GENETIC ALGORITHM BASED LIGHTNING ESTIMATION MODEL

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J. Mech. Cont.& Math. Sci., Special Issue, No.- 6, January (2020) pp 1-14

Copyright reserved © J. Mech. Cont.& Math. Sci.

MUSSE MOHAMUD AHMED et al.

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GENETIC ALGORITHM BASED LIGHTNING ESTIMATION MODEL

Musse Mohamud Ahmed

¹

, Aohammad Kamrul Hasan

²

, Jong F. Chen

³

, Denis Lee

⁴

1,2,3,4

Dept. Electrical and Electronics Engineering, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia

*Corresponding author: [email protected]

https://doi.org/10.26782/jmcms.spl.6/2020.01.00001 Abstract

When lightning strikes to the transmission line, orifices in the insulation can be created. As a result, the insulation co-ordination between phases is breakdown and over- voltage will propagate across the transmission line in the form of electrical fields. Hence, the system will encounter under-frequency and prolonged type of destruction. In a worst-case situation, it may lead blackout. One of the effective ways to reduce lightning impact is to identify the lightning activity. This researchhas been carried out to familiarize the lightning activity in Sarawakarea;hence, the Genetic Algorithm (GA) is utilized to optimize the crucial constants of the lightning empirical equation. As the constant values are successful to be optimized, estimation of Ground Flash Density (GFD) can be performed. The performance is evaluated using Matlab. Using the GA optimized parameter the estimations areprecise. To achieve estimation that is more accurate many trials are required to be carried out in order to determine the best fitness value. In this article, three casesare carried out in determining the optimal solution in term of constant “a” and “b” for each sub-region in Sarawak.

Keywords : GA, Optimization, Ground Flash Density (GFD), Lightening

I. Introduction

Lightning is one of the destructive phenomena. The earth, which experiences the loudest sound and brightest light, is usually produced by lightning. In worldwide, there are about 9 million lightning discharged in every single day.

Lightning can be seen virtually but it is hard for us to well understand. Lightning occurs everywhere and the range of lightning can be very wide, the total discharge can be from tens of nanoseconds to almost a second, and its obscuration had made it even hard to be studied[IV-VII]. Nevertheless, an integrated diagram of the

JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES

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ISSN (Online) : 2454 -7190 , Special Issue, No.-6, January (2020) pp 1-14 ISSN (Print) 0973-8975

The Paper Presented at 5th International Conference on Recent Trends in Computer Sciences and Electronics (RTCSE)

Organized by University of Hawaii, USA and Gyancity Research Lab, Haryana, India

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phenomenon of lightning is acquired after decades of measurement. Figure 1 presents the lightning and its categories in order to model the lightning.

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Figure. 1.3: Types of cloud to ground lightning: types of lightning (a), downward lightning negatively charged leader (b), upward lightning positively charged leader (c), downward lightining positively-charged leader (d), upward lightning negatively charged leader (e) [IV].

Geneticalgorithm is a useful method to optimize the constrained and unconstrained problems nowadays. The utilization of this approach is based on the natural selection concept and it is highly related to biological evolution. The population is considered as the chromosomes or parents, where they have the ability to produce the child or offspring. As this process is conducted continuously, a generation will be kept replacing by a new generation. Throughout this flow, there are three rules, which are important.

 Selection rule: Selection is carried out to determine the winner individual, which is essential for contributing the next generation.

 Crossover rule: Combination of two parents from the population to produce children.

 Mutation rule: Application of the random change to the chromosomes and genes [I].

This study is conducted with the scope of familiarizing to the formation of lightning in Sarawak. Besides, derivation of the constants of the Ground Flash Density (GFD)- Thunderstorm Days (TD) empirical formula from recorded empirical data and measured lightning detection system data using a genetic algorithm is carried out by using Matlab. The formula developed by Cigre in 1991 was based on data obtained from a specific locality but it has been generally used as given in Eqn. (1) [II];

GFD = 0.04 TD 1.25 (1)

However,it could be distinct for other geographical locations due to differing lightning characteristics, so it may be able to generalize it Eqn. (2) [VIII];

GFD = a TD b (2)

where a, b are constants to be estimated.

