Parallel 3-D Finite Element Modeling for Electromagnetic Transient Simulation

• Author / Creator

  Jiacong Li

• Electromagnetic devices, such as transformers and power reactors, are widely used in power systems. Traditionally, these essential components are simplified into lumped net-works in power system electromagnetic transient (EMT) simulations. However, the traditional lumped network model cannot always accurately represent the transient behaviors of these inductive components, especially when complex physical phenomena are encountered (such as magnetic saturation, eddy currents, and hysteresis). On the other hand, the finite element method (FEM) has become a powerful tool to solve complex physical fields, due to its superior accuracy, and the ability to handle complex geometries and material properties. Therefore, researchers have been giving increasing attention to finite element models for energy system EMT simulations in recent years to achieve high precision designs.
  Despite the excellent accuracy, finite element models, comparing with lumped networks, require a dramatically larger amount of computational power. This is a result of the following facts. The device space and electromagnetic field are discretized into many smaller elements and innumerable degree of freedoms (DOF or unknowns) to be solved. This leads to an ‘oversized’ nonlinear matrix system. Also, to handle the nonlinearity, traditional Newton-Rapson (NR) solvers need to repetitively form and factorize the large matrix system, which significantly slows down the simulation.
  With the fast development of parallel computing hardware, researchers have recently introduced the transmission line modeling (TLM) and the nodal domain decomposition method to boost 2-D finite element models. These novel ideas eliminate the traditional repetitive matrix assembly (forming) and factorization during the NR solving process, and their DOF-level parallelism leads to significant speed-up compared with commercial FEM software. However, the above fast algorithms are based on 2-D nodal finite elements, while in reality, power system devices are in 3-D geometry, and simplification from 3-D to 2-D causes excessive information loss. Also, the nodal element leads to significant errors around sharp geometries. 3-D edge finite elements, in contrast, do not have the above shortages, while similar algorithms are rarely seen in 3-D edge FEM.
  In this thesis, the above high-performance massively-parallel methods are further ex-tended to 3-D edge-finite-elements-based EMT simulation models. Challenges due to the different nature between 2-D nodal and 3-D edge element formulations are successfully tackled, and parallelism is explored from different perspectives.
  First, the TLM algorithm is developed to solve nonlinear 3-D edge element problems with parallelism explored at each elements’ viewpoint. Transmission lines are deployed to decouple each element’s local nonlinearity from the global ‘oversized’ matrix. Benefitting from such isolation, the method only requires massively-parallelized small local Newton-Rapson iterations in each element, which is perfectly suitable for GPU architectures. The decoupling also allows constant global admittance matrix. Thus, the repetitive formation and factorization process of the large global matrix are avoided.
  Second, from edge’s view, the edge domain decomposition (EDD) method is proposed to parallelize nonlinear 3-D edge element problems at edge DOF level. The electromagnetic device’s entire space is divided into many sub-domains that only contain one edge unknown. The solution of light-weight nonlinear sub-domain systems can be massively parallelized, and the neighbor-to-neighbor communication scheme eliminates the need to form a global finite element matrix. From the perspective of time, the well-known parallel-in-time method is also adapted to the EDD FEM system to achieve the space-time parallelism.
  In addition, the thesis also proposes a novel coupling scheme to interface the 3-D finite element models with external circuits under large eddy currents without having to com-bine circuit and FEM system in one matrix. Implementations of these massively-parallel algorithms indicate excellent efficiency and accuracy

• Subjects / Keywords

  • Domain Decomposition
  • Finite element method
  • Time Parareal
  • Transmission line modeling

• Graduation date

  Spring 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-qakf-c507

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.