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

The synchronous dq based small-signal stability using the eigenvalue analysis and impedance methods is widely employed to assess system stability. Generally, the harmonics are ignoredin stability analysis which may lead to inaccuracies in stability predictions, particularly, when the system operates in a harmonic-richenvironment. Typically, the harmonic state-space method (HSS) facilitates stability studies of linear time-periodic (LTP) systems, which considersthe impact of harmonics. The use of the dq-dynamic phasor state space and impedance method offers significant advantages over the HSS counterpart, as it reduces system order, is more suitable for studying control systems, retains mutual coupling of harmonics, and simplifies the stability study under unbalanced conditions. This paper extends dynamic phasor modelling for studying stability of modern power systems that include power converters. It is shown that the proposed method reproduces the typical response of STATCOM at the fundamental frequency as well as at 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.