Distribution-dynamic characteristic index dimensionality reduction-based daily load curve clustering method
Through the dimensionality reduction method based on distribution-dynamic feature index and the clustering method of Canopy algorithm, the problems of incomplete curve feature extraction and excessive dimensions in daily load curve clustering are solved, and the clustering quality and computing efficiency are improved.
Patent Information
- Application Number
- CN202411939045.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-26
- Publication Date
- 2025-04-18
AI Technical Summary
The existing daily load curve clustering method has low algorithm computing efficiency caused by incomplete curve feature extraction and excessive dimensions.
The dimensionality reduction method based on the distribution-dynamic feature index is adopted. By calculating the load distribution characteristics and dynamic features, the distribution-dynamic feature dimension reduction curve is merged to reduce the data dimension, and the clustering center is determined using the Canopy algorithm, and Euclidean distance is used for clustering.
The clustering quality and computing efficiency are improved, the clustering results are consistent with the actual situation, the algorithm is strongly robust, and can better reflect the electricity consumption characteristics of each typical industry.
Smart Images
Figure CN119848582A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of power system analysis and control, and in particular relates to a daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction. Background Art
[0002] The clustering of daily load curves of power users aims to identify and extract typical characteristics of users, classify them into categories, and obtain typical daily load curves of various power consumption industries. It is an important basis for many power big data applications such as power load forecasting, load characteristic identification, and demand side management. Therefore, it is necessary to select appropriate and accurate curve characteristic indicators as the basis for curve feature extraction to achieve high-quality clustering of daily load curves.
[0003] With the further construction and improvement of the power grid power big data platform, the number and dimensions of user daily load curves have increased significantly, posing a huge challenge to the computational quality and efficiency of clustering algorithms. However, most of the existing traditional daily load curve clustering methods (such as k-means algorithm, fuzzy C-means algorithm, etc.) use Euclidean distance as the similarity measurement method, directly perform clustering analysis on the normalized multidimensional data group, and the clustering quality is low. There are two main reasons for this: ① The curve feature extraction is imperfect, and the overall distribution characteristics of the curve are evaluated only based on the sampling values at each sampling time, ignoring the dynamic characteristics of the curve, resulting in deviations in category division; ② The curve is not feature extracted and dimensioned, and the dimension of the clustering object set is too high, resulting in low algorithm computational efficiency. Summary of the invention
[0004] In order to solve the technical problems in the prior art of low algorithm operation efficiency caused by imperfect curve feature extraction and too high dimensionality of clustering object sets, the present invention provides a daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, which can accurately extract curve features and improve operation efficiency through effective dimensionality reduction.
[0005] In order to achieve the above technical objectives, the technical solution of the present invention is:
[0006] A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction includes the following steps:
[0007] Step 1) Collect daily load curve data to obtain an n-dimensional data set X=[X1,X2,…,X m], then according to the high and low variation law of power load in a day, the load distribution characteristics of each curve in X are calculated, so as to obtain the distribution characteristic dimension reduction curve corresponding to each curve; next, the representative value of each curve in X is calculated in the sampling time period, and the difference between each representative value is calculated, so as to obtain the dynamic characteristic dimension reduction curve corresponding to each curve; finally, the distribution characteristic dimension reduction curve and the dynamic characteristic dimension reduction curve are merged to obtain the distribution-dynamic characteristic dimension reduction curve, and a dimension reduction data set is formed;
[0008] Step 2) using the distribution-dynamic feature dimensionality reduction curve as the clustered data set, and using the Canopy algorithm to determine the number of cluster centers and the initial cluster center of the clustered data set after dimensionality reduction;
[0009] Step 3) Euclidean distance is used to measure the similarity between each clustered curve and the cluster center of each category curve;
[0010] Step 4) comparing the Euclidean distances between each clustered curve and each cluster center, and dividing the clustered curve into the category with the smallest Euclidean distance, thereby achieving category division;
[0011] Step 5) Calculate the mean of the set of clustering objects in each category, use the mean to find a new clustering center as the new clustering result, and then calculate whether the new clustering result converges. If it converges, end the entire clustering method. Otherwise, check whether the number of iterations reaches the preset value. If it reaches the preset value, end the entire clustering method. Otherwise, return to step 3) to continue the loop iteration.
[0012] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in step 1), the distribution characteristic dimensionality reduction curve is obtained by the following process:
[0013] According to the power consumption law, the peak load period and the flat load period in a day are defined; then, for any curve X in the data set i =[x1,x2,…,x n ], calculate the corresponding daily load rate t1, daily average load t2, daily peak-valley rate t3, peak load rate t4 and valley load rate t5, and thus obtain the distribution characteristic dimension reduction curve T of the original curve i =[t1,t2,t3,t4,t5].
