CN118194074B - Load curve clustering method based on improved rough C-means - Google Patents

Abstract

The present invention belongs to the technical field of load classification of power systems, and discloses a load curve clustering method based on improved rough C-means. First, the original daily load data is normalized, and the number of target clusters, initial cluster centers, lower approximate weights, upper approximate weights, and distance judgment thresholds are determined. Then, the distance from each load curve to each cluster center is calculated, and each load curve is classified into the upper/lower approximate set of the corresponding cluster. Finally, considering the distance between the load curve and the cluster center and the data distribution density in the neighborhood, a mixed imbalance metric is introduced into the iterative formula of the cluster center to quantify the degree of influence of the imbalanced spatial distribution of the load curve within the cluster on the iteration of the cluster center. The present invention can effectively deal with the problem of uneven distribution of load curves, improve the clustering effect, and better provide technical support for demand response, load forecasting, etc.

Description

A load curve clustering method based on improved rough C-means

Technical Field

The invention belongs to the technical field of power system load classification, and in particular relates to a load curve clustering method based on improved rough C-means.

Background Art

With the massive deployment of data collection devices such as smart meters and the development of information and communication technology, the historical electricity consumption data on the user side has exploded. How to mine potential information from the massive load data with low value density and grasp the electricity consumption characteristics and internal connections of different types of users is of great significance for assisting grid dispatchers in carrying out demand response, load forecasting, and electricity price setting. Realizing diversified and flexible load control is an inevitable trend in the development of new power systems.

Cluster analysis is an effective method to mine the potential information of massive load data. Its basic idea is to divide a large number of load curves into several clusters. The load curves within a cluster have a high degree of similarity, while the load curves between clusters have a high degree of difference. At present, most of the research on load curve clustering focuses on data dimension reduction, clustering algorithm performance optimization, optimal number of clusters, and selection of initial cluster centers. However, due to the opening of the power market, user behavior has become more free, resulting in more complex distribution of load curves, resulting in overlapping and uneven distribution of load curves between clusters. For example, industrial users and administrative users are both single-peak loads, but the number of users and adjustable capacity of the two are very different. The existing load curve clustering method will produce a "uniform effect" when processing such data, that is, samples in a large category will be incorrectly divided into small categories. Therefore, in order to achieve refined perception of flexible load resources, it is necessary to strengthen the analysis of load curves in boundary areas to reduce the possibility of incorrect clustering.

The rough C-means clustering algorithm integrates the rough set theory into the C-means clustering algorithm, and regards each cluster as a rough set. Each data object either belongs to the lower approximate set of a certain cluster, or belongs to the upper approximate set of multiple clusters at the same time. The existing rough clustering and its derivative algorithms consider different weighting coefficients of different boundary areas, which has improved the clustering accuracy of load curves in the power market to a certain extent. However, it still gives the same weight to data objects in the same boundary area, ignoring various unbalanced distribution situations within the same boundary area, which will still lead to load curve clustering errors and cannot accurately provide technical support for demand response, load forecasting, etc.

Summary of the invention

To solve the above technical problems, the present invention provides a load curve clustering method based on improved rough C-means, which comprehensively considers the distance between different load curves and the cluster center in the same boundary area and the mixed imbalance measurement of the data distribution density in the neighborhood, and can effectively quantify the influence of the spatial distribution imbalance of the load curve within the cluster on the iteration of the cluster center, which can greatly improve the clustering accuracy of the load curve in the boundary area and open up a new direction for the clustering method of load curves.

The load curve clustering method based on improved rough C-means described in the present invention comprises the following steps:

Step 1: Collect historical daily load data and obtain N original daily load curves on the same day , and the maximum normalization method is used to normalize the original daily load curve to obtain N load clustering object curves that need to be clustered , ;

Step 2: Determine the number of target clusters c and c initial cluster centers , lower approximate weight W _low , upper approximate weight W _up and distance judgment threshold Δ, ;

Step 3: For the load clustering object curve X _k , , calculate its Euclidean distance to each cluster center, and assign _Xk to the upper approximate set of cluster _Ui corresponding to the nearest cluster center _Ci ;

Step 4: If there is another cluster center C _j such that the difference between the distance from X _k to C _j and the distance from X _k to _Ci is less than the threshold Δ, then X _k is simultaneously included in the upper approximate set of the cluster U _j corresponding to C _j. Otherwise, classify _Xk into the lower approximation set of cluster _Ui ;

Step 5: Update the cluster center according to the following iterative formula:

,

Among them, h _ik is the mixed imbalance measure, the difference between the upper approximation set and the lower approximation set represents the boundary set of cluster U _i ;

Step 6: Repeat steps 2 to 5 until the clustering converges.

