Index Matrices—Based Software Implementation of Power Electronic Circuit Design

Abstract

This article aims to present a comprehensive approach with corresponding software that uses index matrices. They have been developed by the authors for an automated model-based design. One of the main goals of this paper is to propose a simple model solving technique for powering electronic devices (particularly, for all subsystems: power supplies, static power converters, electric filters, electrical loads, control systems, etc.). Index matrices, which contain first-order discrete dynamical system parameters, with real numbers as elements, are constructed in order so that voltages, amperages, and discrete values can be calculated. Simulations on a three-phase converter, as well as simulations on buck and boost DC-DC converters with PI controllers, are presented. The function of the proposed software (with examples on the aforementioned devices) is considered, and diagrams of its basic programming classes are shown. The latter draws electronic schemes and their respective graphics, and provides important characteristics. Simulink is used to verify results. Advantages of the proposed approach are a higher speed of calculations (compared to Simulink, due to a lack of differential equations) and a simpler handling of various electronic components. Additionally, a computational scalability is demonstrated.

Index Matrix-Based Modeling and Simulation of Buck Converter

“…All index matrices with real numbers as elements (R-IM) [13,14] have the form A = K, L, a k,l k∈K,l∈L ⊂R (1) with index sets (called the first and second one, respectively) K = k 1 , k 2 , . .…”

“…On the other hand, because of the presence of power and control parts (controllers), which are quite different and mutually influence and complement each other, in many approaches, electronic converters are not susceptible to modeling as a whole unified system. One of the main purposes of the authors' papers has been to present a joint technique based on the apparatus of index matrices [1,2].…”

“…In the present paper, each switch is considered to have two modes too, but the transistor and the diode work out of sync. Such a principle requires variants to be checked and, similarly, determines the exponential dependence of the number of variants on the number of switches [1]. However, the latter is not large in power electronic devices; in the following sections, the transistor and the diode determine four modes.…”

“…Data structures, which implement index matrices in the programming class IndexMatrix, are demonstrated in [1]. There are implementations of all operations from Section 2, except the new one, in this class too.…”

“…There are implementations of all operations from Section 2, except the new one, in this class too. The .NET application, which is presented in [1], concerns analog and digital electronic components and circuits, model solvers, graphics, etc. Its basic feature is the shorter simulation duration compared to Simulink; it has about a 20 times shorter runtime in the case of the considered buck converter and about a 10 times shorter runtime in the case of a three-phase converter.…”