CN114037005A - Power load prediction method based on optimized selection of typical daily load curve - Google Patents
Power load prediction method based on optimized selection of typical daily load curve Download PDFInfo
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Abstract
The invention relates to a power load prediction method based on an optimized selection typical daily load curve, which comprises the following steps: acquiring load original data; preprocessing load original data to obtain a characteristic index; an improved PFCM algorithm is adopted and combined with a fuzzy linear discriminant method (FLDA) to perform cluster analysis on the preprocessed load original data to determine a cluster center matrix; determining a reference day, respectively calculating the correlation between the reference day of each month and each clustering center according to a Pearson correlation coefficient method, and determining the category of each month; and taking the sample point with the maximum membership degree in each class as a typical daily load curve, and performing power load prediction based on the typical daily load curve to obtain a corresponding prediction result. Compared with the prior art, the method has the advantages that the PFCM algorithm is improved, and the FLDA method is combined, so that the typical daily load curve closer to the clustering center can be optimally selected, and the accuracy of power load prediction is effectively improved.
Description
Technical Field
The invention relates to the technical field of power load prediction, in particular to a power load prediction method based on an optimized selection typical daily load curve.
Background
The power load prediction is an important component of power system planning and also is the basis of economic operation of the power system, and is extremely important to the planning and operation of the power system. The key of the load forecasting work is to collect a large amount of historical data, establish a scientific and effective forecasting model, adopt an effective algorithm, take the historical data as the basis, perform a large amount of experimental researches, summarize experiences, and continuously correct the model and the algorithm so as to truly reflect the load change rule.
Before forecasting the power load, a typical daily load curve is often required to be selected in advance, and the traditional method is to select the typical daily load curve by a certain characteristic index, or directly select the daily load curve with the maximum load in the whole month, or select a certain fixed working day in the month as the daily load curve in the month. Wherein, a typical daily load curve is selected according to a certain characteristic index, and the problem of partial completeness of the overall description of the load curve exists; if the daily load curve with the maximum load in the whole month is directly selected or a certain fixed working day in the month is selected as the daily load curve in the month, the method has the problems of applicability and lack of representativeness.
In addition, in the existing research, a machine learning method is also adopted to select a typical daily load curve, for example, a single clustering algorithm or an integrated clustering algorithm is used to obtain a clustering center matrix, and then a sample point closest to the clustering center is obtained by different methods to serve as the typical daily load curve. However, the existing possible fuzzy C-means clustering algorithm (PCM) attaches importance to typicality and does not consider the compactness of sample points, which can cause the result of clustering consistency; the probability fuzzy C-means algorithm (PFCM) overcomes the defects of PCM clustering consistency and FCM sensitivity to distorted data, but the parameter in FCM needs to be calculated first in the process of solving the target function, so that the calculation cost is increased. This can result in a lack of accuracy in the selection of typical daily loads, which in turn reduces the accuracy of the subsequent power load predictions.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a power load prediction method based on an optimized selection typical daily load curve, and the accuracy of power load prediction is improved by optimally selecting the typical daily load curve closer to a clustering center.
The purpose of the invention can be realized by the following technical scheme: a power load prediction method based on an optimized selection typical daily load curve comprises the following steps:
s1, acquiring load original data;
s2, preprocessing the load original data to obtain a characteristic index;
s3, adopting an improved PFCM algorithm, and combining with a fuzzy linear discriminant method (FLDA) to perform cluster analysis on the preprocessed load original data to determine a cluster center matrix;
s4, determining a reference day, respectively calculating the correlation between the reference day of each month and each clustering center according to a Pearson correlation coefficient method, and determining the category of each month;
and S5, taking the sample point with the maximum membership degree in each class as a typical daily load curve, and performing power load prediction based on the typical daily load curve to obtain a corresponding prediction result.
Further, step S2 is specifically to sequentially perform normalization processing and distortion data filtering processing on the load raw data.
Further, the step S3 specifically includes the following steps:
s31, according to the clustering number, initializing a cluster center;
s32, respectively calculating the covariance, the sample typical value, the fuzzy membership matrix and the clustering center matrix of the sample;
s33, further calculating to obtain a fuzzy inter-scattering matrix and a fuzzy total scattering matrix;
s34, determining a characteristic value and a characteristic vector according to the inter-fuzzy dispersion matrix and the fuzzy total dispersion matrix, and projecting the original sample to a characteristic space to obtain transformed sample data;
s35, calculating a fuzzy membership degree, a typical value and a clustering center matrix in the feature space;
and S36, judging whether the iteration termination condition is met, if so, ending the calculation, and outputting the cluster center matrix obtained by the current calculation, otherwise, returning to the step S33.
