Dynamic phasor based frequency scanning for grid-connected power electronic systems

Frequency scanning is a method of obtaining the frequency response of a system by injecting a small-amplitude wide-band signal as an input in a time domain simulation of the system. This is an alternative to analytical derivation of small-signal models, especially for complex grid-connected power electronic systems (PESs). These models are required for the study of adverse interaction of PES with lightly damped oscillatory modes in a power system. The use of the frequency scans for conventional small-signal stability analysis is predicated upon the time-invariance of the underlying model. Since PES are generally time-periodic, time-invariance may be achieved in some transformed variables. Although the DQ transformation is suitable in many situations, it is not so for systems with low-order harmonics, individual-phase schemes, unbalanced or single-phase systems, and PES with negative-sequence controllers. This paper proposes the use of dynamic phasor variables in such situations since the underlying model in these variables is time-invariant. The procedure for dynamic phasor based scanning is, however, intricate because wide-band signal injection results in the simultaneous presence of harmonic dynamic phasor components. The paper outlines this procedure and presents illustrative case studies of Thyristor Controlled Series Compensator (TCSC) and STATCOM. For the TCSC, a comparison of the frequency response obtained from the scanning method and the one obtained from an approximate analytical dynamic phasor model is also presented.