Line Blocking Early Warning Method for New Energy Power System Based on Martingale Model

Abstract

The present invention discloses a method for warning line congestion in a new energy power system based on a martingale model, belonging to the field of electrical engineering technology. The method comprises the following steps: S1: Based on an improved sequence, a Gaussian mixture model is used to segment historical data of the new energy power system to obtain classification results, and Gaussian samples in the classification results are matched to obtain a Gaussian distribution sequence; S2: a martingale model is used to perform correlation decoupling on the Gaussian distribution sequence to obtain a reduction matrix and an independent distribution sequence; S3: an independent distribution sequence is simulated to generate independent sampling samples, and the independent sampling samples are restored to feature sampling samples that meet the distribution characteristics of the classification results through a reduction matrix; S4: a warning is issued based on the prediction error interval obtained from the feature sampling samples and the constraints of the new energy power system. The method solves the technical problem of low line congestion prediction accuracy due to failure to consider the evolution of prediction errors over time, and significantly improves the accuracy of line congestion prediction.

Description

Technical Field

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

[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 is extremely important to provide early warning of line congestion.

[0003] On this basis, accurately predicting line congestion has become an essential step in ensuring the safe and stable operation of the power grid. Existing technologies mainly focus on the performance of the prediction model itself and its applicable scenarios. For example, patent publication number CN109345142A discloses a method and system for obtaining line congestion in a power system, including: calculating the DC power transmission distribution factor of the power system; establishing a priority matrix; judging whether line congestion occurs in the power system at a certain priority level based on the DC power flow of the power system; determining the reduction ratio of the blocked lines in the power system at that priority level when line congestion occurs; determining the proportional relationship between the power reductions of each generator at that priority level; solving the pre-established power system line congestion model to obtain the line congestion result of the power system at that priority level. However, the above scheme does not pay attention to the evolution of the prediction error brought about by load and new energy prediction technology over time. Moreover, 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

[0004] To address the technical problem that the existing technology fails to consider the evolution of prediction errors over time, resulting in low accuracy in line congestion prediction, the present invention provides a new energy power system line congestion early warning method based on a martingale model. Gaussian samples are matched and processed using a Gaussian mixture model to obtain a Gaussian distribution sequence that can be processed by the martingale model. The memoryless nature of the martingale model is used to decouple the Gaussian distribution sequence from its correlation to obtain a reduction matrix and mutually independent independent distribution sequences. A large number of independent sampling samples are further generated based on the mutually independent independent distribution sequences. Feature reduction is then performed on the large number of independent sampling samples using the reduction matrix to obtain feature sampling samples, which are then used to make predictions. This method solves the technical problem of low line congestion prediction accuracy due to failure to consider the evolution of prediction errors over time, significantly improving the accuracy of line congestion prediction.

[0005] To solve the above technical problems, the present invention provides a new energy power system line congestion early warning method based on a martingale model, comprising the following steps:

[0006] S1: Based on the improved sequence, the Gaussian mixture model is used to segment the historical data of the new energy power system to obtain classification results, and the Gaussian samples in the classification results are matched to obtain the Gaussian distribution sequence;

[0007] S2: Use the martingale model to decouple the Gaussian distribution sequence to obtain the restored matrix and the independent distribution sequence;

[0008] 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;

[0009] S4: Provide early warning based on the prediction error interval obtained from feature sampling samples and the constraints of the new energy power system.

[0010] After adopting the above technical solution, the present invention has the following advantages:

[0011] Considering that when the sample size is large enough, all prediction error situations, including extreme situations, can be reproduced, and the existing technology consumes a lot of time and resources in the process of obtaining a large number of samples. In particular, since extreme situations are rare, samples related to extreme situations are scarce. 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 high. Therefore, the memoryless property of the martingale model is used to decouple the correlation of the Gaussian distribution sequence to obtain mutually independent independent distribution sequences. Then, simulation is performed based on the mutually independent independent distribution sequences to obtain a sufficient number of independent sampling samples. Furthermore, considering that Gaussian samples are difficult to be directly processed by the martingale model, the Gaussian samples are matched and processed through a Gaussian mixture model to obtain a Gaussian distribution sequence that can be processed by the martingale model. After obtaining a sufficient number of independent sampling samples, the features of a large number of independent sampling samples are restored through the reduction matrix to obtain feature sampling samples, realizing the restoration of time correlation. Finally, an early warning is issued through the feature sampling samples, solving the technical problem of low accuracy in line congestion prediction due to failure to consider the evolution law of prediction error over time, and significantly improving the accuracy and efficiency of line congestion prediction.

