Generalised dq-dynamic phasor modelling of a STATCOM connected to a grid for stability analysis

The synchronous d-q based small-signal stability using the eigenvalue analysis and impedance methods is widely employed to assess system stability. Generally, the harmonics are ignored in the stability analysis, and such assumption may lead to inaccuracies in the stability predictions, particularly, in harmonic-polluted ac grids. Typically, the harmonic state-space method (HSS) facilitates stability studies of linear time-periodic systems, which considers the impact of harmonics. The use of the d-q dynamic phasor state space and impedance methods offer significant advantages over the HSS counterpart, as they reduce system order, suitable for studying control systems, retain coupling between harmonics, and simplify the stability study under unbalanced conditions. This study extends dynamic phasor modelling for studying stability of modern power systems that include power converters. It is shown that the proposed methods reproduce the typical response of STATCOM at the fundamental frequency, as well as, in the presence of significant low-order harmonics, using both eigenvalues and impedance analysis. Quantitative validations of the proposed extended models against synchronous dq small-signal models confirm their validity.