Modeling and Simulation of Power Electronic Circuits using Piecewise Smooth Differential Algebraic Equations

In the fields of power electronics and power systems, the modeling and simulation of switching converter circuits is often performed using idealized switch models instead of detailed semiconductor models. For such circuits, conventional circuit simulation methods are not directly applicable because the resulting differential algebraic equations (DAEs) are non-smooth and possibly discontinuous. Therefore, most existing power electronic circuit simulation tools reconfigure the circuit equations after each switch event so that the resulting DAE can be considered as smooth between switch events. This approach introduces several difficulties, necessitating advanced mathematical treatment and specialized numerical methods. This thesis introduces piecewise smooth differential algebraic equations as a new mathematical model class to facilitate the analysis of power electronic circuits with idealized switches. The new model class is used to formalize the required solution procedures and clarify the difficulties associated with switch events. Two other contributions of the thesis focus on improving the computational efficiency of existing methods. First, a new method for integration and interpolation is developed. With this method, fewer simulation steps are needed between switch events to achieve the same accuracy. The method is therefore useful for the simulation of circuits with a high switching frequency. Second, a circuit partitioning technique is introduced to reduce the computation time for matrix refactorization at switch events in simulation studies with a large number of switching devices.1. Introduction 2. Literature Review 3. Model Composition 4. Piecewise Smooth DAEs 5. Similarities with Complementarity Modeling 6. Solving Power Electronic Circuits 7. Numerical Integration and Interpolation 8. Circuit Partitioning 9. Conclusionsnrpages: 284status: publishe