The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be-modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current I-p, the elongation kappa, the triangularity delta, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma beta(p), and the internal self inductance l(i) also show acceptable agreement. The evolution of the growth rate gamma is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.