[0012] At the same time, by effectively restoring the 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.

[0013] Preferably, the S1 includes:

[0014] S11: obtaining 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 forecast evolution martingale, and obtaining an improved sequence based on the difference;

[0015] 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.

[0016] Preferably, in S1, performing matching processing on Gaussian samples in the classification results to obtain a Gaussian distribution sequence includes:

[0017] S1a: Obtain the initial values of the parameters in the Gaussian mixture model through the clustering algorithm;

[0018] S1b: Obtain the probability that the Gaussian sample belongs to the Gaussian distribution based on the initial parameter value, and update the initial parameter value based on the probability until the preset requirements are met and execute S1c. Otherwise, execute S1b again in the round;

[0019] S1c: Normalize the Gaussian samples based on the initial parameter values, unbias the Gaussian samples based on the mean of the initial parameter values to obtain unbiased distribution samples, and obtain a Gaussian distribution sequence based on the unbiased distribution samples.

[0020] Preferably, the S1c further comprises:

[0021] The unbiased distribution samples are filled with the longest unbiased distribution sample in the unbiased distribution samples as the filling basis.

[0022] Preferably, the S2 includes:

[0023] 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;

[0024] S22: Decouple the Gaussian distribution sequence based on the lower triangular matrix to obtain an independent distribution sequence.

[0025] Preferably, the independent distribution sequence in S22 is expressed as follows:

[0026] ;

[0027] Where, represents a Gaussian distribution sequence, Represents a lower triangular matrix The transpose of represents an independently distributed sequence.

[0028] Preferably, the S3 includes:

[0029] 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.

[0030] Preferably, the feature sampling samples in S31 are expressed as follows:

[0031] ;

[0032] Where, represents independent sampling samples, Represents a lower triangular matrix The transpose of Represents a feature sampling sample.

[0033] Preferably, the S4 includes:

[0034] S41: Update the feature sampling sample by the mean of the initial parameter value obtained in S1a;

[0035] 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;

[0036] 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 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.

[0037] Preferably, 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.

[0038] Beneficial effects of this program:

[0039] Considering that all prediction error situations, including extreme situations, can be reproduced when the sample size is large enough, a sufficient number of independent sampling samples are obtained through simulation. However, before the simulation, due to the time correlation between Gaussian distribution sequences, the simulation complexity is relatively high. Therefore, the memoryless characteristic of the martingale model is used to decouple the correlation of the Gaussian distribution sequence to obtain independent independent distribution sequences, and then simulation is performed based on the independent independent distribution sequences to obtain a sufficient number of independent sampling samples. Furthermore, considering that Gaussian samples are difficult to be directly processed by the martingale model, the Gaussian samples are matched and processed through the 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 features of a large number of independent sampling samples are restored through the reduction matrix to obtain feature sampling samples, realizing the restoration of time correlation. Finally, the feature sampling samples are used to issue an early warning, solving the technical problem of low accuracy in line congestion prediction due to failure to consider the evolution of the prediction error over time, and significantly improving the accuracy and efficiency of line congestion prediction.

[0040] At the same time, by effectively restoring the extreme cases of abnormal fluctuations in forecast errors, the accident losses caused by abnormal fluctuations in forecast errors are reduced, and the safety, stability and reliability of the new energy power system are improved;

[0041] In order to preserve the data characteristics of unbiased distribution samples and meet the requirements of obtaining the reduction matrix using the martingale model, the longest unbiased distribution sample is used as the filling basis to fill the unbiased distribution samples, so that the characteristics of independent sampling samples can be restored according to the reduction matrix. Then, predictions are made based on a large number of feature sampling samples after feature restoration, further improving the accuracy of line congestion prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Other features, objects, and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings. The drawings are provided for the purpose of illustrating preferred embodiments only and are not to be construed as limiting the present invention. Like reference characters are used throughout the drawings to designate like parts.

