Multirate and multi-stage holomorphic embedding for dynamic simulation of systems of differential-algebraic equations

Abstract

In this paper, we present a novel multirate (MR) extension to the multi-stage holomorphic embedding (MSHE) method and use it to dynamically solve systems of differential-algebraic equations. As a test of real-world applicability, we analyze the algorithm for typical power system cases. When applied to the IEEE 34 bus and IEEE 9 bus benchmark system, the multirate approach significantly reduces the number of recalculations of most variables as compared to the existing MSHE algorithm, thus offering the chance of decreasing simulation time while providing simple means of error control. This integration of a multirate ansatz into the well-established MSHE solver potentially opens up systems for dynamic simulation that were up to now out of numerical reach.