## 1 Introduction
The last two scenarios mentioned above are far away from this paper target. Another studied solution is to face FCL under the assumption that the inverter is droop-based in both operation modes. In [38; 39], examples for three-phase three-wire microgrids are exposed. Different types of short circuits are studied in [38], but the fault current limitations offer dynamics of about 200 ms to achieve steady-state, while in [39] only a tetrapolar short-circuit is evaluated obtaining time responses of about 100 ms. In [40], some results are just simulated for AC droop-based four-wire systems. Finally, other alternatives exist applied to series filters or obtaining FCL by changing the output inductances as detailed in [41; 42]. The main contribution of the present paper is the demonstration by simulation and real results of the advantages and flexibility of a fast time response hybrid combination of voltage control techniques that ensures proper FCL capabilities introducing two strategies for this purpose: one for each operation mode. This allows for applying specific control strategies and solutions in a context of increasing complexity scenarios avoiding the use of generic solutions that are not always the most appropriate ones. Firstly, the AC droop control based on dynamic phasors is adopted for the grid-connected mode, but a master voltage-frequency (V/f) control strategy is embraced for the grid-disconnected mode, offering better dynamic responses during the grid-disconnected operation thanks to disabling the AC droop loop. The use of a variable virtual resistance supports not only soft-starts but also the transference between the operation modes. Varying virtual resistance enhances the voltage restoration during the transference. Secondly, two control strategies will assist the FCL capability of the inverter connected to an AC microgrid. An over-load supervisor is proposed to characterize and limit the over-load magnitude, providing thermal recovery when extra current has to be dispatched during grid-connected mode. In addition, a short-circuit proof strategy supports the operation of the inverter under different short-circuit situations and fault clearances for grid-disconnected operation, obtaining time responses below 60 ms. To achieve the same response from the protective devices' viewpoint, the short-circuit proof algorithm allows for maintaining current and voltage sinusoidal and totally controlled, as required in a microgrid operation framework. All strategies are thought to be compatible with a four-wire microgrid because, as detailed in [43; 44; 45], this is the proper solution for addressing independently three-phase current control and facing imbalances. These strategies become an efficient way to face common situations in low voltage microgrids interfaced with distribution networks. Thus, the paper is organized as follows. Section 2 defines the system. Section 3 describes the proposed strategies for the FCL and the adaptive virtual resistance mechanism adopted for a seamless smooth transference. Section 4 presents the simulated results using Matlab/Simulink (R2017b, The MathWorks, Inc., Natick, MA, USA, 1984) and exposes the experimental ones validated in the experimental ATENEA four-wire microgrid at The National Renewable Energy Centre (CENER). Finally, Section 5 provides the conclusions.