Resolution of nodal analysis with support of Numerical Methods

Caison Rodrigues Ramos, Bruno Pereira do Nascimento, Aline Brum Loreto

Abstract


Usually for the knowledge of the voltages in the electrical circuits it is used the nodal analysis. The nodal analysis is based on Kirchoff’s Law of Currents and Ohm’s Law, where we determine the potential difference between nodes in an electric circuit. Each node produces an equation, thus forming a system of equations that can be solved by numerical methods. This work aims to perform the nodal analysis of a base circuit using the numerical methods Gauss Elimination, LU Factoration, QR Factoration and Crout Method for the solution of linear systems. All numerical methods were implemented in C programming language and the analysis of the accuracy of the results was given by the relative error in comparison to the results obtained by MatLab software. For this process, a base circuit was used that in its nodal analysis generated a linear system of seven equations and seven unknowns. After the conclusion, it was possible to assume that the development of the work provided the application and programming of numerical methods for solution of linear systems in Problems of Electrical Engineering, presenting solutions as exact as those obtained by commercial mathematical software.

Keywords


Electric circuits; Nodal analysis; Numerical methods

References


ALEXANDER CK, SADIKU MNO. Fundamentos de Circuitos Elétricos. 5th ed., Porto Alegre: AMGH; 2003.

CHAPRA SC, CANALERP. Métodos numéricos para engenharia. 5th ed., São Paulo: McGraw-Hill, 2008.

FRANCO NB. Cálculo numérico. 1st ed., Pearson Prentice Hall; 2016.

GRIGOLETTIPS, DIMURO G.P., BARBOZA L.V., REISER R.H.S. Análise intervalar de circuitos elétricos. Trends in Applied and

Computational Mathematics. 2006; v. 7:n. 2:p. 287-296,.

GROBE JR. Sistemas lineares – 2015 [Internet]. Pato Branco: Universidade Tecnológica do Paraná; 2015 Mar 30 [cited 2018 ago 30]. Available from: http://paginapessoal.utfpr.edu.br/grobe/calculo-numerico-das-engenharias/capitulo_2_sistemas_lineares_A.pdf/at_download/file.

HALLIDAYD, RESNICK R, WALKER J. Fundamentos da Física Vol. 3 - Eletromagnetismo. 9th ed., Rio de Janeiro:LTC; 2014.

HILDEBRAND FB. Introduction to Numerical Analysis. 1st ed., Nova Deli: TMH Edition, 1956.

PEREIRA CS, NETO LA, SANTOS MDS, NASCIMENTO TMM, GAMA EDP, SANTOS JJ. Aplicação da Álgebra Linear em circuitos elétricos. Cadernos de graduação - Ciências exatas e tecnológicas. 2015;v. 3:n. 1:p. 35-44,.

POOLE D. Álgebra Linear.1st ed., São Paulo: Pioneira Thomson Learning, 2004.

JVC, BOSO ACMR, NIIYAMA CA. Determinação de Correntes em Circuitos Elétricos Usando Decomposição de Cholesky e Pseudo-inversão. IN: Anais do 34º Congresso Nacional de Matemática Aplicada e Computacional [Internet]. 2012. Maio 17-21; Águas de Lindóia, Brasil. 2012 [cited 2018 ago 30]. Available from: https://sbmac.org.br/eventos/cnmac/xxxiv_cnmac/pdf/219.pdf




DOI: https://doi.org/10.5902/2179460X35502

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