New energy power system line blocking early warning method based on yoke model

Abstract

The invention discloses a new energy power system line blocking early warning method based on a yoke model, and belongs to the technical field of electrical engineering, and the method comprises the steps: S1, segmenting the historical data of a new energy power system through a Gaussian mixture model based on an improved sequence, and obtaining a classification result, carrying out matching processing on Gaussian samples in the classification result to obtain a Gaussian distribution sequence; s2, performing correlation decoupling on the Gaussian distribution sequence by using a yoke model to obtain a reduction matrix and an independent distribution sequence; s3, simulating the independent distribution sequence to generate an independent sampling sample, and restoring the independent sampling sample into a feature sampling sample meeting classification result distribution features through a restoration matrix; and S4, performing early warning based on the prediction error interval obtained by the feature sampling sample and the constraint condition of the new energy power system. The technical problem of low line congestion prediction accuracy caused by the fact that the evolution rule of prediction errors along with time is not considered is solved, and the accuracy of line congestion prediction is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electrical engineering, and specifically to a method for early warning of line congestion in a new energy power system based on a martingale model. Background Technique

[0002] With the vigorous development of new energy, its large-scale grid connection has brought more severe challenges to the power distribution network. In order to ensure the stable operation and high reliability of the power distribution network, it has become extremely crucial to give early warning of line congestion. On this basis, accurately predicting line congestion has become an essential link to ensure the safe and stable operation of the power grid. The existing technologies mainly focus on the performance of the prediction model itself and the adaptation scenarios. For example, a method and system for obtaining line congestion in a power system with the patent publication number CN109345142A includes: calculating the direct current power transfer distribution factor of the power system; establishing a priority matrix; judging whether there is line congestion in the power system under a certain priority according to the direct current power flow of the power system under the priority; determining the reduction ratio of the congested line in the power system under the priority where line congestion occurs; determining the proportional relationship between the reduced power of each generator under the priority; solving the pre-established power system line congestion model to obtain the line congestion result of the power system under the priority. However, the above scheme does not pay attention to the evolution law of the prediction error with time brought by load and new energy prediction technologies. And due to the high randomness and volatility of new energy output, even if the accuracy of the prediction model itself is carefully optimized, it is difficult to avoid abnormal fluctuations in the prediction error. Therefore, the accuracy of line congestion prediction is low. Summary of the Invention

[0003] Aiming at the technical problem that the existing technology does not consider the evolution law of the prediction error with time, resulting in low accuracy of line congestion prediction, the present invention provides a method for early warning of line congestion in a new energy power system based on a martingale model. By using a Gaussian mixture model to match Gaussian samples, a Gaussian distribution sequence that can be processed by the martingale model is obtained. Through the memoryless property of the martingale model, the Gaussian distribution sequence is decoupled in terms of correlation to obtain a reduction matrix and an independent distribution sequence that are mutually independent. Further, a large number of independent sampling samples are generated according to the mutually independent independent distribution sequence. Then, the reduction matrix is used to restore the features of the large number of independent sampling samples to obtain feature sampling samples, and prediction is carried out through the feature sampling samples. The technical problem that the low accuracy of line congestion prediction is caused by not considering the evolution law of the prediction error with time is solved, and the accuracy of line congestion prediction is significantly improved.

[0004] To solve the above technical problems, the present invention provides a method for early warning of line congestion in a new energy power system based on a martingale model, including the following steps: S1: Based on the improved sequence, use the Gaussian mixture model to segment the historical data of the new energy power system to obtain the classification results, and perform matching processing on the Gaussian samples in the classification results to obtain the Gaussian distribution sequence; S2: Use the martingale model to decouple the correlation of the Gaussian distribution sequence to obtain the reduction matrix and the independent distribution sequence; S3: Simulate the independent distribution sequence to generate independent sampling samples, and restore the independent sampling samples into characteristic sampling samples that meet the distribution characteristics of the classification results through the reduction matrix; S4: Issue a warning based on the prediction error interval obtained from the characteristic sampling samples and the constraint conditions of the new energy power system.

[0005] After adopting the above technical solutions, the present invention has the following advantages: Considering that when the sample size is large enough, all prediction error situations including extreme cases can be reproduced. In the process of obtaining a large number of samples in the prior art, a large amount of time and resources are consumed. In particular, due to the rarity of extreme cases and the scarcity of samples related to extreme cases, sufficient independent sampling samples are obtained by simulation. However, before simulation, due to the temporal correlation between Gaussian distribution sequences, the simulation complexity is relatively high. Therefore, the martingale model's memoryless property is used to decouple the correlation of the Gaussian distribution sequence to obtain mutually independent independent distribution sequences, and then sufficient independent sampling samples are obtained by simulating the mutually independent independent distribution sequences. Further, considering that Gaussian samples are difficult to be directly processed by the martingale model, the Gaussian samples are matched through the Gaussian mixture model to obtain a Gaussian distribution sequence that can be processed by the martingale model. After obtaining sufficient independent sampling samples, the characteristics of a large number of independent sampling samples are restored through the reduction matrix to obtain characteristic sampling samples, realizing the restoration of temporal correlation. Finally, a warning is issued through the characteristic sampling samples, solving the technical problem of low accuracy of line congestion prediction caused by the failure to consider the evolution law of prediction errors over time, and significantly improving the accuracy and efficiency of line congestion prediction; At the same time, by effectively restoring extreme cases of abnormal fluctuations in prediction errors, the accident losses caused by abnormal fluctuations in prediction errors are reduced, and the safety, stability, and reliability of the new energy power system are improved.

