  Coordinate transformations significantly simplify power systems computations.
Most notably, the classical Clarke and dq0 transformations are widely used in
three-phase systems, as together they transform balanced abc quantities into
constant-valued signals. However, during unbalanced operation, the utility of
these transformations diminishes, since a null 0 coordinate cannot be ensured
and oscillating signals emerge. While recently proposed transformations ensure
a null 0 coordinate, they still do not lead to constant-valued signals in the
dq0 domain. In this letter, we propose a generalized vector locus
transformation that ensures both a null 0 coordinate and constant-valued
signals. Moreover, we show that, in the balanced case, the classical
amplitude-invariant Clarke transformation is an instance of the proposed
transformation.
