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 Thevenin 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.