[0006] Preferably, the S1 includes: S11: Obtain the difference between the prediction errors at adjacent moments in the rolling prediction error data in the historical data according to the definition of the prediction evolution martingale, and obtain the improved sequence based on the difference; S12: Using the characteristics of the improved sequence as the segmentation benchmark, segment the historical data through the Gaussian mixture model to obtain the classification results.

[0007] Preferably, in S1, the process of obtaining the Gaussian distribution sequence by matching the Gaussian samples in the classification results includes: S1a: Obtain the initial values of the parameters in the Gaussian mixture model through a clustering algorithm; S1b: Obtain the probability that the Gaussian samples belong to the Gaussian distribution based on the initial values of the parameters, update the initial values of the parameters based on the probability, and execute S1c until the preset requirements are met, otherwise execute S1b in rounds; S1c: Perform normalization processing on the Gaussian samples based on the initial values of the parameters, perform unbiased processing on the Gaussian samples based on the mean in the initial values of the parameters to obtain unbiased distribution samples, and obtain the Gaussian distribution sequence based on the unbiased distribution samples.

[0008] Preferably, S1c further includes: Taking the longest unbiased distribution sample in the unbiased distribution samples as the filling benchmark, fill the unbiased distribution samples.

[0009] Preferably, S2 includes: S21: Obtain the reduction matrix based on the variance and covariance of the Gaussian distribution sequence, and perform Cholesky decomposition on the reduction matrix to obtain a lower triangular matrix; S22: Decouple the correlation of the Gaussian distribution sequence based on the lower triangular matrix to obtain an independent distribution sequence.

[0010] Preferably, the independent distribution sequence in S22 is expressed as follows: ; In the formula, represents the Gaussian distribution sequence, represents the lower triangular matrix is the transpose of, represents the independent distribution sequence.

[0011] Preferably, S3 includes: S31: Perform Monte Carlo simulation on the independent distribution sequence to generate independent sampling samples, perform Cholesky decomposition on the reduction matrix to obtain a lower triangular matrix, and obtain characteristic sampling samples that meet the distribution characteristics of the classification results based on the lower triangular matrix.

[0012] Preferably, the characteristic sampling samples in S31 are expressed as follows: ; In the formula, represents the independent sampling samples, represents the lower triangular matrix is the transpose of, represents the characteristic sampling samples.

[0013] Preferably, S4 includes: S41: Update the feature sampling samples using the mean value in the initial parameter values obtained in S1a; S42: Obtain the quantiles according to the engineering accuracy requirements, and obtain the prediction error intervals corresponding to each prediction moment in the feature sampling samples based on the quantiles; S43: Accumulate the prediction error intervals corresponding to each prediction moment based on the definition of the prediction evolution martingale to obtain the fluctuation interval range. Based on the constraint conditions, use the interval power flow method to obtain the power fluctuation range of the line section at each prediction moment. If the right endpoint of the fluctuation interval range is greater than the right endpoint of the power fluctuation range, give an early warning.

[0014] Preferably, in S4, the constraint conditions at least include ramp rate constraint, unit start-stop time constraint, and section limit constraint.

[0015] Beneficial effects of this solution: Considering that when the sample size is large enough, all prediction error situations including extreme cases can be reproduced. Therefore, a sufficient number of independent sampling samples are obtained through simulation. However, before simulation, due to the time correlation between Gaussian distribution sequences, the simulation complexity is relatively high. Therefore, the Gaussian distribution sequences are decoupled for correlation through the memoryless property of the martingale model to obtain independent independent distribution sequences, and then a sufficient number of independent sampling samples are obtained through simulation based on the independent independent distribution sequences. Further, considering that Gaussian samples are difficult to be directly processed by the martingale model, the Gaussian samples are matched through a Gaussian mixture model to obtain Gaussian distribution sequences that can be processed by the martingale model. After obtaining a sufficient number of independent sampling samples, the feature reduction matrix is used to perform feature reduction on a large number of independent sampling samples to obtain feature sampling samples, realizing the reduction of time correlation. Finally, early warning is carried out through the feature sampling samples, solving the technical problem of low accuracy of line congestion prediction due to the failure to consider the evolution law of prediction errors over time, and significantly improving the accuracy and efficiency of line congestion prediction; At the same time, by effectively restoring extreme cases of abnormal fluctuations in prediction errors, the accident losses caused by abnormal fluctuations in prediction errors are reduced, and the safety, stability, and reliability of the new energy power system are improved; In order to retain the data characteristics of the unbiased distribution samples and at the same time meet the requirements of using the martingale model to obtain the reduction matrix, the unbiased distribution samples are filled based on the longest unbiased distribution sample as the filling benchmark, so that the independent sampling samples can be feature-reduced according to the reduction matrix, and then prediction is carried out based on a large number of feature sampling samples after feature reduction, further improving the accuracy of line congestion prediction. Description of the Drawings

[0016] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments read in conjunction with the accompanying drawings. The drawings are only for the purpose of illustrating the preferred embodiments and are not considered to be a limitation of the present invention. Also, throughout the drawings, the same reference numerals are used to represent the same components.

