Power system inter-provincial tie line unit transaction cost confidence interval generation method and system

Abstract

The invention discloses a power system inter-provincial tie line unit transaction cost confidence interval generation method. The method comprises the steps of obtaining data information of a target power system and performing data processing; calculating a feature sequence weight based on a generalization theory; screening and constructing a similar day set based on a maximum information coefficient scheme; and based on Tukey distribution, fitting the similar daily error CDF quantile to generate a unit transaction cost confidence interval so as to complete generation of the unit transaction cost confidence interval of the inter-provincial tie line of the target power system. The invention also discloses a system for realizing the power system inter-provincial tie line unit transaction cost confidence interval generation method. According to the method, the unit transaction cost confidence interval of the inter-provincial tie line of the power system can be generated, the reliability is higher, and the accuracy is better.

Description

Technical Field

[0001] This invention belongs to the field of electrical automation, specifically relating to a method and system for generating confidence intervals for unit transaction costs of inter-provincial tie lines in power systems. Background Technology

[0002] With economic and technological development and the improvement of people's living standards, electricity has become an indispensable secondary energy source in people's production and daily life, bringing endless convenience. Therefore, ensuring a stable and reliable supply of electricity has become one of the most important tasks of the power system.

[0003] The safe, stable, and reliable operation of the inter-provincial power market is crucial for ensuring the rational allocation of inter-provincial power resources and guaranteeing regional renewable energy consumption and power balance. The quantity and price of inter-provincial power interconnections are not only important references for the operation of the inter-provincial power market but also directly related to its safe operation, the rational allocation of inter-provincial power resources, and the guarantee of regional renewable energy consumption and power balance. Therefore, research on the confidence interval of unit transaction costs for inter-provincial power interconnections is of great significance for the safe and stable operation of the power system and the consumption of renewable energy.

[0004] Currently, existing schemes for generating confidence intervals for unit transaction costs in power systems generally use globally statistical historical unit transaction cost error samples, or generate error probability distributions or cumulative probability functions based on fixed dataset partitioning methods to serve as confidence interval benchmarks. However, these schemes exhibit significant reliability and accuracy issues when applied to inter-provincial tie lines. Summary of the Invention

[0005] One of the objectives of this invention is to provide a method for generating confidence intervals for unit transaction costs of inter-provincial power system tie lines that is highly reliable and accurate.

[0006] The second objective of this invention is to provide a system for generating the confidence interval of unit transaction cost for inter-provincial power system tie lines.

[0007] The method for generating a confidence interval for unit transaction cost of inter-provincial power system tie lines provided by this invention includes the following steps:

[0008] S1. Obtain data information about the target power system;

[0009] S2. Process the data obtained in step S1;

[0010] S3. Based on the processed data, calculate the feature sequence weights using generalization theory;

[0011] S4. Based on the maximum information coefficient scheme, the similarity set is selected and constructed;

[0012] S5. Based on the Tukey distribution, the CDF quantiles of similar daily errors are fitted to generate the confidence interval for unit transaction cost, thereby completing the generation of the confidence interval for unit transaction cost of inter-provincial tie lines of the target power system.

[0013] Step S1, which involves acquiring data information about the target power system, specifically includes the following steps:

[0014] Acquire data information about the target power system; the data information includes a historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system, a historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system, and a historical input feature sequence for predicting unit transaction cost points; the historical input feature sequence includes inter-provincial tie line power, inter-provincial tie line power ramp-up rate, sending-end node NWP data, receiving-end node NWP data, sending-end inter-provincial unit transaction cost difference, receiving-end inter-provincial unit transaction cost difference, inter-provincial tie line congestion rate, and inter-provincial tie line icing probability.

[0015] Step S2, which involves processing the data obtained in step S1, specifically includes the following steps:

[0016] The historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system and the historical input feature sequence used for unit transaction cost point prediction are aligned in terms of time span and time scale, with the historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system as the benchmark.

[0017] The missing values ​​are filled in using a cubic spline interpolation algorithm.

[0018] The Isolation Forest algorithm is used to filter and correct outliers;

[0019] The unit root test method was used to test and process the stationarity of the data.

[0020] The min-max normalization algorithm is used to standardize the data.

[0021] Step S3, which involves calculating the feature sequence weights based on the processed data and generalization theory, includes the following steps:

[0022] Based on generalization theory, the historical input feature sequence obtained in step S2 is quantized. Historical forecast series of unit transaction costs Historical Real Value Series of Unit Transaction Costs The causal relationship is used to construct three sets. The regression model;

[0023] Based on the obtained regression model, the F-distribution value is used to measure... , and causal relationship;

[0024] Based on the obtained F-distribution values, the historical input feature sequence is calculated. Historical forecast series of unit transaction costs Weighting in similar day filtering.

