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A Comparison of Numerical Integration methods and Discontinuity Treatment for EMT Simulations

A variety of numerical integration methods are currently being used for simulating electromagnetic transients in commercial software and experimental codes. This paper intends to provide a review and comparison of these methods for time-domain in-tegration, including 2S-DIRK, ARTEMiS art 5 solver, and a semi-analytical matrix exponential-based method. The possibil-ity of utilizing these methods is explored for reliable and effi-cient treatment of discontinuity, which is known to give rise to numerical oscillations for the widely used trapezoidal method. Case studies are conducted to show the strengths and limitations of these methods and their combinations.A series of case studies that cover the most typical electromagnetic transient phenomenon and power system devices are conducted to show the strength and limitations of these methods and their combinations. For example the 2S-DIRK method, which provides sufficient accuracy and L-stability from theoretical analysis, is observed to exhibit overly damping and suppress the actual fast transients in some cases, which is contrary to what was reported in previous publications. The matrix exponential method is shown to possess superior accuracy and free from numerical oscillations due to its analytical nature, but its implementation in EMTP framework is not straightforward. This also is the case for Art5, which is a state space solver that uses low order approximation of the exponential. The State-Space-Nodal (SSN) technique is used to integrate these methods into the EMTP framework. More in-depth discussion is provided in the paper.
Finally, recommendations of the numerical methods are made based on their impact on the simulation result accuracy, numerical efficiency, ease of implementation, robustness for handling discontinuity, and scalability to large scale studies.

Author(s):

Xiaopeng Fu    
Polytechnique de Montréal
Canada

Serigne Mouhamadou Seye    
Polytechnique de Montréal
Canada

Jean Mahseredjian    
Polytechnique de Montréal
Canada

Ming Cai    
Polytechnique de Montréal
Canada

Christian Dufour    
OPAL-RT Technologies
Canada

 

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