Equivalent modelling for the fundamental frequency dynamic variation: State-space, impedance, and power-frequency representations

Stability of power electronic converters connected to power grids is commonly assessed by using the impedance criterion while the stability of power grids is typically analysed by using the network state-space representation. It is known that the impedance criterion may lead to erroneous results if the grid frequency dynamics are not considered while eigenvalue analysis is considered as a reliable method for system stability assessment. The equivalence between these two methods has been recently explored, without considering the effect of network frequency variations. Additionally, the link of the impedance criterion with the power-frequency dynamics of power systems also remains largely unexplored. In this paper, the equivalency between the impedance method considering the grid frequency dynamics and the conventional eigenvalue analysis is demonstrated. In addition, the dynamic interaction between the apparent power flow and the network fundamental frequency is formulated and its link with the impedance representation is shown. It is demonstrated that, by using the impedance representation with the network frequency as an additional input port, the network frequency perturbation plot (NFP) can be intuitively expressed by using quantities consistent with the impedance analysis framework. The main findings are verified using detailed numerical simulations of two representative systems.