[0043] Figure 1 The figure is a flow chart of the method for early warning of line congestion in a new energy power system based on the martingale model of the present invention. DETAILED DESCRIPTION

[0044] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific implementation method described herein is only an optimal embodiment of the present invention, which is only used to explain the present invention and does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flow charts. Although the flow charts describe the operations (or steps) as sequential processes, many of the operations (or steps) therein can be performed 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 can also have additional steps not included in the figures; the process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0046] Example 1:

[0047] like Figure 1 As shown, the new energy power system line congestion early warning method based on the martingale model includes the following steps:

[0048] S1: Based on the improved sequence, the Gaussian mixture model is used to segment the historical data of the new energy power system to obtain the classification results, and the Gaussian samples in the classification results are matched to obtain the Gaussian distribution sequence.

[0049] Said S1 comprises:

[0050] S11: obtaining 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 forecast evolution martingale, and obtaining an improved sequence based on the difference;

[0051] 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.

[0052] In S1, performing matching processing on Gaussian samples in the classification result to obtain a Gaussian distribution sequence includes:

[0053] S1a: Obtain the initial values of the parameters in the Gaussian mixture model through the clustering algorithm;

[0054] S1b: Obtain the probability that the Gaussian sample belongs to the Gaussian distribution based on the initial parameter value, and update the initial parameter value based on the probability until the preset requirements are met and execute S1c. Otherwise, execute S1b again in the round;

[0055] S1c: Normalize the Gaussian samples based on the initial parameter values, unbias the Gaussian samples based on the mean of the initial parameter values to obtain unbiased distribution samples, and obtain a Gaussian distribution sequence based on the unbiased distribution samples.

[0056] Said S1c further comprises:

[0057] The unbiased distribution samples are filled with the longest unbiased distribution sample in the unbiased distribution samples as the filling basis.

[0058] The martingale model is a mathematical model based on probability theory, primarily used to describe random processes. Its core principles are "unbiased" and "memoryless," meaning that the expected value of the future depends solely on current information and is unrelated to past history. Martingale models are widely used in financial mathematics, probability theory, statistics, and engineering fields such as signal processing and time series analysis.

[0059] In this embodiment, the forecast evolution martingale is defined as "the reduction of the current forecast error relative to the previous forecast error", that is, the reduction of the forecast error at time c for time t relative to the forecast error at time c-1 for time t, denoted as , the expression is , It represents the prediction error of time c for time t, It represents the prediction error at time c-1 for time t. The above definition of the forecast evolution martingale characterizes the update rule of the error generated by the prediction behavior at different moments in the historical rolling prediction error data for the prediction result at the same future moment. Generally speaking, the later the prediction behavior occurs, the more experience is gained based on historical data, the more accurate the prediction for the same future moment is, and the smaller the error is. It is used to represent the correction amount of the prediction result at the same future moment due to experience update, so It can also be characterized as:

[0060] ;

[0061] Where, It can be expressed as the measured load or new energy power value at time t The sum of the prediction errors at time c and time t The sum of the two is expressed as follows: ; Forecast error for the same future moment , which can be regarded as the cumulative result of the hourly correction of the prediction error in the process of the predicted behavior occurrence time c gradually approaching the predicted time t. Its expression is as follows: ;

[0062] According to mathematical induction, for any predicted time c and future time t, the prediction error can be expressed as follows:

[0063] ;

[0064] Based on the rolling forecast historical data at each moment in the historical data, the difference in the forecast errors of adjacent moments in the rolling forecast error data can be calculated, that is, the forecast improvement value of any forecast moment c compared with the previous moment c-1 for the forecast within the T period after the start of the forecast. The improvement sequence is the sequence composed of the forecast improvement values, which is expressed as:

[0065] ;

[0066] Indicates that time c is The prediction error at time c-1 is relative to the The reduction of the prediction error at the moment, the meaning of other parameters can be based on The meaning can be inferred by analogy.