[0017] Figure 1 This is a flowchart of the method for warning of line congestion in a new energy power system based on the martingale model of the present invention. Detailed implementation manners

[0018] To make the purpose, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the drawings and embodiments. It should be understood that the specific implementation manners described herein are only the best embodiments of the present invention, only for explaining the present invention, and do not limit the protection scope of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0019] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts depict the operations (or steps) as sequential processes, many of the operations (or steps) can be implemented in parallel, concurrently, or simultaneously. In addition, the order of the operations can be rearranged. The process can be terminated when its operations are completed, but there can also be additional steps not included in the drawings; the process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0020] Embodiment 1: As Figure 1 shown, the method for warning of line congestion in a new energy power system based on the martingale model includes the following steps: S1: Based on the improved sequence, use the Gaussian mixture model to segment the historical data of the new energy power system to obtain the classification result, and perform matching processing on the Gaussian samples in the classification result to obtain the Gaussian distribution sequence.

[0021] The S1 includes: S11: Obtain the difference between the prediction errors at adjacent moments in the rolling prediction error data in the historical data according to the definition of the prediction evolution martingale, and obtain the improved sequence based on the difference; S12: Use the Gaussian mixture model to segment the historical data with the characteristics of the improved sequence as the segmentation basis to obtain the classification result.

[0022] In S1, the performing matching processing on the Gaussian samples in the classification result to obtain the Gaussian distribution sequence includes: S1a: Obtain the initial parameter values in the Gaussian mixture model through a clustering algorithm; S1b: Obtain the probability that a Gaussian sample belongs to a Gaussian distribution based on the initial parameter values, update the initial parameter values based on the probability, and execute S1c until the preset requirements are met, otherwise execute S1b in rounds; S1c: Perform normalization processing on the Gaussian samples based on the initial parameter values, perform unbiased processing on the Gaussian samples based on the mean in the initial parameter values to obtain unbiased distribution samples, and obtain a Gaussian distribution sequence based on the unbiased distribution samples.

[0023] The said S1c further includes: Fill the unbiased distribution samples with the longest unbiased distribution sample in the unbiased distribution samples as the filling benchmark.

[0024] The martingale model is a mathematical model based on probability theory, mainly used to describe random processes. The core ideas of the martingale model are "unbiasedness" and "memorylessness", that is, the expected value of the future only depends on the current information and has nothing to do with the past history. The martingale model has wide applications in financial mathematics, probability theory, statistics, and engineering fields (such as signal processing, time series analysis).

[0025] In this embodiment, the definition of the forecast evolution martingale is "the reduction amount of the current prediction error relative to the previous period's prediction error", that is, the reduction amount of the prediction error for the t-th moment at the c-th moment relative to the prediction error for the t-th moment at the (c - 1)-th moment, denoted as and the expression is , represents the prediction error for the t-th moment at the c-th moment, represents the prediction error for the t-th moment at the (c - 1)-th moment. The above definition of the forecast evolution martingale characterizes the update rule of the error generated by the prediction behaviors at different moments in the historical rolling prediction error data for the prediction result of the same future moment. Generally, the later the prediction behavior occurs, the more experience is obtained based on historical data, and the more accurate the prediction for the same future moment is, and the smaller the error. Then it is used to characterize the correction amount for the prediction result of the same future moment due to experience update. Therefore can also be characterized as: ; In the formula, can be expressed as the measured load or new energy power value at the t-th moment and the prediction error of predicting the t-th moment at the c-th moment The sum, and the expression is as follows ; For the prediction error of the same future moment, it can be regarded as the cumulative result of the hourly correction amount of the prediction error during the process that the prediction behavior occurrence moment c gradually approaches the predicted moment t, and its expression is as follows: ; According to mathematical induction, for any prediction time c and future time t, the prediction error can be characterized by the following expression: ;

[0026] Based on the rolling prediction historical data at each moment in the historical data, the difference between the prediction errors at adjacent moments in the rolling prediction error data can be calculated, that is, the prediction improvement value of the prediction within the T time period after the start of the prediction at any prediction time c compared to the previous moment c - 1. The improvement sequence is the sequence composed of the prediction improvement values, which is expressed as: ; It represents the reduction in the prediction error at time c for compared to the prediction error at time c - 1 for . The meanings of the other parameters can be analogized according to the meaning of .

