Advances to the dynamic analysis of power converter-based systems under uncertainty: A reachability approach

Converter-based generation must comply with modern grid-code interconnection requirements. The grid codes typically prescribe broad envelopes of transient voltage profiles for which generation must remain connected while supporting the recovery of the grid by injecting reactive power. Rigorously proving compliance via a finite number of deterministic simulation studies is cumbersome, if not impossible, due to the infinite number of conceivable events within the prescribed curves. This dissertation sets forth a reachability analysis approach to tackle this problem. The advantage of the method is that it permits the study of systems with unknown-but-bounded uncertainties. In particular, the technique yields state-space sets that are guaranteed to contain all possible trajectories of a dynamic system that originate from a set of prescribed initial conditions and/or driven by unknown-but-bounded disturbances. The method is applied to study the voltage ride-through capability of two common converter-based wind turbine systems, which employ permanent magnet synchronous generators and doubly fed induction generators, respectively. In addition, this dissertation contributes a novel reachability analysis framework for studying linear dynamic systems with uncertain initial conditions and inputs. The proposed method accepts uncertain inputs that are constant, arbitrary, or ramp limited. A distinctive characteristic of this method is that reachability analysis is conducted using the modal information of the system dynamics. The method is applied on a notional shipboard power system with uncertain pulsed loads