Frequency-Domain Stability Criteria for Converter-Based Power Systems

Abstract

Frequency-domain stability criteria are developed for converter-based power systems with any number of converters. The converters may be grid following or grid forming, and the grid can be an ac or hybrid ac-dc network. The converters and the network are all modeled in a common (stationary) reference frame based on small-signal sequence immittances. Coupling over frequency and ac-dc coupling are considered in the most general form. For each type of systems, a frequency-domain model is developed first by nodal analysis and then reformulated to fit the form of a feedback loop with open-loop stability guaranteed by practical conditions. System stability is then determined by a Nyquist-like criterion without the need to check openloop right-half-plane poles. Further simplification of the system models is made possible by a) generalized 𝒏-port equivalent circuits that include both types of coupling, b) equivalence of stability at internal and external nodes, and c) relationship between dynamics at the perturbation and the coupling frequency. Reduction of a system model into separate single-input-single-output models is presented for several special systems along with their practical applications. Quantitative and experimental results are presented to verify the developed theories.

A Review of the Research on the Wide-Band Oscillation Analysis and Suppression of Renewable Energy Grid-Connected Systems

“…Impedance analysis [46] The interactive system exhibits negative damping characteristics at the same frequency of impedance amplitude…”

Quantitative evaluation measures for DC-DC converters

“…It is also applicable to the frequency domain. For more details, [33] will be helpful for the Stability Analysis of DC/DC converters in the frequency domain.…”

Extended Nodal Admittance Matrix Based Stability Analysis of HVDC Connected AC Grids

“…is given in the form of continuous function of frequency [26], which is not the case as illustrated in Appendixes A-C, thus the point-by-point numerical manipulation over frequency and the approximation, e.g. by vector fitting [27], on each set of frequency response by a continuous function of frequency is needed, which is a major disadvantage of this approach.…”

“…Performing small-signal analysis to above equations and jointly solving them yields (26) where d0 q0 d0 q0 d0 q0 , , , , , U U I I M M denote the steady state voltages, currents and modulation indexes and can be written in vector form as…”