We present the results of using the statistical model of field-aligned currents (FACs) based on satellite data and the numerical model of the electric potential distribution in order to detect the asymmetric part in FAC structures and ionospheric plasma convection controlled by the IMF azimuthal (B_y) component at different seasons of the year. These structures can be identified by plotting diagrams, which represent differences in corresponding maps for opposite signs of IMF B_y. Circular near-pole current symmetric about the noon meridian and corresponding convection vortices around the pole have been obtained for the summer and equinox periods. It is difficult to detect distinct structures under winter conditions, and the current is most intense on the morning side. A two-cell convection system with the foci in the afternoon and postmid-night sectors is created in the electric potential difference diagrams. Thus, qualitatively different FAC and convection patterns exist during the solstice in opposite hemispheres. The value of the electric potential originating in the near-pole region under the action of the B_y component and a change in the potential under the action of additional factors have been estimated.