A method to identify the shape of tokamak plasmas with a Legendre-Fourier expansion of the vacuum poloidal flux function in toroidal coordinates is improved for the JT-60 Upgrade plasmas. These are pulse plasma discharges that have different sizes, positions, shapes, and internal quantities. The method is based on an analytical solution of the Grad-Shafranov equation in a vacuum region using toroidal coordinates. Although many identification methods previously proposed allow very small perturbations of certain parameters of the nominal plasma, the method presented here can relax the identification restriction on plasmas. Hence, it is applicable to accurate feedback control and real-time visualization of various plasma configurations.