Numerical Methods for Transient Field-Circuit Coupled Simulations Based on the Finite Integration Technique and a Mixed Circuit Formulation

The objective of this work is to propose effective and reliable higher order time integration schemes for electromagnetic field-circuit coupled problems. According to the classification criteria listed above, a strong coupling is implemented, i.e., field and circuit unknowns are treated together. The numerical integration process is implemented in a monolithic way. The structure of the work is as follows: in the next chapter relevant fundamental concepts are discussed. First of all, the foundations of the electromagnetism are in the focus of consideration. Quasistatic field regimes and the conditions required for the appropriate field classification are elaborated. Secondly, a brief introduction to the applied method for spatial discretization, the Finite Integration Technique, is presented. Main principles and ideas of the method are listed. Finally, some elements of linear circuit analysis are discussed. These three sections of the second chapter can be considered as the foundation blocks for the field-circuit coupled analysis. In the first part of the third chapter, the external circuit description and the network topology are considered. After that the basic types of the conductor models are discussed. Finally, a transient electromagnetic field-circuit coupeld formulation is derived. The fourth chapter starts with a numerical analysis of the derived formulation and considers the applications of standard time integration schemes to this formulation using test examples. The subject of the final part of this chapter is the higher order integration methods, namely Runge-Kutta methods, and their usage for the numerical integration of field-circuit transient formulations. Adaptive time integration schemes are then considered and their application to the coupled formulation is illustrated by a test problem. In the first part of the fifth chapter, an efficient numerical technique for adaptive integration of problems with sinusoidal dynamics is developed. An envelope integration of electromagnetic problems based on the separation of slow and fast varying dynamics is presented in the second part of this chapter. All proposed numerical technique are illustrated with appropiate numerical examples. The subsequent sixth chapter covers important aspects of the numerical integration of field-circuit coupled problems with switching elements. A particular approach allowing to use standard time integration schemes for DAE systems with discontinuities appearing in the system due to the presence of switching elements is given. Finally, two numerical examples are presented: a step-up converter with a conduction coil and a three-phase transformer coupled to a power electronic network. The work is concluded with a short summary