Orthogonal Transformation

Instead of the transformation matrix given in (7.13), let us instead use the transformation matrix

We then have

Note from (7.19) and (7.20) that C ^-1 = ( C^T )* . We can therefore state C( C^T )* = I₃ , where I₃ is (3 × 3) identity matrix. Therefore the transformation matrices given in (7.19) and (7.20) are orthogonal. Now since

we can write from (7.17)

We shall now discuss how different elements of a power system are represented in terms of their sequence components. In fact we shall show that each element is represented by three equivalent circuits, one for each symmetrical component sequence.