Distributed Widely Linear Frequency Estimation in Unbalanced Three Phase Power Systems

TL;DR

This paper introduces distributed widely linear Kalman filtering methods for accurate frequency estimation in unbalanced power systems, effectively handling noncircular signals and disturbances, with demonstrated advantages through synthetic and real case studies.

Contribution

It develops novel distributed widely linear Kalman filters that address unbalanced system conditions and improper signals, improving estimation accuracy over traditional linear methods.

Findings

Widely linear estimators outperform linear ones in unbalanced conditions.

The methods effectively handle noncircular Clarke's voltage signals.

Case studies confirm practical benefits in real-world power systems.

Abstract

A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed widely linear extended complex Kalman filter (D-AECKF) employ a widely linear state space and augmented complex statistics to deal with unbalanced system conditions and the generality complex signals, both second order circular (proper) and second order noncircular (improper). It is shown that the current, strictly linear, estimators are inadequate for unbalanced systems, a typical case in smart grids, as they do not account for either the noncircularity of Clarke's \alpha \beta-voltage in unbalanced conditions or the correlated nature of nodal disturbances. We illuminate the relationship between the degree of circularity of Clarke's voltage and system imbalance, and prove that the proposed widely linear estimators are optimal for such conditions, while also accounting for the correlated and noncircular nature of real-world nodal disturbances. {Synthetic and real world} case studies over a range of power system conditions illustrate the theoretical and practical advantages of the proposed methodology.