Design verification of power electronics systems subject to bounded uncertain inputs

Abstract

This thesis proposes a new methodology for design verification of power electronics systems subject to bounded uncertain inputs. In this method, the power electronics system, which consists of the power electronics converter circuit and the associated controller, is described by a switched-linear state-space representation, where some or all of the inputs may vary without control over some bounded range (e.g. load current, source voltage). The method relies on the solution to the reachability problem associated with this system, which is the computation of the set of all possible system trajectories that arise from different initial conditions, uncontrolled inputs, and inherent switching. The system design verification problem is solved by verifying that this set, called the reach set, remains within a region of the state-space defined by performance requirements (e.g. Existing power electronics system design verification methods rely heavily on time-domain simulations. For each simulation, the set of possible inputs is randomly sampled to obtain a particular operating condition. A very large number of simulations are required in order to verify the behavior of the system for all possible operating conditions. These simulation-based methods also typically rely on the small-signal average model of the power electronics system. This model ignores the effects of switching and is only valid ii for small perturbations around the nominal operating point of the system. With the proposed methodology, it is only necessary to solve one set of matrix differential equations to account for all possible operating conditions. Furthermore, the proposed method uses a switched-linear model of power electronics systems, which is capable of capturing the full large-signal behavior of the system. Thus, the proposed methodology aims to produce a complete and computationally tractable solution to the power electronics system design verification problem.iii To Boompa iv

A Reachability-Based Method for Large-Signal Behavior Verification of DC-DC Converters

“…Finally, it follows from (14), (15), and (16) that (17) Therefore, the regulation requirement is met if and only if (18) The conditions given in (18) also apply to all other examples discussed later in this section.…”

“…6 Following the notation in (15), is given as [4.93, 5.48]. From (17), it follows that . From (18), we conclude that meets the 7.5% voltage regulation requirement.…”

“…The use of large-signal switching models was proposed in [17], where input variations were contained in an ellipsoidal set. This paper substantially extends [17] by: i) providing a precise formulation of the reachability problem in dc-dc converters; ii) tailoring ellipsoidal-based reachability tools to cases when the input space is defined by a symmetric polytope; iii) providing a more detailed analysis of open-and closed-loop controlled buck and boost converters; iv) providing a detailed comparison of the computational performance of the proposed method with simulation-based Monte Carlo methods; and v) providing a method to address parametric uncertainty.…”