Further, the covariance calculation formula of the samples in step S32 is:
wherein n is the number of samples, xjIs a sample vector, σ2In the form of a covariance matrix,is the sample vector average; a typical value calculation formula for a sample is:
where c is the number of clusters, m is the fuzzy weight, tijIs a sample xjFor the typical value of the ith class, p is a set first parameter, and gamma is the current iteration frequency;
the fuzzy membership matrix calculation formula of the sample is as follows:
wherein d isijIs a sample xjTo the clustering center ViEuclidean distance of uijThe membership degree of the jth sample point belonging to the ith class;
the cluster center matrix calculation formula of the samples is as follows:
wherein a and b are respectively a second parameter and a third parameter which are set, vijIs as followsThe j sample points belong to the cluster center matrix of the ith class.
Further, the fuzzy interspersion matrix in the step S33 is specifically:
the fuzzy total dispersion matrix is specifically:
further, the fuzzy total scattering matrix needs to be a nonsingular matrix, and if the fuzzy total scattering matrix obtained through calculation is a singular matrix, regularization processing needs to be performed.
Further, the step S34 specifically includes the following steps:
s341, calculating a characteristic value and a characteristic vector:
SfT -1SfBω=λω
wherein, lambda is a characteristic value, and omega is a characteristic vector;
s342, projecting the sample to a feature space:
yj=ωTxj
wherein, yjIs a transformed sample vector.
Further, the specific process of step S35 is as follows:
converting the clustering center matrix into a feature space:
vi '(γ)=ωTvi (γ)
wherein v isiIs a clustering center vector;
calculating a fuzzy membership function in the feature space:
dij '(γ)=|yi-vi '(γ)|
the typical values are computed in the feature space:
calculating a clustering center matrix in the feature space:
further, the iteration termination condition includes a first termination condition and a second termination condition, and when the first termination condition or the second termination condition is met, the iteration termination condition is met, where the first termination condition is specifically that the current iteration number is greater than a set maximum iteration number;
the second termination condition is that the absolute value of the difference between the current clustering center matrix and the previous clustering center matrix is less than or equal to a preset threshold value.
Further, the reference day is specifically a monthly average load day.
Compared with the prior art, aiming at the problem that clustering is inaccurate when a typical daily load curve is selected in the current power load prediction, a new integrated clustering algorithm is realized by improving the PFCM algorithm and combining with the FLDA algorithm, and is used for clustering the load curve, so that the compactness of a data concentration sample can be fully considered, and the clustering precision is improved; iterative computation is carried out on the optimal characteristic space by combining with FLDA (flash data acquisition), an optimal clustering center matrix is obtained, and the clustering effect is further optimized; and finally, selecting a sample point closest to the clustering center point as a typical daily load curve through the Pearson correlation coefficient. Therefore, the accuracy of selecting the typical daily load curve is guaranteed, and meanwhile, the operation cost is reduced, so that the accuracy and the efficiency of predicting the power load are effectively improved.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
fig. 2 is a schematic diagram of the process of the integrated clustering algorithm proposed by the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in fig. 1, a power load prediction method based on an optimized selection of a typical daily load curve includes the following steps:
s1, acquiring load original data;
s2, preprocessing the load original data to obtain characteristic indexes, specifically, sequentially carrying out standardization processing and distortion data screening processing on the load original data;
s3, adopting an improved PFCM algorithm, and combining with a fuzzy linear discriminant method (FLDA) to perform cluster analysis on the preprocessed load original data to determine a cluster center matrix;
s4, determining a reference day, respectively calculating the correlation between the reference day of each month and each clustering center according to a Pearson correlation coefficient method, and determining the category of each month, wherein the reference day is the average load day of each month;
and S5, taking the sample point with the maximum membership degree in each class as a typical daily load curve, and performing power load prediction based on the typical daily load curve to obtain a corresponding prediction result.
By applying the method, a new integrated clustering method is provided by combining the improved probability C-means clustering algorithm (PFCM) and the fuzzy linear discriminant method (FLDA). The algorithm firstly improves the original PFCM to obtain an improved PFCM; and combining the improved PFCM with the FLDA, and applying the integrated clustering algorithm to the clustering of the load curve.
