Abstract: In this paper, a posteriori multi-objective optimisation (MOO) is applied to tune the parameters of a second-order sliding-mode control (2-SMC) scheme commanding the grid-side converter (GSC) of a doubly-fed induction generator (DFIG) subject to unbalanced and harmonically distorted grid voltage. Two variants (i.e., design concepts) of the same 2-SMC algorithm are assessed, which only differ in the format of their switching functions and which contain six and four parameters to be adjusted, respectively. A single set of parameters which stays valid for nine different operating regimes of the DFIG is also sought. As two objectives, related to control performances of grid active and reactive powers, are established for each operating regime, the optimisation process considers 18 objectives simultaneously. A six-parameter set derived in a previous work without applying MOO is taken as reference solution. MOO results reveal that both the six- and four-parameter versions can be tuned to overcome said reference solution in each and every objective, as well as showing that performances comparable to those of the six-parameter variant can be achieved by adopting the four-parameter one. Overall, the experimental results confirm the latter and prove that the performance of the reference parameter set can be significantly improved by using either of the six- or four-parameter versions.