, strong sunlight) occur simultaneously, and once set, it remains unchanged for a long time. Although it is convenient to use, it also has obvious conservativeness. The dynamic thermal rating (DTR) aims to calculate the overhead conductor current-carrying capacity according to the real-time measurement data of the conductor micro-meteorology. Practical applications show that in most cases, the DTR of overhead lines is significantly higher than STR, fully revealing the time-varying nature and exploration potential of the overhead conductor current-carrying capacity, as well as the huge energy-saving and emission-reduction benefits that can be brought by making full use of this transmission potential.

[0004] Compared with the point prediction method that only predicts the expected future value, probability prediction can predict the probability distribution of future values. Therefore, it can highly quantify the uncertainty caused by environmental factors, provide more comprehensive information for the safe and stable operation of the system, and thus better guide the daily dispatching.

[0005] Existing methods for DTR probability prediction include gradient boosting decision tree (GBDT), random forest (RF), and mixture density network (MDN). GBDT and RF obtain the probability density of the predicted value through quantile regression and kernel density estimation. Although quantile prediction is easy to implement and widely used, the problem of quantile crossing is often ignored in quantile prediction, resulting in unreasonable actual quantile prediction results. Moreover, the estimation effect of kernel density estimation is greatly affected by subjective factors when selecting the kernel function and bandwidth. MDN does not have the problems caused by quantile regression and kernel density estimation, but a single MDN network cannot well learn the temporal features in the data, which is not conducive to improving the prediction accuracy. Compared with the above methods, BILSTM-MDN does not have the problems caused by quantile regression and kernel density estimation, and also takes into account the temporal features of the data, having the most comprehensive and accurate probability prediction ability. Summary of the Invention

[0006] Aiming at the problems existing in the prior art, the present invention provides a method for predicting the DTR probability of a transmission line by using power big data and neural network technology to consider the uncertainty of environmental data and improve the accuracy of DTR prediction.

[0007] To achieve the above object, the present application adopts the following technical solutions:

[0008] A method for predicting the DTR probability of a transmission line based on BILSTM-MDN, the method comprising the following steps:

[0009] Step 1: Select a section of transmission line, and normalize the environmental data (including wind speed sequence, wind direction sequence, environmental temperature sequence, and solar irradiance sequence) and DTR sequence data around the transmission line, and its value range is [0,1], and the formula is as follows:

[0010]

[0011] where x is the data to be processed, x min is the minimum value in the data, x max is the maximum value in the data, x * is the normalized value.

[0012] Step 2: Calculate the autocorrelation coefficients of the wind speed sequence, wind direction sequence, environmental temperature sequence, solar irradiance sequence, and DTR sequence respectively. Take the length of the sequence before the time point when the autocorrelation coefficient is less than 0.6 for the first time as the input length of the sequence, and select the largest one among all the input lengths as the common input length M of all the sequences.

[0013] The formula for calculating the autocorrelation coefficient is as follows:

[0014]

[0015] where N is the length of the sequence, k is the length of the lag (when k = 1, it is to calculate the correlation coefficient between two adjacent values in the sequence), x i is the i-th value in the sequence, x i-k is the i-th value in the sequence, is the mean value of the sequence.

[0016] Step 3: Generate sliding window features and labels from the data according to the common input length calculated in Step 2. When the calculated input length is M, the first to M-th rows of the wind speed sequence, wind direction sequence, ambient temperature sequence, solar irradiance sequence, and DTR sequence in the dataset are used as the input data matrix, while the (M + 1)-th of the DTR data is used as the target data (the model iterates by reducing the error between the target data and the output data), and a sliding window dataset is generated by rolling (i.e., the second to (M + 1)-th rows are used as the input data matrix, and the (M + 2)-th of the DTR data is used as the target data, and so on). The sliding window dataset generated by rolling is divided into a training part and a prediction part according to a ratio of 7:3. The training part is used for parameter learning of the model, and the prediction part is used for testing and evaluating the training results;

[0017] Step 4: Build a BILSTM-MDN neural network. After setting relevant hyperparameters, input the training part of the sliding window dataset for learning to obtain the error of the training part, and then adjust the hyperparameters until the error reaches the minimum (i.e., reaching the limit performance of the model).

[0018] The structure of the built BILSTM-MDN neural network is, from front to back, an input layer, a BILSTM layer, a fully connected layer, an MDN layer, and an output layer.

[0019] The network inputs the training data through the input layer, extracts the temporal features in the data through the BILSTM, and then obtains the probability density of the predicted value through the MDN layer. The probability distribution is obtained by integrating the probability density. Among them:

[0020] BILSTM is composed of a forward LSTM neural network that operates from front to back (as Figure 1 shown) and a backward LSTM neural network that operates from back to front stacked together.

