# Mode Shape Estimation using Complex Principal Component Analysis and k-Means Clustering

## TL;DR

This paper introduces an empirical approach combining complex PCA, Hilbert Transform, and k-means clustering to identify low damped modes and mode shapes from frequency data, validated on simulated and real power system data.

## Contribution

The paper presents a novel two-step method for mode shape estimation using complex PCA and clustering, applicable to real power system measurements.

## Key findings

- Method accurately estimates dominant modes in simulated data.
- Initial real data tests show promising results.
- Approach effectively groups mode shape estimates into meaningful clusters.

## Abstract

We propose an empirical method for identifying low damped modes and corresponding mode shapes using frequency measurements from a Wide Area Monitoring System. The method consists of two main steps: Firstly, Complex Principal Component Analysis is used in combination with the Hilbert Transform and Empirical Mode Decomposition to provide estimates of modes and mode shapes. The estimates are stored as multidimensional points. Secondly, the points are grouped using a clustering algorithm, and new averaged estimates of modes and mode shapes are computed as the centroids of the clusters. Applying the method on data resulting from a non-linear power system simulator yields estimates of dominant modes and corresponding mode shapes that are similar to those resulting from modal analysis of the linearized system model. Encouraged by the results, the method is further tested with real PMU data at transmission grid level. Initial results indicate that the performance of the proposed method is promising.