We consider the stabilization problem for an electrodynamic tether system (EDTS) in a circular near-Earth orbit in the position where the tether is stretched along the local vertical. To solve this problem, we propose an original EDTS design scheme that includes a negatively charged collector at the lower end of the tether and a positively charged collector at the upper end of the tether. The magnitude of the charge on the negatively charged collector is controlled by electronic emitters. We show both analytically and numerically that the Lorentz force moment 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. In addition, controlling the charge on the negatively charged collector according to the current angular motion of the tether allows to create a control component of the Lorentz torque that has dissipative nature. The simultaneous operation of restoring and dissipative-like components of the control Lorentz torque allows us to ensure the asymptotic stability of the vertical position of the tether without having to switch off the electric current flowing along the tether. The proposed control method can be used to stabilize the EDTS in order to increase the efficiency of its operation on the removal of space debris.