Optimal Kalman Estimation of Symmetrical Sequence Components

This article reexamines the problem of estimating symmetrical sequence components, more specifically, the optimal estimation of the magnitude and phases of sequence components. We first address and compare different setups for the optimal Kalman filter, including those that make use of three-phase measurements and those where the measurements are transformed by the Clarke transform, in the well-known direct and quadrature (dq) reference frame. Our main contribution is to show that by disregarding some Clarke transformed measurements in the estimation of zero, positive, and negative sequence components, which is the common practice, almost always lead to an estimator with suboptimal performance. Moreover, we show that optimal performance can be recovered if all Clarke transformed measurements are made available to the filter. We use simple numerical examples to explain our results, and we finish this article with a unified set of guidelines or best practices regarding the estimation of sequence components by optimal Kalman filters.