[0025] Step S3 specifically includes the following steps:

[0026] Based on generalization theory, quantification , and Construct three sets of causal relationships. The regression model is expressed as:

[0027] In the formula: τ1-τ3 are the time step indices of the time series; To consider the historical actual value sequence of unit transaction costs in the historical input feature sequence The regression model value; The autoregressive constant coefficients of the historical actual value series of unit transaction costs; The maximum regression lag time step of the historical actual value sequence of unit transaction costs; The maximum regression lag time step for the nth historical input feature sequence; The autocorrelation coefficient of the regression model; The maximum regression lag time step for the historical forecast series of unit transaction costs; This represents the cross-correlation coefficient of the regression model; For the nth historical input feature sequence; For the first The residuals of the regression model for a historical input feature sequence; The regression model values ​​take into account the historical forecast series of unit transaction costs; The cross-correlation coefficient of the historical predicted value series of unit transaction costs in the regression model; A series of historical forecasts for unit transaction costs; For the first Regression model residuals for a series of historical predicted unit transaction costs; The values ​​of the autoregressive model are taken into account for the historical actual values ​​of unit transaction costs; For the first Regression model residuals of historical actual values ​​of unit transaction costs;

[0028] The least squares method is used to minimize the sum of squares of all residuals to achieve three sets of results. The optimal fit of the regression model;

[0029] Measured by F-distribution , and The causal relationship can be expressed as:

[0030] In the formula Let F be the F-distribution value of the nth historical input feature sequence and the historical actual value sequence of unit transaction cost; for The sum of squared residuals of the corresponding model; for The sum of squared residuals of the corresponding model; This represents the total number of time steps in the time series. The F-distribution values ​​of the historical predicted value series and the historical actual value series of unit transaction costs; for The sum of squared residuals of the corresponding model; For a given confidence level The threshold of the F-distribution; for With a given confidence level The ratio of the F-distribution threshold; for With a given confidence level The ratio of the F-distribution threshold;

[0031] The historical input feature sequence is calculated using the following formula. Historical forecast series of unit transaction costs Weighting in similar day filtering:

[0032] In the formula Input feature sequences for history Weight values ​​in similar day filtering; Historical forecast series of unit transaction costs Weighting values ​​in similar day filtering.

[0033] Step S4, which involves filtering and constructing a set of similar days based on the maximum information coefficient scheme, includes the following steps:

[0034] Construct the correspondence between the feature sequence of the test day and the historical input feature sequence on the two-dimensional value domain plane, and simultaneously construct the correspondence between the predicted unit transaction cost sequence of the test day and the historical predicted unit transaction cost sequence on the two-dimensional value domain plane; then divide the two-dimensional value domain plane into grids;

[0035] For each grid partitioning method of each sequence, calculate the mutual information between the daily sequence to be predicted and the corresponding historical daily sequence under each grid partitioning method;

[0036] After normalizing the mutual information, the maximum value is taken, and then a weighted sum is performed with the corresponding weight to obtain the weighted similarity score between the day to be predicted and the historical day.

[0037] Based on the obtained weighted similarity scores, the corresponding set of similar days is selected.

[0038] Step S4 specifically includes the following steps:

[0039] Constructing the feature sequence of the day to be tested Compared with historical input feature sequences The correspondence on the two-dimensional value range plane is established, and the predicted unit transaction cost sequence for the test day is constructed simultaneously. Historical forecast series of unit transaction costs The correspondence on the two-dimensional value range plane; then, the two-dimensional value range plane is divided into a grid of columns a and rows b, with the upper limit of the total number of grids set during the grid division process. ; The rounding up symbol;

[0040] The mutual information between the predicted daily sequence and the corresponding historical daily sequence under each grid partitioning method is calculated using the following formula:

[0041] In the formula Let be the mutual information value between the k-th day to be predicted and the j-th historical day of the n-th historical input feature sequence under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function; Let be the mutual information value between the k-th day to be predicted and the j-th historical day in the historical prediction value sequence of unit transaction cost under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function;

[0042] Simultaneously, it is set that: given the same total number of grid cells, if there are several ways to partition rows and columns, all partitioning methods will be traversed and their corresponding mutual information will be calculated, with the largest mutual information value selected as the optimal value. and ;

[0043] After normalizing the mutual information, the maximum value is taken to obtain the corresponding normalized mutual information value. and ;

[0044] The weighted similarity score between the date to be predicted and historical dates is obtained by weighted summation using the following formula:

[0045] In the formula The weighted similarity score between the k-th day to be predicted and the j-th historical day;

[0046] Will Sort the values ​​and select the top few best ones. The historical day data corresponding to the value is used as the similar day set for the k-th day to be predicted; wherein, the historical day data includes the historical predicted value sequence of unit transaction cost, the historical actual value sequence of unit transaction cost, and the historical input feature sequence used for unit transaction cost point prediction.

