  Stability of power electronic converters connected to power grids is commonly
assessed by using the impedance criterion. On the contrary, stability of power
grids is typically analysed by using network state-space representation and
system eigenvalues. It has been already reported in the literature that the
impedance criterion may lead to erroneous results if the dynamics of the grid
frequency is not taken into consideration. Meanwhile, the eigenvalue analysis
is still considered as a reliable method for finding instabilities. However,
the equivalence between these two methods (impedance criterion with frequency
dynamics included and eigenvalue analysis) has not been thoroughly studied
before. In this paper, the impedance method with frequency dynamics included is
compared with the conventional eigenvalue analysis for a system fully based on
electronic interfaces. Analytical expressions that link both methods are
provided, showing that they are identical under certain conditions. Then, both
methods are applied to a system based on a grid-forming and a grid-following
converter. The results obtained from real-time simulations performed in OPAL-RT
are used to validate the theoretical developments and main contributions of
this work.
