Parallel Field-Oriented Computation for Electromagnetic Transient Simulation of Power System Components

• Author / Creator

  Liu, Peng

• The finite element method (FEM) has been commonly employed to solve the partial differential equations in different physical domains including structural analysis, heat transfer, and electromagnetics due to its field-oriented nature, high accuracy, and capability to consider complex geometries and material properties. As essential components in the power system, traditional models of transformer and transmission line cannot sufficiently represent the often omitted but important physical phenomena like the ionized field, magnetic saturation, eddy currents, and hysteresis. Therefore, finite element models are given increasing consideration in electromagnetic transient (EMT) simulation to provide more accurate results and a comprehensive view of the physical details, which can assist engineers to make better decisions when designing and testing equipment.

  However, when seeking accuracy and detailed field information, the computational cost of the finite element method substantially increases compared with conventional numerical models. The spatial discretization generates innumerable interconnected nodes and elements, which subsequently are assembled into a large system of equations to be solved with matrix solvers. The computational efficiency of the finite element solver, especially for transient studies and nonlinear problems that require repetitive matrix factorization, remains an intractable challenge. The prevalent trend of parallel processing using high-performance computing resources including multi-core CPUs, many-core GPUs, and field-programmable gate arrays (FPGAs) provides a possible solution to resolve the computation efficiency issue, yet the finite element solution procedure needs to be improved and adapted to parallelism and data dependency to efficiently utilize the parallel hardware resources.

  In this thesis, parallelism is explored at both the node-level and element-level to make the finite element computation suitable for massively parallel processing. First, the nodal domain decomposition scheme is proposed to solve the finite element problem with node-level parallelism. Each finite element node and its neighbors make up a sub-domain and each sub-domain can be mapped to one computational unit and solved independently. The assembling phase and matrix of the finite element method are avoided and the algorithms are perfected for single instruction multiple data (SIMD) stream hardware such as GPUs. The sub-domain solver works for both linear and nonlinear problems, and the mixed boundary conditions are incorporated in the sub-domain solver to accelerate the convergence. By fully using the massively parallel computing resources, the computational efficiency can be greatly improved compared with commercial software while maintaining high accuracy. The node-level parallelism is also extended for the finite difference method when computing the ionized field around high-voltage direct-current (HVDC) transmission line, and the Poisson's equation and the current continuity equation are solved alternatively on GPU to speed up the computation.

  Second, the transmission line decoupling technique is employed to solve the nonlinear finite element problem at the element-level parallelism. Each element is decoupled from the interconnected network using the transmission line so the nonlinearity of the decoupled element can be solved independently on each computational core in parallel, which is suitable for SIMD hardware. Instead of repetitively factorizing the Jacobian matrix, a constant admittance matrix is required and matrix factorization is required once for all. Real-Time implementation is carried out on FPGA to explore the hardware concurrency and data pipelining for a 2D nonlinear finite element transformer model.

  Besides, to interface the finite element model with the electrical network, an indirect field-circuit coupling scheme is proposed to extract and exchange the coupling coefficients at each time-step. Multi-physics finite element simulation considering thermal effects is also discussed in this thesis.

• Subjects / Keywords

  • Finite Element Method
  • Parallel Computing
  • Multiphysics
  • Electromagnetic Transient
  • Power Transformer

• Graduation date

  Fall 2020

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-bvbz-0682

• License

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