Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification of the dominant eigenvalues. The methodology is derived by linearization of the Cauchy-Riemann equations, which define the conformal mapping property of the Nyquist trajectories. The proposed technique is of high practical value, since it can be performed from frequency-domain data obtained by small-signal perturbation (i.e., explicit transfer functions are not needed). A detailed study case, focused on a medium-voltage dc microgrid, is provided in order to verify the theoretical approach. The new features and limitations of the proposed technique are summarized in the conclusions.