[en] In this paper, the authors have performed a number of first principles electronic structure calculations for YBa₂Cu₃O_7-y with different oxygen orderings and concentrations. The resulting total energies have been used to assess the applicability of some of the proposed models for oxygen ordering in this system. The authors find that the results are consistent with an Ising-like model with asymmetric next-neighbor interactions between oxygen sites. The authors determine effective interaction parameters from the first principles calculations and use them to compute the phase diagram for the system, which is in excellent agreement with experiment for the tetragonal-orthorhombic I transition