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Solid State Transformers (SST) may become, in the near future, key technological enablers for decentralized energy supply systems. They have the potential to unleash new technologies and operation strategies of microgrids and prosumers to move faster towards a low carbon-based economy. This work proposes a paradigm change in the hierarchically and distributed operated power systems where SSTs are used to asynchronously connect the many small low voltage (LV) distribution networks, such as clusters of prosumers or LV microgrids, to the bulk power system. The need for asynchronously coupled microgrids requires a design that allows the LV system to operate independently from the bulk grid and to rely on its own control systems. The purpose of this new approach is to achieve immune and resilient by design configurations that allow maximizing the integration of Local Renewable Energy Resources (L-RES). The paper analyses from the stability point of view, through simplified numerical simulations, the way in which SST-interconnected microgrids can become immune to disturbances that occur in the bulk power system and how sudden changes in the microgrid can damp out at the Point of Common Coupling (PCC), thus achieving better reliability and predictability in both systems and enabling strong and healthy distributed energy storage systems (DESSs). Moreover, it is shown that in a fully inverter-based microgrid there is no need for mechanical or synthetic inertia to stabilize the microgrid during power unbalances. This happens because the electrostatic energy stored in the capacitors connected behind the SST inverter can be used for a brief time interval, until automation is activated to address the power unbalance for a longer term.