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**|**PLoS One**|**v.12(2); 2017**|**PMC5325478

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PLoS One. 2017; 12(2): e0172118.

Published online 2017 February 24. doi: 10.1371/journal.pone.0172118

PMCID: PMC5325478

Mahdi Izadi,^{1,}^{2,}^{*} Muhammad Syahmi Abd Rahman,^{1} Mohd Zainal Abidin Ab-Kadir,^{1} Chandima Gomes,^{1} Jasronita Jasni,^{1} and Maryam Hajikhani^{1}

Choongho Yu, Editor^{}

Texas A&M Univ, UNITED STATES

**Conceptualization:**MI MSAR MZAAK.**Data curation:**MI MSAR.**Formal analysis:**MI MSAR MH.**Funding acquisition:**MI MZAAK.**Investigation:**MI MSAR.**Methodology:**MI MZAAK.**Project administration:**MI MZAAK.**Resources:**MI MZAAK CG JJ.**Software:**MH.**Supervision:**MI MZAAK.**Writing – original draft:**MI MSAR.**Writing – review & editing:**MI MZAAK.

* E-mail: moc.oohay@esahpayra

Received 2016 June 10; Accepted 2017 January 31.

Copyright © 2017 Izadi et al

This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Protection of medium voltage (MV) overhead lines against the indirect effects of lightning is an important issue in Malaysia and other tropical countries. Protection of these lines against the indirect effects of lightning is a major concern and can be improved by several ways. The choice of insulator to be used for instance, between the glass, ceramic or polymer, can help to improve the line performance from the perspective of increasing the breakdown strength. In this paper, the electrical performance of a 10 kV polymer insulator under different conditions for impulse, weather and insulator angle with respect to a cross-arm were studied (both experimental and modelling) and the results were discussed accordingly. Results show that the weather and insulator angle (with respect to the cross-arm) are surprisingly influenced the values of breakdown voltage and leakage current for both negative and positive impulses. Therefore, in order to select a proper protection system for MV lines against lightning induced voltage, consideration of the local information concerning the weather and also the insulator angles with respect to the cross-arm are very useful for line stability and performance.

Lightning affects the performance of power lines by both direct and indirect effects where the transient high voltages may cause flashover on the electrical equipment on the power line. Direct lightning strikes, may intercept with line conductors, towers or shielding wires. The probability of direct strike in a given region increases with line height, thus, high voltage (HV) lines may subject to direct strikes more than medium voltage (MV) or low voltage (LV) lines.

On the other hand, when lightning strikes the ground or any object close to a line, the electromagnetic fields will propagate in all directions. The inductive and capacitive coupling of such electromagnetic fields with conducting wires induce voltage impulses in the power system [1–5]. These lightning induced overvoltage (LIOV) may cause significant problems in MV and LV power lines because of the low value of critical flashover (CFO) voltage compared to that of HV line [5]. Moreover, the chance of an indirect effect is higher than that of a direct strike as for any lightning event around a power line, LIOV can appear on the power line.

The high lightning ground flash density makes Malaysia more vulnerable to both direct and indirect lightning effects on power systems. In fact, many parts of Malaysia experience up to 200 thunderstorm days per year which serves as one of the countries with a very high flash density in the world. Local electrical utility, TNB, has claimed that about 50% of total failures in their system are caused by lightning strikes [6]. Therefore, it is necessary to consider the effect of lightning on most electrical components, including insulators.

The selection of powerline insulators should be done after thorough investigation on the weather conditions of a particular region and voltage conditions of the system [7–12]. The configuration of the line and the radial distance between conductors with respect to the ground may also affect the electric field distribution along an insulator and the value of the breakdown voltage under various conditions [11–13].

The combined influence of the weather conditions and the inclination of insulators with respect to the cross arm have not been studied in detail in the literature. Unintended and undesired inclination of isolators in real MV power lines have been reported from many parts of Malaysia (personal communication with TNB Officers). Such distortions may be due to the forces act on an insulator as a result of cornering or external forces such as fallen trees, high wind shear with excessive rainfall etc. Therefore, the electrical performance of an insulator will change and this should be considered in the design or modification of line. To address this issue, in this paper, the electrical behaviour of a 10 kV polymer insulator under an impulse voltage (due to lightning induced voltage) was considered and the effects of weather conditions and inclination of insulator on the power line performance under LIOV has been investigated. Polymer insulator has been considered for the analysis due to the wide-usage of such insulators based on their many advantages in power system applications.