[0047] Step S5, which involves fitting the CDF quantiles of similar day errors based on the Tukey distribution to generate a confidence interval for unit transaction cost, includes the following steps:

[0048] Based on the similar day set obtained in step S4, the prediction error of the unit transaction cost of inter-provincial connecting lines is statistically analyzed.

[0049] Define the quantile function for the Tukey distribution;

[0050] Select several typical probability values ​​to construct a probability set;

[0051] Calculate the empirical distribution quantiles of the probability corresponding to the prediction error of the unit transaction cost of inter-provincial connecting lines, define the parameter optimization objective function of the Tukey distribution based on the empirical distribution quantiles, and solve for it.

[0052] Based on the solution results, select the confidence level and calculate the corresponding error confidence interval boundaries;

[0053] The obtained error confidence interval boundary is superimposed with the unit transaction cost prediction sequence for the date to be predicted, and the normalization is removed to obtain the final unit transaction cost confidence interval.

[0054] Step S5 specifically includes the following steps:

[0055] For each forecast date, the forecast error of the unit transaction cost of the inter-provincial connection line is calculated and expressed as: ;in The prediction error for the u-th unit transaction cost in the similar day set is... Let be the actual unit transaction cost at time t on the s-th similar day. Let $t$ be the predicted unit transaction cost at time $t$ on the $s$-th similar day.

[0056] Define the quantile function of the Tukey distribution , is represented as:

[0057] In the formula is the first adjustable parameter of the Tukey distribution; This is the second adjustable parameter of the Tukey distribution; The p-quantile of the standard Gaussian distribution CDF; This is a probability value;

[0058] Select several typical probability values ​​to construct a probability set. for ;

[0059] Calculate the prediction error of unit transaction cost for inter-provincial connecting lines Corresponding probability empirical distribution quantiles Based on empirical distribution quantiles Define and solve the objective function for optimizing the parameters of the Tukey distribution, using the benchmark as an example; where the defined objective function for optimizing the parameters of the Tukey distribution is expressed as:

[0060] In the formula This represents the total number of typical probability values. Let be the weight of the c-th typical probability value, and ;

[0061] Based on the optimal parameters obtained from the solution and Select confidence level Calculate the corresponding error confidence interval boundary, expressed as:

[0062] In the formula For confidence level The lower boundary of the confidence interval for the unit transaction cost error; For confidence level The upper boundary of the confidence interval for the unit transaction cost error; for The mean; for Standard deviation;

[0063] The obtained error confidence interval boundaries are superimposed on the unit transaction cost prediction series for the date to be predicted, and then normalized is removed to obtain the final unit transaction cost confidence interval, expressed as:

[0064] In the formula For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; This represents the predicted unit transaction cost for the k-th day to be predicted. For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For the first normalization Actual value of unit transaction cost.

[0065] This invention also provides a system for generating the confidence interval for unit transaction cost of inter-provincial tie lines in a power system, comprising a data acquisition module, a data processing module, a weight calculation module, a set construction module, and an interval generation module; the data acquisition module, data processing module, weight calculation module, set construction module, and interval generation module are connected in series; the data acquisition module acquires data information of the target power system and uploads the data information to the data processing module; the data processing module processes the acquired data information based on the received data information and uploads the data information to the weight calculation module; the weight calculation module calculates the feature sequence weights based on generalization theory based on the received data information and the processed data information, and uploads the data information to the set construction module; the set construction module filters and constructs a set of similar days based on the maximum information coefficient scheme based on the received data information, and uploads the data information to the interval generation module; the interval generation module fits the CDF quantile of the similar day error based on the Tukey distribution based on the received data information to generate a confidence interval for unit transaction cost, thereby completing the generation of the confidence interval for unit transaction cost of inter-provincial tie lines in the target power system.

[0066] The method and system for generating confidence intervals for unit transaction costs of inter-provincial power system tie lines provided by this invention are based on generalization theory for weight calculation, and on the construction and screening of similar day sets based on the maximum information coefficient scheme. Finally, error fitting and confidence interval generation are performed based on the Tukey distribution. Therefore, this invention can not only generate confidence intervals for unit transaction costs of inter-provincial power system tie lines, but also has higher reliability and better accuracy. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0068] Figure 2 This is a schematic diagram of the functional modules of the system of the present invention. Detailed Implementation

[0069] like Figure 1 The diagram shown is a flowchart of the method of the present invention: The method for generating the confidence interval of unit transaction cost of inter-provincial power system tie lines disclosed in this invention includes the following steps:

[0070] S1. Obtain data information of the target power system; specifically including the following steps:

[0071] Acquire data information of the target power system; the data information includes the historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system, the historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system, and the historical input feature sequence for unit transaction cost point prediction; the historical input feature sequence includes inter-provincial tie line power, inter-provincial tie line power ramp rate, sending-end node NWP data, receiving-end node NWP data, sending-end inter-provincial unit transaction cost difference, receiving-end inter-provincial unit transaction cost difference, inter-provincial tie line congestion rate, and inter-provincial tie line icing probability;

[0072] S2. Process the data obtained in step S1; specifically, this includes the following steps:

[0073] The historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system and the historical input feature sequence used for unit transaction cost point prediction are aligned in terms of time span and time scale, with the historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system as the benchmark.

