Monte Carlo simulation convergences’ percentage and position in future reliability evaluation

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 6, December 2022, pp. 6218~6227
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i6.pp6218-6227  6218
Journal homepage: http://ijece.iaescore.com
Monte Carlo simulation convergences’ percentage and position
in future reliability evaluation
Nur Nabihah Rusyda Roslan, NoorFatin Farhanie Mohd Fauzi, Mohd Ikhwan Muhammad Ridzuan
Department of Electrical Engineering, Universiti Malaysia Pahang, Pahang, Malaysia
Article Info ABSTRACT
Article history:
Received Sep 10, 2021
Revised Jul 23, 2022
Accepted Aug 15, 2022
Reliability assessment is a needed assessment in today's world. It is required
not only for system design but also to ensure the power delivered reaches the
consumer. It is usual for fault to occur, but it is best if the fault can be
predicted and the way to overcome it can be prepared in advance. Monte
Carlo simulation is a standard method of assessing reliability since it is a
time-based evaluation that nearly represents the actual situation. However,
sequential Monte Carlo (SMC) typically took long-time simulation. A
convergence element can be implemented into the simulation to ensure that
the time taken to compute the simulation can be reduced. The SMC can be
done with and without convergence. SMC with convergence has high
accuracy compared to the SMC without convergence, as it takes a long time
and has a high possibility of not getting accurate output. In this research, the
SMC is subjected to five different convergence items to determine which
converge simulation is the fastest while providing better performance for
reliability evaluation. There are two types of convergence positions, namely
input convergence and output convergence. Overall, output convergence
shows the best result compared to input convergence.
Keywords:
Convergence position
Monte Carlo
Percentage convergence
This is an open access article under the CC BY-SA license.
Corresponding Author:
Mohd Ikhwan Muhammad Ridzuan
Department of Electrical Engineering, College of Engineering, Universiti Malaysia Pahang
Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia
Email: ikhwanr@ump.edu.my
1. INTRODUCTION
Reliability assessment is a must in today society. The development of the world is becoming more
and more complex, and this is also true for the power system network. The increase in the number of people
in the society and the need for more houses, and buildings. This leads to the need for a sufficient power
supply to provide enough power supply to the user [1]. However, a system is not enough if it is not
interrupted because interruption will always occur in the network [2] and fully reliable system is not exist
because of few factors [3]. Monte Carlo simulation (MCS) is one of the preferred methods for reliability
assessment [4], [5]. The purpose of reliability assessment is to ensure that the end user receives sufficient
supply from the network [6]. The distribution system must supply power without interruption. Since
reliability needs to be assessed, an assessment method is mandatory. There are two types of methods that can
be used to evaluate reliability, enumeration and simulation. As for enumeration, the analytical method is one
of the types. It use analytical model to represent the network and used mathematical solution to evaluate
reliability for the network [3]. It is very time consuming and is suitable only for the simplest networks, as it
requires a large number of calculations. Since the network used in this research is quite large and complex, an
accurate method is needed to analyze the network in a very short time. Therefore, MCS is the answer when
the analytical calculation are not adaptable [7]. In MCS, there are two methods that are commonly used for

Int J Elec & Comp Eng ISSN: 2088-8708 
Monte Carlo simulation convergences’ percentage and position in future … (Nur Nabihah Rusyda Roslan)
6219
evaluation: sequential Monte Carlo (SMC) and nonsequential Monte Carlo (NSMC) [4]-[8]. MCS usually
apply for complex and large network [9]-[10] and it also generates the system through random sampling [11].
Complex networks means all the needed component in the power system networks is present [12]. Thus, the
common steps in evaluating reliability are 1. Generates the distribution system in random states, 2. Minimize
the number of faults in random states and lastly 3. Calculate reliability indices [5].
The difference between SMC and NSMC is that SMC is a time-based simulation, which means that
it evaluate the system in time sequence [13]. Other than that, SMC also arranged the sample in
chronologically states, and the frequency of the interruption and the duration for the interruption can be
calculated [14]. In terms of this analysis, time to failure (TTF) and time to repair (TTR) [15] are used to
evaluate the reliability for the network. They are two types of TTF which are for non-repairable system, and
for repairable system [16]. Basically, TTF is the expected time from the repair time to the next break down.
