In the last decade, the concept of grid-forming (GFM) converters has been introduced for microgrids and islanded power systems. Recently, the concept has been proposed for use in wider interconnected transmission networks, and several control structures have thus been developed, giving rise to discussions about the expected behaviour of such converters. In this paper, an overview of control schemes for GFM converters is provided. By identifying the main subsystems in respect to their functionalities, a generalized control structure is derived and different solutions for each of the main subsystems composing the controller are analyzed and compared. Subsequently, several selected open issues and challenges regarding GFM converters, i. e. angle stability, fault ride-through (FRT) capabilities, and transition from islanded to grid connected mode are discussed. Perspectives on challenges and future trends are lastly shared.

Synchronverters have gained interest due to their capability of emulating synchronous machines (SMs), offering self-synchronization to the grid. Despite the simplicity of the control structure, the adoption of an LCL-filter makes the overall model complex again, posing questions regarding the tuning of the synchronverter and its robustness. The multi-inputs multioutputs (MIMO) formulation of the problem requires multivariable analysis. In this paper, the effects of control parameter and grid conditions on the stability of the system are investigated by means of structured singular values (SSV or µ-analysis). A stepby-step design procedure for the control is introduced based on a linearized small-signal model of the system. Then the design repercussions on the stability performance are evaluated through the performed robustness analysis. The developed linearized model is validated against time-domain simulations and laboratory experiments. These have been carried out using a power hardware-in-the-loop (PHIL) test bench, which allows to test the synchronverter under different grid conditions. As a conclusion the paper offers a simple guide to tune synchronverters but also a theoretical solid framework to assess the robustness of the adopted design. Index Terms-Synchronverter robust stability analysis, µanalysis, synchronverter design, power hardware-in-the-loop tests.

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Recent studies have shown how synchronization units of converters operating nearby may interact with each other, affecting the stability of the system. Synchronverters are able to self-synchronize to the grid without the need of a dedicated unit because they can reproduce the power synchronization mechanism of synchronous machines (SMs). Recently, the robust stability of a synchronverter has been investigated by means of structured singular values (SSV or µ-analysis).In this paper, µ-analysis is performed to investigate how the robust stability of a synchronverter is affected by the presence of another converter of the same type operating in parallel. It is demonstrated that the parallel operation of synchronverters reduces their robust stability and a possible solution is proposed, based on the implementation of virtual impedances in the control algorithm. An accurate state-space model of the system under study is developed by adopting the component connection method (CCM) and the robust stability analysis is validated against time-domain simulations in MATLAB/Simulink/PLECS and experimental results with a power-hardware in the loop (PHIL) test bench.