Stability assessment of power-converter-based AC systems by LTP theory: eigenvalue analysis and Harmonic Impedance estimation

Stability analysis of power-converter-based AC systems poses serious challenges not only because of the non-linear nature of power converters, but also because linearisation is not generally applied around a steady-state operating point, as in the DC case, but around a time-periodic operating trajectory. Typical examples are single-phase and unbalanced three-phase systems. In this paper, two general methods to assess stability of the aforementioned systems are presented. Both are based on the Linear Time Periodic (LTP) systems theory. The first is model-based and relies on the evaluation of the eigenvalues of the linearised model, assuming a complete knowledge of the parameters. By contrast, the second proposes a set of small-signal current injections to measure the Harmonic Impedances and applies the LTP Nyquist Criterion, so that stability of the system can be assessed with a black-box approach, without relying on knowledge of the system parameters. The basic LTP systems theory is reviewed in order to provide a mathematical justification for the second method. As case study, a simple network, consisting of a source full-bridge converter in AC voltage-control mode and a load full-bridge converter in AC current-control mode including PLL, is considered. Analytical results based on average modelling and simulations based on both average and switching models are presented, showing good accuracy in the identification of the stability thresholds for both the proposed methods