  In a power system, when the participation factors of generators are computed
to rank their participations into an oscillatory mode, a model-based approach
is conventionally used on the linearized system model by means of the
corresponding right and left eigenvectors. This paper proposes a new approach
for estimating participation factors directly from measurement data on
generator responses under selected disturbances. The approach computes extended
participation factors that coincide with accurate model-based participation
factors when the measured responses satisfy an ideally symmetric condition.
This paper relaxes this symmetric condition with the original measurement space
by identifying and utilizing a coordinate transformation to a new space
optimally recovering the symmetry. Thus, the optimal estimates of participation
factors solely from measurements are achieved, and the accuracy and influencing
factors are discussed. The proposed approach is first demonstrated in detail on
a two-area system and then tested on an NPCC 48-machine power system. The
penetration of inverter-based resources is also considered.