The main process comprises the following steps:
1. improved PFCM algorithm
Aiming at the problem that the PFCM method needs to calculate the parameter in the FCM algorithm to increase the operation cost, the PCM algorithm is firstly improved as follows:
in the formula: c is the number of clusters; n is the number of samples; m is fuzzy weighting number; dijIs a sample xjTo the clustering center ViThe Euclidean distance of; x is the number ofjIs a sample vector; u. ofijThe membership degree of the jth sample point belonging to the ith class; t is tijIs a sample xjTypical values for class i; sigma2Is a covariance matrix;is the sample vector average.
Improved PFCM objective function:
typical values for the samples:
class center matrix:
fuzzy membership matrix:
in the formula: a, b and p are set first, second and third parameters; and gamma is the iteration number.
2. FLDA-improved PFCM Algorithm
In the processed data space, the FLDA is used for solving the optimal transformation vector to project the original matrix to the optimal space, so that the distance between classes is larger, and the samples in the classes are more compact.
Fuzzy inter-class scatter matrix:
fuzzy total scatter matrix:
fuzzy total dispersion matrix SftIn subsequent calculation, a non-singular matrix needs to be satisfied, and if the non-singular matrix is a singular matrix, regularization processing needs to be performed firstly.
Calculation of eigenvalues and eigenvectors:
SfT -1SfBω=λω (9)
in the formula, lambda is a characteristic value, and omega is a characteristic vector;
projecting the sample into a feature space:
yj=ωTxj (10)
the clustering effect can be improved by effectively combining the two algorithms, the optimal transformation vector can be obtained by iterative computation on the optimal characteristic space by a fuzzy linear discriminant method (FLDA), and the clustering precision can be improved by combining the fuzzy clustering algorithm. Combining FLDA with the modified PFCM algorithm results in the following algorithm.
Converting the clustering center matrix into a feature space:
vi '(γ)=ωTvi (γ) (11)
calculating a fuzzy membership function value in the feature space:
dij '(γ)=|yi-vi '(γ)| (12)
the typical values are computed in the feature space:
calculating a clustering center matrix in the feature space:
the FLDA-improved PFCM algorithm is applied to clustering of load curves, as shown in fig. 2, and the specific steps are as follows:
step 1: initializing the improved PFCM algorithm, and calculating the covariance sigma of the sample by the formula (2)2U is obtained by the formula (4-6)ij,tij,vijA value of (d);
step 2: calculating the interspersion matrix S by the formula (7, 8)fBAnd fuzzy total scatter matrix SfT;
Step 3: calculating a characteristic value lambda and a characteristic vector omega through a formula (9);
step 4: the original sample x is expressed by equation (10)jProjecting into feature space to obtain yj;
Step 5: u is obtained by the formula (11-15)ij ’(γ+1),tij ’(γ+1),vij ’(γ+1);
Step 6: γ ═ γ +1, and mixing uij ’(γ+1),tij ’(γ+1),vij ’(γ+1)Are respectively assigned to uij ’(γ),tij ’(γ),vij ’(γ)Then, repeating the following steps of Step2, if gamma is less than or equal to gammamaxOr | vij ‘(γ+1)-vij ‘(γ)And if | ≦ ζ, the iteration is terminated.
3. Selection of typical daily load curve
And calculating a reference day (a monthly average load day) by taking the maximum Pearson correlation coefficient of the monthly reference day vector and the central vector of each class as a classification basis. And selecting the sample point with the maximum membership degree in each class as the typical daily load curve, namely the typical daily load curve containing months.
In summary, the invention firstly uses the characteristic index to reduce the dimension of the original data and introduces sigma2The covariance concept optimizes parameters in the existing PCM and then combines the parameters with FCM to obtain an improved PFCM method, the compactness of samples in a data set is considered, and the clustering precision is improved. And performing iterative computation on the optimal feature space through FLDA (flash data acquisition), so as to obtain an optimal clustering center matrix and further optimize the clustering effect. And selecting the sample point closest to the cluster center point as a typical daily load curve through the Pearson correlation coefficient. On one hand, the improved PFCM method makes up the defects of PCM consistency and the defects of FCM sensitivity to distortion data, on the other hand, FLDA is utilized to further perform alternate optimization in a fuzzy space, clustering precision is improved, and finally, classification results are determined through Pearson correlation coefficients, and the sample point with the maximum membership degree in each class is taken as a typical day; through parameter optimization, the operation cost is reduced, and the working efficiency is improved.