[0067] In this embodiment, the characteristics of the improved sequence are used as the segmentation basis, and the historical data is segmented by the Gaussian mixture model. Specifically, the mean and variance are extracted from the improved sequence, and the historical data is clustered using the Gaussian mixture model based on the mean and variance. 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 kth Gaussian distribution parameter be ,in is the mean, is the covariance. Since the data used in the Gaussian mixture model in the present invention are all one-dimensional arrays, the following Represents variance. According to the initial value of Gaussian distribution parameters, the probability that the Gaussian sample belongs to Gaussian distribution is calculated, that is, the posterior probability. , the posterior probability that it belongs to the kth Gaussian distribution is:

[0068] ;

[0069] in, is the prior probability of the k-th Gaussian distribution, that is, the weight coefficient of the probability density function, satisfying: ;

[0070] Representation sample The probability density under the k-th Gaussian distribution, is a latent variable, representing the sample the type of distribution from; 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 a sample The probability density under the j-th Gaussian distribution, Represents a sample The weighted probability density of the j-th Gaussian distribution, Represents a sample The weighted sum of probability densities under all Gaussian distributions;

[0071] Update the initial value of the parameter based on the probability, that is, re-estimate the parameter based on the sample posterior probability get 、 、 , the formula is as follows:

[0072] ;

[0073] ;

[0074] ;

[0075] The requirement is met when the "obtaining the probability of a Gaussian sample belonging to a Gaussian distribution based on the initial parameter values" operation is executed more than the preset number of times. The preset number is set based on the effectiveness of the initial parameter values in segmenting the historical data. When the current initial parameter values can classify all historical data into different classification results, the preset number of times is met. The initial parameter values obtained through the Gaussian mixture model, i.e., the estimated parameters, are used to normalize the Gaussian samples, ensuring that they meet the Gaussianity assumption in the martingale model, providing the initial conditions for the martingale model to decouple the correlation of the Gaussian samples.

[0076] In this embodiment, the Gaussian samples are unbiased based on the mean of the initial parameter values to obtain unbiased distribution samples. Specifically, the normalized Gaussian samples are processed according to the mean of the initial parameter values. Rearrange the normalized Gaussian samples in ascending order and renumber them in this order, and change the mean The same Gaussian samples are divided into the same category, and the renumbered Gaussian samples are shifted. Units are used to make each type of Gaussian sample satisfy a Gaussian distribution with a mean of 0 to obtain unbiased distribution samples. Gaussian distribution sequences are obtained by unbiased distribution samples that satisfy the unbiasedness assumption in the martingale model, which provides conditions for the martingale model to decouple the correlation of the Gaussian distribution sequence. In order to obtain the reduction matrix to restore the independent sampling samples obtained subsequently, the reduction matrix requires that the unbiased distribution samples are of equal length. Therefore, the unbiased distribution samples are padded so that the unbiased distribution samples belonging to the same category are of the same length as the longest unbiased distribution sample in the category. Through the above processing, the Gaussian samples are converted into Gaussian distribution sequences 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 independent sampling samples can be restored according to the reduction matrix, and then prediction is made based on a large number of feature sampling samples after feature restoration, thereby improving the accuracy of line congestion prediction.

[0077] S2: Use the martingale model to decouple the correlation of the Gaussian distribution sequence to obtain the restored matrix and the independent distribution sequence.

[0078] The S2 includes:

[0079] 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;

[0080] S22: Decouple the Gaussian distribution sequence based on the lower triangular matrix to obtain an independent distribution sequence.

[0081] The independent distribution sequence in S22 is expressed as follows:

[0082] ;

[0083] Where, represents a Gaussian distribution sequence, Represents a lower triangular matrix The transpose of represents an independently distributed sequence.

