Analysis and control of power converters with instantaneous constant-power loads
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This dissertation examines the effects of instantaneous constant-power loads (CPLs) on power converters. These CPLs are prevalent in distributed power architectures and are also present in certain motor-drive applications. CPLs introduce a destabilizing nonlinear effect on power converters through an inverse voltage term that leads to significant oscillations in the main bus voltage or to its collapse. Boundary control is studied in order to stabilize dc-dc converters with instantaneous CPLs. The three basic topologies are studied: buck, boost, and buck-boost. Converter dynamics are analyzed in both switching states and the various operating regions of switch interaction with a first-order switching surface are identified. The analysis reveals important characteristics of CPLs. For non-minimum phase converters, in order to avoid issues related with the fact that the closed-loop state-dependent switching function is undefined on the switching surface, reflective mode solutions to both converter systems are defined in the sense of Filippov. Sufficient conditions for large-signal stability of the closed loop converter operating points are established. It is shown that first-order switching surfaces with negative slopes achieve large-signal stability, while positive slopes lead to instability. In particular, for the boost converter it is illustrated via simulations and experiments that positive slopes may lead to another closed-loop limit cycle. It is also shown that instability as well as system-stalling, which is termed the invariant-set problem, may still occur in reflective mode. However, a hysteresis band that contains the designed boundary may be used to prevent system-stalling, and also allow for a practical implementation of the controller by avoiding chattering. Regulation is also achieved. The dynamic behavior of single-phase full-wave uncontrolled rectifiers with instantaneous CPLs is also explored. Stable operation is shown to be dependent on initial condition and circuit parameters, which must fall within reasonable ranges that validate a CPL model. A necessary condition for stable operation of the rectifier system is thus derived. Furthermore, input and output characteristics of the rectifier with a CPL are investigated, and comparisons are made with the resistive case. A more complete model for the rectifier system that incorporates line-voltage distortion is also utilized to study the rectifier system. Simulations and experimental results are included for verification.