Claims (10)
1. A power load prediction method based on an optimized selection typical daily load curve is characterized by comprising the following steps:
s1, acquiring load original data;
s2, preprocessing the load original data to obtain a characteristic index;
s3, combining an improved PFCM algorithm with a fuzzy linear discrimination method to perform cluster analysis on the preprocessed load original data to determine a cluster center matrix;
s4, determining a reference day, respectively calculating the correlation between the reference day of each month and each clustering center according to a Pearson correlation coefficient method, and determining the category of each month;
and S5, taking the sample point with the maximum membership degree in each class as a typical daily load curve, and performing power load prediction based on the typical daily load curve to obtain a corresponding prediction result.
2. The method for predicting the power load based on the optimized selection of the typical daily load curve according to claim 1, wherein the step S2 is to perform a normalization process and a distortion data screening process on the load raw data in sequence.
3. The method for predicting the power load based on the optimized selection of the typical daily load curve according to claim 1, wherein the step S3 specifically comprises the following steps:
s31, according to the clustering number, initializing a cluster center;
s32, respectively calculating the covariance, the sample typical value, the fuzzy membership matrix and the clustering center matrix of the sample;
s33, further calculating to obtain a fuzzy inter-scattering matrix and a fuzzy total scattering matrix;
s34, determining a characteristic value and a characteristic vector according to the inter-fuzzy dispersion matrix and the fuzzy total dispersion matrix, and projecting the original sample to a characteristic space to obtain transformed sample data;
s35, calculating a fuzzy membership degree, a typical value and a clustering center matrix in the feature space;
and S36, judging whether the iteration termination condition is met, if so, ending the calculation, and outputting the cluster center matrix obtained by the current calculation, otherwise, returning to the step S33.
4. The method for predicting power load based on optimized selection of typical daily load curve according to claim 3, wherein the covariance calculation formula of the samples in the step S32 is as follows:
wherein n is the number of samples, xjIs a sample vector, σ2In the form of a covariance matrix,is the sample vector average;
a typical value calculation formula for a sample is:
where c is the number of clusters, m is the fuzzy weight, tijIs a sample xjFor the typical value of the ith class, p is a set first parameter, and gamma is the current iteration frequency;
the fuzzy membership matrix calculation formula of the sample is as follows:
wherein d isijIs a sample xjTo the clustering center ViEuclidean distance of uijThe membership degree of the jth sample point belonging to the ith class;
the cluster center matrix calculation formula of the samples is as follows:
wherein a and b are respectively a second parameter and a third parameter which are set, vijAnd the j sample point belongs to the clustering center matrix of the i class.
6. the power load prediction method based on the optimized selection of the typical daily load curve as claimed in claim 5, wherein the fuzzy total scattering matrix is a nonsingular matrix, and if the calculated fuzzy total scattering matrix is a singular matrix, a regularization process is performed.
7. The method for predicting the power load based on the optimized selection of the typical daily load curve according to claim 5, wherein the step S34 specifically comprises the following steps:
s341, calculating a characteristic value and a characteristic vector:
SfT -1SfBω=λω
wherein, lambda is a characteristic value, and omega is a characteristic vector;
s342, projecting the sample to a feature space:
yj=ωTxj
wherein, yjIs a transformed sample vector.
8. The method for predicting the power load based on the optimized selection of the typical daily load curve according to claim 7, wherein the specific process of the step S35 is as follows:
converting the clustering center matrix into a feature space:
vi'(γ)=ωTvi (γ)
wherein v isiIs a clustering center vector;
calculating a fuzzy membership function in the feature space:
dij'(γ)=|yi-vi'(γ)|
the typical values are computed in the feature space:
calculating a clustering center matrix in the feature space:
9. the power load prediction method based on the optimized selection of the typical daily load curve according to claim 3, wherein the iteration termination condition comprises a first termination condition and a second termination condition, and when the first termination condition or the second termination condition is met, the iteration termination condition is met, and the first termination condition is that the current iteration number is greater than the set maximum iteration number;
the second termination condition is that the absolute value of the difference between the current clustering center matrix and the previous clustering center matrix is less than or equal to a preset threshold value.
10. The method for predicting the power load based on the optimized selection of the typical daily load curve according to claim 1, wherein the reference day is a monthly average load day.
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