Abstract. The mathematical generalization of classical model of the global circuit with taking into account the convective current generator, working in the planetary boundary layer was considered. Convective current generator may be interpreted as generator, in which the electromotive force is generated by processes, of the turbulent transport of electrical charge. It is shown that the average potential of ionosphere is defined not only by the thunderstorm current generators, working at the present moment, but by the convective current generator also. The influence of the convective processes in the boundary layer on the electrical parameters of the atmosphere is not only local, but has global character as well. The numerical estimations, made for the case of the convective-unstable boundary layer demonstrate that the increase of the average potential of ionosphere may be of the order of 10% to 40%.