[0084] In this embodiment, the reduction matrix is the variance covariance matrix. For the pre-processed Gaussian distribution sequences of the same order, the variance covariance matrix VCV of the Gaussian distribution sequences in the same category is obtained and Cholesky decomposition is performed to generate the lower triangular matrix V and its transpose. The Gaussian distribution sequence is right-multiplied by the inverse matrix of the transpose of the lower triangular matrix to eliminate the time correlation in the Gaussian distribution sequence, and then generate mutually independent independent distribution sequences, namely standard normal sequences. Taking the correlation decoupling of the Gaussian distribution sequence of the kth category as an example: for the Gaussian distribution sequence in the same category , ,…, Obtain the covariance matrix of the variance, if The variance of (i=1,…,T) is and The covariance of , then the Gaussian distribution sequence of the kth category , ,…, The variance-covariance matrix of It can be expressed as:

[0085] ;

[0086] Considering that the variance covariance matrix is a semi-positive symmetric matrix, The matrix is decomposed by Cholesky to obtain the lower triangular matrix and its transpose , the formula is as follows: ; Multiply the Gaussian distribution sequence of the kth category by the lower triangular matrix obtained by decomposition The inverse matrix of The correlation of the data in the Gaussian distribution sequence of the kth category can be eliminated, and it can be transformed into an independent distribution sequence with a mean of 0 and a variance of 1, that is, a standard normal sequence. The transformation process is as follows:

[0087] ;

[0088] The memoryless property of the martingale model is used to decouple the correlation of Gaussian distribution sequences to obtain mutually independent independent distribution sequences, which reduces the complexity of subsequent simulations and improves the prediction accuracy.

[0089] S3: Simulate the independent distribution sequence to generate independent sampling samples, and restore the independent sampling samples into feature sampling samples that meet the distribution characteristics of the classification results through the restoration matrix.

[0090] The S3 includes:

[0091] 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.

[0092] The characteristic sampling samples in S31 are expressed as follows:

[0093] ;

[0094] Where, represents independent sampling samples, Represents a lower triangular matrix The transpose of Represents a feature sampling sample.

[0095] In this embodiment, in order to describe the distribution characteristics of the independent distribution sequence and thus construct the prediction error interval, a 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 meet the classification result using the lower triangular matrix obtained above. Taking the independent sampling samples of the kth category as an example: if the independent sampling samples of the kth category are (i=1,…,T), whose sequence is expressed as , the feature sampling sample of the kth category is , , whose sequence is represented as , then the following formula:

[0096] ; Feature sampling samples that meet the Gaussian distribution sequence distribution characteristics of the kth 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 performing Monte Carlo simulation on the independent distribution sequence to generate independent sampling samples, the complexity of simulating sequences 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 conditions, including extreme cases, are reproduced, so that the prediction error range can be obtained based on all prediction error conditions. It can effectively predict the worst case of abnormal fluctuation of prediction error. Compared with the traditional method of only optimizing the prediction model itself, this method can effectively restore the extreme cases of abnormal fluctuation of prediction error, thereby reducing the accident losses caused by abnormal fluctuation of prediction error, while also improving the accuracy and flexibility of line blockage anomalies.

[0097] S4: Provide early warning based on the prediction error interval obtained from feature sampling samples and the constraints of the new energy power system.

[0098] The S4 includes:

[0099] S41: Update the feature sampling sample by the mean of the initial parameter value obtained in S1a;

[0100] 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;

[0101] 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 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.

[0102] 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.

[0103] In this embodiment, although the feature sampling samples contain correlation factors between sequences, the mean is 0. Therefore, it is necessary to perform translation restoration based on the mean in the initial parameter value, that is, the original distribution mean obtained by the clustering algorithm, to obtain a mean of All the above feature sampling samples at the same prediction moment are mixed and sorted to obtain the ordered generated sample sequence corresponding to each prediction moment , generate a sufficient number of ordered sample sequences corresponding to each prediction moment , according to the engineering accuracy requirements, a set of quantiles such as 1% and 99% quantiles, 5% and 95% quantiles, etc. are taken to obtain the prediction error interval corresponding to each prediction moment, that is, the upper and lower bounds of the forecast improvement variable fluctuation , (i=1,…,T), according to the deduction based on the definition of the forecast evolution martingale in the previous article, the forecast error for the same forecast target time can be expressed as the hourly accumulation of the forecast improvement value, as follows:

[0104] ;

