Granger Causality for Predictability in Dynamic Mode Decomposition

TL;DR

This paper introduces a method combining Persistence of Excitation and Granger Causality Test to validate measurement data for Dynamic Mode Decomposition, improving the identification of system modes and predictability in complex dynamical systems.

Contribution

It proposes a novel validation framework using PE and GCT conditions to enhance DMD analysis, validated on power system stability data.

Findings

PE condition sets the minimum data length for analysis

GCT determines the model order for causality detection

Method improves mode identification accuracy in power systems

Abstract

The dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data, the DMD algorithm necessitates ensuring the quality of the input measurement data sequences. On that account, for validating the usability of the dataset for the DMD algorithm, the paper proposed two conditions: Persistence of excitation (PE) and the Granger Causality Test (GCT). The virtual data sequences are designed with the hankel matrix representation such that the dimensions of the subspace spanning the essential system modes are increased with the addition of new state variables. The PE condition provides the lower bound for the trajectory length, and the GCT provides the order of the model. Satisfying the PE condition enables estimating an approximate linear model, but the predictability with the identified model is only assured with the temporal causation among data searched with GCT. The proposed methodology is validated with the application for coherency identification (CI) in a multi-machine power system (MMPS), an essential phenomenon in transient stability analysis. The significance of PE condition and GCT is demonstrated through various case studies implemented on 22 bus six generator system.