The paper addresses the problem of attitude stabilization of electrodynamic space tether system (EDTS) in the local vertical position. The EDTS includes a negatively charged collector at the lower end of the tether and a positively charged collector at the upper end. The magnitude of the negative charge is under control. The Lorentz torque acting on the EDTS due to charged collectors at the ends of the tether significantly expands the stability area for the vertical position of the tether. The interaction of charged collectors with near-Earth plasma is analyzed. The results showed that during the continuous operation of the electron gun, the locally equilibrium values of the potentials of the collectors and charges on them can vary by a factor of 2-3, and the values of the currents in the tether and in the electron gun can vary by more than one order of magnitude.