Comparison of time-varying phasor and dq0 dynamic models for large transmission networks

In recent years, with increasing penetration of small distributed generators and fast power electronics based devices, the assumption of quasi-static phasors is becoming increasingly inaccurate. In order to describe fast dynamic behavior and rapid amplitude and phase variations, more accurate dynamic models based on the dq0 transformation are used. To better understand the differences between these two models, in this work we compare their relative accuracy when applied to large-scale transmission networks. In this light, the present work describes the two types of models using similar terminology, which is based on dq0 quantities. Based on this result, we show that quasi-static models may be obtained from dq0 models at low frequencies, and that there exists a frequency range in which quasi-static model approximates the dq0 model well. The obtained results allow to estimate the frequency after which the quasi-static model cannot accurately describe the system dynamics, and dq0 models should be used instead.