With reference to toroidal fusion devices, we solve axisymmetric nonlinear evolutionary equilibrium equations, describing the plasma behaviour, self-consistently coupled to eddy currents equations, describing surrounding three-dimensional (3D) structures. This formulation allows the analysis of nonlinear plasma quasi-static evolution in the presence of 3D volumetric conductors. Several validations and test cases are presented, suggesting the potential applications of the proposed method to the analysis of various situations of scientific and technical interest for future fusion devices such as ITER and DEMO, like for instance disruptions.