s-domain methodology for assessing the small signal stability of complex systems in nonsinusoidal steady state

The paper gives the outline of a generalized small signal stability analysis of the periodic steady state, which includes harmonics, for systems with complex components. These could be (switched) time-varying, or nonlinear components, possibly also rotating machines and transmission lines represented as elements with distributed and frequency-dependent parameters. It is assumed that a harmonic power flow solution exists. Its stability analysis by linearization along the known limit cycle should be computationally too expensive. However, linearization of the individual components results in linear, time-periodic (LTP) models. The proposed solution is based on equivalencing the LTP models with standard linear time-invariant (LTI) components. The methodology is illustrated on a small system with a periodic steady state that may be either stable or unstable.