Abstract
In this paper, a novel massively space-time parallel finite element (FE) transformer model is proposed for power system electromagnetic transient simulations. The method utilizes the reduced magnetic vector potential (RMVP) formulation to solve the electromagnetic field in the transformer, and the 3-D tetrahedral edge element is applied to discretize the RMVP formulation. The discretized nonlinear system is solved by adaptive transmission line modeling (TLM) and matrix-free conjugate gradient iterator, which allows parallelism at the elemental-level and eliminates the need for Newton-Raphson (NR) iterations over the large-scale global matrix. The paper also integrates the parallel-in-time method with the finite element solver to further parallelize the model at space-time level, and the GPU implementation of the model realized a speedup of over 55 and high accuracy, compared with a commercial FE software.
Highlights
Transformers are one of the most utilized components in energy and power systems, due to their ability to change voltages and isolate currents between different coils
If the Parareal iterations required are less than the number of time windows, the parallel-in-time algorithm becomes faster than the traditional time-serial method, and the Parareal-adaptive-transmission line modeling (TLM) transformer model is boosted with both space and time parallelism
Compared with the traditional fixed-impedance transmission line technique, the new method changes the characteristic impedance based on the operating point, which dramatically improves the convergence speed of TLM iterations
Summary
Transformers are one of the most utilized components in energy and power systems, due to their ability to change voltages and isolate currents between different coils. To simplify the equations for power system application, one usually omits dielectric (high frequency) related terms and introduce potential functions to reduce jump of solution at different material interfaces [16] This leads to the reduced magnetic vector potential (RMVP or A) formulation [16]:. To obtain a consistent solution over the entire domain for all elements, the local restrictions of 6 edge DOFs in (7) related to each element need to be assembled into a global system During this process, all elements interact with each other at surfaces between different elements with respect to Maxwell’s equations [17]: 1) Continuity of tangential A is automatically ensured by the edge-based DOF discretization format.
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