[0105] Improved sequences generated at different forecast moments They are independent of each other. For any forecast start time and forecast target time with the same time span, the forecast improvement value can be represented by a random variable that satisfies the distribution law of the historical data at the corresponding forecast target time. Furthermore, the fluctuation of the forecast improvement value can be represented by the forecast improvement fluctuation interval generated by the quantile obtained from the distribution of the historical data at the corresponding forecast target time. Therefore, at the interval operation level, variables with the same forecast time span but different forecast start times can be converted to each other. Therefore, at the interval operation level, the forecast error can be obtained by accumulating the forecast improvement interval variables at the same forecast start time c. The expression is as follows:

[0106] ;

[0107] The prediction start time is c-1. According to the above derivation, for the sample sequence generated in an ordered manner (i=1,…,T) The forecast improvement interval variable at the same forecast start time obtained by taking the quantile [ ](i=1,…,T), the power fluctuation range of the line section at each prediction moment in the time span T can be represented by hourly accumulation, that is, the fluctuation range of the prediction error of each time section. The expression for obtaining the fluctuation range of the prediction error of each time section is as follows:

[0108] In this embodiment, the constraints include the forecast error interval fluctuation constraint, power balance constraint, PTDF-based DC power flow constraint, unit ramp rate constraint, unit start-up and shutdown time constraint, and unit output and section limit constraint. , ],[ , ]and[ , ] is the fluctuation range of the load, wind power and photovoltaic prediction errors of grid node i when the target time is t, 、 、 are random variables of grid node i load, wind power and photovoltaic power fluctuations within the error fluctuation range, In order to predict the branch flow of the power grid line L at time t, the interval flow method is used to solve the maximum value of each branch flow when the load, wind power and photovoltaic forecast values of the grid node i at the forecast time t fluctuate within an interval, that is, the upper bound and lower bound of the branch flow. The objective function for solving the upper bound and lower bound of the branch flow is: ; , and That is, the power fluctuation range of the line section at each prediction moment. Since the power fluctuation range of the line section at each prediction moment is affected by the power system constraints, the power fluctuation range of the line section at each prediction moment 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 through ① to ⑥: ① According to the definition of prediction error, record is the load forecast value of node i at time t, is the true load value of node i at time t, is a random variable that fluctuates within the error fluctuation interval, , The upper and lower bounds of the prediction error fluctuation at the prediction time t are selected based on the time span between the current time and the prediction time for the prediction error fluctuation intervals corresponding to the different time spans generated above. Similarly, the wind power and photovoltaic related variables are defined accordingly. 、 、 、 、 、 、 、 , is the load forecast value of wind power at time t, is the true value of wind power load at time t, is a random variable that fluctuates within the prediction error fluctuation range of wind power when the target time is t. 、 are the upper and lower bounds of the wind power prediction error fluctuation range when the target time is t, is the predicted load value of photovoltaic at time t, is the actual value of the photovoltaic load at time t, is a random variable that fluctuates within the prediction error fluctuation interval of photovoltaic power when the target time is t. 、 are the upper and lower bounds of the photovoltaic prediction error fluctuation range when the target time is t; then:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] ②Record is the generator output corresponding to node i at time t, Inject power to node i, Boolean variable is the switch state of the generator set at node i at time t, =1 means the generator set is turned on, =0 means the generator set is turned off and the output is 0, and the output limit of the generator set at node i is [ , ], then:

[0116]

[0117]

[0118] At the same time, the power balance constraint can be expressed as:

[0119] ③ Let the power grid branch association matrix be A, the rows represent the branch numbers, the columns represent the node numbers, for each branch, that is, each row in the matrix, the number 1 represents the branch starting node, the number -1 represents the branch end point, and the number 0 represents an irrelevant node. It is stipulated that the starting number is on the left of the end number. is a diagonal matrix, the diagonal elements are the susceptances of each branch, and B is the grid susceptance matrix. is the voltage phase angle of node i. According to the DC power flow formula and the grid susceptance matrix definition, we have: remember is the voltage phase angle of node j associated with node i. According to Kirchhoff’s law, the node injection power can be expressed as:

[0120] ;

