In the analysis of power-electronic-based energy conversion systems, it is important to identify the operational modes of the associated converters and inverters. However, as the number of switching elements increases, it becomes more difficult to analytically establish all possible modes of operation. In this paper, a modelling technique is described wherein a state-space representation of the overall system is generated automatically and updated dynamically as each new topology is encountered. Utilizing this approach, it becomes possible to identify the operational modes of converters and inverters based upon the cyclically repeated sequences of topologies that can be observed during steady-state operation. To demonstrate this technique, an example system comprised of a 6-phase synchronous machine, rectifier, and interphase transformer is considered. This system exhibits several distinct modes of operation that depend upon specific circuit connections. These operating modes are automatically identified using the proposed methodology and the results are compared with measured dynamic performance.