Parallel 2-D Finite Element Modeling for Transmission Line and Power Transformer for Electromagnetic Transient Study

  • Author / Creator
    Xu, Qingjie
  • The energy exchange between the electric field and the magnetic field is the foundation for electromagnetic equipment in power systems. However, not all exchange is desirable. Some sudden exchanges with a large amount of energy involved such as overvoltages and overcurrents may have an adverse impact on the equipment’s operation and reliability. The electromagnetic transient (EMT) simulation was traditionally utilized to study the effects of these troublesome energy exchanges. Lumped models have been widely used in EMT simulation, ut they are incapable of capturing transient behaviors accurately. As the most prevalent numerical method to solve field-oriented Maxwell’s equations to describe the electromagnetic problem accurately, the finite element method (FEM) has attracted increasing attention in EMT simulation. FEM is a powerful tool to provide the capability of modeling irregular geometries, the ability of handling complex material properties, and superior accuracy. Regardless of the outstanding accuracy and detailed insight provided, the finite element method leads to a significant increase in computational burden for a simulation program. On the other hand, the involvement of the repetitive computation of large matrix systems when using the traditional Newton-Raphson method to solve nonlinear problems also slows down the simulation. The development of parallel computing with high-performance computing hardware provides a path forward. The parallel computing hardware provides the inherent parallel architecture to execute a program in parallel and thus has the potential to shorten execution time. To accelerate FEM computation with parallel computing hardware, an algorithm design to modify the traditional FEM process to fit in parallelism is required. In this thesis, parallel algorithms are designed to solve EMT in both ionized field modeling and power transformer modeling efficiently on the appropriate parallel computing platform.
    First, a massively parallel algorithm to solve a hybrid ionized field around AC/DC transmission lines is proposed. A fine-grained nodal domain decomposition scheme, which enables each sub-domain with only one unknown to be solved independently in a massively parallel fashion, was employed to solve Poisson’s equation. Meanwhile, an upwind nodal charge conservation method is applied to solve the current continuity equation without numerical oscillation at node level. The computation of nodal domain decomposition and upwind nodal charge conservation can both be vectorized and mapped to massive computational cores and utilize the computing power of GPUs. The interaction between HVAC and HVDC was solved without Deutsch’s assumption to guarantee the accuracy, and the wind influence can be considered. The performance of the proposed method is tested and compared with commercial software showing a significant speedup with guaranteed accuracy.
    Second, the transmission-line modeling (TLM) technique is integrated into a parallel and deeply pipelined algorithm to decouple the nonlinear finite elements caused by nonlinear material in a power transformer. The transmission line is utilized to separate the nonlinear finite elements from the linear network and then these decoupled elements can be solved individually in a parallel manner. Without losing the merit of traditional transmission-line modeling, an adaptive transmission-line modeling method is employed to reduce TLM iteration number. The other component of this algorithm is the preconditioned conjugate gradient method, which can be deployed on FPGA to achieve high parallelism. The accuracy of the transformer solver under both current-excited and voltage-excited conditions was validated against the commercial FE simulation tool. In addition, a field-circuit coupling approach to interface the FE model for the transformer and external circuits is also discussed and implemented on FPGAs. The accuracy for the combination between the field-circuit coupling and the above finite element model is also verified.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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.