Automated sequence impedance modeling of three-phase converters based on computer algebra

Sequence impedance models have been accepted as an effective method for resonance and stability analysis of renewable energy, high-voltage dc transmission and other three-phase power electronics systems. While such impedance models can be obtained in numerical form by simulation or measurement, the analytical models such as those presented in [2, 3] provide invaluable insight into how impedance behavior relates to circuit and control design. Developing such analytical models, however, requires special skills and has been limited to few specialists. To facilitate the application of the method, this paper presents automated generation of sequence impedance models using computer algebra. The preliminary program that is capable of performing this function is developed based on a new matrix formulation of the underlying harmonic linearization method [7] and is implemented in Mathematica. Applications in two-level voltage-source converter and modular multilevel converters are presented to demonstrate the feasibility of the method.