We investigate the performance of the upcoming ACES (atomic clock ensemble in space) space mission in terms of its primary scientific objective, the test of the gravitational redshift. Whilst the ultimate performance of that test is determined by the systematic uncertainty of the on-board clock at 2–3 ppm, we determine whether, and under which conditions, that limit can be reached in the presence of coloured realistic noise, data gaps and orbit determination (OD) uncertainties. To do so we have developed several methods and software tools to simulate and analyse ACES data. Using those we find that the target uncertainty of 2–3 ppm can be reached after only a few measurement sessions of 10–20 d each, with a relatively modest requirement on OD of  ∼300 m.