[0014] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in the step 1), the daily load rate t1 is calculated by the following formula:
[0015] t1=X av / X max
[0016] The daily average load t2 is calculated by the following formula:
[0017] t2=X sum / 48
[0018] The daily peak-to-valley rate t3 is calculated by the following formula:
[0019]
[0020] The peak load rate t4 is calculated by the following formula:
[0021] t4=X av.peak / X av
[0022] The valley load rate t5 is calculated by the following formula:
[0023] t5=X av.val / X av
[0024] Among them, X av is the average load for the whole day, X av =X sum / n,X sum represents the total daily load, X max is the maximum load of the day, X min is the lowest load of the day, X av.peak is the average load during peak period, X av.val is the average load during the valley period.
[0025] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in the step 1), the process of obtaining the dynamic characteristic dimensionality reduction curve includes:
[0026] Calculate the load average value in each sampling period as the representative value of the sampling period, and obtain the division representative curve G i =[g1,g2,...,g8], where g i represents the representative value of the i-th sampling time period, k represents the maximum number of sampling time periods, and its value is 8;
[0027] Then calculate the difference t between each adjacent sampling time period i ′=g i+1 -g i , thus obtaining the dynamic feature dimensionality reduction curve T i ′=[t1′,t2′,...,t7′].
[0028] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in step 1), the distribution-dynamic characteristic dimensionality reduction curve is obtained by:
[0029] The distribution feature dimension reduction curve Ti = [t1, t2, t3, t4, t5] is merged with T i ′ = [t1′, t2′,..., t7′] to obtain the distribution - dynamic feature dimensionality reduction curve R of the load curve i = [t1, t2,..., t5, t1′, t2′,..., t7′], that is, R i = [r1, r2,..., r 12 .
[0030] The described daily load curve clustering method based on distribution - dynamic feature index dimensionality reduction, step 2) of which includes:
[0031] Set threshold parameters T1 and T2, where T2 is taken as 2 times the average curve distance, and T1 > T2;
[0032] Select any curve R in the dataset to be clustered i That is, point R i , as the center of the first cluster Canopy, and remove the points selected into Canopy from the dataset to be clustered;
[0033] Calculate the distance U between each point in the dataset to be clustered and the j - th Canopy center i-j ; If U i-j < T2, then classify it into this Canopy and remove it from the dataset to be clustered; If the distance from the point to all current Canopy centers satisfies U i-j > T1, then take it as the center of a new Canopy and remove it from the dataset to be clustered; If the distance U of the point to all current Canopies i-j < T1, and it has not been classified after all points in the dataset to be clustered have been calculated, then take it as the center of a new Canopy and remove it from the dataset to be clustered; Repeat the above classification steps until there are no more points in the dataset to be clustered, thereby obtaining the initial cluster center set C = [C1, C2,..., C p , where p is the number of initial cluster centers.
[0034] In the described daily load curve clustering method based on distribution - dynamic feature index dimensionality reduction, in step 2), for the threshold parameters T1 and T2, where T1 = 2T2, the calculation formula of T1 is:
[0035]
[0036] where m represents the total number of curves in the dataset to be clustered, R i represents the i - th curve in the dataset to be clustered, and R j represents the j - th curve in the dataset to be clustered.
[0037] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in the step 3), the similarity is measured according to the size of the Euclidean distance, wherein the smaller the Euclidean distance, the higher the similarity. The Euclidean distance is calculated by the following formula:
[0038]
[0039] Among them, D(R i ,C j ) is R i and the jth initial cluster center C j The Euclidean distance of , n is the dimension.
[0040] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in the step 5), the mean of the clustering object set of each category is calculated by the following formula:
[0041]
[0042] Among them, C j (I+1) is the j-th cluster center curve after the I+1th iteration; m j is the number of daily load curves classified into the jth category; R e is the daily load curve belonging to the jth class;
[0043] In the daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, in the step 5), whether the new clustering result converges is calculated by the following process:
[0044] After calculating the mean of the clustered object set of each category, the square error and J of the clustered object set are calculated. If |J I+1 -J I |<e, where e is the preset convergence limit value, the new clustering result is considered to be converged; the sum of square errors J of the clustered object set is calculated by the following formula:
[0045]
[0046] Among them, J I is the sum of square errors after the Ith iteration.