[0027] In this embodiment, taking the characteristics of the improvement sequence as the segmentation benchmark, the historical data is segmented by the Gaussian mixture model as follows: the mean and variance are extracted from the improvement sequence. According to the mean and variance, the historical data is segmented by using the Gaussian mixture model for clustering. The clustering algorithm, i.e., the k-means algorithm, is used to generate the initial values of the parameters, i.e., the initial values of the Gaussian distribution parameters. Let the initial value of the Gaussian distribution parameter of the k-th Gaussian distribution be , where is the mean, is the covariance. Since the data used in the Gaussian mixture model of the present invention are all one-dimensional arrays, the following represents the variance. The probability that a Gaussian sample belongs to a Gaussian distribution, i.e., the posterior probability, is calculated according to the initial values of the Gaussian distribution parameters. For the sample , its posterior probability of belonging to the k-th Gaussian distribution is: ; Among them, is the prior probability of the k-th Gaussian distribution, i.e., the weight coefficient of the probability density function, which satisfies: ; represents the sample under the k-th Gaussian distribution, is a latent variable, representing the distribution type from which the sample comes; represents the set of all means, covariances, and prior probabilities in the Gaussian mixture model. K represents the total number of Gaussian distributions, is the prior probability of the j-th Gaussian distribution, represents the sample The probability density under the j-th Gaussian distribution denotes the sample The weighted probability density of the sample under the j-th Gaussian distribution denotes the sample The sum of the weighted probability densities under all Gaussian distributions Updating the initial parameter values based on probability, that is, re-estimating the parameters based on the posterior probability of the sample obtain 、 、 , and the formula is as follows: ; ; ; When the number of times of "obtaining the probability that a Gaussian sample belongs to a Gaussian distribution according to the initial parameter values" is greater than the preset number of times, the preset requirements are met. The preset number of times is set according to the effect of dividing the historical data according to the initial parameter values. When all the historical data can be classified into different classification results according to the current initial parameter values, it means that the preset number of times is reached. The initial parameter values obtained through the Gaussian mixture model, that is, the estimated parameters, normalize the Gaussian samples, making the Gaussian samples satisfy the Gaussianity assumption in the martingale model, providing a preliminary condition for the martingale model to decouple the correlation of the Gaussian samples.

[0028] In this embodiment, the unbiased distribution samples are obtained by unbiased processing of the Gaussian samples based on the mean value in the initial parameter values. Specifically: the normalized Gaussian samples are re-sorted in ascending order according to the mean value in the initial parameter values and re-numbered according to this order. At the same time, the Gaussian samples with the same mean value are divided into the same category, and the re-numbered Gaussian samples are translated units to make each category of Gaussian samples satisfy the Gaussian distribution with a mean of 0 to obtain the unbiased distribution samples. The Gaussian distribution sequence is obtained through the unbiased distribution samples that satisfy the unbiasedness assumption in the martingale model, providing a condition for the martingale model to decouple the correlation of the Gaussian distribution sequence. In order to obtain the reduction matrix to restore the subsequent independently sampled samples, and it is required that the unbiased distribution samples are of equal length when obtaining the reduction matrix. Therefore, the unbiased distribution samples are filled to make the unbiased distribution samples belonging to the same category have the same length as the longest unbiased distribution sample in this category. Through the above processing, the Gaussian samples are converted into a Gaussian distribution sequence that can be processed by the martingale model, thereby improving the prediction efficiency. At the same time, it provides conditions for obtaining the reduction matrix, so that the independently sampled samples can be feature-restored according to the reduction matrix, and then predictions are made based on a large number of feature-sampled samples after feature restoration, improving the accuracy of line congestion prediction.

[0029] S2: Use the martingale model to decouple the correlation of the Gaussian distribution sequence to obtain the reduction matrix and the independent distribution sequence.

[0030] The said S2 includes: S21: Obtain the reduction matrix based on the variance and covariance of the Gaussian distribution sequence, and perform Cholesky decomposition on the reduction matrix to obtain the lower triangular matrix; S22: Decouple the correlation of the Gaussian distribution sequence based on the lower triangular matrix to obtain the independent distribution sequence.

[0031] The independent distribution sequence in the said S22 is expressed as follows: ; In the formula, represents the Gaussian distribution sequence, represents the lower triangular matrix transpose, represents the independent distribution sequence.

[0032] In this embodiment, the reduction matrix is the variance-covariance matrix. For the preprocessed Gaussian distribution sequences with the same order, calculate the variance-covariance matrix VCV of the Gaussian distribution sequences within the same category and perform Cholesky decomposition (Cholesky decomposition) to generate the lower triangular matrix V and its transpose. Multiply the Gaussian distribution sequence on the right by the inverse matrix of the transpose of this lower triangular matrix to eliminate the time correlation in the Gaussian distribution sequence, and then generate the mutually independent independent distribution sequence, that is, the standard normal sequence. Taking the decoupling of the correlation of the Gaussian distribution sequence of the kth category as an example: For the Gaussian distribution sequences within the same category , , …, calculate the variance-covariance matrix. If (i = 1, …, T) has a variance of and the covariance between is , then the Gaussian distribution sequence of the kth category , , …, the variance-covariance matrix can be expressed as: ; Considering that the variance-covariance matrix is a positive semi-definite symmetric matrix, so for matrix perform Cholesky decomposition to obtain the lower triangular matrix and its transpose , the formula is as follows: ; Multiply the Gaussian distribution sequence of the kth category on the right by the inverse matrix of the lower triangular matrix obtained by decomposition It is possible to eliminate the correlation of the data in the Gaussian distribution sequence of the k-th category, so that it is transformed into an independent distribution sequence that is independent of each other and satisfies a mean of 0 and a variance of 1, that is, a standard normal sequence. The transformation process is as follows: ; By using the memoryless property of the martingale model, the Gaussian distribution sequence is decoupled for correlation to obtain an independent distribution sequence that is independent of each other. While reducing the complexity of subsequent simulations, the prediction accuracy is improved.

