The space debris occupies the orbit resources greatly, which seriously threats the safety of spacecraft for its high risks of collisions. Many theories about space debris removal have been put forward in recent years. The Electro Dynamic Tether (EDT), which can be deployed under gravity gradient, is considered to be an effective method to remove debris in low orbit for its low power consumption. However, in order to generate sufficient Lorentz force, the EDT needs to be deployed to several kilometers, which increases the risks of tangling and the instability of the EDT system. In the deployment process, different initial in-plane/out-of-plane angles, caused by direction error at initial release or the initial selection of ejection, affect the motion of EDT system seriously. In order to solve these problems, firstly, this paper establishes the dynamic model of the EDT system. Then, based on the model, safety metrics of avoiding tangling and assessing system stability during EDT deployment stage are designed to quantitatively evaluate the EDT system security. Finally, several numerical simulations are established to determine the safety ranges of the initial in-plane/out-of-plane angles on the EDT deployment.