Several works have shown interest in lightning induced voltage over the past few decades. For example, a group of Japanese researchers [14] studied induced voltage waveforms while simultaneously measuring lightning stroke current waveforms for both positive and negative polarities. Three continuous years of study has demonstrated the behaviour of induced voltages along a length of distribution line. A reduced scale work was conducted by [15] to simulate a lightning channel with consideration of a lossy ground in order to evaluate lightning induced voltage on overhead lines. Meanwhile, a study by [16] focused on the effect of voltage attenuation on shielded wires and surge arrestors due to lightning induced voltage. To date, works for the evaluation of lightning induced voltage by numerical methods have become more popular. Regarding the simple Rusck formula, some elaborate models e.g. [17–19] have been developed. In addition, as presented by Yutthagowith et al., the Cooray-Rubinstein expression has been used for the calculation of lightning induced voltage due to a flat ground and a tall structure flash [20].

A lightning induced voltage can be created on the power line by coupling between the lightning electromagnetic fields and the power line [1, 3, 4], as shown in Fig 1.

In order to evaluate the lightning induced voltage on the power line, the lightning current wave shape of the channel base (striking point and at different heights along the channel) should be modelled. In this study, the channel base current was simulated using the sum of two Heidler functions as expressed by Eq (1) and the typical current parameters are listed in Table 1 as follows [1, 3];

$$\text{i}\left(0,\text{t}\right)=\left[\frac{{\text{i}}_{01}}{{\mathrm{\eta}}_{1}}\frac{{\left(\frac{\text{t}}{{\mathrm{\u0413}}_{11}}\right)}^{{\text{n}}_{\text{c}1}}}{1+{\left(\frac{\text{t}}{{\mathrm{\u0413}}_{11}}\right)}^{{\text{n}}_{\text{c}1}}}\mathrm{exp}\left(\frac{-\text{t}}{{\mathrm{\u0413}}_{12}}\right)+\frac{{\text{i}}_{02}}{{\mathrm{\eta}}_{2}}\frac{{\left(\frac{\text{t}}{{\mathrm{\u0413}}_{21}}\right)}^{{\text{n}}_{\text{c}2}}}{1+{\left(\frac{\text{t}}{{\mathrm{\u0413}}_{21}}\right)}^{{\text{n}}_{\text{c}2}}}\mathrm{exp}\left(\frac{-\text{t}}{{\mathrm{\u0413}}_{22}}\right)\right]$$

(1)

Where

i_{01},i_{02} are the amplitudes of the channel base current,

Γ_{11},Γ_{12} are the front time constants,

Γ_{21},Γ_{22} are the decay- time constants,

n_{c1},n_{c2} are the exponents (2~10),

$${\mathrm{\eta}}_{1}=\mathrm{exp}\left[-\left(\raisebox{1ex}{${\mathrm{\Gamma}}_{11}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{\Gamma}}_{12}$}\right.\right){\left({\mathrm{n}}_{\mathrm{c}1}\frac{{\mathrm{\Gamma}}_{12}}{{\mathrm{\Gamma}}_{11}}\right)}^{\frac{1}{{\mathrm{n}}_{\mathrm{c}1}}}\right],$$

$${\mathrm{\eta}}_{2}=\mathrm{exp}\left[-\left(\raisebox{1ex}{${\mathrm{\Gamma}}_{21}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{\Gamma}}_{22}$}\right.\right){\left({\mathrm{n}}_{\mathrm{c}2}\frac{{\mathrm{\Gamma}}_{22}}{{\mathrm{\Gamma}}_{21}}\right)}^{\frac{1}{{\mathrm{n}}_{\mathrm{c}2}}}\right].$$

Fig 2 shows the channel base current with a current peak of 18.1 kA and a time to peak of about 1.5 μs [3].

In this study, the current waveshape at different heights along the channel was modelled using the MTLE current model as expressed by Eq (2) whereby the values of λ and v were set at 1500 m and 1 x 10^{8} m/s, respectively [3, 21].

