A Numerical Matrix-Based Method for Stability and Power Quality Studies Based on Harmonic Transfer Functions

Some couplings exist between the positive-and negative-sequence impedances of a voltage-sourced power converter especially in the low frequency range due to the nonlinearities and low-bandwidth control loops such as the phase-locked loop. In this paper, a new numerical method based on the harmonic transfer function for analysis of the linear time periodic systems is presented, which is able to handle these couplings. In a balanced three-phase system, there is only one coupling term, but in an unbalanced (asymmetrical) system, there are more couplings, and therefore, in order to study the interactions between these couplings a matrix-based method should be used. No information about the structure of the converter is needed and elements are modeled as black boxes with known terminal characteristics. The proposed method is applicable for both power quality (harmonic and interharmonic emissions) and stability studies, which is verified by simulations in this paper.