[0021] The network structure of the mixture density network (MDN) consists of two hidden layers and an output layer. The output layer outputs the σ, μ, and π parameters of the Gaussian mixture model. When the input variable x is given, the Gaussian mixture model gives the conditional probability distribution p(y|x) in the form of formula (3):

[0022]

[0023] where m is the number of mixture distribution components, and π i (x) is the mixing coefficient of the i-th Gaussian component, and μ i (x) and σ i (x) correspond to the mean and variance of the i-th Gaussian component, respectively.

[0024] It should be noted that the sum of all mixing coefficients should be 1, as shown in formula (4).

[0025]

[0026] Usually, the softmax function is used to output the value of π i (x), and its expression form is as shown in formula (5)

[0027]

[0028] In formula (5) is the output of the previous layer network. The softmax function ensures that the sum of the output mixture component coefficients is 1, and each mixing coefficient is within the range of [0, 1].

[0029] The standard deviation σ i (x) and the mean μ i (x) are output in the following form to ensure that they are greater than 0:

[0030]

[0031]

[0032] where and are the output values of the previous layer network.

[0033] Finally, the loss function of the mixture density network is constructed through the maximum likelihood function, and its defined formula is as follows:

[0034]

[0035] The value of logL(y|x) will gradually decrease with iterations during the training process, indicating that the prediction error decreases.

[0036] Step 5: Save the trained model, evaluate the prediction accuracy of the model using the prediction part of the data separated in Step 3, and obtain the final prediction result and prediction error. After predicting the probability density through BILSTM-MDN, calculate its confidence interval by integration. After calculating its confidence interval, evaluate the prediction accuracy using four criteria: average coverage error (ACE), prediction interval normalized averaged width (PINAW), interval sharpness (IS), and continuous rank probability score (CRPS).

[0037] ACE = PIC - PINC (9)

[0038]

[0039]

[0040]

[0041]

[0042] In equations (9) and (12), PINC is the nominal confidence level, and PIC is the average coverage rate (i.e., the proportion of the true value between the upper and lower limits).

[0043] In equations (10), (11), (12), and (13), n is the total number of data in the prediction part, y i is the predicted value, is the lower limit of the prediction interval, is the upper limit of the prediction interval.

[0044] In equation (13), CDF f,i (x) is the predicted probability distribution corresponding to y i , and H(y - y i ) is 1 when y is greater than or equal to y i , and 0 otherwise.

[0045] In the present invention, the pre-network of MDN is replaced by BILSTM, combining the time-series feature extraction ability of BILSTM and the ability of MDN to output probability density, so as to accurately predict the probability of DTR.

[0046] Compared with the existing methods, the beneficial effects of the present invention are as follows: (1) BILSTM can well learn the temporal features in the data, which is beneficial to improving the accuracy of the model. (2) By predicting the probability density of the predicted value, the uncertainty of environmental factors can be well quantified, providing the most comprehensive information and better guiding the day-ahead scheduling. (3) Instead of predicting the environmental value first and then calculating DTR through the IEEE738 standard, the direct prediction method of directly predicting the future DTR value through the historical DTR value and environmental value reduces the influence of human factors between links. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a schematic diagram of the LSTM structure;

[0048] Figure 2 is the autocorrelation coefficient of the environmental temperature feature;

[0049] Figure 3 is the prediction confidence interval of BILSTM-MDN. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] In order to make the objectives, technical solutions and advantages of the present application more clear and understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0051] In the embodiment of the present application, DTR data and environmental data (including wind speed, wind direction, environmental temperature and solar irradiance) with a time resolution of 1h from March 1, 2015 to June 1, 2015 of an overhead conductor with a model of LGJ 400 / 35 at a 220kv voltage level in Liaoning Province are collected as experimental data.

[0052] The experiment is based on the Pycharm IDE, Python 3.9 language, Pytorch framework and various other function libraries.

[0053] In the first step, the obtained data is in csv format. The dataset is read through the pandas function library and saved in Dataframe format. The collected data is normalized, and the calculation method is shown in formula (1).

[0054] In the second step, the common input length M of all sequences is determined by calculating the autocorrelation coefficient. According to the definition of the autocorrelation coefficient, when the autocorrelation coefficient is greater than 0.6, the sequence has strong correlation. In this example, it is calculated that the sequence with the longest correlation is the environmental temperature feature, and the sequence length is 29. Therefore, 29 is selected as the common input length M.

[0055] In the third step, the data is generated into a sliding window dataset with a length of 29, and the first 70% of the data is used as the training part, and the last 30% of the data is used as the prediction part.

[0056] In the fourth step, put part of the training data into the established BILSTM-MDN model for iterative training until the best effect is achieved.

[0057] First, initialize the hidden layer of the BILSTM network according to the set hyperparameters (including num_directions, stacked_layers, batch_size, hidden_size).

