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Analysis of the fundamental modes of oscillation plays a crucial role in assessment of the power system dynamic performance and control design to suppress undesirable modes. Multivariable state space representation overcomes some of the hidden dynamics related difficulties. Only a small part of the system pole spectrum is controllable-observable. Modal approximations of the transfer function matrix using dominant poles identified through dominant residues reduce computation volume. Projecting the state-space on the dominant eigen space preserves the system behaviour.