Modeling and Simulation of a Metal Oxide Lightning Surge Arrester for 132kV Overhead Transmission Lines

Power system outages are affected by many direct and indirect factors, of which lightning is the most important one. Lightning causes disruption in the power distribution system that directly or indirectly affect the end consumer. Lightning occurs because of friction between oppositely charged clouds. Lightning strikes usually target conductive material as well as electrically charged regions of the earth such as Power Transmission Systems, antennas, and other conductive surfaces [1]. It is a natural phenomenon in which millions of volts and thousands of amperes of current strike the stratosphere or ground where conductive or electrical equipment are present. This phenomenon produces a breakage in the insulating layers of air between the clouds and the earth; so a visible flash of light is seen [2]. The waveform of a strike for 8/20us  is shown below:

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Figure 1. Standard waveform of a lightning strike

During decades of observation on lightning strikes and lab experiments with Tesla coils and artificially produced lightning inside labs, concluded the above waveform, which roughly stands for the type of waveform possible in nature.

Figure 1 shows the main categorization of lightning strike which reaches its peak value in 8 microseconds and then drops to half its peak value in 20 microseconds [3].

Underground transmission system is completely insulated below the layers of soil, while the overhead transmission system is exposed to air as well as lightning strikes. In third world countries, overhead distribution systems are a common practice. For a lightning strike to damage a distribution system, it does not need to touch the transmission system physically. All it has to do is to strike at the vicinity of the transmission system. This type of a lightning strike at the vicinity of a distribution system typically induces about 300 thousand volts of electricity in the nearby electrical transmission lines. There is no way of safeguarding the distribution system or the nearby transmission lines from such a high voltage. Typical protective techniques such as compensators are not enough to safeguard the nearby transmission lines from the effects of the induced voltage of this order [4].

In a normal overhead transmission system, insulator strings are attached as a safety measure that can absorb voltage swells up to specific limits. This limit is called Critical Flashover Voltage (CFOV) rating. CFOV is defined as, “a maximum value of the absorption power of the insulator string in a voltage swell phenomena in the distribution system”. In the event of exceeding this rating, the transmission system could be damaged by the voltage swell, resulting in damage to very expensive equipment in the nearby substation. The phenomenon of exceeding voltages over the ratings of the critical flashover voltage of the insulator string is called a flashover. Researches are carried out everywhere in the world to test this threshold limit of an insulating string, or another insulating equipment, by creating an artificial flashover.

Table 1. Arrester models

IEEE Model

1111111111111.png $\begin{aligned} \mathrm{L} 1 &=15 \mathrm{d} / \mathrm{n}[\mu \mathrm{H}] \\ \mathrm{R} 1 &=65 \mathrm{d} / \mathrm{n}[\Omega] \\ \mathrm{L} 0 &=0.2 \mathrm{d} / \mathrm{n}[\mu \mathrm{H}] \\ \mathrm{R} 0 &=100 \mathrm{d} / \mathrm{n}\lceil\Omega] \\ C &=\frac{100 n}{d}[p F] \end{aligned}$ d is the estimated height of the arrester in meter n is the number of parallel columns of MO in the arrester

Pinceti Model

2.png $\begin{aligned} L_{1} &=\frac{1}{4}\left(\frac{\frac{U_{r 1}}{T_{2}}-U_{\frac{r 8}{T_{2}}}}{U_{\frac{r 8}{T_{2}}}}\right) U_{r}[\mu H] \\ L_{0} &=\frac{1}{12}\left(\frac{\frac{U_{r 1}}{T_{2}}-U_{\frac{r 8}{T_{2}}}}{U_{\frac{r 8}{T_{2}}}}\right) U_{r}[\mu H] \end{aligned}$ Ur is the rate voltage $U_{r 1 / T 2}$ is the residual voltage at 10 kA fast front current surge $1 / T 2 \mu s$ $U_{\frac{r 8}{20}}$ is the residual voltage at current surge with $8 / 20 \mu s$ shape $R_{0}=1 M \Omega$