[0058] Then, input the training data into the BILSTM network. The forward propagation layer of the BILSTM contains 64 neurons, and the backward propagation layer contains 64 neurons. The output shape of the BILSTM layer is [num_output, M, hidden_size], where num_output is the number of points predicted by the model (in this example, num_output = 1), and hidden_size is the number of neurons.

[0059] Then, use three independent fully connected networks to perform fully connected calculations on the output of the BILSTM layer. The process of the fully connected calculation can be expressed as y t = ω d x t + b d , where ω d , b d are parameters to be learned, and y t is the output value of this step. The outputs of the three fully connected networks respectively correspond to π, μ, and σ in the MDN network, and the output shape is [num_output, M, m], where m is the number of Gaussian components in the Gaussian mixture model.

[0060] Take the last time step of the outputs of the three fully connected networks (i.e., code[:, -1, :]) as the output results of π, μ, and σ respectively. Process π using the softmax function to ensure that the sum of the output mixture component coefficients is 1, and each mixture coefficient is within the range of [0, 1]; use the exp function for μ and σ to ensure that they are greater than 0.

[0061] Substitute the calculated π, μ, and σ into the loss function composed of the maximum likelihood function, update the network parameters through backpropagation, and continuously iterate until the value of the loss function reaches the lowest.

[0062] Adjust the hyperparameters through Bayesian optimization, and repeat the above process until the optimal hyperparameters are found.

[0063] The final hyperparameters in this example are as follows: the learning rate is 0.0003, the batch_size is 12, the drop_out is 0.4, the optimizer is Adam, the weight_decay is 0.0001, and the n_epochs is 350.

[0064] Step 5: Evaluate the accuracy of the model by predicting some data: After predicting the probability density through BILSTM-MDN, calculate its confidence interval through integration, calculate four metrics: ACE, PINAW, IS, and CRPS, and compare the prediction effects with those of three models: MDN, GBDT-QR-KDE, and RF-QR-KDE. Among them, GBDT refers to Gradient Boosting Decision Tree, RF refers to Random Forest, QR refers to Quantile Regression, and KDE refers to Kernel Density Estimation.

[0065] Table 1 Comparison of prediction effects of several models

[0066]

[0067] From the perspective of ACE, RF is the best, BILSTM-MDN is the second best, MDN is the third best, and GBDT has the worst effect; from the perspective of PINAW, BILSTM-MDN is the best, MDN is the second best, GBDT is the third best, and RF is the worst; from the perspective of IS, BILSTM-MDN is the best, MDN is the second best, GBDT is the third best, and RF is the worst; from the perspective of CRPS, BILSTM-MDN is the best, GBDT is the second best, MDN is the third best, and RF is the worst. Considering the above several metrics, although RF has better performance in terms of the average coverage error, its comprehensive performance is relatively low due to the large width, while BILSTM-MDN is superior to other models in the remaining metrics. It can be seen that BILSTM-MDN has certain superiority in DTR probability prediction.

[0068] The above content is only to illustrate the technical idea of this application and cannot be used to limit the protection scope of this application. Any changes made on the basis of the technical solution according to the technical idea proposed in this application fall within the protection scope of the claims of this application.

[0069] In addition, unless expressly stated in the claims, the order of the processing elements and sequences, the use of numerical letters, or the use of other names described in this application are not used to limit the order of the processes and methods of this application. Although some currently useful embodiments are discussed through various examples in the above disclosure, it should be understood that such details are for illustrative purposes only. The appended claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that conform to the essence and scope of the embodiments of this application. For example, although the system components described above can be implemented by hardware devices, they can also be implemented only through software solutions, such as installing the described system on existing servers or mobile devices.

[0070] Similarly, it should be noted that, in order to simplify the description of the disclosure of this application and thus help the understanding of one or more embodiments, in the foregoing description of the embodiments of this application, sometimes multiple features are merged into one embodiment, drawing, or description thereof. However, this disclosure method does not mean that the features required by the subject matter of this application are more than those mentioned in the claims. In fact, the features of the embodiments are fewer than all the features of the individual embodiments disclosed above.

[0071] For each patent, patent application, patent application publication, and other materials cited in this application, such as articles, books, specifications, publications, documents, etc., their entire contents are hereby incorporated into this application by reference. Except for the application history documents that are inconsistent with or conflict with the content of this application, and except for the documents that limit the broadest scope of the claims of this application (currently or subsequently appended to this application). It should be noted that if there are inconsistencies or conflicts between the descriptions, definitions, and / or uses of terms in the supplementary materials of this application and the content described in this application, the descriptions, definitions, and / or uses of terms in this application shall prevail.

