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This is just one of the ways:

Choose the variables couple in question defining the SISO form of the system. Write out the state space matrix commonly denoted as "A" of the synchronous machine. Calculate the eigenvalues of that matrix. Then calculate the residues of the matrix with respect to the selected SISO system (the chosen variables in question define the input matrix B and output matrix C). The eigenvalues are the zeros of the transfer function while the residues are the constants in the fractionally partitioned form of the transfer function.

The matrices I was talking about define the linearised system in the form :

dx/dt=Ax+Bu

y=Cx

For a more thorough explanation see

Power System Stability And Control By Prabha Kundur
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Explain open-loop transfer function of a close system?

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