Conformal mapping of impedance stability models for system-level dynamics assessments

Abstract

Abstract-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.Index Terms-ac-dc power conversion, dc power transmission, power system modeling, power system stability, stability criteria.

Stability Analysis of Multi-Port MVDC Distribution Networks for All-Electric Ships

“…7, it can be observed that there are no visual (-1,0) encirclements. In such cases, the conformal mapping property can be considered to assess stability [44]. This property is briefly explained below.…”

“…From (14), in practice, identification of the sign of σ 1 is straightforward by inspection (of each Nyquist trajectory). More details, including a detailed derivation of (14), are given in [44]. Now, from Fig.…”