[0033] S3: Simulate the independent distribution sequence to generate independent sampling samples, and restore the independent sampling samples into characteristic sampling samples that satisfy the distribution characteristics of the classification results through the restoration matrix.

[0034] The said S3 includes: S31: Conduct Monte Carlo simulation on the independent distribution sequence to generate independent sampling samples, perform Cholesky decomposition on the restoration matrix to obtain a lower triangular matrix, and obtain characteristic sampling samples that satisfy the distribution characteristics of the classification results based on the lower triangular matrix.

[0035] The expression of the characteristic sampling samples in the said S31 is as follows: ; In the formula, represents the independent sampling sample, represents the lower triangular matrix transpose, represents the characteristic sampling sample.

[0036] In this embodiment, in order to describe the distribution characteristics of the independent distribution sequence and thus construct a prediction error interval, Monte Carlo simulation is performed on the independent distribution sequence to obtain independent sampling samples, and the independent sampling samples are inversely transformed into the distribution characteristics that satisfy the classification results through the obtained lower triangular matrix. Taking the independent sampling samples of the k-th category as an example: If the independent sampling samples of the k-th category are (i = 1,..., T), its sequence is expressed as , the characteristic sampling samples of the k-th category are , , its sequence is expressed as , then through the following formula: ; The characteristic sampling samples that satisfy the distribution characteristics of the Gaussian distribution sequence of the k-th category can be obtained , , through the above formula, the correlation between independent sampling samples is restored, that is, the distribution characteristics of the Gaussian distribution sequence corresponding to the independent sampling samples are restored. By generating independent sampling samples through Monte Carlo simulation of the independent distribution sequence, the complexity of simulating the sequence with time correlation is reduced, thereby improving the simulation efficiency. At the same time, by obtaining a large number of independent sampling samples, all prediction error situations including extreme situations are reproduced, so as to obtain the prediction error interval according to all prediction error situations, and the worst situation of abnormal fluctuations in prediction errors can be effectively predicted. Compared with the traditional method of only optimizing the prediction model itself, this method can effectively restore the extreme situation of abnormal fluctuations in prediction errors, thereby reducing the accident losses caused by abnormal fluctuations in prediction errors. At the same time, it also improves the accuracy and flexibility of line congestion anomalies.

[0037] S4: Issue a warning based on the prediction error interval obtained from the characteristic sampling samples and the constraint conditions of the new energy power system.

[0038] The said S4 includes: S41: Update the characteristic sampling samples with the mean value in the initial parameter values obtained in S1a; S42: Obtain the quantiles according to the engineering accuracy requirements, and obtain the prediction error interval corresponding to each prediction moment in the characteristic sampling samples based on the quantiles; S43: Accumulate the prediction error intervals corresponding to each prediction moment based on the definition of the prediction evolution martingale to obtain the fluctuation interval range. Based on the constraint conditions, use the interval power flow method to obtain the power fluctuation range of the line section at each prediction moment. If the right endpoint of the fluctuation interval range is greater than the right endpoint of the power fluctuation range, a warning is issued.

[0039] In S4, the said constraint conditions at least include ramp rate constraint, unit start-up and shutdown time constraint, and section limit constraint.

[0040] In this embodiment, although the characteristic sampling samples contain the correlation factors between sequences, the mean value is 0. Therefore, it is necessary to perform translational restoration according to the mean value in the initial parameter values, that is, the original distribution mean value obtained by the clustering algorithm, to obtain the characteristic sampling samples with a mean value of . Mix and sort all the above characteristic sampling samples at the same prediction moment to obtain the ordered generated sample sequence corresponding to each prediction moment , for the sufficient ordered generated sample sequences corresponding to each prediction moment , according to the engineering accuracy requirements, take a set of quantiles such as 1% and 99% quantiles, 5% and 95% quantiles, etc., so as to obtain the prediction error interval corresponding to each prediction moment, that is, the upper and lower bounds of the prediction improvement variable fluctuation , (i = 1, …, T), according to the derivation in combination with the definition of the prediction evolution martingale in the foregoing text, it can be known that for the same prediction target moment, the prediction error can be expressed as the hourly accumulation of the prediction improvement value, and the formula is as follows: ;

[0041] Since the improvement sequences generated at different prediction moments are independent of each other, for any prediction start moment and the prediction target moments with the same time span, the prediction improvement value can be characterized by a random variable that satisfies the historical data distribution law of the corresponding prediction target moment. Further, the fluctuation situation of the prediction improvement value can be characterized by the prediction improvement fluctuation interval generated by the quantile obtained from the historical data distribution of the corresponding prediction target moment. Therefore, at the level of interval operation, variables with the same prediction time span but different prediction start moments can be transformed into each other. Therefore, the prediction error can be obtained by accumulating the prediction improvement interval variables at the same prediction start moment c at the level of interval operation, and the expression is as follows: ;