[0121] Introducing the power transfer distribution factor matrix , this matrix can directly convert the power injected into the grid node into DC power flow, and its definition can be expressed as the following expression:

[0122] according to The definition of the matrix is easy to see that it can be obtained by Simultaneous elimination of expressions But the joint process involves finding The steps of matrix inversion are as follows: Matrices are often singular and there is no mathematical inverse matrix. In order to avoid the computational error introduced in the process of reducing the order of the B matrix by the reference point method, the present invention introduces the Moore-Penrose pseudo-inverse matrix to represent The inverse of a matrix, The Moore-Penrose pseudo-inverse matrix of the matrix is , the calculation method of the matrix can be used by singular value decomposition method, that is, singular value decomposition of the singular matrix B, the process is as follows: in , is an orthogonal matrix, is a diagonal matrix whose diagonals are the singular values of the B matrix, and according to the definition of the Moore-Penrose pseudo-inverse matrix, The following expression can be used to solve it: in for The inverse of the non-zero elements on the diagonal of the matrix is obtained. Based on the above method, the pseudo-inverse matrix of the B matrix can be obtained On this basis, through Simultaneous pairs of expressions Solve the matrix and get The matrix expression is as follows:

[0123] ④Record the state variables of generator set i from time t-1 to time t A change from 0 to 1 is a power-on event, recorded as a Boolean variable ; State variables from time t-1 to time t A change from 1 to 0 is a shutdown event, recorded as a Boolean variable .Regulation is the initial switching state of the generator set, which should be assigned before calculating the optimization problem. and The definition of , whose value can be described as the following constraints:

[0124]

[0125]

[0126]

[0127] Represents the state variables from time t-2 to time t-1, for , The relevant constraints, whose expressions contain the product of Boolean variables, make the constraints nonlinear. The following linear rewriting method is introduced to describe the nonlinear constraints as a combination of linear constraints:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] The maximum upward and downward climbing rates of unit i when it is in the starting state at time t and time t-1 are and , the climbing threshold of the unit during the start-up and shutdown process is and Usually, the ramp threshold of the unit during the start-up and shutdown process will be set to the minimum output of the unit. For units that are always on, the ramp constraint can be expressed as follows: and ,in is the time span; for a unit that is experiencing a startup event, its ramp constraint can be described as the sum of the constraints in two stages, namely, the ramp threshold during the unit startup and shutdown process and the ramp constraints when the unit is turned on For a unit that is experiencing a shutdown event, its ramp constraint cannot exceed the ramp threshold , and the unit that is about to shut down needs to reduce its output to the ramp threshold before shutting down To summarize, the ramp rate constraints considering the switch state changes during unit operation are as follows:

[0135]

[0136]

[0137]

[0138] according to The meaning can be inferred The meaning of is not repeated here;

[0139] ⑤Record the minimum start-up and shutdown time of unit i as follows: and ,Regulation and It is the initial start-up and shutdown time of the unit, and it is stipulated that the unit i is in the initial start-up state = , in the initial shutdown state = . Let the prediction time range be T, then the value range of the optimization problem time variable t is [1, T]. The other value variables of t are meaningless unless otherwise specified. Therefore, when the range of t does not exceed the maximum time scale T, when a startup or shutdown event occurs at time t, the time range of its impact does not exceed or , combined with the initial start-up and shutdown status of the unit, the unit start-up and shutdown time constraints can be expressed as:

[0140]

[0141]

[0142] ;

[0143] ;

[0144] according to The meaning can be inferred The meaning of is not repeated here;

[0145] ⑥ Note is the cross-section limit of line L, then the optimization objective of this optimization problem is The following section limit constraints should be met:

[0146]

[0147] when The optimization result reaches the section limit boundary or When , it can be considered that the line L has a section blockage 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 of the above optimization problem.