Furthermore, in step 1, the sampling interval of the original daily load curve is 1 hour, so the N original daily load curves on the same day are ,in represents the kth original daily load curve, Represents the value of the kth original daily load curve at the i-th hour.

Furthermore, in step 1, the maximum value normalization method is used to normalize the original daily load data. The specific method is as follows:

,

Thus, we can obtain N normalized load clustering object curves. ,in represents the kth load clustering object curve, and X _ki represents the value of the kth load clustering object curve in the ith hour.

Furthermore, in step 3, the Euclidean distance from the kth load clustering object curve _Xk to the initial clustering center _Ci = ( _Ci1 , _Ci2 , ..., _Ci24 ) is calculated as follows:

,

Wherein, d _ik is the Euclidean distance from the kth load clustering object curve X _k to the initial clustering center _Ci .

Furthermore, in step 5, the calculation formula of the mixed imbalance metric h _ik is as follows:

,

in, Denote the distance X _k as The number of load curves within the neighborhood of ; Represents the upper approximation set of cluster _Ui corresponding to cluster center _Ci Number of internal load curves; It represents the distance metric when the k-th load clustering object curve _Xk participates in the iteration of the cluster center _Ci. The farther the distance, the lower the influence of the distance _dik from _Xk to _Ci on the update iteration of _Ci , and the closer the distance, the higher the influence. It represents the local density measurement when the k-th load clustering object curve _Xk participates in the iteration of the cluster center _Ci . The lower the density, the lower the influence of the load curve density in the neighborhood _{of Xk} on the update iteration of _Ci , and the higher the density, the greater the influence.

The beneficial effects described in the present invention are as follows: the method described in the present invention combines distance measurement and domain density measurement, fully considers the influence of cross-overlap and uneven distribution of load curves between clusters, assigns different weighting coefficients to each load curve in the cluster center iteration formula, and quantifies the influence of the imbalanced spatial distribution of load curves within the cluster on the iteration of the cluster center; the closer the load curve is to the center and the higher the data distribution density in the neighborhood, the greater the weighting coefficient, and the greater the contribution to the center iteration; similarly, the farther the load curve is from the center and the lower the data distribution density in the neighborhood, the smaller the weighting coefficient, and the smaller the contribution to the center iteration; by strengthening the analysis of the load curves in the cross-boundary area, the problem of uneven distribution of load curves is effectively dealt with, the clustering accuracy of the load curves in the cross-boundary area is improved, and better technical support is provided for demand response, load forecasting, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of the method of the present invention;

FIG2 is a schematic diagram of load clustering results under the method of the present invention;

FIG3 is a schematic diagram of cluster center results under the method of the present invention;

FIG4 is a schematic diagram of load clustering results under the traditional improved C-means clustering method;

DETAILED DESCRIPTION

In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments in conjunction with the accompanying drawings.

The load curve clustering method based on improved rough C-means described in the present invention, as shown in FIG1 , comprises the following steps:

Step 1: Collect historical daily load data and obtain N original daily load curves on the same day , and the maximum normalization method is used to normalize the original daily load curve to obtain N load clustering object curves that need to be clustered , ;

The sampling interval of the original daily load curve in step 1 is 1 hour, so the N original daily load curves in the same day are ,in represents the kth original daily load curve, represents the value of the kth original daily load curve at the i-th hour;

In step 1, the maximum value normalization method is used to normalize the original daily load data. The specific method is:

,

Thus, we can obtain N normalized load clustering object curves. ,in represents the k-th load clustering object curve, X _ki represents the value of the k-th load clustering object curve at the i-th hour;

Step 2: Determine the number of target clusters c and c initial cluster centers , lower approximate weight W _low , upper approximate weight W _up and distance judgment threshold Δ, ;

Step 3: For the load clustering object curve X _k , , calculate its Euclidean distance to each cluster center, and assign _Xk to the upper approximate set of cluster _Ui corresponding to the nearest cluster center _Ci ;

The kth load clustering object curve X _k to the initial clustering center The Euclidean distance is calculated as follows:

,

Where, d _ik is the Euclidean distance from the kth load clustering object curve X _k to the initial clustering center _Ci ;

