Equations for the three-dimensional equilibrium of a plasma are formulated in the poloidal representation. The magnetic field is expressed in terms of the poloidal magnetic flux Psi and the poloidal electric current F. As a result, three-dimensional equilibrium configurations are analyzed with the help of a set of equations including the elliptical equation for the poloidal flux, the magnetic differential equation for the parallel current, and the equations for the basis vector field b. To overcome the difficulties associated with peculiarities that can arise in solving the magnetic differential equation at rational toroidal magnetic surfaces, small regulating corrections are introduced into the proposed set of equations. In this case, second-order differential terms with a small parameter appear in the magnetic differential equations, As a result, these equations take the form of elliptical equations. Three versions of regulating corrections are proposed. The equations obtained can be used to develop numerical codes for calculating three-dimensional equilibrium plasma configurations with an island structure.