In addition, the values of the lightning electromagnetic fields and the lightning induced voltage were calculated based on Fig 3, using the analytical expressions as shown in the Eqs (2–4) [1, 3].

$${\text{B}}_{\mathrm{\phi}}\left(\text{r},\text{z},{\text{t}}_{\text{n}}\right)={\sum}_{\text{i}=1}^{\text{n}}{\sum}_{\text{m}=1}^{\text{k}+1}\{{\text{a}}_{\text{m}}{\text{F}}_{\text{i},1}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}}_{\text{m},\text{i}}\right)-{\text{a}\prime}_{\text{m}}{\text{F}}_{\text{i},1}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}\prime}_{\text{m},\text{i}}\right)\}$$

(2)

$${\text{E}}_{\text{r}}\left(\text{r},\text{z},{\text{t}}_{\text{n}}\right)={\text{E}}_{\text{r}}\left(\text{r},\text{z},{\text{t}}_{\text{n}-1}\right)+\mathrm{\Delta}\text{t}\times {\sum}_{\text{i}=1}^{\text{n}}{\sum}_{\text{m}=1}^{\text{k}+1}\{{\text{a}}_{\text{m}}{\text{F}}_{\text{i},2}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}}_{\text{m},\text{i}}\right)-{\text{a}\prime}_{\text{m}}{\text{F}}_{\text{i},2}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}\prime}_{\text{m},\text{i}}\right)\}$$

(3)

$${\text{E}}_{\text{z}}\left(\text{r},\text{z},{\text{t}}_{\text{n}}\right)={\text{E}}_{\text{z}}\left(\text{r},\text{z},{\text{t}}_{\text{n}-1}\right)+\mathrm{\Delta}\text{t}\times {\sum}_{\text{i}=1}^{\text{n}}{\sum}_{\text{m}=1}^{\text{k}+1}\{{\text{a}}_{\text{m}}{\text{F}}_{\text{i},3}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}}_{\text{m},\text{i}}\right)-{\text{a}\prime}_{\text{m}}{\text{F}}_{\text{i},3}\left(\text{r},\text{z},{\text{t}}_{\text{n}},{\text{h}\prime}_{\text{m},\text{i}}\right)\}$$

(4)

Where:

r = radial distance with respect to the lightning channel,

z = height of observation point with respect to the ground surface,

$\overrightarrow{{\mathrm{B}}_{\mathrm{\phi}}}$ = magnetic flux density,

$\overrightarrow{{\mathrm{E}}_{\mathrm{r}}}$ = horizontal electric field,

$\overrightarrow{{\mathrm{E}}_{\mathrm{z}}}$ = vertical electric field,

$${\mathrm{t}}_{\mathrm{n}}=\frac{\sqrt{{\mathrm{r}}^{2}+{\mathrm{z}}^{2}}}{\mathrm{c}}+(\mathrm{n}-1)\mathrm{\Delta}\mathrm{t}\phantom{\rule{2em}{0ex}}\mathrm{n}=\mathrm{1,2},\dots ,{\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$$

$${\mathrm{\Delta}\mathrm{h}}_{\mathrm{i}}=\{\begin{array}{l}\mathrm{\beta}{\mathrm{\chi}}^{2}\left\{(\mathrm{c}{\mathrm{t}}_{\mathrm{i}}-\mathrm{c}{\mathrm{t}}_{\mathrm{i}-1}\right)-\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}}-\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}+\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}-1}-\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}\}\phantom{\rule{0.5em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}>1\\ \mathrm{\beta}{\mathrm{\chi}}^{2}\left\{-\left(\mathrm{\beta}\mathrm{z}-\mathrm{c}{\mathrm{t}}_{\mathrm{i}}\right)-\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}}-\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}\right\}\phantom{\rule{11.5em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}=1\end{array}$$