II. Optimazation Using Genetic Algorithm

The approach taken in this project is to use genetic algorithm (GA) [3] to estimate a, b from the empirical recorded data and measured lightning detection system data. To specify the lightning characteristics parameter estimation problem, the i^th chromosome pi is defined with genes and as;

p_i = [a_i, b_i] (4)

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4 where a_max< a_i<a_min, b_max< b_i<b_min. A. Initialize Population

A random population P of N_popchromosome is generated;

P = {p₁, p₂, ..., p_Npop} (4)

p_i, i = 1, ..., Npop may synthesized using a random generator as;

a_i = a_min + R. ( a_max - a_min ), b_i = b_min + R. ( b_max - b_min ) (5) where R∈ [0,1] is a random number.

B. Calculate Chromosome Fitness

The fitness function f (p_i) of chromosome p_i, i = 1, ..., Npop is defined as;

| GFD_meas – GFD_emp | (6)

where GFD_meas are the measured values from the lightning density map in figure 3.3 and GFD_emp are the calculated values from the empirical data in table 3.1 and equation

GFD = a Td ^b (7)

The GFD_meas and GFD_emp for the same region are considered in the calculation to estimate the lightning characteristics parameters.

C. Select Winner Populations

First, a probability q_i to each chromosome p_i is assigned using its fitness value as;

qi = ^{( )}

∑ ( ) , 0 < qi< 1 (8)

Next, the cumulative probability 𝑞 for p_i is defined as;

𝑞 = ∑ 𝑞 i = 1, ..., Npop] (9)

Then, a roulette wheel competition is held to select two winner parents, p_iand p_j, from the population. A parent p_i is a winner if;

𝑞 < 𝑑 ≤ 𝑞 , d = R∈ [0,1] (10)

D. Genes Crossover

With two winner parents, four candidate offspring c_k, k = 1, 2, 3, 4 are synthesized to produce one winner offspring o. These are;

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5 𝐶 = 𝑝 + 𝑝

2

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𝐶 = 𝑝 (1 − 𝜇 ) + max ( 𝑝 , 𝑝 ).𝜇 (12)

𝐶 = 𝑝 (1 − 𝜇 ) + min ( 𝑝 , 𝑝 ).𝜇 (13)

𝐶 = (𝑝 𝑝 )(1 − 𝜇 ) + (𝑝 + 𝑝 ) 2

(14) Where the crossover weightage 𝜇 is user assigned and

max (𝑝 , 𝑝 ) = [max (𝑎 , 𝑎 ) ,max (𝑏 , 𝑏 )] (15)

min (𝑝 , 𝑝 ) = [min (𝑎 , 𝑎 ) ,min (𝑏 , 𝑏 )] (16)

𝑝 = [𝑎 ,𝑏 ] (17)

𝑝 = [𝑎 ,𝑏 ] (18)

The candidate offspring are designed to span across diverse regions of the parameter space as illustrated in figure 1, in order to enhance the effectiveness of the global optimum search.

Fig. 1.Geometric Distribution ofCandidate Offspring in Parameter Space

The winner offspring o is determined from c_k, k = 1, 2, 3, 4 as;

o = c_i | min_i f (c_k), k = 1, 2, 3, 4 (19)

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6 where o = [𝑎 ,𝑏 ].

E. Mutation

The winner offspring, o next undergo mutation to synthesize three mutated offspring m_k, k = 1, 2, 3 as;

m_k = o + [𝑏 ∆ , 𝑏 ∆ ] = [𝑎 + 𝑏 ∆ , 𝑏 + 𝑏 ∆ ] (20)

where 𝑏 , 𝑏 ∈ { 0, 1}

∆ = 𝑅. min (𝑎 − 𝑎 , 𝑎 − 𝑎 ) (21)

∆ = 𝑅. min (𝑏 − 𝑏 , 𝑏 − 𝑏 ) (22)

and R = [-1, 1] is a random number.Thus, m_k are determined as;

m₁ = [𝑎 + 𝑏 ∆ , 𝑏 ] (23)

m2 = [𝑎 , 𝑏 + 𝑏 ∆ ] (24)

m₃ = [𝑎 + 𝑏 ∆ , 𝑏 + 𝑏 ∆ ] (25)

F. Reproduction

Let m = m_i | min_i f (m_k), k = 1, 2, 3, and

p = p_i | max_i f(P) (26)

p' = p'_i | max_i f(P') (27)

p'' = p''_i | max_i f(P'') (28)

Where,P, P' and P'' are the population of Npop size each.

