| The main contribution of this thesis is to analyze, and also to propose design criteria for, linear and nonlinear controllers applied to DC-DC converters feeding downstream power converters. This topology is the basic configuration for power electronics based distributed power systems (DPS). DPS share a common characteristic, which is the connection in cascade of power converters. In this architecture, a primary power converter regulates the voltage of a common DC distribution bus where power converters acting as load are connected. Load power converters can be motor drivers or DC-DC converters that perform, in stages, the final voltage regulation required by the final loads. Due to the voltage regulation loop included in the load converters, these units present a behavior similar to a constant power load (CPL) at input terminals. Its dynamic behavior is equivalent to a dynamic negative resistance, destabilizing the DC bus and consequently the system.; This work develops a systematic non-linear analysis of power converters operating in cascade based on the phase-plane and geometric considerations of the vector field defined by the differential equation modeling the system. A large-signal averaged model of the converter is considered to include in the controller design not only the behavior around the operation point but also the behavior of the converter operating in different modes and in saturation. The topology of the vector field for different power converters and simple controllers is first analyzed considering an ideal CPL to model the load presented to the primary converter by the downstream converters. DC-DC power converters loaded by ideal CPL present a unique phase portrait with several equilibrium points defining only local convergence of the operation point of the system. For simple cases, the region of attraction can be analyzed using the phase-plane, where the boundary of that basin is mainly defined by the stable manifold of the unstable equilibrium points. This preliminary study allows extending the analysis to more realistic cases, which are DC-DC power converters including over-current protections and load models that consider the start-up behavior of downstream converters. The additional non-linearities included in the model set new equilibrium points and redefine the region of convergence of the operation point. For low order systems, the phase plane analysis gives a simple tool to analyze the interaction between the primary source and load converters and design the primary controller and its protections. Based on general properties of the model, the analysis can be extended to higher order systems that include both dynamics in the controller and more complex converters. Similar conclusions can be extrapolated about the basin of attraction of the operation point for those systems. |