While for TTR, it can be defined as the total time need to perform maintenance for the faulty system divided
by the total number of fault [16]. SMC creates an interruption based on the calculated TTF, while NSMC is
based on random interruption solely. For the SMC, the computation of TTF and TTR is a must, since it has to
decide which time to disrupt. Since the interruptions caused by TTF, the force fault system needs TTR to
repair the system. After all the necessary steps in the simulation have been performed, a stopper is needed to
ensure that the simulation converges. Variance reduction technique (VRT) [17] in the simulation is needed to
reduce the time simulation to achieve fast convergence [17]. In addition to reducing the time required, it can
also increase the speed of computer, since in the research, there are certain small probabilities of fault which
it may take a longer time to execute a simulation even though the computer is a modern computer [18]. There
are a few VRTs that are commonly used in MCS. Which are, Antithetic variates that introduce negative
correlation between two samples [19] to evaluate the reliability in the system, importance sampling [20] that
operates by changing the probability distribution of the sample by keeping the expectation of reliability
indices stable [21], stratified sampling that operates by dividing the sample into a small region [22], and a
few more.
There are a few parts that convergence can be added, overall, it can be grouped into two types which
are convergence at the input and convergence at the output. For the convergence at input, there are three
types of convergence at input which are TTF, TTR, and both of TTF and TTR. To determine the convergence
in TTF and TTR, the accuracy limit is used, which is the percentage of the acceptance range for the
simulation. The percentage determines the range of accepted intermittency that is close to the expected one.
The smaller the accuracy limit, the longer it takes to reach convergence. Finally, for output convergence,
there are two elements that make the simulation converge, namely the system indices and the customer
indices. For output convergence, the variance calculates the difference between the current value and the
previous value. When the difference becomes smaller a few times, the system starts to become stable, and
then convergence is achieved. At the end of the simulation, reliability indices: system average interruption
frequency index (SAIFI), system average interruption duration index (SADI), and customer average
interruption duration index (CAIDI) [23] will be calculated to observe which methods is accurate based on
time and percentage accuracy. SAIFI is system average interruption frequency index, SAIDI is system
average interruption duration index, and lastly CAIDI is customer average interruption duration index [24].
Table 1 shows the input data used to run the simulation. The fault rate is used to determine the
expected interruption at the component. The repair time is only used if a fault occurs on the component. The
fault rate for the overhead line was expressed in kilometers (km). Therefore, to use it in the simulation, the
fault rate must be expanded based on the length of the overhead line. The longer the overhead line, the
greater the fault rate. This means that overhead lines with a greater length have a higher tendency to interrupt.
The display in Figure 1 is IEEE-14 buses. This network contains 20 components consisting of 17 overhead
lines and 3 transformers. Each overhead line represents with different length. The greater the length, the
higher the fault susceptibility of the lines.
In output convergence, convergence occurs at the end of the simulation, either in the system indices
(SAIFIs, SAIDIs, CAIDIs) or in the customer indices (SAIFIc, SAIDIc, and CAIDIc). Convergence at the
output is different from convergence at the input. Input convergence focuses on the mean of the outcome,
which should converge to the expected mean, while output convergence focuses on the calculation of the
variance between the current value and the previous value. The calculation of the variance decreases until it
reaches a steady state, which means that convergence has been achieved.
