In the upcoming “smart grid” era, advanced control schemes are required for inverter- interfaced DERs to guarantee stability of inverter-dominated feeders and microgrids. Nevertheless, in many of the recently proposed methods, the safe and stable operation of inverters can not be analytically guaranteed under normal and abnormal grid conditions. In this thesis, single-phase grid-connected inverters are initially considered and an enhanced Current-Limiting Droop (CLD) controller is proposed. In contrast to the original CLD, which limits the inverter current under a lower value than its maximum during faults, the proposed controller fully utilizes the inverter capacity. An inherent current limitation is proven through nonlinear ultimate boundedness theory and is shown to facilitate the operation of Fault-Ride-Through (FRT) schemes. Furthermore, conditions for asymptotic stability of the closed-loop system are derived. Additionally, a new CLD scheme is proposed, which operates without the need of a PLL and introduces a virtual inertia property to DERs. In the sequel, three-phase grid-connected inverters are investigated and a new controller in the dq-frame is proposed to deal with FRT in three-phase systems. Initially, a novel method to divide the current into its symmetrical components during unbalanced faults is proposed. Hence, based on an adaptive bounded integral controller, the proposed scheme provides voltage support to both positive and negative sequences, while ensuring the current boundedness and asymptotic stability of the closed-loop system. In the final part of this thesis, the safe and stable operation of three-phase inverter-based microgrids is investigated. Particularly, an advanced controller is proposed to deal with extreme load conditions. Through the proposed scheme, the limitation of the inverter current during transients is guaranteed, without the need of online adaptation techniques. Furthermore, the proposed approach significantly simplifies the stability analysis of microgrids, since it can be investigated through a Jacobian matrix of reduced size
