An application of the statistical theory of feedback to power system identification

Two processes are termed strongly (respectively weakly) feedback free when the canonical innovations representation (IR) of the joint process has one of two specified structures respectively [1-4]. The property that two processes are feed-back free captures the notion of a unique direction of influence between two processes. A set of equivalent characterizations of this property is presented in this paper. These characterizations yield a set of statistical tests for feed-back. When feedback exists between two processes it is possible to identify the separate loops of the IR by prediction error methods [5-9]. However, it is only when the disturbances in each loop are mutually orthogonal, and one of the loops contains a delay, that the loops so identified constitute the feedforward and feedback loops of the observed physical system. In this paper we describe how closed loop identification problems arise in load and generating source identification in power systems. We present some initial simulation results obtained by applying a spectral factorization algorithm to the problem of closed loop system identification. Further, we describe the application of this algorithm to real power system data [18-20].