Frédéric Plumier

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

This paper deals with a new scheme for coupling phasor-mode and electromagnetic transients simulations. In each simulation, an iteratively updated linear equivalent is used to represent the effect of the subsystem treated by the other simulation. Time interpolation and phasor extraction methods adapted to this scheme are presented and compared to existing methods. Finally, simulation results obtained with a 74-bus test system are reported.

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

Co-simulation opens new opportunities to combine mature electromagnetic transients (EMT) and phasor-mode (PM) solvers, and takes advantage of their respective high accuracy and execution speed. In this paper, a relaxation approach is presented, iterating between an EMT and a PM solver. This entails interpolating over time the phasors of the PM simulation, extracting phasors from the time evolutions of the EMT simulation, and representing each subsystem with a proper multiport equivalent when simulating the other subsystem. Various equivalents are reviewed and compared in terms of convergence of the PM-EMT iterations. The paper also considers the update with frequency of the Thévenin impedances involved in the EMT simulation, the possibility to compute the EMT solution only once per time step, and the acceleration of convergence through a prediction over time of the boundary variables. Results are presented on a 74-bus, 23-machine test system, split into one EMT and one PM subsystem with several interface buses.

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

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 of finite element and circuit solvers using optimized waveform relaxation

This paper focuses on a comparison of the co-simulation schemes for coupled problems with application to coupled electromagnetic field and power-electronic simulations. A co-simulation framework between a finite element solver and a circuit solver based on the waveform relaxation scheme results in an iterative process whose convergence depends on the kind of transmission coupling conditions (TCC) on the interface between the sub-problems. The convergence of TCC is illustrated on two test cases: a boost converter and a switched reluctance motor drive.