Linearization of periodic power electronic-based power systems for small-signal analysis

Integrating power electronics to the grid has introduced new small signal-signal stability challenges, which are commonly studied with average time-invariant models and, more recently, with harmonic state-space models. In both approaches, it is common to obtain the models by following an analytical formulation, which can be tedious and impractical in systems with different controllers and topologies, just to mention a few examples. This paper proposes a numerical approach based on shooting methods and the recursive evaluation of the time-variant Jacobian along the steady-state orbits to construct automatically a periodic linear time variant model and its respective linear time-invariant model using the extended harmonic domain; these models include explicitly the harmonic components. The proposed modeling approach can be applied to systems with different converter topologies, controllers, and modulation techniques. A nonlinear periodic switched system (grid-connected parallel inverter-based microgrid) is used to validate the proposed linearization approach.