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Newton-Type Iterative Solvers for Power Flows

International Journal of Electrical and Electronics Engineering
© 2024 by SSRG - IJEEE Journal
Volume 11 Issue 11
Year of Publication : 2024
Authors : Ruben Villafuerte Diaz, Victorino Juarez Rivera, Ruben Abiud Villafuerte Salcedo, Jesus Medina Cervantes
10.14445/23488379/IJEEE-V11I11P118
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How to Cite?

Ruben Villafuerte Diaz, Victorino Juarez Rivera, Ruben Abiud Villafuerte Salcedo, Jesus Medina Cervantes, "Newton-Type Iterative Solvers for Power Flows," SSRG International Journal of Electrical and Electronics Engineering, vol. 11,  no. 11, pp. 172-181, 2024. Crossref, https://doi.org/10.14445/23488379/IJEEE-V11I11P118

Abstract:

Starting from a Newton-type method of third order and two steps, a five-step and a seven-step method is adapted to solve nonlinear equations and the power function f(V1,V2,...V3) is applied to calculate the voltage at each node of an electrical power system and the load flow in the transmission lines. The procedure involves iteratively calculating the nonlinear function and its first and second derivatives. At each node i of the system under study, the original formula of Newton's method, or an adaptation of it, is applied, and the approximations of the voltage at each node are calculated. To reduce the execution time, an acceleration function that depends on the first and second derivatives of the power function was used. The power function is generated at each node and iteratively solved for each node separately, thus avoiding the formation of the Jacobian matrix. Test systems from 9 to 118 nodes were analyzed; the maximum errors found were 0.333% for the 30-node system in the Voltage magnitude, 5.62% in the angle one node of the same system, For the 118-node system, the maximum error in the voltage magnitude was 2.254%, in one node of the system. The applied methods reduce the execution time from 1048.875 to 78.125 milliseconds with the accelerated seven-step method and with a tolerance of 1.0e-04. We foresee the possibility of applying methods with more steps and higher acceleration factors from the results obtained.

Keywords:

Load flows, Nonlinear equations, Numerical Methods, Newton-type methods, Power systems.

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