Table 1. Exact input data
Component kV Fault rate (Fault/km) Repair time (hours/fault)
Overhead line (per km) 0.4 0.168 5.7
Transformer 0.4 0.002 5

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 6, December 2022: 6218-6227
6220
(A)
1
2
G1
(C)
5
(E)
(B)
4
(F)
6
(L)
12
11
(R)
10
9
(P)
(T)
14
(Q)
7
(O)
8
(G)
(J)
(I)
(H)
1.5 km
0.7 km 3.0 km
0.75 km
2.0 km
0.65 km
2.3 km
0.5 km
1.0 km
0.64 km 0.8 km
0.9 km
0.6 km
1.4 km
1.6 km
0.3 km
(N)
13
3
2.5 km
C3
C1
C2
(S)
(K)
G2
Figure 1. IEEE 14-bus
2. RESEARCH METHOD
In the Figure 2, shows the flow chart for each positioning is shown. The figure lists some
positioning for convergence that can be performed. Five positioning have been listed, namely convergence at
TTF and TTR, convergence at TTF or TTR only. Basically, there are three convergence positions at the input
of the simulation. While the remaining two convergences are at the output of the simulation. Which of the
output convergences, occur at system indices and customer indices. In general, the convergences were
dependent on the variance calculated. The first step for reliability assessment simulation is to generate fault
rates (denoted as lambda) and repair times. These fault rates represent the probability of fault for each
component. They are used to estimate the expected interruptions that should occur on the representative
components. Then, uniformly distributed random numbers in the range between 0 and 1 are generated then
incorporated with CDF. The TTF (1) is used to determine the time in which the component would fail. Later,
the calculation of TTR (2) is performed after the generation of random number for TTR based on the created
interruption in TTF.
𝐹−1(𝑡) =
− log(𝑅)
𝜆
(1)
𝐹−1(𝑡) = 𝜎(− ln( 𝑅))
1
𝛽 (2)
After the calculation of TTF and TTR is completed, the power flow, which consists of
20 components and 14 buses, is force fault based on the calculated TTF and TTR. Finally, after running the
network with faulty components, an observation of the buses is performed. It is determined which buses are
affected by the interruption at the components. The number of interruptions and the duration of interruptions
at each bus are recorded to calculate reliability indices for the buses. Normal variance reduction is the
common method that being use by the researcher to converge simulations. Usually in normal variance
reduction convergence can be obtained by calculating the expected value and the variance of the estimate
function by using stated formula. After obtained the expected and variance of the estimate function, then, the
coefficient of variation needs to obtain make sure that the chosen reliability index is less than the tolerance
level. If it is exceeded the tolerance level, then the simulation needs to repeat again from the beginning.
𝐸(𝐹) = (
1
𝑁
) ∑ 𝐹(𝑈𝑖)
𝑁
𝑖=1 (3)

6221
Where, E (F) is estimate of the expected value [25], N is number of simulations, and F (Ui) is test result for
the ith
sampled value:
𝑉(𝐹) = (
1
𝑁−1
) ∑ (𝐹(𝑈𝑖) − 𝐸(𝐹))
2
𝑁
𝑖=1 (4)
where, V (F) is variance of the estimate function F.
𝜀 =
√𝑉(𝐹)
√𝑁.𝐸(𝐹)
(5)
Start
Input Lambda, λ and
Repair Time
Generate Random Number for TTF, R1
I=1
TTF=(-1/lambda)*(log R1)
Converge
Force Fault on selected branch in IEEE14 bus based
on TTF and TTR
I=1000
Calculate Reliability Indices
End
TTR=σ(-log R2)^1/β
Yes
Yes
No
No
Run Power Flow
Record number of Interruption and
Duration of Interruption at each Buses
I=I+1
Converge
Yes
No
Converge
Yes
Converge
Yes
No
No
TTF and TTR
TTF
TTR
Customer
System
Converge at:
I=I+1
Generate Random Number for TTR, R2
Figure 2. Convergence flowchart for different positioning for convergence
2.1. Convergence at input
Input convergence focus on the input data of fault rates and repair time as the expected values. In
addition, percentage limits have been added to the simulation. The function of the percentage limit is to
extend the range of the expected value. If the expected TTF is set to 0.25 faults/years. This means that the
expected interruptions would be 250 interruptions in 1,000 years. However, it is somewhat difficult to
determine the exact number of 250. Therefore, the interruptions that are around 250 should be accepted based
on the percentage limit. As shown in Figure 2, the green box shows convergence on two input data, namely
TTF and TTR as example. The blue and red boxes show that convergence occurs on one of the input data. It
depends on the researcher himself which part he allows to converge. Almost the same process for
convergence on the output.

