On the convergence of relaxation schemes to couple phasor-mode and electromagnetic transients simulations

Abstract

Abstract-Hybrid simulations combining phasor-mode and electromagnetic transients models aim at taking advantage of computational speed of the former and accuracy of the latter. For simulation accuracy, a relaxation process is used, which consists of iterating between both models. The convergence properties of this relaxation process are investigated. The speed of convergence is assessed when the variables exchanged at the interface between both models are respectively pure voltage/current sources, Norton/Thévenin equivalents, or a combination of them. Iteratively updated Norton/Thévenin equivalents are shown to drastically reduce the number of relaxation iterations.

Co-Simulation of Electromagnetic Transients and Phasor Models: A Relaxation Approach

“…One issue tackled in this paper is the proper choice and update of the multi-port equivalent attached to those interface buses. This is an extension of the authors' previous work reported in [9], [10].…”

“…It was found that the conditions of type (a) did not make the iterations converge (even in steady-state conditions). All other boundary conditions led to convergence, and yielded the same dynamic response [9]. The performances of type (c) vary too much from one case to another; type (d) is consistently the best.…”

“…It must be noted that the choice between Norton and Thévenin is arbitrary, as for each one there is an equivalent model in the other representation. This approach can be already found in [13], while further investigations have been reported in [7], [9], [10]. Nevertheless, the above references report on results with a single boundary bus, and on small test systems.…”

“…The terms of higher frequency present in the EMT simulation outputs are filtered out as "measurement noise" by the leastsquare fitting. Owing to the presence of the cosine component in (9), T x should be at least equal to one period at fundamental frequency ω nom /2π.…”

A relaxation scheme to combine phasor-mode and electromagnetic transients simulations

“…This assertion is supported by numerical results in [8], where the rate of convergence of the relaxation scheme is assessed under the assumption that the EMT and PM subsystem behave linearly.…”