[0074] The missing values ​​are filled in using a cubic spline interpolation algorithm.

[0075] The Isolation Forest algorithm is used to filter and correct outliers;

[0076] The unit root test method was used to test and process the stationarity of the data.

[0077] The min-max normalization algorithm is used to standardize the data.

[0078] S3. Based on the processed data, and using generalization theory, calculate the weights of the feature sequences; this includes the following steps:

[0079] Based on generalization theory, the historical input feature sequence obtained in step S2 is quantized. Historical forecast series of unit transaction costs Historical Real Value Series of Unit Transaction Costs The causal relationship is used to construct three sets. The regression model;

[0080] Based on the obtained regression model, the F-distribution value is used to measure... , and causal relationship;

[0081] Based on the obtained F-distribution values, the historical input feature sequence is calculated. Historical forecast series of unit transaction costs Weighting in similar day filtering;

[0082] In practice, the following steps can be taken:

[0083] Given that the prediction of unit transaction cost for inter-provincial connecting lines is essentially about identifying the causal relationship between feature sequences and unit transaction cost (i.e., unit transaction cost is the result of a specific input feature sequence), quantification is performed based on generalization theory (GT). , and Construct three sets of causal relationships. The regression model is expressed as:

[0084] In the formula: τ1-τ3 are the time step (moment) indices of the time series; To consider the historical actual value sequence of unit transaction costs in the historical input feature sequence The regression model value; The autoregressive constant coefficients of the historical actual value series of unit transaction costs; The maximum regression lag time step of the historical actual value sequence of unit transaction costs; The maximum regression lag time step for the nth historical input feature sequence; The autocorrelation coefficient of the regression model; The maximum regression lag time step for the historical forecast series of unit transaction costs; This represents the cross-correlation coefficient of the regression model; For the nth historical input feature sequence; For the first The residuals of the regression model for a historical input feature sequence; The regression model values ​​take into account the historical forecast series of unit transaction costs; The cross-correlation coefficient of the historical predicted value series of unit transaction costs in the regression model; A series of historical forecasts for unit transaction costs; For the first Regression model residuals for a series of historical predicted unit transaction costs; The values ​​of the autoregressive model are taken into account for the historical actual values ​​of unit transaction costs; For the first Regression model residuals of historical actual values ​​of unit transaction costs;

[0085] in, The model is a regression model that takes into account the nth historical feature sequence; The model is a regression model that takes into account historical prediction sequences; The model is an autoregressive model based on the historical actual unit transaction cost series;

[0086] The least squares method is used to minimize the sum of squares of all residuals to achieve three sets of results. The optimal fit (i.e., optimization) of the regression model , and );

[0087] Measured by F-distribution , and The causal relationship can be expressed as:

[0088] In the formula Let F be the F-distribution value of the nth historical input feature sequence and the historical actual value sequence of unit transaction cost; for The sum of squared residuals of the corresponding model; for The sum of squared residuals of the corresponding model; This represents the total number of time steps (moments) in the time series. The F-distribution values ​​of the historical predicted value series and the historical actual value series of unit transaction costs; for The sum of squared residuals of the corresponding model; For a given confidence level The threshold of the F-distribution; for With a given confidence level The ratio of the F-distribution threshold; for With a given confidence level The ratio of the F-distribution threshold; and The larger the value, the stronger the causal relationship between the two sequences on the actual unit transaction cost;

[0089] The historical input feature sequence is calculated using the following formula. Historical forecast series of unit transaction costs Weighting in similar day filtering:

[0090] In the formula Input feature sequences for history Weight values ​​in similar day filtering; Historical forecast series of unit transaction costs Weight values ​​in similar day filtering;

[0091] S4. Based on the maximum information coefficient scheme, the similarity set is selected and constructed; including the following steps:

[0092] Construct the correspondence between the feature sequence of the test day and the historical input feature sequence on the two-dimensional value domain plane, and simultaneously construct the correspondence between the predicted unit transaction cost sequence of the test day and the historical predicted unit transaction cost sequence on the two-dimensional value domain plane; then divide the two-dimensional value domain plane into grids;

[0093] For each grid partitioning method of each sequence, calculate the mutual information between the daily sequence to be predicted and the corresponding historical daily sequence under each grid partitioning method;

[0094] After normalizing the mutual information, the maximum value is taken, and then a weighted sum is performed with the corresponding weight to obtain the weighted similarity score between the day to be predicted and the historical day.

