Fractal geometry for distribution grid topologies

Barakou, F.; Koukoula, Despina; Hatziargyriou, Nikos D.; Dimeas, Aris

doi:10.1109/ptc.2015.7232496

Cited by 9 publications

(3 citation statements)

References 2 publications

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“…Hence, fractal dimension is used to extract and identify characteristics of droplet distribution based on the fractal geometry. Sarkar and Chaudhuri proposed a Differential Box-Counting (DBC) method to calculate fractal dimension of droplet distribution image [19]- [21]. If N is the number of boxes that cover the pattern, r is the box size, the fractal dimension (FD) is given by: As shown in the Figure 3, original image (Figure 3(a)) is converted to gray scale and then edge detector is applied to the gray-scale image (Figure 3(b)).…”

Section: A the Dynamic Behavior Of Water Dropletmentioning

confidence: 99%

Dynamic Behavior of Droplets and Flashover Characteristics for CFD and Experimental Analysis on SiR Composites

Liu

Kong

et al. 2019

IEEE Access

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The dynamic mechanism of water droplet formation has recently drawn considerable attention in research and application toward silicon rubber composite insulators. This paper is aimed at numerical simulations and experiments on the dynamic mechanism of water droplet formation with different applied voltages and droplet distribution and induced surface discharges on the insulator surface under the impact of AC electric field. The computational fluid dynamics model and experimental setup of multiple droplets were established to analyze the dynamic behavior of droplets and flashover characteristics. The obtained results reveal that the fusion first occurs between larger size droplets and the fusion is hard to happen along with the rise of the fractal dimension (FD) of droplet distribution. The elongation of droplets merges with more droplets and finally affects the electric field distribution on the insulator surface. With the increase of FD, the maximum electric field intensity shows an increasing tendency. Meanwhile, the experimental results show that with the increase of electric field intensity, the droplet fusion phenomenon becomes more obvious, which is consistent with the simulation results. The flashover voltage on the surface of silicon rubber decreases with the decrease of the FD of droplets, indicating that the complexity of droplet distribution has a significant effect on the flashover voltage. INDEX TERMS Droplet elongation, flashover voltage, discrete droplet, sir composite, fractal dimension.

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Section: A the Dynamic Behavior Of Water Dropletmentioning

confidence: 99%

Dynamic Behavior of Droplets and Flashover Characteristics for CFD and Experimental Analysis on SiR Composites

Liu

Kong

et al. 2019

IEEE Access

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“…Generally, some patterns that repeat themselves in different scales through specific processes are hiding behind the complexity of many objects, composing the fractal objects observed …”

Section: Fractal Theorymentioning

confidence: 99%

“…Generally, some patterns that repeat themselves in different scales through specific processes are hiding behind the complexity of many objects, composing the fractal objects observed. 27 The short and strict definition always eliminates some fractal sets, as stated in Falconer. 28 A fractal is a set F characterized by the following properties:…”

Section: Definitionmentioning

confidence: 99%

A power grid partitioning optimization method based on fractal theory

Zhang

Han

et al. 2018

Int Trans Electr Energ Syst

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Summary It is important to identify characteristics of power grid structures in many applications. In a power system, large grids are divided into areas to meet planning and control requirements. Topological structures are considered in partitioning methods to guarantee the reliability and extendibility of power grids. However, the representation of structures is complex. To apply topological structures efficiently, this paper presents a new method for quantizing topological structures of power grids based on fractal theory. The fractal property of power grids is proved, and the fractal dimension of power grids is measured by a box‐counting algorithm. A fractal dimension‐based prediction method of short‐circuit current is proposed to identify problem regions quickly. Then a power‐grid‐partitioning optimization method based on the quantization results of power grids is introduced for power grids. Finally, the IEEE 118‐bus test system and an actual power grid in China are employed to illustrate the validity of the proposed method.

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