Mitarbeitende

The efficient energy conversion between different voltage levels is an essential part of today's energy supply. In recent years electronic power conversion has become more and more important. Examples can be found in many household appliances (e.g., mobile phone charging, computer power supply), regenerative energies (e.g., wind, photovoltaic), transportation (e.g., electric vehicles, trains), and industrial applications (e.g., welding, induction heating). The conversion is accomplished using power electronics (e.g., buck converters, inverters) instead of conventional transformers. These devices are cheap in production, light in weight, require little space and are easily controllable if a compensation of changing load is necessary. Electronic power converters use transistors to switch on and off the DC input voltage to obtain in average the desired output voltage at the output of the converter. Filters, mostly passive low-pass filters, are used to smoothen the output voltage. To obtain a well designed power converter in terms of efficiency, computer simulations are a reliable tool. Time stepping algorithms are often used to solve the differential equations describing the converters. If simplifications are used, e.g., ideal transistors and diodes, the algorithm needs to be equipped with an additional switch event detection. Since the switching frequency of modern converters can be very high, i.e., up into the MHz range, this conventional time stepping is inefficient since every switching event has to be resolved to guarantee a reasonable accuracy. This research focuses on developing a more efficient means to simulate power converters. A mathematical concept called Multirate Partial Differential Equations (MPDEs) is used. It allows to split the solution into components of different rates. These components evolve along different artificial time scales. The MPDEs are solved using two methods namely a Ritz-Galerkin approach combined with a conventional time stepping. Speedups in computation time of up to 1000 could be observed so far.