The combination of multi-rate integration algorithms with automatic error control and equation-based, object-oriented Modelica models opens up very interesting perspectives for the flexible and efficient simulation of smart grid systems. In this paper, the model of an idealized power system possessing some of the multi-domain, multiple-time-scale dynamics of smart grid models is presented and used as a test case for a novel TR-BDF2 multi-rate integration algorithm. Promising results are obtained, which motivate further research in this direction.