Identification of groups of -coherent generators

It is observed that for a power system after a disturbance certain groups of generators have similar waveforms for their rotor-angle response curves. We define generators to be coherent if the waveforms of the rotor-angle curves are identical. In practice, however, they may be very close but not identical. We say that generators are -coherent if the maximum of the difference of their angle curves is less than . We present necessary and sufficient conditions for a group of generators to be -coherent under a set of disturbances. The condition is expressed in terms of the controllability Grammian of the model. Singular-value decomposition (SVD) of the Grammian is used to provide insights to the results. We also derive an approximate expression for the Grammian and suggest a method for identifying groups of -coherent generators.