[0042] The prediction start moment is c - 1. According to the above derivation, for the prediction improvement interval variables (i = 1, …, T) of the same prediction start moment obtained by taking the quantile of the ordered generated sample sequence (i = 1, …, T), the power fluctuation range of the line section at each prediction moment within the time span of T in this prediction behavior, that is, the fluctuation interval range of the prediction error at each time section, can be characterized by the hourly accumulation method, and the expression for obtaining the fluctuation interval range of the prediction error at each time section is as follows: ; In this embodiment, the constraint conditions include prediction error interval fluctuation constraint, power balance constraint, DC power flow constraint based on PTDF, unit ramp rate constraint, unit start-up and shutdown time constraint, and unit output and section limit constraint. Denote , , , and , as the prediction error fluctuation intervals of the load, wind power and photovoltaic power of grid node i at the prediction target moment t, , , are the random variables of the load, wind power and photovoltaic power of grid node i fluctuating within the error fluctuation interval respectively, To predict the branch power flow of the power grid line L at the prediction time t, the interval power flow method is used to solve the maximum and minimum values of the branch power flow when the predicted values of the load, wind power, and photovoltaic power at the power grid node i fluctuate within an interval at the prediction time t, that is, the upper bound and the lower bound of the branch power flow. The objective functions for solving the upper bound and the lower bound of the branch power flow are as follows: ; , and That is, they constitute the power fluctuation range of the line section at each prediction time. Since the power fluctuation range of the line section at each prediction time is affected by the constraints of the power system, the power fluctuation range of the line section at each prediction time is obtained through the constraints, which improves the rationality of the power fluctuation range and also improves the security of the power system. The constraints are described below from ① to ⑥: ① According to the definition of the prediction error, denote as the predicted value of the load at node i at time t, as the true value of the load at node i at time t, as the random variable that fluctuates within the error fluctuation interval, , as the upper and lower bounds of the prediction error fluctuation at the prediction time t. Their values need to be selected according to the time span between the current time and the prediction time from the prediction error fluctuation intervals corresponding to different time spans generated above. Similarly, the relevant variables of wind power and photovoltaic power are defined accordingly 、 、 、 、 、 、 、 , as the predicted value of the wind power load at time t, as the true value of the wind power load at time t, as the random variable that fluctuates within the prediction error fluctuation interval of the wind power at the prediction target time t, 、 are respectively the upper and lower bounds of the prediction error fluctuation interval of the wind power at the prediction target time t, as the predicted value of the photovoltaic load at time t, as the true value of the photovoltaic load at time t, as the random variable that fluctuates within the prediction error fluctuation interval of the photovoltaic at the prediction target time t, 、 are respectively the upper and lower bounds of the prediction error fluctuation interval of the photovoltaic at the prediction target time t; then there are:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] ② Denote as the generator output corresponding to node i at time t, as the injection power of node i, and the Boolean variable as the switch state of the generator set at node i at time t. = 1 indicates that the generator set is turned on, = 0 indicates that the generator set is turned off and the output is 0 at the same time. Denote the output limit of the generator set at node i as , , then there is:

[0049]

[0050] At the same time, the power balance constraint can be expressed as:

[0051] ③ Denote the network branch incidence matrix as A, where the rows represent the branch numbers and the columns represent the node numbers. For each branch, that is, each row in the matrix, the number 1 represents the starting node of the branch, the number -1 represents the ending node of the branch, and the number 0 represents an unconnected node. It is stipulated that the starting node number is on the left of the ending node number. Denote as the diagonal matrix, and the diagonal elements are the susceptances of each branch. Denote B as the network susceptance matrix. as the voltage phase angle of node i. According to the DC power flow formula and the definition of the network susceptance matrix, there is: Denote as the voltage phase angle of node j associated with node i. According to Kirchhoff's law, the node injection power can be expressed as: ;

[0052] Introduce the power transfer distribution factor matrix , which can directly convert the node injection power of the network into the DC power flow. Its definition can be expressed by the following expression:

[0053] According to the definition formula of the matrix, it is easy to know that it can be obtained by eliminating through the expression. However, the elimination process involves the step of obtaining the matrix inverse. According to the properties of the network susceptance matrix, The matrix is often singular and there is no inverse matrix in the mathematical sense. To avoid the operation errors introduced in the process of reducing the order and inverting the B matrix using the reference point method, the present invention introduces the Moore-Penrose pseudoinverse matrix to represent the inverse matrix of the matrix, The Moore-Penrose pseudoinverse matrix of the matrix is , and the calculation method of this matrix can adopt the singular value decomposition method, that is, perform singular value decomposition on the singular matrix B, and the process is as follows: where , is an orthogonal matrix, is a diagonal matrix with the singular values of the B matrix on the diagonal. According to the definition of the Moore-Penrose pseudoinverse matrix, can be solved by the following expression: where is obtained by taking the reciprocal of the non-zero elements on the diagonal of the matrix. Based on the above method, the pseudoinverse matrix of the B matrix can be obtained. On this basis, by simultaneously solving the expressions for the matrix, the matrix expression is as follows:

