This paper presents a new systematic scheme for designing optimized robust and efficient steady state load shedding (LS) in standalone inverter-based microgrids (IBMGs) considering uncertainties of the load and renewable generations. In order to incorporate different states of non-dispatchable renewable based-Distributed Energy Resources (DERs) and load demand fluctuations, the scenario tree model is implemented. To reduce the computational burden of the proposed model, a scenario-reduction technique using the Kantorovich distance (or Wasserstein distance) criteria is adopted to extract a sufficiently small number of scenarios. To reflect the system frequency in each opted scenario, a new power flow (PF) procedure, in which the system frequency turns up as a supplementary state variable is adopted. This procedure aims at minimizing the required shed loads to maintain the MG frequency over the critical frequency, when the inverters cannot tolerate any overload. According to the optimal curtailed load for different scenarios, a step-wise LS scheme is proposed for applying to an on-line operation manner. The performance of the proposed scheme is evaluated in two typical MV MG in standalone mode, a medium-scale 21 bus test system and a large-scale 118 bus test system, to ensure the efficiency and reliability of the proposed method in real conditions and systems. The obtained results evidence the effectiveness and the correctness of the presented LS scheme to diagnose power shortages and to maintain system frequency in the desirable range. Furthermore, the obtained results by proposed LS model have been compared with the conventional priority-based LS and the superiority of the proposed model over conventional models is proved.