[0047] The technical effect of the present invention is that the daily load curve clustering method based on the distribution-dynamic characteristic index dimensionality reduction proposed by the present invention can effectively solve the two problems faced by the clustering method, and improve the clustering quality while improving the calculation efficiency. Its clustering results are consistent with the actual situation, and the algorithm has strong robustness and high computational efficiency. It can better reflect the electricity consumption characteristics of various typical industries, and provide reliable and effective support for power load data applications such as power load forecasting and demand-side management, and has certain engineering practical value. In the context of big data, the present invention can fully consider the distribution characteristics and dynamic characteristics of the curve, and greatly improve the efficiency and quality of daily load curve clustering. On the other hand, the method in this paper can effectively solve the problem that the initial cluster center and the number of clusters in the clustering algorithm are difficult to determine. The clustering results are consistent with the actual project, and can provide strong support for power grid companies to analyze user electricity consumption behavior and formulate reasonable electricity consumption plans. It has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] Figure 1 Schematic diagram of the dimensionality reduction process of the present invention.
[0049] Figure 2 Schematic diagram of the clustering process of the present invention. DETAILED DESCRIPTION
[0050] See also Figure 1 The present embodiment proposes a daily load curve clustering method based on distribution-dynamic feature index dimensionality reduction. First, according to distribution feature indicators such as daily load rate and daily peak-to-valley difference rate, a distribution feature dimensionality reduction data set is extracted; then, the sampling time period is divided into load peak period, off-peak period and valley period, and the dynamic feature dimensionality reduction data set is extracted according to the difference of sampling values in adjacent sampling time periods; finally, the two types of dimensionality reduction data sets are combined to form a distribution-dynamic feature dimensionality reduction data set.
[0051] See also Figure 2 After the dimensionality reduction is completed, this embodiment uses the characteristic index clustering method to perform cluster analysis on the dimensionality reduction data set to obtain the final clustering result.
[0052] The method proposed in this embodiment specifically includes the following steps:
[0053] Step 1) Data dimensionality reduction. For an n-dimensional data set X = [X1, X2, ..., X m ], and perform dimensionality reduction based on distribution-dynamic feature indicators to obtain the reduced dimensionality data set R = [R1, R2, …, R m ].
[0054] Specifically, in step 1), first, according to the power consumption pattern, the peak load period is defined as: 09:00-12:00, 14:30-17:30, 19:00-22:00; the trough load period is: 22:00-24:00, 00:00-06:00; the flat load period is: 6:00-9:00, 12:00-14:30, 17:30-19:00. Then, for any curve X in the data set, i =[x1,x2,…,x n ], calculate each curve X i =[x1,x2,…,x n ], the daily load rate t1, daily average load t2, daily peak-valley rate t3, peak load rate t4 and valley load rate t5, and the distribution characteristic dimensionality reduction curve T of the original curve is obtained. i =[t1, t2, t3, t4, t5]. The definitions of various indicators are shown in Table 1, and the calculation formulas of relevant indicators in Table 1 are shown in formulas (1) and (2). av is the average load for the whole day, X max is the maximum load of the day, X min is the lowest load of the day, X av.peak is the average load during peak period, X av.val is the average load during the valley period.
[0055]
[0056] In the formula, X sum The total daily load
[0057] X av =X sum / n (2)
[0058] In the formula, X av Indicates the average load.
[0059] Table 1 Load curve distribution characteristic indicators
[0060]
[0061]
[0062] Then, according to formula (3), the representative value of each sampling time period is calculated. In this embodiment, the load average value in each sampling time period is used as the representative value of the sampling time period, and the division representative curve G is obtained. i =[g1,g2,...,g8].
[0063]
[0064] Then, using Equation (4), calculate the differences between adjacent sampling time periods to obtain the dynamic feature dimensionality reduction curve T i ′ = [t1′, t2′,..., t7′].
[0065] t i ′ = g i+1 -g i (4)
[0066] After obtaining T i = [t1, t2, t3, t4, t5] and T i ′ = [t1′, t2′,..., t7′], merge the two to obtain the distribution-dynamic feature dimensionality reduction curve R i = [t1, t2,..., t5, t1′, t2′,..., t7′], that is, R i = [r1, r2,..., r 12 .
[0067] Collect the distribution-dynamic feature dimensionality reduction curves of all load curves to obtain the dimensionality reduction dataset R = [R1, R2,…, R m .
[0068] Step 2) Select the clustering centers. Use the Canopy algorithm to determine the number of clustering centers and the initial clustering centers of the dataset T after dimensionality reduction.
