Quasi two- and three-dimensional models of dense night-time sporadic E-layers of the earth's ionosphere as current generators are developed. The layers are assumed to be situated in an ambient plasma of about fifty times lower density and their neutral particles possess a rather high bulk velocity relative to the ions. The quasi-two dimensionality of the first model results from the assumption that relative electron-ion drifts in the neutral wind direction are almost compensated. The ion current in the neutral wind direction is caused by collisions with neutrals, but the electron current is a result of the appearing electrical polarization field. Within the proposed model the electron current is closed by an external circuit, for which a rough description is developed. The electrical polarization field is considered and estimated taking into account the altitude profile of the electrical conductivity in the external circuit. Further, a quasi-three-dimensional model of local current generation caused by the action of short-duration intense neutral winds on sporadic E-layers of finite horizontal dimensions is presented. In the analysis, the Hall and Pedersen currents in the sporadic layer as well as in the less dense plasma above the sporadic layer are taken into account. Thus, the currents in two horizontal plasma layers of different density and the field-aligned currents connecting the borders of these two layers are considered. A two-fluid hydrodynamic analysis of the system shows that maximum Hall currents occur if the sporadic layer-generator is situated at altitudes of about 120 km. The bulk electron velocity in these currents can reach values of the order of the neutral wind velocity.