[0054] ④ Denote that the state variable of the generator set i changes from 0 to 1 from the (t - 1)th moment to the tth moment as a startup event, denoted as the Boolean variable ; the state variable changes from 1 to 0 from the (t - 1)th moment to the tth moment as a shutdown event, denoted as the Boolean variable . It is stipulated that is the initial switch state of the generator set and should be assigned a value before calculating the optimization problem. According to and 's definitions, their values can be described by the following constraints:

[0055]

[0056]

[0057] represents the state variable from the (t - 2)th moment to the (t - 1)th moment. For the constraints related to , , the product of Boolean variables in their expressions makes the constraints show non-linear characteristics. The following linear rewriting method is introduced to describe the non-linear constraints as a combination of linear constraints:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Denote the maximum upward and downward ramping rates of unit i when it is in the on state at both time t and t-1 as and , and denote the ramping threshold of the unit during the start-up and shutdown processes as and . Usually, the ramping threshold of the unit during the start-up and shutdown processes is set to the minimum output of the unit . For units that are always in the on state, the ramping constraint can be expressed according to the definition as: and , where is the time span; for units that are experiencing a start-up event, its ramping constraint can be described as the sum of the constraints in two stages, that is, the ramping threshold during the start-up and shutdown processes of the unit and the ramping constraint when the unit is in the on state; for units that are experiencing a shutdown event, its ramping constraint cannot exceed the ramping threshold , and the unit preparing to shut down needs to reduce its output to below the ramping threshold before it can shut down at the next moment. To sum up, the ramping rate constraint considering the change of the switch state during the operation of the unit is as follows:

[0064]

[0065]

[0066] According to , the meaning of can be inferred, which will not be elaborated here; ⑤ Denote the minimum start-up and shutdown times of unit i as and , and stipulate that and are the initial start-up and shutdown times of the unit, and stipulate that under the initial start-up state of unit i = , under the initial shutdown state = 。Let the prediction time range be \(T\). Then the value range of the time variable \(t\) of the optimization problem is \([1, T]\). Variables with other values of \(t\) are meaningless without special regulations. Therefore, when the power-on or power-off event occurs at time \(t\) within the range of \(t\) not exceeding the maximum time scale \(T\), the affected time range does not exceed or . Combining with the initial start-stop state of the unit, the start-stop time constraint of the unit can be expressed as:

[0067]

[0068] ;

[0069] ;

[0070] According to the meaning of, it can be inferred that the meaning of, which will not be elaborated here; ⑥ Denote as the section limit of line \(L\). Then the optimization objective of this optimization problem should satisfy the following section limit constraints:

[0071] When the optimization result touches the section limit boundary or , it can be considered that the section of line \(L\) is blocked at the time \(t\) calculated by the optimization problem. This criterion is used to identify the section blockage of the power grid according to the solution result of the above optimization problem.

[0072] Based on the processing of the constraint conditions of the optimization problem in steps ① to ⑥, the conditions originally defined as non-linear constraints can be transformed into linear constraints, so that the non-linear programming problem is converted into a mixed integer linear programming problem (MIP). For the mixed integer linear programming problem, a commercial solver can be used for solution. Its solution idea is a combination of branch and bound, cutting plane method and heuristic algorithm. Through the above steps, the optimal is obtained. Through the optimal the upper bound of the branch power flow and the lower bound of the branch power flow are obtained, which improves the upper bound of the branch power flow and the lower bound of the branch power flow The rationality and adaptability of the power fluctuation range formed thereby. Furthermore, by analyzing the fluctuation interval range and the power fluctuation range, when the right endpoint of the fluctuation interval range is greater than the right endpoint of the power fluctuation range, a warning is issued, which also improves the timeliness of power system warning and the safety of the power system.

[0073] As can be seen from the above embodiments, at least the following substantial effects are achieved: According to the above idea, the DC interval power flow problem of a high-proportion new energy power system with a prediction time range of T is solved, and the blocking situation prediction of each branch of the power grid can be generated under the condition that the prediction error changes within the fluctuation interval generated based on the improved martingale model within the T time range, so as to guide the power grid dispatching to prepare for the contingency plan of possible section blocking situations, thereby avoiding the loss of line blocking accidents caused by abnormal fluctuations in load and new energy prediction; The present invention can generate a rolling prediction and forecast improvement sequence based on historical rolling prediction error data to characterize the time evolution law of the prediction error, and can generate a sufficient number of samples with the same distribution to restore the distribution law of historical rolling prediction error forecast improvement, so as to depict the prediction error fluctuation situation at each time point within the prediction time window of the rolling prediction model adopted by the power grid, and can effectively predict the worst situation of abnormal fluctuations in prediction errors. Compared with the traditional method that only optimizes the prediction model itself, this method can effectively restore the extreme situation of abnormal fluctuations in prediction errors, thereby reducing the accident losses caused by abnormal fluctuations in prediction errors; At the same time, a method combining a mixture Gaussian model and a forecast evolution martingale model is used to extract and restore the distribution characteristic information of the rolling prediction and forecast improvement sequence, and it also has an excellent fitting effect on the real prediction and forecast improvement data that satisfies the biased non-Gaussian distribution and has time-correlated coupling; The power transfer distribution factor is used to directly characterize the relationship between the injected power of the DC interval power flow node and the branch power flow, and the Moore-Penrose pseudoinverse matrix, that is, the Moore-Penrose pseudoinverse matrix, is introduced to avoid the calculation error caused by manually selecting the reference point during the calculation process. This method can effectively simplify the operation process of the DC interval power flow, thereby simplifying the relevant constraints and intermediate variables of the power flow equation in the optimization problem, and effectively accelerating the solution efficiency of the final mixed integer programming problem (MIP).

