Modeling, Design and Control of Power Converters

This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck) regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current (DC-AC) inverter. These are widely used for power transfer in a variety of industrial and personal applications. This motivates the precise quantification of conditions under which existing modeling and design methods yield satisfactory designs, and the study of alternatives when they don’t. This dissertation describes a method utilizing Fourier components of the input square wave and the inductor-capacitor (LC) filter transfer function, which doesn’t require the small ripple approximation. Then, trade-offs associated with the choice of the filter order are analyzed for integrated buck converters with a constraint on their chip area. Design specifications which would justify using a fourth or sixth order filter instead of the widely used second order one are examined. Next, sampled-data (SD) control of a buck converter is analyzed. Three methods for the digital controller design are studied: analog design followed by discretization, direct digital design of a discretized plant, and a “lifting” based method wherein the sampling time is incorporated in the design process by lifting the continuous-time design plant before doing the controller design. Specifically, controller performance is quantified by studying the induced-L2 norm of the closed loop system for a range of switching/sampling frequencies. In the final segment of this dissertation, the inner-outer control loop, employed in inverters with an inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the loop broken at the error and the control are examined, demonstrating that traditional methods only address these properties for one loop-breaking point. New controllers are then provided for improving both sets of properties.