Modified Halley's Method for Solving Nonlinear Functions With Convergence of Order Six and Efficiency Index 1.8171

Nazeer, Waqas; Tanveer, Muhmmad; Munir, Mobeen; Jan, A.; Kang, Shin-Min

doi:10.12732/ijpam.v111i1.6

Cited by 1 publication

(2 citation statements)

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“…A flow chart to solve equation ( 4) is shown in figure 2; it shows the main steps to solve equation ( 4) by means of the Halley-type method [20]. In each block of the flow diagrams of figures 2 and 3, the activities carried out are as follows; 1.…”

Section: Resultsmentioning

confidence: 99%

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Two Algorithms for Load Flow Analysis in Balanced Radial Distribution Systems

Villafuerte¹,

Medina²,

Villafuerte³

et al. 2021

ujeee

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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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Section: Resultsmentioning

confidence: 99%

“…Equation ( 5) is used to iteratively calculate the voltage at any node in the network. For node i, using Halley's formula [20]. Where; N is the number of nodes and α is an acceleration factor between 2.5 and 10.…”

Section: Proposed Methodsmentioning

confidence: 99%