Contribuição ao uso de métodos formais no estudo de circuitos de eletrônica de potência.

Abstract

This thesis presents an alternative method to the simulation process of power electronic circuits, composed by power processors and a controller, named conversor. Computer simulations are normally used to analyze the behavior of power electronic circuits, and do not guarantee a reliable adjustment to the results attained while evaluating, for example, the effect of either any set of initial conditions or parametric deviation in the circuit components. The alternative technique proposed in this work comprehends the use of formal methods to obtain a model for power circuits, to analyze and verify the behavior of these systems, and to redesign a new controller from a set of desired specifications as well. Power electronic circuits exhibit a continuous and discrete dynamics, which is a typical feature of hybrid systems. This work introduces a systematic procedure to derive a mathematical model that captures the hybrid behavior of these systems as hybrid automata. The model of the hybrid automaton obtained is based on the representation of the structure of a converter, as a result of an assembly method of blocks that represent the components of such converter. The modeling procedure allows dealing with the improvement of semiconductor circuit devices as well as the existence of uncertainties in the input signal, for both constant and time variant input. Once obtained the hybrid automaton, which represents the formal model of the power circuit, methods are developed to verify its properties by using the reachability analysis on the hybrid system state-space itself. The methods of verification make possible the analysis of properties such as the compatibility of current and voltage values in the circuit components under specified limits, the fault occurrences when the current and voltage values exceeds the rupture limits, the voltage level necessary to turn on a semiconductor device, the compliance of the steady-state current and voltage values as desired, etc. Finally, methods to automatically redesign a controller were implemented. The controller goal is to guarantee that every reachable state of the system will converge to a set of reliable configurations, as specified in the design. By using this approach it is possible to get around several problems that may occur in the industrial automation, and in particular, concerning the power electronic circuits.