An acceptance probability 𝜀 , 0 <𝜀 < 1 is defined. Then, a random probability 𝜌 , 0 <𝜌 < 1 is generated, such that;

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7 i. If 𝜀 < 𝜌 , then

 m ↔ p and thus the population become P' = {P, m | p ∉ P}

ii. If 𝜀 > 𝜌 , then

 m₁↔ piff (m1) < f (p) and thus the population becomes P' = {P, m₁ | p ∉ P}, else P' = P if f (m₁) > f (p).

 m2↔ p' if f (m2) < f (p') and thus the population becomes P'' = {P', m₂ | p' ∉ P'}, else P'' = P' if f (m₂) > f (p').

 m3↔ p'' if f (m3) < f (p'') and thus the population becomes P''' = {P'', m₃ | p'' ∉ P''}, else P''' = P'' if f (m₃) > f (p'').

G. Stopping Criteria

The GA iteration will stop if the following criteria are satisfied;

 f (p) <𝛿

 Generation exceeds a maximum, G_max

 | f ^G+1(p) - f ^G(p) | <𝛿 where f ^G (.) denotes the G^th generation fitness values.

III. Result And Discussion

The GA parameters are presented in Table 1. The optimization process of this study, each region in Sarawak is categorized as case 1, case 2 and case 3 where each case is used different values of amax, amin, bmaxand bmin.

Case 1: amax = 0.10, amin = 0.01, bmax =1.6, bmin = 1.0 Case 2: amax = 0.15, amin = 0.01, bmax =1.6, bmin = 0.9 Case 3: amax = 0.20, amin = 0.01, bmax =1.6, bmin = 0.8 Range of maximum and minimum constants:

case 1 < case 2 < case 3.

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Table 1. Parameter of Constants [8-17]

III.i. Optimization Result For Kuching Region

From the Vaisala lightning detection system in SEB, the measured value of GFD in Kuching is 16 flashes/km2/year as shown in table 2. On the other hand, based on the result of three cases in Kuching, each case presents the empirical value of GFD which is approximately same to the measured value of GFD. In case 1, empirical value of GFD is 16.022 flashes/km2/year, which is higher than the measured value of GFD about 0.022. For case 2, the empirical value of GFD is 16.038 flashes/km2/year, it is 0.038 higher than measured value of GFD. In case 3, the empirical value of GFD is 15.982, and it is 0.018 lower than the measured value of GFD.

Table 2. GFDmeas VS GFDemp

GA Parameter User Defined Value

Population size, Npop 300

a_min,a_max 0.02, 0.06

b_min, b_max 0.625, 1.875

Crossover weight, 𝜇 0.5 – 0.9

Mutation acceptance probability, 𝜀 0.1

Absolute fitness tolerance, 𝛿 0.01

Relative fitness tolerance, 𝛿 0.001

Maximum generation, Gmax 500

Measured value of GFD, flashes/km²/year

Empirical value of GFD, flashes/km²/year

(Td = 184)

Case 1 Case 2 Case 3

16.000 16.022 16.038 15.982

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In figure 2, empirical formula of case 1, case 2 and case 3 are combined and presented. Based on the graph, the red line, blue line and green line are nearly-close to each other. This means the constant values of three cases are approximately same even though the range of the constants are enlarged. This revealed that the constant a and b are neared to the optimal solution since the equations are converged.

Fig. 2. Empirical Formula of All Cases for Kuching Region III.ii. Optimization Result For Sri Aman Region

Using Vaisala lightning detection system in SEB, the measured value of GFD in Sri Aman is 6 flashes/km2/year as shown in table 3. On the other hand, based on the result of three cases in Sri Aman, each case presents the empirical value of GFD which is approximately same to the measured value of GFD. In case 1, empirical value of GFD is 6.027 flashes/km2/year, which is higher than the measured value of GFD about 0.027. In case 2, the empirical value of GFD is 5.993, and it is 0.007 lower than the measured value of GFD. For case 3, the empirical value of GFD is 6.032 flashes/km2/year, and it is 0.032 higher than measured value of GFD.

