RELIABILITY ASSESSMENT ON NETWORK EQUIVALENT USING MONTE-CARLO SIMULATION TECHNIQUE
M.F.N-F. Farhanie, R.N.N. Rusyda, M.I.M. Ridzuan
Faculty of Electrical & Electronics Engineering, Universiti Malaysia Pahang, Malaysia E-mail: [email protected]
ABSTRACT
Reliability in an electrical power system is the ability of the system to deliver electrical energy without any interruption.
In the literature review, the analysis of the power system in low voltage (LV) network is less focused compared to the medium voltage (MV) and high voltage (HV) due to the absence of general exact data and sizing of the LV network.
The LV network becomes complex when the sizing of the network increases. Thus, in this research, the performance of reliability in the LV network will be evaluated using an equivalent network by simplifying the network. This simplified network will reduce the simulation time. The performance in a complex network should first be evaluated before reliability assessments are carried out. The assessment of reliability is carried out using Monte-Carlo Simulation.
The reliability indices, SAIFI, SAIDI and CAIDI between these two networks (detailed and equivalents network) are compared. The expected output in the detailed network will have the same or close readings of reliability indices as in an equivalent network.
Keywords: low voltage, medium voltage, reliability. failure rate, repair time, interruptions
INTRODUCTION
In this modern era, electricity is one of the essential sources in order to carry out various daily activities.
Thus, the utility company needs to ensure the customers will receive the continuous supply of electricity with no interruption happens. A distribution system failure causes the most interruption experienced amongst customers. Although the system is always interrupted, yet customers often expect more reliability and stability at all times [1].
Reliability in power systems, particularly in distribution systems, always linked to the continuity of electricity.
Overages ago, the reliability of the power system assessment is more concerned with the generation and transmission in comparison with the distribution system, especially in low voltage systems [2]. The LV network spreads out from these substations to create a ‘tree-like’ structure in the distribution system. Since
LV located at downstream of the MV system, hence the interruption in LV will have a huge effect on the performance of reliability in the power system.
LV and MV are always clearly represented in an aggregate lumped model in most large power systems because of the complexity of calculation and the LV and MV volume [3]-[8]. Due to the increase in size and volume of the network, this network becomes more complex; thus, the performance of reliability is difficult to analyze. Hence, in this research, the complex network will be represented by a single equivalent network. The representation of the equivalent network will simplify the network complexity; thus, it will reduce the computational time using a simulation method.
The main purpose of this research is to represent the entire LV network with one equal component. Two
basic input data which are failure rate and repair time are required for the reliability analysis. Thus, accurate mean time to repair, MTTR and mean time to failure, MTTF are required to this reliability assessment. The analysis in this project is carried out using the Monte- Carlo simulation. Before the assessment of reliability in the equivalent network done, the performance in the complex network should be analyzed first. The reliability indices between these two networks are compared and observed. The reliability analysis in a detailed network will provide further information and specific details.
METHODOLOGY
Monte-Carlo Simulation Technique
The performance of reliability in the system can be evaluated using two types of methods; analytical and probability assessment.
The failure of components or systems in reliability analysis is evaluated in the presence of randomness.
Monte-Carlo Simulation (MCS) is an appropriate method to be used in the reliability analysis due to its characteristic, which considers the stochastic nature of the power system. Monte Carlo is a method used over the last few decades. This method is widely used in many fields, such as finance, weather, etc. In this reliability assessment, the Monte-Carlo is used to check for the probability of the event.
Monte Carlo is the only proven, probabilistically accurate and computationally efficient process [9]. Since a power system consists of a large and complex network, the most suitable technique used to assess the performance of networks is the sequential Monte-Carlo simulation technique instead of the analytical method [10]-[12]. The sequential MCS technique simulates the chronological system behaviour by sampling the system states sequences for several periods while the analytical method
Assign fault rate, lambda of the component
Interrupt selected component based on TTF Set total simulation, n=1000
Generate Random Number, R TTF=-(1/λ) x In R
Calculate reliability indices n==1
N=n Yes
END Model Analysed
network
No N=n+1
Figure 1 Flowchart of Monte-Carlo Simulation
uses a mathematically based approach to evaluates the performance of reliability in the power system using the mathematical solution. In the sequential Monte-Carlo technique, the system conditions and corresponding times are reported on the basis of which the reliability indices can be determined for a sufficiently long time after the simulation. For this approach, it is important first to define the two fundamental inputs that are fault rate and repair time before it can randomly generate [13]-[14]. This MCS technique will damage the components in the system based on fault rate and repair time. When there is any failure component in the system, it will cause interruption to most of the customers’ end due to no supplies. This event of interruption will be recorded and measured in reliability indices.
This MCS application is a corner pillar in sensitivity and quantitative probability analysis. This sequential MCS needs more computational efforts that non- sequential technique. The MCS flowchart above can be summarised as below,
1. Two models of the bus system, which are Case 14 and Case4gs, are used to represent the distribution network in this project. Case14 represents LV distribution system while Case4gs represents MV distribution system.
