To read the Quran in the Salat, and out of it in Ramadan, is something praised/praiseworthy. But in the Taraweeh (and in the other Salat), you may read as much as you can, even if it is a short Surah, and if you are an Imam then be conscious of those who are following. Lastly, it is not necessary for you to complete the entire Quran in The salat. Also it is Sunnah on the Imam to read the whole Quran once in Taraweeh during Ramadan (and this is the position taken by the Hanabalah and the majority of the Hanafiyah), but if he cannot then it is ok.
فَاقْرَءُوا مَا تَيَسَّرَ مِنَ الْقُرْآنِ
so recite what is easy [for you] of the Qur'an
Surat Al Muzzamil Ayah 20
Sources, and links for more information (in Arabic): this, this, and this.