Evaluating Time Step Effects in Shifted-Frequency Analysis for Converter-Dominated Power Systems

Open Source Modelling and Simulation of Energy Systems (OSMSES), pp. 1–6

Abstract

Modern power systems are increasingly dominated by power electronic converters, motivating simulation approaches that balance accurate representation of electromagnetic and control dynamics with feasible computational effort. Shifted-Frequency Analysis (SFA) using Dynamic Phasors (DP) provides an approach intermediate between Electromagnetic Transient (EMT) and Root Mean Square (RMS) simulations. This paper analyzes how time step selection affects shifted-frequency resistive companions for linear dynamic elements using the Trapezoidal Rule (TR) and Backward Euler (BE) integration methods. For both TR and BE, small time steps recover the corresponding EMT resistive companions written in DP variables, while large time steps yield the Quasi-Static Phasor (QSP) admittances. The main difference lies in the history current sources: for TR, their vanishing in the large time step limit requires a steady-state phasor assumption, whereas for BE they decay asymptotically for bounded signals. Using the open-source library DPsim, the paper further evaluates how these effects manifest in a non-linear converter-dominated system. In the numerical example, SFA-TR remains closer to the EMT reference at small time steps, whereas SFA-BE introduces numerical damping at RMS-size time steps and approaches the RMS response more closely.

Authors 3

1. Georgii Tishenin Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Aachen,Germany

2. Armin Teskeredžić Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Aachen,Germany

3. Antonello Monti Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Aachen,Germany