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2.2. Convergence at output
From the Table 2, E1 shows the smallest percentage limit compared to E20. For E1, due to the
smaller percentage accuracy, hence it took long time to complete a simulation, as the range for the percentage
limit (positive limit and negative limit) for this case is smaller. Thus, it is difficult to complete a simulation
when the range of the percentage limit small, compare to E20, the number of years for this case is only
9 years, and referring to the negative and positive limit, the range for this case is wider. It can be concluded
that, the larger the percentage accuracy the shortest the time taken for the simulation to complete, as the
range for the percentage limit is wider, thus it easy to achieve convergence.
The percentage accuracy for E1 is 1%, so the simulation took 62 years to converge the simulation.
While for E20, the simulation used larger percentage accuracy which are 20% and it took only a moment to
converge, which 9 years. From the figure itself, it can be seen that if the percentage accuracy small, it took
longer time to complete a simulation and vice versa.
Table 2. Limit for each percentage accuracy for case E
Case Percentage Accuracy Number of Years Positive Limit Negative limit
E1 1% 62 62.62 61.38
E5 5% 13 13.65 12.35
E10 10% 11 12.1 9.9
E15 15% 10 11.5 8.5
E20 20% 9 10.8 7.2
3. RESULTS AND DISCUSSION
3.1. Interruptions at component
Figure 3 shows the interruption at component D see Figure 1. The reason for choosing component D
is that component D has the longer length in the network of IEEE -14 buses. Thus, it also has a higher failure
rate since the failure rate for overhead lines depends on the length of the overhead line. The figure therefore
shows the number of interruptions for component D for each case. The number of interruptions for case A,
case B and case C are almost the same, since the convergence were occurred at the input of the simulation.
However, convergence at TTR shows better performance as it reduced the time required to compute a
simulation.
Figure 3. Number of interruptions at component D
In output convergence, convergence on system indices shows better performance because it able to
converge. Compared to convergence at customers, convergence does not occur even though the number of
years has already been extended to 4,000 years. It seems that the simulation cannot calculate the variance
because it cannot converge. Therefore, convergence should be applied in the system when convergence is at
the output. Roughly, the number of interruptions for case A, case B, case C and case D are almost the same.
If referring to the Figure 3, case D shows the highest number of interruptions due to the non-convergence
simulation. However, if the number of interruptions being divided into 500 years (limit number of years for
case A to C) then the number of interruptions for case D would be 244 interruptions (488 interruptions
divided half of the years).
3.2. Interruptions at bus 8
Figure 4 shows the average interruption that occurs at bus 8. Out of all 14 buses in the network,
only bus 8 was affected by component interruption. Basically, bus 8 is the only bus that connected with one
225 225 217
488
5
0
100
200
300
400
500
600
Case A Case B Case C Case D Case E (20%)
Number
of
Interruptions
Cases

6223
overhead line. Figure 1 for bus 13 shows that the bus is connected to 3 overhead lines. When one of the
overhead lines is broken, the other two overhead lines back up the broken line. Basically, SMC tends not to
interrupt the buses at the same time compared to NSMC because it randomly interrupts the component one at
a time (in sequences), so the interruptions do not occur at the same time. Figure 4 shows that cases A to D are
similar in terms of the average of interruptions that occur.
Case E, however, shows a low average. This is because the years converge only up to 9 years.
Moreover, the accuracy limit for E20 is also very high. When the accuracy limit is large, it is easy to achieve
convergence. Therefore, for E20, the percentage accuracy needs to be adjusted to obtain an average similar to
the other cases. The smaller the percentage accuracy, the longer of time (years of simulation) to achieve
accuracy.
