Mathematical model of frequency inverter with autonomous voltage inverter

An analytical analysis of the processes occurring in the systems of an electric drive with a frequency converter, which are characterized by discrete, nonlinear properties, is practically impossible. This predetermines the need to use methods of mathematical modeling and mathematical experiment to study the properties of such systems. Purpose of the work: building a model of a frequency converter with formalization in the form of mathematical relationships of the relationships between the variables characterizing its functioning, based on the analysis of physical processes in each of its elements. Mathematical models of each element must be represented by structural diagrams, which are subsequently combined into a common block diagram of the frequency converter in accordance with the method of structural modeling. Research methods: to solve the set tasks, the methods of the theory of electronics and electrical engineering, induction devices and the concept of switching functions were used. Software implementations of the proposed mathematical models and numerical studies of the processes reproduced by them were performed in the MATLAB computing environment (SIMULINK application software package). Results: the method of structural modeling made it possible to create a fairly universal and flexible version of a complete mathematical model of a frequency converter, due to the possibility of a fairly simple inclusion in it of various options for mathematical models of elements included in a specific real frequency converter. In this case, the resulting model preserves the topology of a real frequency converter and the observability of all its real physical variables. The use of the theory of induction devices and the concept of switching functions made it possible, on a single methodological basis, to create physically and mathematically grounded mathematical models of all the main elements of the frequency converter. The constructed model makes it possible to clarify the relationship between the physical variables of the individual elements of the frequency converter and their mutual influence.