Index Matrix-Based Modeling and Simulation of Buck Converter

The approach described in this paper handles the parameters and characteristics (analog and discrete ones) of a Buck DC-DC converter (in its power and control parts) in a common manner. The usage of probably complicated differential equations for discrete dynamical systems is avoided by means of index matrix equations, which can be easily understood. Compared to classical matrix models, the proposed index matrix models are more descriptive and also smaller in size. Such functionality is widely applied by the authors, and a new operation is defined and used as well. The relevance of the proposed techniques in power electronics, because of switching topologies and a limited numbers of components, is argued. Respective examples of functioning modes of the considered converter, in which power circuits and controllers are modeled jointly, are given. Estimations of analog values are based on partly linear dependencies, which are shown to be adequate in first-order analyses. Specific expressions for a Buck DC-DC converter are presented. A model-solving technique and an exhaustive search on a parameter space are considered in detail and automated via well-formalized algorithms. Nested parameter intervals and verifications with normal probability distributions are used in an optimization procedure. The full agreement of implementation via MATLAB source code with results obtained via Simulink is demonstrated. The short simulation times of this software (compared to Simulink and a .NET desktop application developed by the authors) justify the search for optimal variants in a wide multi-dimensional space. A max–min procedure with 10,000 simulations in each verification step is presented.