This article examines power issues for the ADF and four break models (Perron, 1989; Zivot and Andrews, 1992) when the DGP corresponds to one of the break models. Choosing to test an incorrect break model can, but need not, greatly reduce the probability of rejecting the null. Break points that are relatively early in the sample period have substantial effects of increasing power. For modest shifts in time trends, simply including a time trend without shift in the model preserves power, but not for large time-trend shifts.
Maican, Florin and Richard J. Sweeney (2014),
"Costs of Misspecification in Break-model Unit-root Tests".