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(copyright) 2020Recent advances in Transmission Network Expansion Planning (TNEP) have demonstrated that two-stage adaptive robust optimization (ARO) renders the expansion planning problem tractable for real systems and, at the same time, constitutes a relevant approach to deal with uncertain demand and generation capacity in the TNEP problem. However, the use of cardinality and polyhedral uncertainty sets does not consider the correlation of uncertain parameters and makes the interpretation of final results difficult from a probabilistic view-point. The recent use of level II structural-reliability and decomposition techniques allows the incorporation of ellipsoidal uncertainty sets, which permits the use of expected values and the variance-covariance matrix of uncertain parameters (First-Order Second-Moment, FOSM). However, it also constitutes an approximation. This paper presents an iterative method which, using FOSM and appropriately modifying the reliability index associated with the desired objective function quantile, transforms the model into a level III structural-reliability method that allows the consideration of the complete probabilistic structure of the uncertain parameters. Numerical results from a realistic case study are presented and discussed.