[0095] Based on the obtained weighted similarity scores, select the corresponding set of similar days;

[0096] In practice, the following steps can be taken:

[0097] Given that the autocorrelation of each characteristic sequence and the autocorrelation of the predicted unit transaction cost both exhibit strong nonlinear characteristics on different days, this invention uses MIC, which can mainly measure the nonlinear relationship between time series, as the basis for screening similar days.

[0098] Constructing the feature sequence of the day to be tested Compared with historical input feature sequences The correspondence on the two-dimensional value range plane is established, and the predicted unit transaction cost sequence for the test day is constructed simultaneously. Historical forecast series of unit transaction costs The correspondence on the two-dimensional value range plane; then, the two-dimensional value range plane is divided into a grid of columns a and rows b, with the upper limit of the total number of grids set during the grid division process. ; The rounding up symbol;

[0099] The mutual information between the predicted daily sequence and the corresponding historical daily sequence under each grid partitioning method is calculated using the following formula:

[0100] In the formula Let be the mutual information value between the k-th day to be predicted and the j-th historical day of the n-th historical input feature sequence under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function; Let be the mutual information value between the k-th day to be predicted and the j-th historical day in the historical prediction value sequence of unit transaction cost under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function;

[0101] Simultaneously, it is set that: given the same total number of grid cells, if there are several ways to partition rows and columns, all partitioning methods will be traversed and their corresponding mutual information will be calculated, with the largest mutual information value selected as the optimal value. and ;

[0102] After normalizing the mutual information, the maximum value is taken to obtain the corresponding normalized mutual information value. and ; and The larger, the more and , and The stronger the nonlinear correlation;

[0103] The weighted similarity score between the date to be predicted and historical dates is obtained by weighted summation using the following formula:

[0104] In the formula The weighted similarity score is given between the k-th day to be predicted and the j-th historical day. The larger the value, the higher the similarity between the two.

[0105] Will Sort the values ​​and select the top few (preferably the top 30-50 with the largest values). The historical day data corresponding to the value is used as the similar day set for the k-th day to be predicted; wherein, the historical day data includes the historical predicted value sequence of unit transaction cost, the historical actual value sequence of unit transaction cost, and the historical input feature sequence used for unit transaction cost point prediction;

[0106] S5. Based on the Tukey distribution, fit the CDF quantiles of similar daily errors to generate a confidence interval for unit transaction cost, thus completing the generation of the confidence interval for unit transaction cost of inter-provincial tie lines in the target power system; including the following steps:

[0107] Based on the similar day set obtained in step S4, the prediction error of the unit transaction cost of inter-provincial connecting lines is statistically analyzed.

[0108] Define the quantile function for the Tukey distribution;

[0109] Select several typical probability values ​​to construct a probability set;

[0110] Calculate the empirical distribution quantiles of the probability corresponding to the prediction error of the unit transaction cost of inter-provincial connecting lines, define the parameter optimization objective function of the Tukey distribution based on the empirical distribution quantiles, and solve for it.

[0111] Based on the solution results, select the confidence level and calculate the corresponding error confidence interval boundaries;

[0112] The obtained error confidence interval boundaries are superimposed with the unit transaction cost prediction series for the date to be predicted, and the normalization is removed to obtain the final unit transaction cost confidence interval.

[0113] In practice, the following steps can be taken:

[0114] For each forecast date, the forecast error of the unit transaction cost of the inter-provincial connection line is calculated and expressed as: ;in The prediction error for the u-th unit transaction cost in the similar day set is... Let be the actual unit transaction cost at time t on the s-th similar day. Let $t$ be the predicted unit transaction cost at time $t$ on the $s$-th similar day.

[0115] Define the quantile function of the Tukey distribution , is represented as:

[0116] In the formula is the first adjustable parameter of the Tukey distribution; This is the second adjustable parameter of the Tukey distribution; The p-quantile of the standard Gaussian distribution CDF; This is a probability value;

[0117] Select several typical probability values ​​to construct a probability set. for ;

[0118] Calculate the prediction error of unit transaction cost for inter-provincial connecting lines Corresponding probability empirical distribution quantiles Based on empirical distribution quantiles Define and solve the objective function for optimizing the parameters of the Tukey distribution, using the benchmark as an example; where the defined objective function for optimizing the parameters of the Tukey distribution is expressed as:

[0119] In the formula This represents the total number of typical probability values. Let be the weight of the c-th typical probability value, and ;

[0120] The solution process can be efficiently solved using least squares-related algorithms (such as the trust region method, Levenberg-Marquardt method, etc.);

[0121] Based on the optimal parameters obtained from the solution and Select confidence level Calculate the corresponding error confidence interval boundary, expressed as:

[0122] In the formula For confidence level The lower boundary of the confidence interval for the unit transaction cost error; For confidence level The upper boundary of the confidence interval for the unit transaction cost error; for The mean; for Standard deviation;

[0123] The obtained error confidence interval boundaries are superimposed on the unit transaction cost prediction series for the date to be predicted, and then normalized is removed to obtain the final unit transaction cost confidence interval, expressed as:

[0124] In the formula For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; This represents the predicted unit transaction cost for the k-th day to be predicted. For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For the first normalization Actual value of unit transaction cost.

