The paper presents a method to describe the evolution of the plasma equilibrium in an iron core transformer tokamak. It is shown that for any possible discharge scenario for a circular cross-section plasma, full information on the poloidal magnetic field system is contained in a set of two-dimensional characteristics. Using a boundary integral equations method, a large number of equilibrium states have been computed to obtain the necessary two-dimensional characteristics for describing discharge scenarios in the T-15 tokamak.