Solution of State Equations in Terms of Separated Modes with Applications to Synchronous Machines

Using a special linear transformation, a linear time invariant state model can be changed into a new form defined as the separated mode model. As this transformation is repeated, the state model tends to be separated into two decoupled or independent parts. Each of them is a lower dimensional state model. The solutions of the two are the fast and slow components of the original state model respectively. Applying this approach to induction and synchronous machines, new linearized reduced order models are obtained. Computation results have shown that the new models have lower dimension and higher accuracy than the common one which neglects stator transients (pψ terms).