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In the last decade, different control concepts for the synchronisation of voltage-controlled power converters have been proposed in order to form converter-based power systems. The interoperability of these grid-forming power controls is often analysed based on reduced-order models covering only the slow controls or modes. In this article, the coupling of the outer, power-related and inner, inverter output-related control of multiple grid-forming power converter systems is analysed, based on a minimal working example. The elementary study cases each consist of a different grid-forming converter coupled with an external (and passive) grid. Here, the investigated stability problems are already manifested in the simplest possible setup. The analysis of these coupling effects is performed by modelling the system in impedance-based, state-space and phase portrait-based frameworks. In particular, small coupling impedances, like short transmission lines or small short circuit impedances, can be challenging for the controller stability of grid-forming converters while the inner controls can even enhance this issue. The impact of this phenomenon and the participating subsystems are identified in this work. Thus, recommendations concerning modelling techniques and their legitimate assumptions are given. Laboratory experiments validate the performed analysis by indicating a close correlation between analytical models and experimental results.

On the Coupling of Power-Related and Inner Inverter Control Loops of Grid-Forming Converter Systems