$${\mathrm{\Delta}\mathrm{h}\mathrm{\prime}}_{\mathrm{i}}=\{\begin{array}{l}\mathrm{\beta}{\mathrm{\chi}}^{2}\left\{(\mathrm{c}{\mathrm{t}}_{\mathrm{i}-1}-\mathrm{c}{\mathrm{t}}_{\mathrm{i}}\right)+\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}}+\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}-\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}-1}+\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}\}\phantom{\rule{0.5em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}>1\\ \mathrm{\beta}{\mathrm{\chi}}^{2}\left\{-\left(\mathrm{\beta}\mathrm{z}+\mathrm{c}{\mathrm{t}}_{\mathrm{i}}\right)+\sqrt{{\left(\mathrm{\beta}\mathrm{c}{\mathrm{t}}_{\mathrm{i}}+\mathrm{z}\right)}^{2}+{\left(\frac{\mathrm{r}}{\mathrm{\chi}}\right)}^{2}}\right\}\phantom{\rule{11.5em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}=1\end{array}$$

$${\mathrm{h}}_{\mathrm{m},\mathrm{i}}=\{\begin{array}{l}\frac{({\mathrm{m}-1)\times \mathrm{\Delta}\mathrm{h}}_{\mathrm{i}}}{\mathrm{k}}+{\mathrm{h}}_{\mathrm{m}=\mathrm{k}+1,\mathrm{i}-1}\\ \frac{({\mathrm{m}-1)\times \mathrm{\Delta}\mathrm{h}}_{\mathrm{i}}}{\mathrm{k}}\phantom{\rule{2.5em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}=1\end{array}$$

$${\mathrm{h}\mathrm{\prime}}_{\mathrm{m},\mathrm{i}}=\{\begin{array}{l}\frac{({\mathrm{m}-1)\times \mathrm{\Delta}{\mathrm{h}}^{\mathrm{\prime}}}_{\mathrm{i}}}{\mathrm{k}}+{\mathrm{h}\mathrm{\prime}}_{\mathrm{m}=\mathrm{k}+1,\mathrm{i}-1}\\ \frac{({\mathrm{m}-1)\times \mathrm{\Delta}{\mathrm{h}}^{\mathrm{\prime}}}_{\mathrm{i}}}{\mathrm{k}}\phantom{\rule{2em}{0ex}}\mathrm{for}\phantom{\rule{0.25em}{0ex}}\mathrm{i}=1\phantom{\rule{0.25em}{0ex}}\end{array}$$

$${\mathrm{F}}_{\mathrm{i},1}\left(\mathrm{r},\mathrm{z},{\mathrm{t}}_{\mathrm{n}},{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)=\left(\frac{{\mathrm{\mu}}_{0}}{4\mathrm{\pi}}\right)\left\{\frac{\mathrm{r}}{{\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{3}}\mathrm{i}\right({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}})+\frac{\mathrm{r}}{{\mathrm{c}\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{2}}\frac{\partial \mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)}{\partial \mathrm{t}}\}$$

$${\mathrm{F}}_{\mathrm{i},2}\left(\mathrm{r},\mathrm{z},{\mathrm{t}}_{\mathrm{n}},{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)=\left(\frac{1}{4\mathrm{\pi}{\mathrm{\epsilon}}_{0}}\right)\{\frac{3\mathrm{r}\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}{{\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{5}}\times \mathrm{i}({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}})+\frac{3\mathrm{r}\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}{{\mathrm{c}\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{4}}\times \frac{\partial \mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)}{\partial \mathrm{t}}+\frac{\mathrm{r}\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}{{{\mathrm{c}}^{2}\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{3}}\times \frac{{\partial}^{2}\mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)}{\partial {\mathrm{t}}^{2}}\}$$

$${\mathrm{F}}_{\mathrm{i},3}\left(\mathrm{r},\mathrm{z},{\mathrm{t}}_{\mathrm{n}},{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)=\left(\frac{1}{4\mathrm{\pi}{\mathrm{\epsilon}}_{0}}\right)\left\{\frac{2{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}-{\mathrm{r}}^{2}}{{\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{5}}\times \mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)+\frac{2{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}-{\mathrm{r}}^{2}}{\mathrm{c}{\left(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}\right)}^{4}}\times \frac{\partial \mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)}{\partial \mathrm{t}}-\frac{{\mathrm{r}}^{2}}{{\mathrm{c}}^{2}{(\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}})}^{3}}\times \frac{{\partial}^{2}\mathrm{i}\left({\mathrm{h}}_{\mathrm{m},\mathrm{i}},{\mathrm{t}}_{\mathrm{n}}-\frac{\sqrt{{\mathrm{r}}^{2}+{\left(\mathrm{z}-{\mathrm{h}}_{\mathrm{m},\mathrm{i}}\right)}^{2}}}{\mathrm{c}}\right)}{\partial {\mathrm{t}}^{2}}\right\}$$