Present in Figure 5 is the average interruptions and duration for case E when using different
percentage accuracy. As stated before, E20 produce lowest number of years as shown in Table 2. However,
due to the huge different between the other cases, another simulation was being done to check which
accuracy that has the same accuracy as the other cases. If referring to Table 2, the reading for E20 is the
lowest, and it seem that case E not suitable with 20% of accuracy. With that, four more simulations were
done with different accuracy (1%, 5%, 10% and 15%).
Figure 4. Average SAIFI, SAIDI and CAIDI at bus 8
Figure 5. Different percentage accuracy for case E
As shown in Figure 5, it shows the average interruptions and duration for bus 8. From the figure, if
comparing with other cases in Figure 4, only 1% of accuracy that almost has the same reading as other cases.
If focusing on 1% of percentage accuracy, the SAIFI for 1% is 0.32, and is almost the same as the rest of the
cases in Figure 4. However, for average SAIDI, the reading for 1% of accuracy is slightly lowest from the
other cases. It could be because the number of interruptions for E1 is lowest compared to other cases, which
result in less time needed to repair the interruption. For CAIDI PDF, the average durations for customer in E1
is in the range with other cases.
Present in Figure 6 is the average interruptions and duration for case D (4,000 years). Among all
cases, only case D fail to converge, as it stops at the decided years (1,000 years). According to Monte Carlo,
the more the number of iterations, it is easy for the simulation to meet the expected input data. Thus, in order
to analyze whether the simulation converge when the number of years were extend for another 3,000 years,
which include the current years, the simulation was done for 4000 years. However, the simulation still fails to
converge. Apart from that, the shocking result shows that the recorded value for case D is almost the same as
0.33 0.33 0.33 0.33 0.11
4.58 4.58 4.58 4.68
1.33
3.95 3.95 3.98 4.02
1.33
0
1
2
3
4
5
C ASE A C ASE B C ASE C C ASE D C ASE E (2 0 % )
PDF
(%)
CASES
Average SAIFI Average SAIDI Average CAIDI
0.32 0.43
0.92
1.45
2.1
3.87
1.21
1.83
2.45
3.2
3.7
0.9
1.1
1.2 1.3
0
1
2
3
4
5
1 5 10 15 20
Average
interruption
at
Bus
8
Percentage Accuracy (%)
SAIFI SAIDI CAIDI

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the other cases. Focusing on Figure 6, the average SAIFI for case D (4,000 years) are 0.33, and it just the
same as the rest cases which are also 0.33 as shown in Figure 4. The same goes for average SAIDI and
CAIDI where the recorded values are similar with average SAIDI and CAIDI in Figure 4.
Figure 7 shows the system average interruption frequency index (SAIFI) PDF for case A through E.
From the figure, E20 has the highest percentage for uninterrupted buses, while the other cases have similar
values. If comparing with case D, case E has highest uninterrupted because of the lowest number of years,
hence result in small interruptions in the system. However, after reducing the percentage accuracy for E20,
the uninterrupted bus was recorded at 70.97% (refer Table 3) almost the same as other cases.
Figure 6. Average interruption and duration for case D (4,000 years)
Figure 7. SAIFI PDF
Since a large accuracy bound was used in case E, it is easy to achieve convergence. In the opposite
case, the simulation would take longer to complete. To achieve a similar percentage in E20 as in the other
cases, the accuracy must be reduced to 1% of the accuracy limit, as shown in Table 2. It may not be the main
intention of this research to obtain a similar percentage of reliability indices, as at the beginning of the
research the accuracy limit was standardized to 20% of accuracy. However, since E20 has an irregular
reading, another research see in Table 2 was conducted to observe which accuracy has a similar value to the
other cases. Refer to the Figure 7, E20 has less interruptions compared to other cases. It stated that, the
0.0714 for E20 is 11.11% which is totally different from the 0.0714 of other cases with the range of 20% of
occurrence. Due to the high percentage accuracy, the PDF tends to get small values since the percentage limit
affected the simulation by decreasing the size of the sample drastically. However, if the percentage accuracy
got smaller, the size of the sample will be increased see in Table 2. Thus, when case E using 1% of
percentage accuracy, the reading for 0.0714 is 27.42%. The reading might be slightly higher compared to the
other cases, however it still in the range of 20% of occurrence.
