Faults in power systems cause voltage sags, which, in turn, provoke large current peaks in gridconnected equipment. Then, a complete knowledge of the inverter behaviour is needed to meet fault ridethrough capability. The aim of this paper is to propose a mathematical model that describes the behaviour of the currents that a three-phase inverter with RL filter inject to a faulty grid with symmetrical and unsymmetrical voltage sags. The voltage recovery process is considered, i.e., the fault is assumed to be cleared in the successive zero-cross instants of the fault current. It gives rise to a voltage recovery in different steps (discrete voltage sag), which differs from the usual model in the literature, where the voltage recovers instantaneously (abrupt voltage sag). The analytical model shows that the fault-clearing process has a strong influence on the injected currents. Different sag durations and depths have also been considered, showing that there exist critical values for these magnitudes, which provoke the highest current peaks. The analytical study is validated through simulations in MATLAB TM and through experimental results.

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This paper presents a systematic model order reduction (MOR) algorithm based on state relevance applied to an islanded microgrid with electronic power generation. MOR of such islanded microgrids may not benefit, a priori, from the well-established time-scale separation usually applied to conventional power systems, and a systematic MOR is still an open issue. The proposed algorithm uses a balanced realization of the linear system, where state variables may not have physical meaning, to obtain the states' energies. It then calculates the relevance of the original system states from those energy values. The newly proposed ``state-relevance coefficient'' should help to choose which states to consider in a reduced model in each study case. Detailed nonlinear simulation results show that the proposed algorithm is able to find the relevant states to include in the reduced model systematically, even in operation points near the stability limit, where ad-hoc MOR techniques are likely to fail. The performance of the algorithm is illustrated in a system with grid-forming converters in various scenarios but can be easily applied to other systems.