[0069] Specifically, in this step 2), first, set the threshold parameters T1 and T2, and satisfy T1 > T2. Among them, T2 is taken as 2 times the average curve distance, and T1 = 2T2. The calculation formula is shown in Equation (5) below;
[0070]
[0071] Then, select any point in the dataset to be clustered as the center of the first Canopy, and the point selected as the Canopy center is removed from the dataset accordingly.
[0072] Finally, according to Equation (6), calculate the Euclidean distance U i between each point R j in the dataset to be clustered and the j-th Canopy center R i-j . If U i-j < T2, then classify it into the j-th Canopy and remove R i from the dataset to be clustered; if the Euclidean distance of R i to all Canopy centers satisfies U i-j > T1, then take R i as a new Canopy center and take Ri Removed from the dataset to be clustered; if R i The distance U to all Canopy centers i-j < T1, and after all points in the dataset to be clustered have been calculated and the classification is still not completed, it is taken as a new Canopy center, and R i Is removed from the dataset to be clustered. Repeat this calculation step until the dataset is empty to obtain the initial clustering center set C = [C1, C2,..., C p , where p is the number of initial clustering centers.
[0073]
[0074] In the formula: D(R i , R j ) is the Euclidean distance between the i-th curve R i and the j-th curve R j in the dataset, and n is the dimension of the time series to be measured.
[0075] Step 3) Similarity measurement. Using the Euclidean distance, successively measure the similarity D(R i = [r i,1 , r i,2 ,..., r i,12 and the clustering center C j = [c j,1 , c j,2 ,..., c j,12 of each category curve D(R i , C j ).
[0076] In this step, also based on Equation (6), replace R j in the formula with C j to calculate the similarity D(R i = [r i,1 , r i,2 ,..., r i,12 and the clustering center C j = [c j,1 , c j,2 ,..., c j,12 of each category curve D(R i , C j ).
[0077] Step 4) Class division. Compare the Euclidean distances of each object to be clustered R i with respect to each clustering center C j , and divide R i into the one with the minimum Euclidean distance (min(D(R i , C1), D(Ri ,C2),...,D(R i ,C K )))'s category.
[0078] Step 5) Update the cluster center. Calculate the mean of the cluster object set of each category as the new cluster center. Then calculate whether the new clustering result converges. If it converges, the entire clustering method ends. Otherwise, check whether the number of iterations reaches the preset value. If it reaches the preset value, the entire clustering method ends. Otherwise, return to step 3) to continue the loop iteration.
[0079] Specifically, this step first calculates the mean of the clustering object set of each category as the new cluster center, as shown in formula (7). If at this time, the sum of the squared errors of the clustered object set J satisfies |J I+1 -J I |<e (e is the convergence limit value), then the result is output and the algorithm ends; otherwise, jump to step 3). The calculation formula is shown in formula (8).
[0080]
[0081] In the formula, C j (I+1) is the j-th cluster center curve after the algorithm's I+1th iteration; m j is the number of daily load curves classified into the jth category; R e is the daily load curve belonging to the jth category.
[0082]
[0083] In the formula, J I is the sum of square errors after the Ith iteration of the algorithm.
Claims
1. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction, characterized in that: The following steps are involved: Step 1) Collect daily load curve data to obtain an n-dimensional data set X=[X1,X2,…,X m ], and then according to the high and low variation law of power load in a day, the load distribution characteristics of each curve in X are calculated, so as to obtain the distribution characteristic dimensionality reduction curve corresponding to each curve; Next, the representative value of each curve in X in the sampling time period is calculated, and the difference between the representative values is calculated to obtain the dynamic feature dimension reduction curve corresponding to each curve; Finally, the distribution feature dimensionality reduction curve and the dynamic feature dimensionality reduction curve are combined to obtain the distribution-dynamic feature dimensionality reduction curve and form a dimensionality reduction data set; Step 2) Using the reduced dimension data set as the clustered data set, the Canopy algorithm is used to determine the number of cluster centers and the initial cluster centers of the clustered data set after the dimension reduction; Step 3) Euclidean distance is used to measure the similarity between each clustered curve and the cluster center of each category curve; Step 4) comparing the Euclidean distances between each clustered curve and each cluster center, and dividing the clustered curve into the category with the smallest Euclidean distance, thereby achieving category division; Step 5) Calculate the mean of the set of clustering objects in each category, use the mean to find a new clustering center as the new clustering result, and then calculate whether the new clustering result converges. If it converges, end the entire clustering method. Otherwise, check whether the number of iterations reaches the preset value. If it reaches the preset value, end the entire clustering method. Otherwise, return to step 3) to continue the loop iteration.
2. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 1, characterized in that: In the step 1), the distribution feature dimensionality reduction curve is obtained by the following process: According to the power consumption law, the peak load period and the flat load period in a day are defined; then, for any curve X in the data set i =[x1,x2,…,x n ], calculate the corresponding daily load rate t1, daily average load t2, daily peak-valley rate t3, peak load rate t4 and valley load rate t5, and thus obtain the distribution characteristic dimension reduction curve T of the original curve i =[t1,t2,t3,t4,t5].
3. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 2, characterized in that: In step 1), the daily load rate t1 is calculated by the following formula: t1=X av / X max The daily average load t2 is calculated by the following formula: t2=X sum / 48 The daily peak-to-valley rate t3 is calculated by the following formula: The peak load rate t4 is calculated by the following formula: t4=X av.peak / X av The valley load rate t5 is calculated by the following formula: t5=X av.val / X av Among them, X av is the average load for the whole day, X av =X sum / n,X sum represents the total daily load, X max is the maximum load of the day, X min is the lowest load of the day, X av.peak is the average load during peak period, X av.val is the average load during the valley period.
4. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 2, characterized in that: In the step 1), the process of obtaining the dynamic feature dimensionality reduction curve includes: Calculate the load average value in each sampling period as the representative value of the sampling period, and obtain the division representative curve G i =[g1,g2,...,g8], where g i represents the representative value of the i-th sampling time period, k represents the maximum number of sampling time periods, and its value is 8; Then calculate the difference t between each adjacent sampling time period i ′=g i+1 -g i , thus obtaining the dynamic feature dimensionality reduction curve T i ′=[t1′,t2′,...,t7′].
5. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 4, characterized in that: In the step 1), the distribution-dynamic feature dimensionality reduction curve is obtained as follows: The distribution feature dimension reduction curve T i =[t1,t2,t3,t4,t5] and T i ′=[t1′,t2′,...,t7′] to obtain the distribution-dynamic characteristic dimension reduction curve R of the load curve i =[t1,t2,...,t5,t1′,t2′,...,t7′], that is, R i =[r1,r2,...,r 12 ].
6. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 1, characterized in that: The step 2) comprises: Set threshold parameters T1 and T2, where T2 is twice the average distance of the curve, and T1>T2; Select any curve R in the clustered data set i That is, point R i , as the center of the first clustering Canopy, and remove the points selected into the Canopy from the clustered data set; Calculate the distance U between each point in the dataset to be clustered and the j-th Canopy center i-j ; if U i-j < T2, then classify it into this Canopy and remove it from the dataset to be clustered; if the distance from the point to all current Canopy centers satisfies U i-j > T1, then use it as the center of a new Canopy and remove it from the dataset to be clustered; if the distance U of the point to all current Canopies i-j < T1, and it has not been classified after all points in the dataset to be clustered have been calculated, then use it as the center of a new Canopy and remove it from the dataset to be clustered; repeat the above classification steps until there are no more points in the dataset to be clustered, thus obtaining the initial cluster center set C = [C1, C2,..., C p , where p is the number of initial cluster centers.
7. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 6, characterized in that: In the step 2), the threshold parameters T1 and T2, where T1=2T2, are calculated as follows: Where m represents the total number of curves in the clustered data set, R i represents the i-th curve in the clustered data set, R j Represents the jth curve in the clustered data set.
8. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 6, characterized in that: In the step 3), the similarity is measured according to the size of the Euclidean distance, wherein the smaller the Euclidean distance, the higher the similarity. The Euclidean distance is calculated by the following formula: Among them, D(R i ,C j ) is R i and the jth initial cluster center C j The Euclidean distance of , n is the dimension.
9. The daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 1 is characterized in that: In the step 5), the mean of the clustering object set of each category is calculated by the following formula: Among them, C j (I+1) is the j-th cluster center curve after the I+1th iteration; m j is the number of daily load curves classified into the jth category; R e is the daily load curve belonging to the jth category.
10. A daily load curve clustering method based on distribution-dynamic characteristic index dimensionality reduction according to claim 9, characterized in that: In step 5), whether the new clustering result converges is determined by the following process: After calculating the mean of the clustered object set of each category, the square error and J of the clustered object set are calculated. If |J I+1 -J I |<e, where e is the preset convergence limit value, the new clustering result is considered to be converged; the sum of square errors J of the clustered object set is calculated by the following formula: Among them, J I is the sum of square errors after the Ith iteration.