[0148] Based on the processing of the optimization problem constraints in steps ① to ⑥, the conditions originally defined as nonlinear constraints can be converted into linear constraints, so that the nonlinear programming problem can be converted into a mixed integer linear programming problem (MIP). For the mixed integer linear programming problem, a commercial solver can be used to solve it. Its solution idea is to combine branch and bound, cutting plane method and heuristic algorithm. The optimal solution is obtained through the above steps. , through the optimal Get the upper bound of branch power flow Lower bound of branch flow , which improves the upper limit of the flow through the branch Lower bound of branch flow The rationality and adaptability of the power fluctuation range formed by the power fluctuation range are analyzed. When the right end point of the fluctuation range is greater than the right end point of the power fluctuation range, an early warning is issued, which also improves the timeliness of the power system early warning and the safety of the power system.

[0149] It can be seen from the above embodiments that at least the following substantial effects are achieved:

[0150] Based on the above ideas, the DC section power flow problem of a high-proportion renewable energy power system with a forecast time range of T is solved. It can generate a forecast of the congestion situation of each branch of the power grid when the forecast error within the time range of T varies within the fluctuation range generated by the improved martingale model. This can guide the grid dispatcher to prepare contingency plans for possible section congestion, thereby avoiding losses caused by line congestion accidents due to abnormal fluctuations in load and renewable energy forecasts.

[0151] This method generates a rolling forecast improvement sequence based on historical rolling forecast error data, thereby characterizing the temporal evolution of forecast errors. It also generates a sufficient number of identically distributed samples to restore the distribution of historical rolling forecast error forecast improvements, thereby depicting the forecast error fluctuations at each point within the forecast time window of the rolling forecast model used by the power grid. This method can effectively predict the worst-case scenario of abnormal forecast error fluctuations. Compared to traditional methods that only optimize the forecast model itself, this method can effectively restore extreme cases of abnormal forecast error fluctuations, thereby reducing accident losses caused by abnormal forecast error fluctuations.

[0152] At the same time, a combination of a mixed Gaussian model and a forecast evolution martingale model is used to extract and restore the distribution characteristics of the rolling forecast forecast improvement sequence. This method also has an excellent fitting effect on real forecast improvement data that meets biased non-Gaussian distribution and has time correlation coupling.

[0153] The power flow transfer distribution factor is used to directly characterize the relationship between the injected power of the DC section power flow node and the branch power flow, and the Moore-Penrose pseudo-inverse matrix is introduced to avoid the computational errors caused by manually selecting reference points during the calculation process. This method can effectively simplify the calculation process of the DC section power flow, thereby simplifying the relevant constraints and intermediate variables of the power flow equation in the optimization problem, and effectively speeding up the solution efficiency of the final mixed integer programming problem (MIP).

[0154] The specific implementation described above is a preferred implementation of the new energy power system line congestion warning method based on the martingale model of the present invention, and is not intended to limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to this specific implementation. All equivalent changes made in accordance with the shape and structure of the present invention are within the scope of protection of the present invention.

Claims

1. A new energy power system line congestion warning method based on a martingale model is characterized by: The following steps are involved: S1: Based on the improved sequence, the Gaussian mixture model is used to segment the historical data of the new energy power system to obtain 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 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: Provide early warning based on the prediction error interval obtained from feature sampling samples 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, characterized in that: Said S1 comprises: S11: obtaining 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 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, characterized in that: In S1, performing matching processing on Gaussian samples in the classification result 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 based on the initial parameter value, and update the initial parameter value based on the probability until the preset requirements are met and execute S1c. Otherwise, execute S1b again in the round; S1c: Normalize the Gaussian samples based on the initial parameter values, unbias the Gaussian samples based on the mean of the initial parameter values to obtain unbiased distribution samples, and obtain a Gaussian distribution sequence 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: Said 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, 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 the lower triangular matrix; S22: Decouple the Gaussian distribution sequence based on the lower triangular matrix 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, characterized in that: The independent distribution sequence in S22 is expressed as follows: ； Where, represents a Gaussian distribution sequence, Represents a lower triangular matrix The transpose of represents an independently distributed sequence.

7. The method for early warning of line congestion in a new energy power system based on a martingale model according to claim 3, 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, characterized in that: The characteristic sampling samples in S31 are expressed as follows: ； Where, 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, characterized in that: The S4 includes: S41: Update the feature sampling sample by the mean of the initial parameter value 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 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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