[0125] This invention's method, based on the GT-MIC similar day set selection method, starts from the mathematical essence of the feature sequence and the unit transaction cost prediction sequence. It generates adaptive weights based on the causal correlation strength of each sequence to the actual unit transaction cost sequence and quantitatively evaluates the nonlinear dependence between the predicted day and historical day sequences, thereby constructing an objective similar day set with strong mathematical basis. The method also utilizes the Tukey distribution and the similar day set to generate confidence intervals for unit transaction costs. This allows for direct explicit fitting of error samples to quantiles, demonstrating significant computational efficiency and model analytical power compared to traditional Gaussian distributions, general distributions, and kernel density estimation methods. Furthermore, the Tukey distribution explicitly controls the tail shape through the tail parameter h and incorporates extreme probability points (e.g., 1% / 99%) for fitting. Compared to composite distributions such as Gaussian mixtures, it more efficiently matches the potential "fat-tailed" characteristics of inter-provincial link unit transaction costs and avoids local optima problems in multi-parameter optimization. Therefore, this invention's method offers higher reliability and better accuracy.

[0126] like Figure 2 The diagram shows the functional modules of the system of the present invention: The system disclosed in this invention for generating the confidence interval of unit transaction cost for inter-provincial tie lines in a power system includes a data acquisition module, a data processing module, a weight calculation module, a set construction module, and an interval generation module; the data acquisition module, data processing module, weight calculation module, set construction module, and interval generation module are connected in series; the data acquisition module is used to acquire data information of the target power system and upload the data information to the data processing module; the data processing module is used to process the acquired data information according to the received data information and upload the data information to the weight calculation module; the weight calculation module is used to calculate the feature sequence weights based on generalization theory according to the received data information and the processed data information, and upload the data information to the set construction module; the set construction module is used to screen and construct similar day sets according to the received data information based on the maximum information coefficient scheme, and upload the data information to the interval generation module; the interval generation module is used to fit the CDF quantile of similar day errors according to the Tukey distribution according to the received data information to generate the confidence interval of unit transaction cost, thereby completing the generation of the confidence interval of unit transaction cost for inter-provincial tie lines in the target power system.

Claims

1. A method for generating a confidence interval for unit transaction cost of inter-provincial power system tie lines, comprising the following steps: S1. Obtain data information about the target power system; S2. Process the data obtained in step S1; S3. Based on the processed data, calculate the feature sequence weights using generalization theory; S4. Based on the maximum information coefficient scheme, the similarity set is selected and constructed; S5. Based on the Tukey distribution, the CDF quantiles of similar daily errors are fitted to generate the confidence interval for unit transaction cost, thereby completing the generation of the confidence interval for unit transaction cost of inter-provincial tie lines of the target power system.

2. The method for generating the confidence interval of unit transaction cost for inter-provincial power system interconnection lines according to claim 1, characterized in that... Step S1, which involves acquiring data information about the target power system, specifically includes the following steps: Acquire data information about the target power system; the data information includes a historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system, a historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system, and a historical input feature sequence for predicting unit transaction cost points; the historical input feature sequence includes inter-provincial tie line power, inter-provincial tie line power ramp-up rate, sending-end node NWP data, receiving-end node NWP data, sending-end inter-provincial unit transaction cost difference, receiving-end inter-provincial unit transaction cost difference, inter-provincial tie line congestion rate, and inter-provincial tie line icing probability.

3. The method for generating the confidence interval of unit transaction cost for inter-provincial power system tie lines according to claim 2, characterized in that... Step S2, which involves processing the data obtained in step S1, specifically includes the following steps: The historical predicted value sequence of unit transaction cost of inter-provincial tie lines of the target power system and the historical input feature sequence used for unit transaction cost point prediction are aligned in terms of time span and time scale, with the historical actual value sequence of unit transaction cost of inter-provincial tie lines of the target power system as the benchmark. The missing values ​​are filled in using a cubic spline interpolation algorithm. The Isolation Forest algorithm is used to filter and correct outliers; The unit root test method was used to test and process the stationarity of the data. The min-max normalization algorithm is used to standardize the data.