Step 4: If there is another cluster center C _j such that the difference between the distance from X _k to C _j and the distance from X _k to _Ci is less than the threshold Δ, then X _k is simultaneously included in the upper approximate set of the cluster U _j corresponding to C _j. Otherwise, classify _Xk into the lower approximation set of cluster _Ui ;

Step 5: Update the cluster center according to the following iterative formula:

;

Among them, h _ik is the mixed imbalance measure, the difference between the upper approximation set and the lower approximation set represents the boundary set of cluster U _i ;

The calculation formula of the hybrid imbalance metric h _ik is as follows:

,

in, Denote the distance X _k as The number of load curves within the neighborhood of ; Represents the upper approximation set of cluster _Ui corresponding to cluster center _Ci Number of internal load curves; It represents the distance metric when the k-th load clustering object curve _Xk participates in the iteration of the cluster center _Ci. The farther the distance, the lower the influence of the distance _dik from _Xk to _Ci on the update iteration of _Ci , and the closer the distance, the higher the influence. It represents the local density measurement of the kth load clustering object curve _Xk when participating in the iteration of the cluster center _Ci . The lower the density, the lower the influence of the load curve density in the neighborhood _{of Xk} on the update iteration of _Ci. The higher the density, the higher the influence.

Step 6: Repeat steps 2 to 5 until the clustering converges.

The daily load curve of 1910 users (including 200 industrial users, 300 administrative users, 400 commercial users, 350 residential users, 360 catering users, and 300 street lamp and high energy consumption enterprise users) measured on a certain working day in August 2015 in a certain area was selected as the research object. The daily load sampling interval was 1h, with a total of 24 sampling points per day. The number of algorithm target clusters c was set to 6, the lower approximate weight W _low was set to 0.9, the upper approximate weight W _up was set to 0.1, the distance judgment threshold Δ was set to 0.1, and the neighborhood range Set to 0.2.

The result of the load curve clustering method based on improved rough C-means described in the present invention is shown in FIG2, and the user load curves are divided into 6 categories, with 202 load curves in category 1, 304 load curves in category 2, 401 load curves in category 3, 350 load curves in category 4, 363 load curves in category 5, and 300 load curves in category 6. Categories 1 and 2 are both single-peak loads, but the electricity consumption time of category 1 is concentrated in the period of 06:00-21:00, and the electricity consumption time of category 2 is concentrated in the period of 08:00-19:00, and the average load level of category 1 is higher than that of category 2. Category 1 is mainly industrial users, and category 2 is mainly administrative industry users such as schools, hospitals, and governments. Category 3 and 4 are both bimodal loads. The two peaks of Category 3 appear at around 12:00 and 18:00, respectively. This category mainly includes commercial users such as hotels and supermarkets. The two peaks of Category 4 appear at around 07:00 and 21:00, respectively. This category mainly includes residential users such as apartments. Category 5 is a trimodal load, mainly for users in the catering industry. There is a peak power consumption phenomenon in the morning, noon and evening, and the power consumption decreases during the morning working hours, lunch break and afternoon working hours. Category 6 is a peak avoidance load, mainly for public street lamps and high-energy-consuming enterprise users. The cluster centers of the six types of loads are shown in Figure 3.

The method proposed in the present invention is compared with the traditional improved C-means load clustering method. The traditional improved C-means load clustering method only improves the algorithm performance and does not consider the impact of the unbalanced distribution of the load curve. The clustering result of the traditional improved C-means load clustering method is shown in Figure 4. The user load curves are divided into 6 categories. There are 226 load curves in category 1, 276 load curves in category 2, 373 load curves in category 3, 352 load curves in category 4, 383 load curves in category 5, and 300 load curves in category 6. Under the traditional improved C-means load clustering method, a considerable part of the load in category 2 is incorrectly classified into category 1, and a considerable part of the load in category 3 is also incorrectly classified into category 5. From the above analysis, it can be seen that the load curve clustering method based on improved rough C-means proposed in the present invention has fewer incorrectly clustered load curves and has a better classification effect.

In order to further verify that the proposed mixed imbalanced metric considering distance and density can improve the performance of clustering methods, the C-means algorithm and the rough C-means algorithm are selected as comparison algorithms, and the clustering results are evaluated from the following four aspects:

1) DBI index: This index reflects the dispersion between clusters and the compactness within clusters. The smaller the value, the higher the clustering quality. The calculation formula is as follows:

,

Where: is the average distance from all samples in the i-th class to its cluster center; is the distance between the cluster centers of the i-th and j-th categories; The smaller it is, the better the clustering effect is;

2) SSE index: This index reflects the intra-cluster cohesion of all clusters. The smaller the value, the higher the clustering quality. The calculation formula is as follows:

;

3) SC index: This index reflects the density between clusters. The closer its value is to 1, the farther the clusters are from each other.