Fernandez-Diaz model

$\begin{align}  & \text{L1}=\frac{2}{5}\frac{{{U}_{\frac{r8}{T2}}}-Uss}{{{U}_{\frac{r8}{T2}}}}{{U}_{r[\mu H]}} \\ & \text{C}=\frac{1}{55}\frac{{{U}_{\frac{r8}{T2}}}-Uss}{{{U}_{\frac{r8}{T2}}}}{{U}_{r[pF]}} \\\end{align}$ Ur  is the rated voltage 3.png Ur8/20  is the residual voltage at 10kA  current surge with $8 / 20 \mu s$ shape in kV Uss  is the residual voltage at at $500 \mu s$ or $30 / 70 \mu s$ in $k V$ $R_{0}=1 M \Omega$

In the past few decades, transmission line arresters (TLAs) have shown promising results for protection of distribution systems at substation as well as transmission line level [3, 5, 6]. Transmission line arrester are specifically designed electrical circuits that can absorb electrical power above a certain rating up to a certain limit. Most of the absorbed power is diverted to the nearby ground level; and is discarded from the distribution system safely, while the remaining is dissipated as heat. Table 1 describe surge arrester models.

Overvoltage occurs from various effects both naturally, as well as from system faults in the electrical power system. They are classified into two classes, switching over-voltage and lightning over-voltage. For designing of extra high-voltage parameters of a power system distribution, it is necessary that switching over-voltages are taken into account. For instance, designing of an arrester for an extremely high-voltage line requires the 1/2 μs front-of-wave (FOW) switching Surge analysis [7]. Specific interest is the lightning strike that occurs in the vicinity or directly on a substation, or a part of a power distribution system. Lightning strikes are typically in the range of millions of volts, with thousands of amperes of current. A direct hit on a transmission system causes drastic damage to the equipment if the system is unprotected. However, it is not necessary that the lightning strike should hit the transmission system directly, a nearby hit can also cause the collapse of insulating airfield, and can cause induced voltages and induced current in the transmission system. The induced voltages can reach as high as 300 kilovolts with currents as large as 10000 amperes [3].

In the research [8], authors proposed an Ultra High Voltage TLA, which was tested on a 828kV overhead transmission line system. The design was tested in parallel combination with the existing fixed arrester. The tests were carried out in collaboration with energy Supplier Company, and the arrester proved its working for the said purpose. However, TL protection parameters were not calculated in the research paper. A study in Malaysia was conducted recently on the design and selection of a sure arrester for a 500kV overhead transmission line system. It was concluded that a 132kV arrester with suitable modifications can be utilized to work for the 500kV line, and that in order to protect the line, the surge arrester must be installed [9].

This paper is an intimate understanding of the working of a transmission line arrester installed on an overhead transmission line system for protection of the nearby substation as well as the transmission system.

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3.2 Lightning model simulation

The model of the Lightning surge has been designed on the model proposed by, time series of the Lightning Voltage Surge as well as the current surge is shown in Figure 4 and 5 consecutively:

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Figure 4. Max value of the lightning source

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Figure 5. Lightning current waveform (8/20 μs) showing peak value of ~10kA

The maximum value of the lightning strike is about 1M Volts on an 8/20 μs waveform.

The current waveform shows the following series:

3.3 Curve fitting results in Matlab

Matlab curve fitting toolbox is used for curve fitting on the values obtained from the IEEE group for A₀ and A₁ that gives equations from which any dependent value for an independent input could be found out. The graphs shown in Figure 6 and 7, both for A₀ and A₁ are generated with general model power2 with 95% confidence bounds.