2. Two input data (fault rate and repair time) are selected based on the categories of the distribution system.
3. The total simulation has been set to 1000 years. In each simulation, the random number is generated for each component. The generated random number is converted into time to failure (TTF) according to the corresponding fault rate.
4. From the value of TTF obtained from step (3), check whether TTF == 1 or not. If TTF==1, hence the selected component, will interrupt, if TTF ≠ 1, it will generate the random number again.
5. The simulation will run until it follows the simulation duration stated as in this project, the simulation time is set until 1000 years.
6. The reliability indices can be calculated; thus, the performance of reliability assessment in the distribution system is obtained.
A distribution system consists of a set of series components such as lines, cable, transformer, etc. A customer connected to any load points such a system requires the operation of all components between itself and the supply point. Thus, the average failure rate, λs is the sum of every failure rate of the component. The formula λs =
Σ
iλi is used to simplify the extensive network and turn the large network into an equivalent network. This equivalent network will be implemented at the endpoint of the MV system.Figure 1 shows the flowchart of reliability assessment in this project. IEEE 14 represents the LV network, while IEEE 4gs represents MV network in the distribution system. Before simulating the simulation, a modification in MatPower for all the networks should be done first. The networks are modified to be supplied by only one generator to evaluate reliability performance. A few analyze in both LV and MV networks are required before an assessment in the equivalent network. There are four different cases required to be analyzed, as shown in Table 1. Although this research is intended to evaluate the reliability in the LV network, it also included an analysis of the MV network to quantify and justify the importance of detailing the distribution network.
Table 1 Description of cases
Case Description
1 LV network consists of 14 buses and 20 branches 2 MV network consists of 4 buses & 4 branches
3 Detailed (a combination of MV and LV) network consist of 56 buses & 84 branches 4 Equivalent network (a combination of MV and LV equivalent) network
Network
i. LV network (Case 1)
Figure 2 LV network
In this project, the performance of reliability is analyzed in both LV and MV network, but the main focus is on the LV network. The purpose of this project is to do an equivalent network in the LV system.
This LV equivalent network will be implemented at the endpoint of the MV network. Thus, in order to analyze the equivalent network, the assessment in a complex LV network (Case 1) needs to do the analysis first. The first analysis to be done is in IEEE 14. In this
analysis, it is required to calculate the R equivalent and X equivalent for the assessment in the equivalent network. By using formula P=I2R and Q=I2X, the value of R and X equivalent can obtain. All the parameters are obtained from the MatPower. This equivalent impedance, Zeq will represent the total LV network impedance. This impedance will insert into MatPower in order to analyze the performance of LV equivalent.
ii. MV network (Case 2)
In this case, IEEE Case4gs will represent an MV network.
The LV network will be located at the endpoint of each MV network. In this case, IEEE Case4gs will represent an MV network. The LV network will be located at the endpoint of each MV network. Although the research is focused on the LV network, analysis to quantify and justify the significance of the detailed MV network also should be done.
1 29
15 43
Bus (1-14) G1 Branch (1-20)
Bus (15-28) Branch (21-40)
Bus (29-42) Branch (41-60)
Bus (43-56) Branch (61-80) 0.8km
1.5km
2.5km
1km
Branch 81
Figure 3 MV network
Figure 4 MV and detailed LV networks (Case 3)
iii. MV and detailed LV networks (Case 3)
This network is the combination of MV and LV detailed network. As mentioned before, IEEE Case14 and IEEE Case4gs are used to represent LV and MV networks, respectively. Since LV network is located at the downstream of the MV point, hence at every point of MV network, there will consist of 14 LV network buses.
Thus, there are about 56 buses and 84 branches in this detailed network. Due to a huge number of buses
and branches, the network becomes more complex and difficult to do analysis. Thus, the simplification of the network made the analysis much more accessible.
In this network, Buses 1, 15, 29 and 43 represent MV network, as shown in Figure 4.
Input Data, Fault Rate and Repair Time
As mentioned earlier, the fault rate and repair time are two fundamental inputs in the reliability evaluation.
It is very crucial to choose the precise value for both inputs is as it indirectly affects reliability efficiency.
iv. MV and equivalent LV networks (Case 4)
1
29
15
43 G1
Bus (1-14) Branch (1-20)
Bus (15-28) Branch (21-40)
Bus (29-42) Branch (41-60)
Bus (43-56) Branch (61-80) 0.8km
1.5km
2.5km
1km Branch
81
EquivalentLV LV
Equivalent
EquivalentLV LV
Equivalent
Figure 5 MV and equivalent LV networks (case 4)
Table 2 Parameter for reliability analysis in LV and MV networks [15]-[16]
Component Voltage (kV) Fault rates
(failure/year)
Repair times (hours/fault)
Overhead lines 11 0.1230 5.00
0.4 0.0706 6.44
Transformer 11/0.4 0.1809 5.00
After simplification of Network 3 (detailed network), then a simplified network is obtained. The equivalent failure rate and repair time in the equivalent network is obtained by evaluating the failure rate and repair time of each of the components in the aggregate part of the system. In this network, the input data used are obtained by evaluating the average failure rate and repair time in Case 1.