4. The method for generating the confidence interval of unit transaction cost for inter-provincial power system tie lines according to claim 3, characterized in that... Step S3, which involves calculating the feature sequence weights based on the processed data and generalization theory, includes the following steps: Based on generalization theory, the historical input feature sequence obtained in step S2 is quantized. Historical forecast series of unit transaction costs Historical Real Value Series of Unit Transaction Costs The causal relationship is used to construct three sets. The regression model; Based on the obtained regression model, the F-distribution value is used to measure... , and causal relationship; Based on the obtained F-distribution values, the historical input feature sequence is calculated. Historical forecast series of unit transaction costs Weighting in similar day filtering.

5. The method for generating the confidence interval of unit transaction cost for inter-provincial power system tie lines according to claim 4, characterized in that... Step S3 specifically includes the following steps: Based on generalization theory, quantification , and Construct three sets of causal relationships. The regression model is expressed as: In the formula: τ1-τ3 are the time step indices of the time series; To consider the historical actual value sequence of unit transaction costs in the historical input feature sequence The regression model value; The autoregressive constant coefficients of the historical actual value series of unit transaction costs; The maximum regression lag time step of the historical actual value sequence of unit transaction costs; The maximum regression lag time step for the nth historical input feature sequence; The autocorrelation coefficient of the regression model; The maximum regression lag time step for the historical forecast series of unit transaction costs; This represents the cross-correlation coefficient of the regression model; For the nth historical input feature sequence; For the first The residuals of the regression model for a historical input feature sequence; The regression model values ​​take into account the historical forecast series of unit transaction costs; The cross-correlation coefficient of the historical predicted value series of unit transaction costs in the regression model; A series of historical forecasts for unit transaction costs; For the first Regression model residuals for a series of historical predicted unit transaction costs; The values ​​of the autoregressive model are taken into account for the historical actual values ​​of unit transaction costs; For the first Regression model residuals of historical actual values ​​of unit transaction costs; The least squares method is used to minimize the sum of squares of all residuals to achieve three sets of results. The optimal fit of the regression model; Measured by F-distribution , and The causal relationship can be expressed as: In the formula Let F be the F-distribution value of the nth historical input feature sequence and the historical actual value sequence of unit transaction cost; for The sum of squared residuals of the corresponding model; for The sum of squared residuals of the corresponding model; This represents the total number of time steps in the time series. The F-distribution values ​​of the historical predicted value series and the historical actual value series of unit transaction costs; for The sum of squared residuals of the corresponding model; For a given confidence level The threshold of the F-distribution; for With a given confidence level The ratio of the F-distribution threshold; for With a given confidence level The ratio of the F-distribution threshold; The historical input feature sequence is calculated using the following formula. Historical forecast series of unit transaction costs Weighting in similar day filtering: In the formula Input feature sequences for history Weight values ​​in similar day filtering; Historical forecast series of unit transaction costs Weighting values ​​in similar day filtering.

6. The method for generating the confidence interval for unit transaction cost of inter-provincial power system tie lines according to claim 5, characterized in that... Step S4, which involves filtering and constructing a set of similar days based on the maximum information coefficient scheme, includes the following steps: Construct the correspondence between the feature sequence of the test day and the historical input feature sequence on the two-dimensional value domain plane, and simultaneously construct the correspondence between the predicted unit transaction cost sequence of the test day and the historical predicted unit transaction cost sequence on the two-dimensional value domain plane; then divide the two-dimensional value domain plane into grids; For each grid partitioning method of each sequence, calculate the mutual information between the daily sequence to be predicted and the corresponding historical daily sequence under each grid partitioning method; After normalizing the mutual information, the maximum value is taken, and then a weighted sum is performed with the corresponding weight to obtain the weighted similarity score between the day to be predicted and the historical day. Based on the obtained weighted similarity scores, the corresponding set of similar days is selected.

7. The method for generating the confidence interval of unit transaction cost for inter-provincial power system tie lines according to claim 6, characterized in that... Step S4 specifically includes the following steps: Constructing the feature sequence of the day to be tested Compared with historical input feature sequences The correspondence on the two-dimensional value range plane is established, and the predicted unit transaction cost sequence for the test day is constructed simultaneously. Historical forecast series of unit transaction costs The correspondence on the two-dimensional value range plane; then, the two-dimensional value range plane is divided into a grid of columns a and rows b, with the upper limit of the total number of grids set during the grid division process. ; The rounding up symbol; The mutual information between the predicted daily sequence and the corresponding historical daily sequence under each grid partitioning method is calculated using the following formula: In the formula Let be the mutual information value between the k-th day to be predicted and the j-th historical day of the n-th historical input feature sequence under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function; Let be the mutual information value between the k-th day to be predicted and the j-th historical day in the historical prediction value sequence of unit transaction cost under the g-th grid partitioning method; for and The joint probability density function; for The marginal probability density function; for The marginal probability density function; Simultaneously, it is set that: given the same total number of grid cells, if there are several ways to partition rows and columns, all partitioning methods are traversed and their corresponding mutual information is calculated, and the largest mutual information is selected as the... and ; After normalizing the mutual information, the maximum value is taken to obtain the corresponding normalized mutual information value. and ; The weighted similarity score between the date to be predicted and historical dates is obtained by weighted summation using the following formula: In the formula The weighted similarity score between the k-th day to be predicted and the j-th historical day; Will Sort the values ​​and select the top few best ones. The historical day data corresponding to the value is used as the similar day set for the k-th day to be predicted; wherein, the historical day data includes the historical predicted value sequence of unit transaction cost, the historical actual value sequence of unit transaction cost, and the historical input feature sequence used for unit transaction cost point prediction.

