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

Abstract

Abstract-Co-simulation opens new opportunities to combine mature ElectroMagnetic Transients (EMT) and Phasor-Mode (PM) solvers, and take 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 sub-system by a proper multiport equivalent when simulating the other sub-system. 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 sub-system with several interface buses.

Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits

“…Finally, also the phase currents can be readily obtained by the inverse Clarke transformation (19). After simple algebra, we obtain:…”

“…The proposed analytical approach provides theoretical insight into the comprehension of asymmetrical transients by explaining the role of each Clarke modal circuit in the determination of the time-domain phase variables. A comparable analytical contribution is not available in the relevant literature, whereas the literature concerning the numerical simulation of transients in three-phase systems is vast (e.g., see [7,[18][19][20][21][22]). In particular, time-domain and frequency-domain analysis of asymmetrical transients has proved to be effective in the characterization of faults in electrical machines, power lines, and power electronics systems [23][24][25][26][27][28][29][30][31][32].…”

Multi‐platform real‐time microgrid simulation testbed with hierarchical control of distributed energy resources featuring energy storage balancing

“…The network is modelled in the phasor domain to reduce the computational burden incurred by typical electromagnetic transient (EMT) or transient stability (TS) simulations. However, this method does not capture transients between steady-state conditions, so for accuracy and speed, a hybrid EMT-TS simulation, like those described in [23,24] is implemented. The OPAL-RT is capable of real-time simulation using phasor domain TS simulation via its ePHASORsim component, and EMT simulation via its eMEGAsim component to make a more accurate model for approximately the same computational burden while retaining the ability to interact with the system realistically during simulation.…”

Research, Development and Application of Hybrid Model of Back-to-Back HVDC Link

“…Mainly such hybrid simulators are based on a combination of different simulation approaches [3,5,6,7,8,9,10]. For instance, in [3,5,7], the authors have proposed both applications of Electro-Magnetic Transient (EMT) and Phasor-Domain simulation methods. In such cases, the EMT is used to simulate a detailed three-phase mathematical model of EPS and the typical calculation of the time-step is found to be less than 10µs, but only for small and the most interesting part of EPS due to the limited computational resource of a processor.…”