,

Where a(X _k ) represents the average distance from X _k to other samples in the same cluster; b(X _k ) represents the minimum average distance from X _k to samples in other clusters;

4) Clustering accuracy AC: This indicator refers to the percentage of correctly clustered data objects in the data set compared with the decision attribute values of the original data set. The calculation formula is:

.

Table 1 Comparison of clustering effects

Table 1 is a comparison of clustering effects. From the perspective of clustering indicators, the DBI index of the improved clustering method proposed in the present invention has the smallest value, indicating that the clusters are closer and the clusters are more dispersed; the SSE index of the improved clustering method proposed in the present invention has the smallest value, indicating that the cohesion of each cluster is optimal; the SC index of the improved clustering method proposed in the present invention has the largest value, indicating that the clusters are more sparse; the clustering accuracy of the improved clustering method proposed in the present invention is the highest, indicating that the clustering is more accurate.

The above description is only a preferred embodiment of the present invention and is not intended to be a further limitation of the present invention. All equivalent changes made using the contents of the present specification and drawings are within the protection scope of the present invention.

Claims (5)

1. The load curve clustering method based on the improved rough C-means is characterized by comprising the following steps of:

step 1, acquiring historical daily load data, and acquiring N original daily load curves of the same day Normalizing the original daily load curve by adopting a maximum normalization method to obtain N load clustering object curves needing to be clustered，；

Step 2, determining the number c of target clusters and c initial cluster centersA lower approximation weight W _low, an upper approximation weight W _up, and a distance determination threshold delta,；

Step 3, for the load clustering object curve X _k,Calculating Euclidean distance from the cluster center to each cluster center, and classifying X _k into the upper approximation set of the cluster U _i corresponding to the nearest cluster center C _i ；

Step 4, if another cluster center C _j exists so that the difference between the distance from X _k to C _j and the distance from X _k to C _i is smaller than the threshold delta, classifying X _k into the upper approximate set of the cluster U _j corresponding to C _j at the same time; Otherwise, X _k is classified into the lower approximation set of cluster U _i ；

Step 5, updating the clustering center according to the following iterative formula:

，

Wherein h _ik is the mixed imbalance metric, the difference between the upper approximation set and the lower approximation set A boundary set representing a cluster-like U _i;

and 6, repeating the steps 2-5 until the clustering converges.

2. The method for clustering load curves based on improved coarse C-means according to claim 1, wherein in step 1, the sampling interval of the original daily load curves is1 hour, and then N original daily load curves in the same day areWhereinThe kth raw daily load curve is shown,The value of the kth original daily load curve at the ith hour is shown.

3. The load curve clustering method based on the improved rough C-means according to claim 1, wherein the method for normalizing the original daily load data by adopting a maximum normalization method in the step 1 is as follows:

，

thereby obtaining N normalized load clustering object curves WhereinAnd X _ki represents the value of the kth load clustering object curve at the ith hour.

4. The load curve clustering method based on modified coarse C-means according to claim 1, wherein in step 3, the euclidean distance from the kth load cluster object curve X _k to the initial cluster center C _i=(C_i1, C_i2, … , C_i24) is calculated as follows:

，

Wherein d _ik is the Euclidean distance from the kth load clustering object curve X _k to the initial clustering center C _i.

5. The load curve clustering method based on modified coarse C-means according to claim 1, wherein in step 5, the mixing unbalance measure h _ik is calculated as follows:

，

wherein, Indicating a distance X _k ofThe number of load curves in the neighborhood range; Representing the upper approximation set of class cluster U _i corresponding to cluster center C _i The number of internal load curves; The distance measurement when the kth load clustering object curve X _k participates in the iteration of the clustering center C _i is shown, the farther the distance is, the lower the influence degree of the distance d _ik from X _k to C _i on the updating iteration of C _i is, and the higher the influence degree is when the distance is closer; The k-th load clustering object curve X _k is represented to participate in local density measurement when the clustering center C _i iterates, the lower the density is, the lower the influence degree of the density of the load curve in the X _k neighborhood range on the C _i updating iteration is, and the higher the density is, the higher the influence degree is.