Coherent Clustering Method Based on Weighted Clustering of Multi-Indicator Panel Data

Abstract

The identification of coherent clusters plays an important role in dynamic equivalence and active split control of power systems. The existing coherent clustering methods often adopt a single indicator, e.g. only based on the power angle curve to identify coherent clusters. In addition, in the coherency identification process, the feature extraction is not sufficient, which may cause the problem of inaccurate grouping. In this paper, a coherent clustering method based on weighted clustering of multi-indicator panel data (WCMPD) is proposed. First, the measurements including power angle increment, terminal voltage, and rotor kinetic energy increment from phasor measurement units (PMU) are selected from panel data to reflect the coherence of the generators. Second, the indicator weights and time weights are calculated based on the cross-sectional and time dimension of the panel data. In order to suppress the shortcomings of the coherent clustering method based on Euclidean distance, three distance functions (''horizontal absolute value,'' ''rate of change at adjacent time points,'' and ''fluctuation variation degree'') are defined, and then aggregated. At last, the distance matrices among generators are calculated and the coherent generators can be obtained based on the system cluster method. The simulation results on the EPRI-36 bus system and the North China power grid demonstrate that the proposed method has better clustering results than traditional methods.INDEX TERMS Coherency clustering, weighted clustering algorithm of panel data, multiple indicator, index weight, system clustering.

A Robust Scheme for Coherency Detection in Power Systems

“…Table 3 shows the C-index evaluated for various number of clusters for both consistent and inconsistent delay cases. It can be observed that for a cluster search range of [2,7], the cluster number K=4 has the least index, indicating the optimal number of clusters is 4. The coherent groups thus identified are as shown in Table 4.…”

“…When a stressed power system is subject to large disturbances that could result in instability, it is necessary to perform emergency control to prevent cascading failures and the collapse of the entire network [2]. The first line of control actions is the engagement of conventional protection systems and controls, e.g., protective relays.…”

Review of Clustering Methods for Slow Coherency-Based Generator Grouping

“…In particular, the Gini coefficient measures the inequality among the indices, while the Kendall rank correlation coefficient measures the correlations. The exploitation of multiple indicators is also addressed in [18], where a multi-indicator panel data is constructed by considering, for each generator m = 1,…, M, the amplitude of the voltage at the generator terminal, the increment of the rotor kinetic energy (with respect to the initial instant t 0 ), and the voltage phase angle variation Δδ mt at time t with respect to the voltage phase angle 0 ä mt at the initial instant t 0 :…”

“…The need for considering a distance notion that does not strictly refer to the same time instants is recognised as well in [18], where an integrated weighted distance is used. This distance is based on the definition of three distance functions: (i) "horizontal absolute value"; (ii) weighted distance of "rate of change at adjacent time points"; (iii) weighted distance of "coefficient of variation''.…”

K-means method for clustering learning classes

“…Class grouping is important and implemented by educational institutions when beginning learning, this grouping aims to group students into the variables that have been determined so that they can gather students into the right group [1]. The purpose of this class grouping is to facilitate the instructor in adjusting the material presented by paying attention to the categories of student groups that have been determined, so that students have the readiness or ability to accept lessons that will be given by the instructor [2].…”