For the SAIDI PDF, it was calculated based on the time taken to repair the interruption created at
SAIFI PDF. For the uninterrupted system, repair time is not needed since the system remain on state. For the
rest of the interrupted systems, there will be its own time to repair, and it is not the same for each
interruption. From the Figure 8, in E20, low number of repair time is taken. As mentioned earlier, the reason
for less repair time is that the number of years for E20 was drastically reduced from 1,000 years, and this
happened because the percentage of accuracy for E20 is too large. Among the convergence items, E20
converges faster and reduces drastically as it reaches a convergence of less than 1,000 years. Table 2 shows
0.33
4.68
4.02
0
1
2
3
4
5
SAIFI SAIDI CAIDI
Avergae
interruptions
and
durations
at
Bus
8
Reliability Index
Case A
Case B
Case C
Case D (1000 years)
Case E (20%)
0
50
100
0 0.0714 0.1429 0.2143
71.2
24.54
4.06
0.2
71.2
24.54
4.06
0.2
71.1
24.89
3.8
0.21
72.1
23.7
3.8
0.4
88.89
11.11
Cases
PDF
(%)
Reliability Indices
SAIFI PDF

6225
that at 1% accuracy, E1 took 62 years to converge, while at 20% accuracy, it took only 9 years to converge. It
can be seen by referring to the Table 3. For the 0.8571, for E20, the probability of occurrence for this
reliability indices are 11.11%, however, when the case E used 1% of percentage accuracy, the 0.8571
reliability indices have 25.81% of occurrence. Which is E1 has almost the same reading as case A, case B,
case C and case D.
Table 3. PDF for E1
SAIFI SAIDI CAIDI
Reliability Indices PDF (%) Reliability Indices PDF (%) Reliability Indices PDF (%)
0 70.97 0 70.97 0 70.97
0.0714 27.42 0.8571 25.81 12 27.42
0.1429 1.61 1.7143 3.23 24 1.61
Figure 8. SAIDI PDF
For the Figure 9, CAIDI PDF it just basically the same as the previous average CAIDI PDF at bus 8.
Where CAIDI used to measure time taken for the customer will experience for one interruption. CAIDI is
differ from SAIDI, as SAIDI used to measure the time taken for all interruptions occurred. From the figure,
case D has the longer hours for one interruption, which is 48 hours/interruption. If referring to Figure 3, case
D has the highest interruptions at component thus for the interruptions at Bus 8 it is quite severe, as there is
interruption that required 48 hours to repair. The most common time needed to repair for one interruption are
12 hours/interruption for every cases. For E20, it shows that only two repair times experience by the
customer. That is because, the number of years for E20 is only 9 years. Hence, due to low number of years,
less interruptions were created in the system. Thus, that is explains why only two repair times were recorded
in E20, compared to other cases. For case E, by using 1% of percentage accuracy, the number of repair times
that being recorded for this simulation are three see in Table 3, CAIDI. Since the percentage accuracy being
reduced, the number or years will be increased as it is difficult to converge when the percentage accuracy
small. Due to the increase of number of years, the interruptions created in the system also will be increased
along with the number of years. Referring to the 12 hours reliability indices in Figure 9, the E20 recorded
11.11% of occurrence, however, when the limit accuracy being decreased to 1%, the occurrence for 12 hours
reliability indices increased to 27.42% possibility.