$${\mathrm{a}}_{\mathrm{m}}=\{\begin{array}{l}\frac{{\mathrm{\Delta}\mathrm{h}}_{\mathrm{i}}}{2\times \mathrm{k}}\phantom{\rule{2em}{0ex}}\mathrm{f}\mathrm{o}\mathrm{r}\phantom{\rule{0.25em}{0ex}}\mathrm{m}=1\phantom{\rule{0.25em}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0.25em}{0ex}}\mathrm{m}=\mathrm{k}+1\\ \phantom{\rule{0.75em}{0ex}}\frac{{\mathrm{\Delta}\mathrm{h}}_{\mathrm{i}}}{\mathrm{k}}\phantom{\rule{1.5em}{0ex}}\mathrm{f}\mathrm{o}\mathrm{r}\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{s}\phantom{\rule{0.25em}{0ex}}\end{array}$$

$${\mathrm{a}\mathrm{\prime}}_{\mathrm{m}}=\{\begin{array}{l}\frac{{\mathrm{\Delta}{\mathrm{h}}^{\mathrm{\prime}}}_{\mathrm{i}}}{2\times \mathrm{k}}\phantom{\rule{2em}{0ex}}\mathrm{f}\mathrm{o}\mathrm{r}\phantom{\rule{0.25em}{0ex}}\mathrm{m}=1\phantom{\rule{0.25em}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0.25em}{0ex}}\mathrm{m}=\mathrm{k}+1\\ \phantom{\rule{0.75em}{0ex}}\frac{{\mathrm{\Delta}{\mathrm{h}}^{\mathrm{\prime}}}_{\mathrm{i}}}{\mathrm{k}}\phantom{\rule{1.35em}{0ex}}\mathrm{f}\mathrm{o}\mathrm{r}\phantom{\rule{0.25em}{0ex}}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{s}\phantom{\rule{0.25em}{0ex}}\end{array}$$

k is division factor (≥2)

Fig 4 illustrates the evaluated lightning induced voltage on the line where striking distance is 50m and the conductor height is 10m, respectively. Considering the problem geometry in Figs Figs11 and and3,3, and the fact that this particular distance of 50m is within the critical area to cause the flashover, therefore these parameters are used as the basis to carry out the experimental work. Whilst the 1.2/50μs standard lightning impulse voltage waveform generated in the laboratory is to replicate the similarity of the real waveform obtained in natural environment. In addition, the 10m height is to reflect the actual and typical height of an overhead distribution line. Thus, with these several considerations, the peak induced voltage of 122kV obtained is very much reasonable to be chosen and to be injected as a source voltage in experimental work. It is worth to note that the typical Basic Insulation Lightning Level (BIL) for 33 kV distribution line is around 110kV and much less for lower voltage system, such as 22kV or 11kV. That’s mean the higher the voltage above the BIL, the higher the probability of the equipment damages due to this induced voltage.

Insulators, as their name indicates, are used to isolate live conductors from the grounded supporting structure. Insulators are designed with appropriate shapes according to their application. In early times, native materials were used for manufacturing insulators such as porcelain from clay, feldspar and quartz, and glass from silica, soda ash, dolomite, limestone, feldspar and sodium sulphate [22].

Due to material advancement about four decades ago, electrical industries found a solution to overcome the low performance of traditional insulators by introducing the polymer insulator [23]. Indeed, polymer insulators have shown excellent performance under heavily polluted conditions as compared to ceramic and glass types. The superior material also allowed for easy handling and maintenance, e.g. installation and washing. However, the organic compounds of the polymer are much more likely to age in time, mainly caused by electrical overstress and radiation [22–27].

In this study, a 10kV polymer insulator was studied as shown in Fig 5 and the specifications of the insulator are tabulated in Table 2 as follows:

It is known that the insulator was prone to environmental degradation. Perhaps, the mechanical characteristic of the insulator is highly at risk. Occasionally, some insulator will bend due to the weight load of the power line or results of the external force like a fallen tree or faulty pole. On field observation has recorded that the insulators were inclined (as shown in Fig 6) due to the events which consequently influence the clearance of the line to the nearby grounded parts such as cross-arm.

