Laplace transform inversion through the theta algorithm for power-system EMT analysis

•This paper shows that the conventional Laplace transform inversion method used in EMT analysis, referred to here as WNLT, has at least two major shortcomings. One is that its level of accuracy cannot be guaranteed. The other is that its precision is limited to levels between 10^−3 and 10^−5, and th...

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Bibliographic Details
Published in:Electric power systems research Vol. 197; p. 107342
Main Authors: Castañón, L.J., Naredo, J.L., Zuluaga, J.R., Bañuelos-Cabral, E., Gómez, Pablo
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.08.2021
Elsevier Science Ltd
Subjects:
Algorithms
Cost analysis
Electricity distribution
Electromagnetic transients
Epsilon algorithm
Frequency-domain
Integrals
Laplace transform
Laplace transforms
Numerical analysis
Padé approximants
R&D
Research & development
Shanks transformation
Theta algorithm
Transient analysis
Shanks transformation
Theta algorithm
Padé approximants
Epsilon algorithm
Electromagnetic transients
Frequency-domain
Laplace transform
ISSN:0378-7796, 1873-2046
Online Access:Get full text
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Summary:•This paper shows that the conventional Laplace transform inversion method used in EMT analysis, referred to here as WNLT, has at least two major shortcomings. One is that its level of accuracy cannot be guaranteed. The other is that its precision is limited to levels between 10^−3 and 10^−5, and that higher accuracies (up to 10^−9) could be achieved with excessive computational cost.•The paper presents a new method for the numerical solution of the Laplace inversion integral and proposes it to replace the WNLT as an R&D tool in EMT analysis and as a reference method to evaluate EMT models and results.•The new method is based on Brezinski's theta algorithm. Apparently, this is the first time that the theta algorithm has been applied in the numerical inversion of the Laplace transform, as well as in the EMT analysis of power systems.•The accuracy and computational efficiency of the new method are evaluated through a set of 36 test functions established by the numerical analysis community.•The new method achieves a guaranteed accuracy of the order of 10^−9 at moderate computational costs.•The usefulness of the new method for the EMT analysis of power systems is demonstrated by its application to a three-phase network composed of three generators, three transformers, eight overhead transmission lines and five loads with reactive components. The results being obtained compare favourably well with those of a well-known industrial grade EMT analysis software. Laplace transform analysis of electromagnetic power system transients generally is based on a technique in which the Laplace inversion integral is truncated with a suitable data window. This technique, being referred to as WNLT, is appropriate for most practical cases. Nevertheless, it results inadequate for certain R&D tasks. This paper presents a new technique for numerical Laplace inversion that does not require truncation with a data window; it instead uses Brezinski's theta algorithm to account for the infinite range of the Laplace inversion integral. As opposed to the WNLT, the new technique guarantees consistent and high accuracy levels at low computational costs. Finally, the new technique is applied to the transient analysis of a power-system network. Its results compare favorably well with those from the PSCAD/EMTDC program.
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ISSN:0378-7796
1873-2046
DOI:10.1016/j.epsr.2021.107342