Passivity of Electrical Power Networks Modelled Using Rectangular and Polar Variables

The proliferation of converter-interfaced distributed energy resources has highlighted the need for decentralized small-signal stability criteria for such interconnected systems. Passivity of the admittance based on rectangular D-Q variables is a promising grid-connectivity criterion for devices connected to the network. This is facilitated by the inherent passivity of the D-Q based impedance of the electrical network. However, this criterion has been found to be too restrictive for the connected devices that have voltage magnitude and frequency-dependent power injection characteristics. Therefore in this paper, alternative formulations involving polar variables and active and reactive power are examined. The results presented in this paper indicate that (a) the wide-band polar formulation of the network is not passivity compliant, and (b) the polar formulation is suitable for developing passivity-based stability criteria for low frequency models, while the rectangular formulation can be retained for the high frequency models.