In this research, the values for electrical breakdown under a negative and positive standard impulse voltage (1.2/50 μs) was investigated assuming weather conditions of wet and wet with 4% salt. In order to represent the effect of the insulator angle with respect to the cross-arm (due to the force axis on the line as shown in Fig 7), a metal grounded plate was set at the bottom of the insulator and the electrical behaviour of the insulator under different angles with respect to the metal plate was investigated and the values of the leakage current and breakdown voltage were determined.

Figs Figs88 and and99 show the values of the 50% breakdown voltage and leakage current for different angles with respect to the cross arm under a negative impulse voltage (1.2/50μs) and wet conditions.

Moreover, Fig 10 illustrates the value of the 50% breakdown voltage for different angles with respect to the cross arm under a positive impulse voltage (1.2/50μs) and wet conditions.

Referring to Fig 10, by applying such smaller angles to the insulator, the breakdown voltage decreased significantly. It has been noticed that the time taken for breakdown also shorten within 1.5 μs which is noteworthy for lightning protection study.

Figs Figs1111 and and1212 show the electrical breakdown for different insulator angles with respect to the cross-arm. Both figures indicate the different path of flashover due to the changes of clearance distance.

As illustrated in Figs Figs1111 and and1212 the electrical discharge path for 90° is different from 60° because of an increase in the electric field in the area between the insulator and the cross-arm. The values of the 50% breakdown voltage and leakage current for different angles with respect to the cross arm under a negative impulse voltage (1.2/50 μs) and wet conditions with 4% salt conditions is demonstrated in Figs Figs1313 and and1414.

Moreover, the values of the 50% breakdown voltage and leakage current for different angles with respect to the cross arm under negative impulse voltage (1.2/50μs) and wet with 4% salt conditions are shown in Figs Figs1515 and and1616.

Fig 17 shows the peak values of the breakdown voltage and leakage current under different impulses, insulator angle and wet conditions. The results show that the insulator angle with respect to the cross-arm has an effect on the values of electrical breakdown for both positive and negative impulses and also under both wet and salty wet conditions. This is because of changes in the field distribution in the space between the insulator and the cross-arm. Moreover, by reducing the insulator angle, the values of the leakage current at breakdown show a reducing trend.

In order to consider the electrical behaviour of an insulator under different inclination angles, the finite element analysis (FEA) method was used. This method assisted the efficient analysis of field distributions across different materials. A full scale model of a 10 kV polymer insulator was modelled using the Ansys HFSS software. Fig 18 shows the model attached to a cross-arm structure and surrounded by air. In addition, Fig 19 shows the profile of the electric field versus time for three different insulator angles (angles with respect to the cross-arm) during dry conditions while Fig 20 shows the same simulation but under humid conditions. The model was energised by a lightning induced voltage as presented in Fig 4 which recorded as high as 122 kV. The measurement of the electric fields was taken at the reference point marked as “probe”.

As shown in Figs Figs1919 and and20,20, the insulator angle has a significant effect on the profile of the electric field within the space near to the insulator, especially for the smaller angles. Note that the electric field increased for the smaller angles because of the shorter live-to-ground distance which means the possibility of flashover occurring is increased. Similarly, the rate of degradation of the polymer insulator could be amplified. Fig 21 shows the electric field distribution within the space around the insulator with an inclination angle. The maximum and mean values of the electric field in the space between the insulator and cross-arm for different angles are summarised accordingly in Table 3.

The results show that the insulator angle can effectively escalate the field distribution in the space between the insulator and the cross-arm regardless of the air humidity. It was calculated that the percentage difference of the electric field (between 90° and 45°) can be up to 88%. The significant increase of the electric field due to the small inclination angle reduces the electrical breakdown values as the ionisation of the air takes place at a lower voltage. Moreover, Table 3 also indicates that the value of the electric field at the reference point is slightly increased by about 0.4% - 0.7% of difference due to changes in humidity in the surrounding air. Particularly, the electric field increases when the humid air has a high volume conductivity compared to dry air.