8. The method for generating a confidence interval for unit transaction cost of inter-provincial power system tie lines according to claim 7, characterized in that... Step S5, which involves fitting the CDF quantiles of similar day errors based on the Tukey distribution to generate a confidence interval for unit transaction cost, includes the following steps: Based on the similar day set obtained in step S4, the prediction error of the unit transaction cost of inter-provincial connecting lines is statistically analyzed. Define the quantile function for the Tukey distribution; Select several typical probability values ​​to construct a probability set; Calculate the empirical distribution quantiles of the probability corresponding to the prediction error of the unit transaction cost of inter-provincial connecting lines, define the parameter optimization objective function of the Tukey distribution based on the empirical distribution quantiles, and solve for it. Based on the solution results, select the confidence level and calculate the corresponding error confidence interval boundaries; The obtained error confidence interval boundary is superimposed with the unit transaction cost prediction sequence for the date to be predicted, and the normalization is removed to obtain the final unit transaction cost confidence interval.

9. The method for generating a confidence interval for unit transaction cost of inter-provincial power system tie lines according to claim 8, characterized in that... Step S5 specifically includes the following steps: For each forecast date, the forecast error of the unit transaction cost of the inter-provincial connection line is calculated and expressed as: ;in The prediction error for the u-th unit transaction cost in the similar day set is... Let be the actual unit transaction cost at time t on the s-th similar day. Let $t$ be the predicted unit transaction cost at time $t$ on the $s$-th similar day. Define the quantile function of the Tukey distribution , is represented as: In the formula is the first adjustable parameter of the Tukey distribution; This is the second adjustable parameter of the Tukey distribution; The p-quantile of the standard Gaussian distribution CDF; This is a probability value; Select several typical probability values ​​to construct a probability set. for ; Calculate the prediction error of unit transaction cost for inter-provincial connecting lines Corresponding probability empirical distribution quantiles Based on empirical distribution quantiles Define and solve the objective function for optimizing the parameters of the Tukey distribution, using the benchmark as an example; where the defined objective function for optimizing the parameters of the Tukey distribution is expressed as: In the formula This represents the total number of typical probability values. Let be the weight of the c-th typical probability value, and ; Based on the optimal parameters obtained from the solution and Select confidence level Calculate the corresponding error confidence interval boundary, expressed as: In the formula For confidence level The lower boundary of the confidence interval for the unit transaction cost error; For confidence level The upper boundary of the confidence interval for the unit transaction cost error; for The mean; for Standard deviation; The obtained error confidence interval boundaries are superimposed on the unit transaction cost prediction series for the date to be predicted, and then normalized is removed to obtain the final unit transaction cost confidence interval, expressed as: In the formula For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; This represents the predicted unit transaction cost for the k-th day to be predicted. For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized lower boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For confidence level The normalized upper boundary value of the confidence interval for the unit transaction cost at time t on the k-th day to be predicted; For the first before normalization Actual value of unit transaction cost.

10. A system for implementing the method for generating confidence intervals for unit transaction costs of inter-provincial power system tie lines as described in any one of claims 1 to 9, characterized in that... It includes a data acquisition module, a data processing module, a weight calculation module, a set construction module, and an interval generation module; the data acquisition module, data processing module, weight calculation module, set construction module, and interval generation module are connected in series; the data acquisition module is used to acquire data information of the target power system and upload the data information to the data processing module; The data processing module is used to process the acquired data based on the received data information and upload the data information to the weight calculation module; The weight calculation module is used to calculate the weights of the feature sequences based on the received data and the processed data, and based on generalization theory, and then upload the data to the collection construction module. The set construction module is used to filter and construct similar day sets based on the received data information and the maximum information coefficient scheme, and then upload the data information to the interval generation module. The interval generation module is used to fit the CDF quantile of similar daily errors based on the received data information and the Tukey distribution to generate the confidence interval of unit transaction cost, so as to complete the generation of the confidence interval of unit transaction cost of inter-provincial tie lines of the target power system.

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