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 ignored in stability analysis which may lead to inaccuracies in stability predictions, particularly, when the system operates in a harmonic-rich environment. Typically, the harmonic state-space method (HSS) facilitates stability studies of linear time-periodic (LTP) systems, which considers the 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. Acronyms and definitions STATCOM dc side capacitor ℎ Harmonic order. STATCOM dc link current STATCOM Direct and quadrature currents vector An integer number representing harmonic order, which is the axis to which referred STATCOM controller proportional gains STATCOM controller integral gains ℒ , ℒ The number of states and inputs of the studied system Return ratio matrix of grid-load , STATCOM resistance and inductance STATCOM dc link voltage Direct and quadrature voltages vector at ℎ harmonic () A function of time representing the complex Fourier coefficient 'dynamic phasor parameter' of the periodic signal Coupling impedance caused by harmonic at fundamental frequency. , Coupling impedance caused by the fundamental frequency at harmonic A coupling impedance which caused by the existence of positive and negative harmonics at a specific harmonic