Modeling power networks using dynamic phasors in the dq0 reference frame

The dynamic behavior of large power systems has been traditionally studied by means of time-varying phasors, under the assumption that the system is quasi-static. However, with increasing integration of fast renewable and distributed sources into power grids, this assumption is becoming increasingly inaccurate. In this paper, we present a dynamic model of general transmission and distribution networks that uses dynamic phasors in the dq0 reference frame. The model is formulated in the frequency domain, and is based on the network frequency dependent admittance matrix. We also present a simplified version of this model that is obtained by a first-order Taylor approximation of the dynamic equations. The proposed models extend the quasi-static model to higher frequencies, while employing dq0 signals that are static at steady-state, and therefore combine the advantages of high bandwidth and a well-defined operating point. The models are verified numerically using the 9-, 30-, and 118-bus test-case networks. Simulations show that frequency responses of all models coincide at low frequencies and diverge at high frequencies. In addition, responses of the dq0 model in the time domain and in the abc reference frame are very close to those of the transient model.