Claims

1. A dynamic thermal rating probability prediction method for transmission lines based on BILSTM-MDN, characterized in that, It includes the following steps: Step 1: Select a section of transmission line, and normalize the environmental data and DTR sequence data around the transmission line, with the value range being [0, 1]. Among them, the environmental data includes the wind speed sequence, wind direction sequence, environmental temperature sequence, and solar irradiance sequence; Step 2: Calculate the autocorrelation coefficients of the wind speed sequence, wind direction sequence, environmental temperature sequence, solar irradiance sequence, and DTR sequence respectively; Take the length of the sequence before the time point when the autocorrelation coefficient is less than 0.6 for the first time as the input length of the sequence, and select the largest one among all the input lengths as the common input length M of all sequences; Step 3: Generate sliding window features and labels from the data according to the common input length calculated in Step 2; When the calculated input length is M, take the first to the M-th rows of the wind speed sequence, wind direction sequence, environmental temperature sequence, solar irradiance sequence, and DTR sequence in the dataset as the input data matrix, and the (M + 1)-th of the DTR data as the target data, and generate a sliding window dataset by rolling; Divide the generated sliding window dataset into a training part and a prediction part. The training part is used for parameter learning of the model, and the prediction part is used for testing and evaluating the training results; Step 4: Build a BILSTM-MDN neural network. After setting the hyperparameters, input the training part of the sliding window dataset for learning to obtain the error of the training part, and then adjust the hyperparameters until the error reaches the minimum; Replace the pre-network of the traditional MDN with BILSTM, and combine the ability of BILSTM to extract temporal features and the ability of MDN to output probability density to make an accurate probability prediction for DTR; Step 5: Save the trained model, evaluate the prediction accuracy of the model through the prediction part data separated in Step 3, and obtain the final prediction result and prediction error; After predicting the probability density through BILSTM-MDN, calculate its confidence interval through integration; After calculating its confidence interval, evaluate the accuracy of the prediction.

2. The dynamic thermal rating probability prediction method for transmission lines based on BILSTM-MDN according to claim 1, characterized in that In the above-mentioned Step 4, the built BILSTM-MDN neural network structure is, from front to back, the input layer, BILSTM layer, fully connected layer, MDN layer, and output layer; The network inputs the training data through the input layer, extracts the temporal features in the data through BILSTM, and then obtains the probability density of the predicted value through the MDN layer. The probability density obtained by integration is the probability distribution; Among them: BILSTM is composed of a forward LSTM neural network operating from front to back and a backward LSTM neural network operating from back to front stacked together; The network structure of the mixture density network MDN includes two hidden layers and an output layer. The output layer outputs the σ, μ, and π parameters of the Gaussian mixture model; When a given input variable x is given, the Gaussian mixture model gives the conditional probability distribution p(y|x) in the form of formula (3): where m is the number of mixture distribution components, and π i (x) is the mixing coefficient of the i-th Gaussian component, and μ i (x) and σ i (x) correspond to the mean and variance of the i-th Gaussian component; It should be noted that the sum of all mixing coefficients should be 1, as shown in formula (4); The softmax function is usually used to output the value of π i (x), and its expression is shown in formula (5) In formula (5) is the output of the previous layer network. The softmax function ensures that the sum of the output mixture component coefficients is 1, and each mixture coefficient is within the range of [0, 1]; Standard deviation σ i (x) and mean μ i (x) is output in the following form to ensure that it is greater than 0: Among them, and are the output values of the upper-layer network; Finally, construct the loss function of the mixture density network through the maximum likelihood function, and its defined formula is as follows: The value of logL(y|x) will gradually decrease with iterations during the training process, indicating a reduction in the prediction error.

3. A method for predicting the probability of dynamic thermal rating of a transmission line based on BILSTM-MDN according to claim 1, characterized in that In step 5, after calculating its confidence interval, the accuracy of the prediction is evaluated by four criteria: the average coverage error ACE, the average width of the prediction interval PINAW, the interval sharpness IS, and the continuous ranked probability score CRPS. The specific formulas are as follows: ACE = PIC - PINC (9) In equations (9) and (12), PINC is the nominal confidence level, and PIC is the average coverage rate (i.e., the proportion of the true value between the upper and lower limits). In formulas (10), (11), (12), and (13), n is the total number of prediction part data, y i is the predicted value, is the lower limit of the prediction interval, is the upper limit of the prediction interval; In Equation (13), CDF f,i (x) is the predicted probability distribution corresponding to y i , and H(y - y i ) is 1 when y is greater than or equal to y i ; otherwise, it is 0.

4. A dynamic thermal rating probability prediction method for transmission lines based on BILSTM-MDN according to claim 1, characterized in that, In step 2, the formula for calculating the autocorrelation coefficient is as follows: where N is the length of the sequence; k is the length of the lag, and when k is 1, it is to calculate the correlation coefficient between two adjacent values in the sequence; x i is the i-th value in the sequence, x i-k is the i-th value in the sequence, is the mean value of the sequence.

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