Figure 9. CAIDI PDF
Case A
Case B
Case C
Case D (1000 years)
Case E (20%)
0
50
100
0 0.8571 1.7143 2.7143 3.4286
71.2
21.5
5.68 1.22 0.41
71.2
21.5
5.68 1.22 0.41
71.1
21.73
5.49 1.27 0.42
72.1
19.9
5.4 2.1 0.5
88.89
11.11
Cases
PDF(%)
Reliability Indices
SAIDI PDF
Case A
Case B
Case C
Case D (1000 years)
Case E (20%)
0
50
100
0 12 16 18 24 36 48
71.2
24.54
0.2 0.81 2.84 0.41
71.2
24.54
0.2 0.81 2.84 0.41
71.1
24.47
0.21 0.84 2.95 0.42
72.1
22.4
0.2 1.4 3.2 0.5 0.2
88.89
11.11
Cases
PDF
(%)
Reliability Indices
CAIDI PDF

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4. CONCLUSION
In conclusion, from the overall results, it can be stated that the value of the convergence plays their
own parts very well. However, to get the precise result as the expected, the percentage of accuracy also need
to be considered at the first place. As for E20, the accuracy limit for case E need to be small in order to get
the similar result as the other cases. Since, due to the large percentage accuracy, the simulation converged
faster and reduced the number of years drastically comparing to the other cases. Based on the new simulation
for case E, by using 1% of percentage accuracy, the accuracy for the case E is almost similar as the other
cases which is, to converge a system indices, the researcher needs to used small percentage accuracy in order
to get high accuracy. For other cases, the number of years being reduced around 450 to 500 years. Except for
case D, where it failed to converge even though the simulation were being extend to 4,000 years. However, it
can be stated that, even though the number of years being extend, the accuracy for case D (4,000 years) is
remained the same as case D (1,000 years). Even the simulation failed to converge, the result from case D
can be classified as reliable because the recorded value for this case it similar as the cases that manage to
converge. As for the input convergence, it can be seen that, the convergence only occurs for the input data
that were set to converge. If the simulation were set to converge at TTF and TTR than both of the input data
will converge. However, if the convergence were set at one of the input data, example TTR, then only TTR
will converge, and the TTF will be ignored since the convergence were set at TTR only. The same goes for
the convergence at TTF only. Lastly, it is important for the researcher to know what kind of result that they
want at the end of their research. Because each convergence shows different output with different
characteristic of the simulation.
ACKNOWLEDGEMENTS
The authors would like to thank the Ministry of Higher Education for providing financial support
under Fundamental Research Grant Scheme (FRGS) No. FRGS/1/2018/TK04/UMP/02/16 (University
reference RDU190186).
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BIOGRAPHIES OF AUTHORS
Nur Nabihah Rusyda Roslan received B.Eng. (Hons) Electrical Engineering
(Power System) from University Malaysia Pahang (Pekan Campus), Pekan, Pahang. She is
currently pursuing the M.S. degree with the College of Engineering, University Malaysia
Pahang, Gambang Campus, Kuantan, Pahang, Malaysia as a part-time student. She is currently
a protégé at Tenaga Nasional Berhad (TNB). Her research interest is in reliability evaluation
using Monte Carlo simulation for distribution system, and the characteristics for convergence
and variance reduction methods in Monte Carlo simulation. She can be contacted at email:
nabihahrusyda96@gmail.com.
NoorFatin Farhanie Mohd Fauzi received B.Eng. (Hons) Electrical Engineering
(Power System) from University Malaysia Pahang (Pekan Campus), Pekan, Pahang is
currently pursuing the M.S. degree with the College of Engineering, University Malaysia
Pahang, Gambang Campus, Kuantan, Pahang, Malaysia as a part-time student. She is currently
works as Project Engineer and her research interests is in reliability evaluation using Monte
Carlo simulation for distribution system, and the probability distribution function for Monte
Carlo simulation. She can be contacted at email: fatinfarhanie96@gmail.com.
Mohd Ikhwan Muhammad Ridzuan is currently the senior lecturer in the
department of electrical engineering, Universiti Malaysia Pahang. His research covers
reliability, distribution network performance and design. Mohd Ikhwan holds a bachelor
degree in electrical engineering from Universiti Teknologi Malaysia, Malaysia and a PhD in
Energy Systems from University of Edinburgh, United Kingdom. He has almost 4 years’
experience in electrical operation and maintenance with Tenaga Nasional Berhad. He is a
registered Professional Engineer with Board of Engineer Malaysia and a registered
Professional Technologies with Malaysia Board of Technologies. He can be contacted at
ikhwanr@ump.edu.my.

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