Electromagnetic transient simulation algorithm for nonlinear elements based on Rosenbrock numerical integration method

Traditional nonlinear elements of the electromagnetic transient simulation program (EMTP) use the numerical integration method, often employing the trapezoidal integration method as an implicit algorithm. However, when the number of nonlinear elements is high, the iterative format becomes computatio...

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Bibliographic Details
Published in:IEEE access Vol. 12; p. 1
Main Authors: Ye, Jing, Xie, Jihao, Wang, Yong, Zhang, Liang, Li, Binshan, Lv, Jinwei, Li, Ke, Jin, Shengpeng, Xu, Yang, Ma, Wei
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Accuracy
Algorithms
Calahan algorithm
Computational efficiency
Electromagnetic transient
Format
Jacobi matrix method
Jacobian matrices
Jacobian matrix
Mathematical models
Numerical integration
Numerical models
Oscillators
Power system stability
Precise integration method
Real-time systems
Rosenbrock algorithm
Simulation
Time integration
Transient analysis
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:Traditional nonlinear elements of the electromagnetic transient simulation program (EMTP) use the numerical integration method, often employing the trapezoidal integration method as an implicit algorithm. However, when the number of nonlinear elements is high, the iterative format becomes computationally cumbersome. The semi-implicit format algorithms, based on the Rosenbrock real-time integration method, do not require iterations and can be applied directly in a recursive manner. However, as the number of nonlinear elements increases, it becomes necessary to invert the matrix that contains the Jacobian matrix, resulting in an increase of both algorithmic computation and inversion time with the dimensionality of the system. In this paper, a new numerical solution method is adopted, which combines the precise integration method. Specifically, the Calahan algorithm, with 2-stage and 3-order, is used to numerically integrate the Duhamel integration terms, and the accuracy of the Calahan algorithm is enhanced through Richardson extrapolation. The new algorithm can avoid the inverse of the matrix containing the Jacobian matrix, and the computational efficiency is equivalent to an explicit method, which greatly improves the computational efficiency of the Rosenbrock integration algorithm. The results verify the effectiveness and accuracy of the algorithm for typical power system nonlinear element electromagnetic transient simulation cases.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2024.3398772