Measured value of GFD

Empirical value of GFD (Td = 105)

6.000 6.027 5.993 6.032

100 110 120 130 140 150 160 170 180 190 200

6 8 10 12 14 16 18 20

Annual Thunderstorm Days, Td Ground Flash Density, GFD (flashes/km2/year)

Case 1: GFD = 0.010Td^1.415 Case 2: GFD = 0.022Td^1.264 Case 3: GFD = 0.014Td^1.350

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Fig. 3. Empirical Formula of All Cases for Sri Aman Region III.iii. Optimization Result For Sibu Region

From the Vaisala lightning detection system in SEB, the measured value of GFD in Sibu is 12 flashes/km2/year as shown in table 4. On the other hand, based on the result of three cases in Sibu, each case presents the empirical value of GFD which is approximately same to the measured value of GFD. In case 1, empirical value of GFD is 11.986 flashes/km2/year, which is lower than the measured value of GFD about 0.014. In case 2, the empirical value of GFD is 12.071, and it is 0.029 higher than the measured value of GFD. For case 3, the empirical value of GFD is 12.078 flashes/km2/year, and it is 0.078 higher than measured value of GFD.

12.000 11.986 12.071 12.087

100 110 120 130 140 150 160 170 180 190 200

5 6 7 8 9 10 11 12

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Fig. 4. Empirical Formula of All Cases for Sibu Region III.iv. Optimization Result For Bintulu Region

From the Vaisala lightning detection system in SEB, the measured value of GFD in Bintulu is 6 flashes/km2/year as shown in table 5. On the other hand, based on the result of three cases in Bintulu, each case presents the empirical value of GFD which is approximately same to the measured value of GFD. In case 1, empirical value of GFD is 5.985 flashes/km2/year, which is lower than the measured value of GFD about 0.015. In case 2, the empirical value of GFD is 5.992, and it is 0.008 lower than the measured value of GFD. For case 3, the empirical value of GFD is 6.018 flashes/km2/year, and it is 0.018 higher than measured value of GFD.

6.000 5.985 5.992 6.018

100 110 120 130 140 150 160 170 180 190 200

10 15 20 25

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Fig. 5. Empirical Formula of All Cases for Bintulu Region

The execution time of the GA coding in Matlab software is long. This is because the execution system contains many iterations that required the looping process. Long execution time may lead the users have to spend a lot of time to execute the GA coding and not every execution can be succeeded. This means that the high specification of the computer is preferable in running the optimization process of GA. Besides, low population size consideration in GA process can lead the results to be low accuracy. In this project, low population size is selected due to the execution time is too long. In other words, if the project is carried out in a longer term, the high population size can be selected and this will definitely improve the accuracy of the results. In the GA coding implementation, the constant a and b that have to go through the optimization process do not have the standard maximum value and minimum value. The selection of the maximum and minimum values of the constants are based on the investigation of the previous journal papers. Hence, more researches should be carried in advance, hence it can contribute in determining the maximum and minimum values of constants a and b. Furthermore, the number of generations in GA coding plays a crucial role to enhance the reliability of the results. In every generation, the result will be corrected and the results’ tolerance is reduced.

Increasing the number of generations in GA process will not result the execution time to be too long.

100 110 120 130 140 150 160 170 180 190 200

4.5 5 5.5 6 6.5 7 7.5 8 8.5 9

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IV. Conclusion And Future Recommendation

As the geographical area in Sarawak state is much different as compared to other foreign countries, the existing empirical formula of lightning activity is possible to be modified by adding other factors to increase the effectiveness of the empirical equation in ground flash density estimation. For instance, the parameters such as temperatures, humidity, and wind speed are different among the countries.

Hence, more researches have to be carried out to establish a new modified empirical formula. The empirical formula can be improved by adding certain constants which may suit with its typical country. In conclusion, the objectives of this project are achieved where the GA technique is successful to be utilized in optimizing the constants of existing empirical formula. Although the results are still experiencing the tolerances, the results are still beneficial in estimation the ground flash density of each region in Sarawak. As the approximate values of the lightning activity parameters are determined, the power instruments can be protected in more effective manner against lightning strikes.

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