Lightning induced voltage is one of the major electrical problems for MV lines because of the length of the line and the low value of the CFO of the line compared to transmission lines. On the other hand, when considering the indirect effects of lighting, the lightning electromagnetic field is the source of the lightning induced voltage which can be created by any lightning events around the line [11, 28, 29]. Therefore, in distribution networks the chance of indirect effects is higher than direct effects. Moreover, in order to design appropriate values for lightning protection and also to increase the insulation level of the line, consideration of the weather conditions, the structure of line and also the insulator angle will be required, otherwise neglecting these factors will cause the stability of the line to be reduced. It is important to take account of the peak value of the lightning induced voltage in Fig 4 and also the behaviour of the lightning induced voltage versus the current and radial distance changes (as illustrated in Figs Figs2222 and and2323 respectively). Based on Fig 22 the induced voltage on the power line increases linearly with the peak current, thus indicating that serious measures should be taken when designing both the current and voltage withstand capabilities of electrical systems.

The behaviour of the lightning induced voltage presented in Fig 22 is dependently changes according to the striking distance. In contrast, the results in Fig 23 depicts a decreasing trend of induced voltage over the striking distance, r.

This work studied the behaviour of a polymer insulator under different weather conditions and also insulator angles (with respect to the cross-arm) and can be helpful to set proper lightning protection on a MV line. Ultimately, the high lightning density in Malaysia requires more research in this field in order to optimise the entire system to avoid costly failure in advance.

In this paper, the electrical performance of a 10 kV polymer insulator was determined experimentally under negative and positive impulse conditions for different types of weather and insulator angles. Moreover, the behaviour of the electric field and voltage along an insulator for different insulator angles was studied by modelling the insulator and the results were discussed appropriately. Results showed that the insulator angle and weather conditions reduced the value of the breakdown voltage and thus will reduce the line’s lightning performance. Furthermore, this behaviour provides excellent information on what should be done to protect those lines against the indirect effects of lightning, whereby consideration should be given to different impulse voltages and also the use of local information of the environment.

This work was supported by Universiti Putra Malaysia.

Data Availability

All relevant data are within the paper and its Supporting Information file.

1. Izadi M, Kadir A, Abidin MZ, Hajikhani M. An Algorithm for Evaluation of Lightning Electromagnetic Fields at Different Distances with respect to Lightning Channel. Mathematical Problems in Engineering.2014.

2. Rameli N, Ab Kadir M, Izadi M, Gomes C, Jasni J. Evaluation of Lightning Induced Voltage due to the Effect of Design Parameters on Medium Voltage Distribution Line. Jurnal Teknologi. 2013;64(4).

3. Izadi M, Ab Kadir MZA, Hajikhani M, editors. Effect of lightning induced voltage on the line polymer insulator in a distribution line. 2014 International Conference of Lightning Protection (ICLP); 2014: IEEE.

4. Izadi M, Ab Kadir MZA, Hajikhani M. On the Lightning Induced Voltage Along Overhead Power Distribution Line. Journal of Electrical Engineering & Technology. 2014;9(5):1694–703.

5. Rachidi F. A review of field-to-transmission line coupling models with special emphasis to lightning-induced voltages on overhead lines. IEEE Transactions on Electromagnetic Compatibility,. 2012;54(4):898–911.

6. Rawi IM, Yahaya MP, Kadir M, Azis N, editors. Experience and long term performance of 132kV overhead lines gapless-type surge arrester. 2014 International Conference of Lightning Protection (ICLP); 2014: IEEE.

7. Abd Rahman M, Izadi M, Ab Kadir M, editors. Influence of air humidity and contamination on electrical field of polymer insulator. 2014 IEEE International Conference on Power and Energy (PECon); 2014: IEEE.

8. Abidin NZ, Abdullah A, Norddin N, Aman A, Ibrahim K, editors. Leakage current analysis on polymeric surface condition using time-frequency distribution. 2012 Ieee International Power Engineering and Optimization Conference (PEDCO) Melaka, Malaysia; 2012: IEEE.

9. Ahmadi-Joneidi I, Majzoobi A, Shayegani-Akmal AA, Mohseni H, Jadidian J. Aging evaluation of silicone rubber insulators using leakage current and flashover voltage analysis. Dielectrics and Electrical Insulation, IEEE Transactions on. 2013;20(1):212–20.

