Dynamic Stability Calculations for an Arbitrary Number of Interconnected Synchronous Machines

Describing the small signal performance of a multi- machine synchronous power system by a set of differential equations of the form x = A x allows standard multivariable control theory to be used in dynamic stability studies. The construction of the A matrix for a multimachine power system involves the application of Kron's rotational transformation to the transmission network admittance matrix, and a matrix analysis of the synchronous machines using internal flux linkages as state variables.