An Iterative Method to Solve Nonlinear Equations

Villafuerte, Rubén; Medina, Jesús; Villafuerte, A S Rubén; Juarez, Victorino; Gonzalez, Manuel Losada y

doi:10.13189/ujeee.2019.060102

Cited by 5 publications

(7 citation statements)

References 18 publications

(30 reference statements)

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“…The elements of the submatrix J ij of (1) are generated in each iteration and depend on the partial derivatives of the real power or reactive power with respect to the nodal Voltages. The real and reactive power in each node is calculated with (3) and (4), respectively [11,12,17].…”

Section: Proposed Methods and Convergence Analysismentioning

confidence: 99%

“…The increases in real and reactive power are calculated in each iteration with (9)-(10). ∆ = − i≠ Slack (9) ∆ = − i≠ Slack (10) Where: P i spec Real power load in node i, Q i spec Reactive power load in node i, P i calc Real power calculated at node i, Q i calc Reactive power calculated at node i For the solution of real nonlinear equations, methods of several steps and of high order of convergence have been proposed [13][14][15][16][17]. The method used in this work is four steps and only the function f(x n ) and its derivative f '(x n ) are necessary.…”

Section: Proposed Methods and Convergence Analysismentioning

confidence: 99%

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Two Iterative Methods to Solve Nonlinear Equations of Load Flows

D.,

C.,

et al. 2019

IJEAT

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This paper presents the results obtained when two iterative methods are applied to the solution of non-linear equations that model the load flow in electric power systems. Two iterative methods are applied; the first consists of a simplification of the rectangular form the traditional Newton-Raphson method, the second is a hybrid method and relates the simplified form proposed here and a four-step Newton-type iterative method. The convergence characteristic and the mathematical preliminaries of the iterative four-step method are included in the paper. The methods were used to calculate the voltages at each node of the IEEE test system of 118 nodes and a distribution system of 40 nodes. In each method, the formation of the Jacobian matrix, widely used in traditional forms of load flows, is avoided and only elementary operations are carried out, impacting the execution times for the test systems used, being of the order of 15.6 to 279 milliseconds. The maximum error found is for the 118 node system and is of the order of 3.7%.

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Section: Proposed Methods and Convergence Analysismentioning

confidence: 99%

Section: Proposed Methods and Convergence Analysismentioning

confidence: 99%

Two Iterative Methods to Solve Nonlinear Equations of Load Flows

D.,

C.,

et al. 2019

IJEAT

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“…Figure 4 corresponds to a system of 70 nodes and 6 branches, the data of impedances and demanded powers are in [21], [22], as well as the graph that shows the magnitude of the voltages and the value of the angle of each voltage. Figure 5 shows the voltage obtained with the two algorithms used in this work, with equation ( 5), with equation ( 6), and the results obtained with a method used for interconnected power systems [23]. Figure 6 shows the angle of the voltages obtained with the two algorithms used in this work, with equation ( 5), with equation ( 6), and the results obtained with a method used for interconnected power systems [23].…”

Section: Casementioning

confidence: 99%

“…Figure 5 shows the voltage obtained with the two algorithms used in this work, with equation ( 5), with equation ( 6), and the results obtained with a method used for interconnected power systems [23]. Figure 6 shows the angle of the voltages obtained with the two algorithms used in this work, with equation ( 5), with equation ( 6), and the results obtained with a method used for interconnected power systems [23].…”

Section: Casementioning

confidence: 99%

Two Algorithms for Load Flow Analysis in Balanced Radial Distribution Systems

Villafuerte¹,

Medina²,

Villafuerte³

et al. 2021

ujeee

Self Cite

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This paper was developed with the purpose of knowing the behavior of radial distribution systems that operate in balanced conditions. Two algorithms were used to calculate the voltage at the network nodes and with them the load flow in each line. With the application of Kirchhoff's laws of electrical circuits, a one-dimensional arrangement of order N and a two-dimensional arrangement of order Nx5 are generated, both depend on the impedances and the shunt admittances. With these two arrangements, a non-linear function f (V1, V2 ,,, VN,, Sc) was generated, which depends on the voltages Vi and the complex power Sc demanded at each node of the distribution system. These equations were solved iteratively, two methods were applied; In the first method, the Halley formula with an acceleration factor α was used to solve the non-linear function f (V1, V2 ,,, VN,, Sc), in the second method, the Gaussian method was applied in the same way that it is used for load flows in interconnected systems. The two algorithms were applied to test systems of 40, 70 and 80 nodes, obtaining results similar to those reported in the specialized literature where they make use of other solution methods. In the author's opinion, the proposed algorithms represent alternatives for the study of energy distribution systems. An advantage of the methods is that they are simple code and there are differences between them, the second method has a faster convergence.

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“…Numerical analysis has interesting applications in several branches of pure and applied science that can be studied in the general framework of the non-linear equations [2,12,17,26,32]. Searching out a solution for non-linear equations is highly significant.…”

Section: Introductionmentioning

confidence: 99%

An optimal fourth order method for solving nonlinear equations

Hafiz¹,

Khirallah²

2020

J. Math. Computer Sci.

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In this paper, we use both weight functions and composition techniques together for solving non-linear equations. We designed a new fourth order iterative method to increase the order of convergence without increasing the functional evaluations in a drastic way. This method uses one evaluation of the function and two evaluations of the first derivative. The new method attains the optimality with efficiency index 1.587. The convergence analysis of our new methods is discussed. Furthermore, the correlations between the attracting domains and the corresponding required number of iterations have also been illustrated and discussed. The comparison with several numerical methods and the use of complex dynamics and basins of attraction show that the new method gives good results.

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An Iterative Method to Solve Nonlinear Equations

Cited by 5 publications

References 18 publications

Two Iterative Methods to Solve Nonlinear Equations of Load Flows

Two Iterative Methods to Solve Nonlinear Equations of Load Flows

Two Algorithms for Load Flow Analysis in Balanced Radial Distribution Systems

An optimal fourth order method for solving nonlinear equations

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