[0074] The above-described specific implementation manner is the preferred implementation manner of the method for warning line blocking of a new energy power system based on the martingale model of the present invention, and does not limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to this specific implementation manner. Any equivalent changes made according to the shape and structure of the present invention are within the protection scope of the present invention.

Claims

1. A new energy power system line congestion warning method based on a martingale model, characterized in that: The following steps are involved: S1: Based on the improved sequence, the historical data of the renewable energy power system is segmented using the Gaussian mixture model to obtain the classification results, and the Gaussian samples in the classification results are matched to obtain the Gaussian distribution sequence; S2: Use the martingale model to decouple the correlation of the Gaussian distribution sequence to obtain the restored matrix and the independent distribution sequence; S3: Simulate the independent distribution sequence to generate independent sampling samples, and restore the independent sampling samples to feature sampling samples that meet the distribution characteristics of the classification results through the restoration matrix; S4: Early warning based on the prediction error interval obtained from feature sampling and the constraints of the new energy power system.

2. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 1 is characterized in that: The S1 includes: S11: obtaining the difference of the prediction errors at adjacent moments in the rolling prediction error data in the historical data according to the definition of the forecast evolution martingale, and obtaining an improved sequence based on the difference; S12: Using the features of the improved sequence as a segmentation benchmark, segment the historical data using a Gaussian mixture model to obtain a classification result.

3. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 2 is characterized in that: In S1, performing matching processing on Gaussian samples in the classification results to obtain a Gaussian distribution sequence includes: S1a: Obtain the initial values ​​of the parameters in the Gaussian mixture model through the clustering algorithm; S1b: Obtain the probability that the Gaussian sample belongs to the Gaussian distribution according to the initial parameter value, and update the initial parameter value based on the probability until the preset requirements are met and S1c is executed. Otherwise, S1b is executed in rounds; S1c: Normalize the Gaussian samples based on the initial parameter values, unbias the Gaussian samples based on the mean in the initial parameter values ​​to obtain unbiased distribution samples, and obtain Gaussian distribution sequences based on the unbiased distribution samples.

4. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 3 is characterized in that: The S1c further comprises: The unbiased distribution samples are filled with the longest unbiased distribution sample in the unbiased distribution samples as the filling basis.

5. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 1 is characterized in that: The S2 includes: S21: Obtain the reduction matrix based on the variance and covariance of the Gaussian distribution sequence, and perform Cholesky decomposition on the reduction matrix to obtain a lower triangular matrix; S22: Based on the lower triangular matrix, the correlation of the Gaussian distribution sequence is decoupled to obtain an independent distribution sequence.

6. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 5 is characterized in that: The independent distribution sequence in S22 is expressed as follows: ； In the formula, represents a Gaussian distribution sequence, Represents a lower triangular matrix The transpose of represents independently distributed sequences.

7. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 3 is characterized in that: The S3 includes: S31: Perform Monte Carlo simulation on the independent distribution sequence to generate independent sampling samples, perform Cholesky decomposition on the reduction matrix to obtain a lower triangular matrix, and obtain feature sampling samples that meet the distribution characteristics of the classification results based on the lower triangular matrix.

8. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 7 is characterized in that: The characteristic sampling samples in S31 are expressed as follows: ； In the formula, represents independent sampling samples, Represents a lower triangular matrix The transpose of Represents a feature sampling sample.

9. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 3 is characterized in that: The S4 includes: S41: updating the feature sampling samples by using the mean of the initial parameter values ​​obtained in S1a; S42: obtaining quantiles according to engineering accuracy requirements, and obtaining prediction error intervals corresponding to each prediction moment in the feature sampling sample based on the quantiles; S43: Based on the definition of the forecast evolution martingale, the prediction error interval corresponding to each prediction moment is accumulated to obtain the fluctuation interval range. Based on the constraint conditions, the interval power flow method is used to obtain the power fluctuation range of the line section at each prediction moment. If the right endpoint of the fluctuation interval range is greater than the right endpoint of the power fluctuation range, an early warning is issued.

10. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 1 or 9, characterized in that: In S4, the constraint conditions include at least a ramp rate constraint, a unit start-up and shutdown time constraint, and a section limit constraint.

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