Blade Element Momentum Theory (BEMT) performance models for wind turbines lead to a robust BEMT model of marine current or tidal stream turbines. It is shown that numerical convergence methods for models reported in the literature are problematic when away from the normal operating range and this paper reports a robust numerical scheme using combined Monte Carlo and sequential quadratic optimisation. The model is extended by Prandtl corrections for losses at the blade tip and hub. Results are validated against an industrial code, Garrad Hassan’s Tidal Bladed Software (GH Tidal Bladed) evaluation version, and a lifting line theory model.