The self-consistency between the current driven by the rf wave at the Lower Hybrid (LH) frequency, the residual Ohmic electric field and the toroidal MHD equilibrium in a tokamak has been investigated in detail. For this purpose, a dedicated simulation framework has been developed, SLUKE, allowing to incorporate with a high flexibility different types of codes which must be chained for the considered study, but also to perform quantitative comparisons between modelling results and experimental observations. The numerical tools in the suite of codes are the tokamak solver METIS (Artaud et al 2018 Nucl. Fusion58 105001), the solver of the Grad–Shafranov equation FEEQS.M (Blum et al 2019 J. Comput. Phys.394 594), the LH wave coupling code ALOHA (Hillairet et al 2010 Nucl. Fusion50 125010), the ray tracing code C3PO (Peysson et al 2012 Plasma Phys. Control. Fusion54 045003), the solver LUKE of the linearized relativistic 3D guiding-centre averaged electron Fokker–Planck equation (Peysson et al 2014 Fusion Sci. and Tech., 65 22), and the R5-X2 quantum relativistic synthetic diagnostic calculating the non-thermal bremsstrahlung (Peysson et al 2008 Phys. Plasmas15 092509). An appropriate set of discharges of the Tore Supra tokamak, particularly well diagnosed, have been selected, where the Ohmic plasma current is either partially or almost fully replaced by the LH-driven one. It is shown that despite a strong absorption of the LH wave in the core plasma, the convergence towards a fully self-consistent solution remains difficult when the fraction of the LH-driven current predominates, which could lead to a bi-stable regime. This numerical instability can be stabilized by an ad-hoc radial transport used as a regularization parameter of the numerical scheme. When the Ohmic part of the plasma current predominates, a fast convergence is observed, even if the electric field profile is significantly modified after a few iterations.