Hey VladV -
Static Shadows are generated via Lightmaps through the Lightmass system and as they are (grossly oversimplified) just textures applied on top of your world, you will have to optimize them to look their best. Every Light has lightmass settings which can be adjusted to better accommodate its use as well as the World Settings under Lightmass. These setting include the distance at which the lightmap fades in and out, the shadow’s penumbra fade (Shadow Exponent), its resolution.
Since their are limitations to Static lighting in close up scenarios, the stationary light was brought in to bridge the shadow difference between the lightmapped shadows and the dynamic shadows of movable lights. At close distances a Stationary light will render dynamic shadows but father away it will switch to built static shadows.
Hopefully this got you on the right track. I would also recommended spending sometime in this section of the documentation, https://docs.unrealengine.com/latest/INT/Engine/Rendering/LightingAndShadows/LightMobility/index.html, and let me know if you still have questions.
Thank You
Eric Ketchum