10. Engelbrecht C, Gutman I, Garcia R, Kondo K, Lumb C, Matsuoka R, et al. Artificial Pollution Test for Polymer Insulators. CIGRE Technical Brochure. 2013(555).

11. Cai L, Wang J, Zhou M, Chen S, Xue J. Observation of natural lightning-induced voltage on overhead power lines. IEEE Transactions on Power Delivery. 2012;27(4):2350–9.

12. Tripathi R, Grzybowski G, Ward R, editors. Electrical degradation of 15 kv composite insulator under accelerated aging conditions. Electrical Insulation Conference (EIC), 2013 IEEE; 2013: IEEE.

13. Su N, Lv X-B, Shen H-B, Zhang B-Y, Lin Y. Research and Analysis on the High Current Impulse Withstand Capability of 10 kV Polymer Housed Arreste. Insulators and Surge Arresters. 2012;5:013.

14. Yokoyama S, Miyake K, Mitani H, Yamazaki N. Advanced observations of lightning induced voltage on power distribution lines. IEEE Transactions on Power Delivery. 1986;1(2):129–39.

15. Ishii M, Michishita K, Hongo Y. Experimental study of lightning-induced voltage on an overhead wire over lossy ground. IEEE Transactions on Electromagnetic Compatibility. 1999;41(1):39–45.

16. Paolone M, Nucci CA, Petrache E, Rachidi F. Mitigation of lightning-induced overvoltages in medium voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters: Modeling and experimental validation. IEEE Transactions on Power Delivery. 2004;19(1):423–31.

17. Nucci C, Rachidi F. Lightning-induced voltages on overhead power lines. Part I: Return stroke current models with specified channel-base current for the evaluation of the return stroke electromagnetic fields. 1995.

18. Rachidi F, Nucci CA, Ianoz M, Mazzetti C. Influence of a lossy ground on lightning-induced voltages on overhead lines. IEEE Transactions on Electromagnetic Compatibility. 1996;38(3):250–64.

19. Rachidi F, Nucci CA, Ianoz M. Transient analysis of multiconductor lines above a lossy ground. IEEE Transactions on Power Delivery. 1999;14(1):294–302.

20. Yutthagowith P, Ametani A, Nagaoka N, Baba Y. Lightning-Induced Voltage Over Lossy Ground by a Hybrid Electromagnetic Circuit Model Method With Cooray–Rubinstein Formula. IEEE Transactions on Electromagnetic Compatibility. 2009;51(4):975–85.

21. Izadi M, Ab Kadir MZ, Gomes C, Wan Ahmad WFH. Analytical expressions for electromagnetic fields associated with the inclined lightning channels in the time domain. Electric Power Components and Systems. 2012;40(4):414–38.

22. Looms J. Insulators for High Voltages, Peter Peregrinus Ltd;
London, United Kingdom, ISBN. 1988;863411169.

23. Vázquez IR. A Study of Nanofilled Silicone Dielectrics for Outdoor Insulation: University of Waterloo; 2009.

24. Farzaneh M, Chisholm WA. Insulators for icing and polluted environments: Wiley.com; 2009.

25. Ghosh S. Insulation Coordination in Power System: Electrical Engineering; 2013 [15 OCTOBER]. Available from: http://www.electrical4u.com/insulation-coordination-in-power-system/.

26. Tavlet M, Ilie S. Behaviour of organic materials in radiation environment. Radiation and Its Effects on Components and Systems, RADECS. 1999;99:210–5.

27. Bojovschi A, Wong K, Rowe W. Impact of electromagnetic radiation on cascaded failure in high voltage insulators. Applied Physics Letters. 2011;98(5):051504.

28. Izadi M, Ab Kadir M, editors. On the Relation between Ground Resistivity and Lightning Induced Voltage Evaluation on the Distribution Lines. IEEE conference, Istanbul Turkey; 2013.

29. Rizzo R, Andreotti A, Del Pizzo A, Verolino L. Lightning induced effects on lossy multiconductor power lines with ground wires and non-linear loads-Part II: simulation results and experimental validation. Przeglad Elektrotechniczny (Electrical Review). 2012;88(9b):305–8.

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