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Figure 6. Curve fitting result for A0

The curve fitting routine run for A₀ gives a binomial power fit with the following equations:

General model Power2:

f(x)= a*x^b+c     (1)

Coefficients (with 95% confidence bounds):

a = 11.62 (4.257,18.98)

b = 0.428 (0.2639,0.5922)

c =112.8 (105.2,120.4)

SSE: 28.9

R-square: 0.982

Adjusted R-square: 0.978

RMSE: 1.792

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Figure 7. Curve fitting result for A1

Similarly, for A₁:

General model Power2:

f(x)= a*x^b+c      (2)

Coefficients (with 95% confidence bounds):

a = 114.8 (-403.7,633.3)

b = 0.04436 (-0.1503,0.2391)

c = -11.61 (-528.7,505.5)

Goodness of fit:

SSE: 31.24

R-square: 0.9582

Adjusted R-square: 0.9489

RMSE: 1.863

3.4 Residual voltages

The time series of residual voltage data is shown in Figure 8:

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Figure 8. Residual voltage in arrester with peak value shown

The residual voltage test shows a peak value of 194kV which is lower than the maximum residual voltage obtained from manufacturer specification that is 291kV, and satisfies the model requirements.

3.5 Footing currents

Footing current is the term used for the current flowing in the low impedance resister at the base of the tower. It is used for providing a high conductive path to the current appearing on the arrester in the event of a lightning Strike. Typical values of this resistor lie between 20 to 25 ohms.

Figure 9 shows a discharge current maximum value of 4.79kA which passes from the footing resistor and drops to 0 Amperes at about 25µs, which shows the stability for arrester.

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Figure 9. Footing current of the arrester showing peak value

3.6 Simulation results after parameter adjustment

For a 20 μs duration of simulation, after the adjusted parameters of the L1 from default value to 2.905 in multiple runs of the simulation, the resulting waveform shows promising results given below:

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Figure 10. Residual voltage on the designed arrester

The Figure 10 above shows a peak value of 294.239 kV of residual voltage which is upto the standards and the consistency is assured as well.

3.7 Design parameters summary

The arrester design parameters are tabulated in Table 2:

Table 2. Designed parameters of the arrester

3.8 Analysis

The analysis of the designed arrester is done visually from the graphs considering the various requirements of the manufacturer as well as the design criteria. However, a few of the analysis is done mathematically to prove the arrester’s efficacy in the desired voltage rating installation. For this study, the following parameters are analyzed mathematically for the justification of the design.

3.8.1 Lightning impulse withstand voltage – LIWV

The lightning impulse withstand voltage is defined using the following equation:

LIWV = BIL /VrPeak

LIWV $_{\frac{8}{20}}=550 \mathrm{kV} / 322 \mathrm{kV}=1.708$      (3)

322kV is the peak residual voltage from the manufacturer specification table provided in Table 3. The higher this value, the better the insulation level. So, LIWV value is satisfactory.

3.8.2 Energy absorption capability

The instantaneous energy absorption at 0.5 μs is thus calculated as:

Energy $=\mathrm{Pd}$

Energy $=\mathrm{Vid}$

Energy $=294239 \times 5000 \times 0.5 \times 10^{-6}$

735.59 Jouls@10kA $\in 0.5 \mu \mathrm{s}$

This value of energy is also in agreement and is in fact improved from previous designs.

The total energy absorbed in 20 μs of the lightning strike is calculated as below:

Total Energy$=\int_{1009}^{9950} \mathrm{VI} \Delta t d x\\=\int_{1009}^{9950}|-7786.95 x+294239| d x \Delta t\\=378869094867.025 \Delta \mathrm{t}\\=378869094867.025 \times 20\\\times 10^{-6}JoulesTotalEnergy$

Total Energy $=7.577$ MegaJoules        (4)

This value is greater than the required minimum of 5kJ that justifies the energy absorption capability of the designed arrester.

3.8.3 Relative error

Referring to the manufacturer’s data sheet reproduced in Table 3: 

Table 3. Ohio brass EP series 120kV arrester for 132kV system

The relative error is defined as:

$\epsilon=\frac{\left(V_{S}-V_{d}\right)}{V_{d}} \times 100 \%$     (5)

In this study:

$\epsilon=\frac{294.239 k V-291 k V}{291 k V} \times 100 \%$

$\epsilon=1.113 \%$

This value is targeted to result between 0 and 4%, and the resulting value is quiet expectedly good and relates to the manufacturer’s specs, hence the designed arrester is improved in its relative error, LIWV, as well as its energy absorption capability.