Poomsae and Ki
Now let me talk about whether the poomsae produces Ki.
Poomsae is the series of attacking and defending actions. Thus, considering the direct meaning of poomsae, it is difficult to explain its relation to Ki. I think we should depend on the wisdom of elders and of nature, to find out the relation.
I suppose that the poomsae is the evolved system of attacking and defending skills of a man. It must have evolved(developed) by many people, to be a natural series of natural movements.
Here, its naturality is important. Natural movements converge to the harmony of the principles of life and the whole world. Then the ultimate form can be helpful for almost everything. We can find another kinds of examples similar to this. The musicians, who are not aware of the biology or medicine, are trying to make a just beautiful music. But we say some music of a great musician is good for health or some thing else. It is because the ultimate form of music might be the best harmony of everything. So I can conclude that the poomsae can produce Ki.
However, to do poomsae is not always to produce Ki, I think. In order to produce Ki, the poomsae should have the harmony of its function and structure of man's body. It can be obtained by the long-time history, which generates the wisdom of nature beyond that of a certain man. Usually such poomsae is not specially characteristic so that those who didn't understand the deep meaning of the essence of martial arts cannot discern it from what are not. For the poomsaes of Taekwondo, some of them are made up and reconstructed recently, and they have some trivial faults I think.
Although those problems are prevailed in every kinds of martial arts, it should be noticed I think. However, it can be said that the poomsae of TKD is helpful to produce Ki when it were trained in the right way; that is, the motions should accord to the breathing. Its accordance consisted of its rhythm and the changes of mind.
You should see PPT in order to know the relations among them.