The reliability performance of every part of the network, such as the transformers, circuit breakers, etc., is taken into consideration for each failure rate and repair time. In this research, two components are included which are transformers and overhead line, however, the overhead line is the main focus because the network is the most dominant component
Reliability Indices
In the distribution system, the assessment of the reliability can be divided into two different groups -load indices and system indices [17]. There a few reliability indices used as a parameter to evaluate the performance of reliability in the system which are SAIDI, SAIFI, MAIFI, CAIDI, ENS and AENS [18]. In this analysis, only three common indices are considered, which are SAIDI, SAIFI and CAIDI. These indices are very important, especially to the service provider to record the performance of reliability in the power system in order to ensure the better quality of services receives to the customer ends [19],
1. SAIFI = Total number of customers interrupted (LI) /Total number of customer served 2. SAIDI = Total number of interruption durations
(by LI)/Total number of customer served 3. CAIDI = SAIDI / SAIFI = Total number of interruption
durations / Total number of customers Interrupted
RESULT AND DISCUSSIONS
Figure 6 shows the average indices of 4 different cases. Based on Figure 6, the average of SAIFI in case 1 network is the lowest among the other cases.
As mentioned before, the failure rate is one of the reliability inputs, which directly will affect the total of interruptions. Based on Table 2, the failure rate of the overhead line in the LV network is lower than in the MV network. Hence, the total interruption in Case 1 is lower compared to Case 2. As the SAIFI equation is related to the total interruption, thus increasing interruptions in the system also will increase the value of SAIFI. The LV network interruption will have a huge effect on the total of interruptions in MV for Cases 3 and 4 since this LV is located at the downstream of MV. Thus, the total interruption in MV is higher in LV. In this research, the repair time used for the overhead line in LV and MV is 6.44 hours/fault and 5 hours/fault, respectively, while the repair time for the transformer is 5 hours/
fault for both networks. Index CAIDI is related to the repair time of the component. This can be shown based on the formula above; CAIDI is equal to the
Figure 6 Reliability results for four cases
total number of interruption durations/Total number of custom Interrupted Based on Figure 6, it shows the varies average of CAIDI in four different cases. The average of CAIDI in Case 2 is the lowest compared to the others. This is because the average of interruption hours (CAIDI) is inversely proportional to the average failure rate (SAIFI), hence the higher the value of SAIFI, the lower the value of CAIDI. The value of SAIFI in Case 2 is the highest; thus, it has the lowest value of CAIDI compared to the others. While for Case 3 and Case 4, the average value of CAIDI in Case 3 is slightly higher than in Case 4. The average of SAIDI in Case 3 is higher than in Case 4. Hence it will affect the value of CAIDI.
The result is acceptable since it is difficult to obtain a close value of SAIDI between Case 3 and Case 4. This is because in Case 3, there are about 56 busloads, which equal to the number of customers compared in Case 4, which has four busloads. Thus, these busloads will experience different repair times. Increase the number of busloads will increase the total duration of customers interrupted; hence it will affect the average value of CAIDI. In this research, the repair time in the LV network, which represents an average of CAIDI is used as an equivalent repair time in the equivalent network. Hence, the average of CAIDI in Case 1 is similar to the average of CAIDI in Case 4, which is 5.11 hours/faults. Since the repair time of the same type of components is the same, hence the average of CAIDI in Case 4 is similar to its repair time.
Table 3 below shows the percentage error between detailed (Case 3) and equivalent network (Case 4). The average of SAIFI between Case 3 and Case 4 are close to each other. Hence, the percentage error between these two is the lowest. Since Case 3 is the combination of LV and MV network; hence the repair time of the components is different according to the types of networks. Thus, the percentage error in the average of CAIDI between Case 3 and Case 4 is about 4.31 %, which is higher than the percentage error in SAIFI.
Lastly, the percentage of error in SAIDI is the highest compare to the others. The SAIDI index is the total duration of interruption over the total of customers.
The total duration of interruptions is related to the repair time and interruptions of components. Since the interruptions in the detailed network are varies, and there are a few customers are not interrupt at all;
hence it will affect the average of SAIDI in the detailed network.
Thus, the percentage error of SAIDI between these two networks is the highest. The expected percentage error should get lower than the current percentage error. This percentage error of SAIDI can be reduced by increasing the simulation time.
Table 3 Comparison between Case 3 and Case 4 for different indices
Average Index Case 3 Case 4 Percentage Error (%)
SAIFI 0.06473 0.06400 1.13
SAIDI 0.39532 0.32704 17.27
CAIDI 5.34 5.11 4.31
Simulation time
(in seconds) 127.43 s 57.46 s 54.91
The comparison of the value of SAIDI for each customer between Case 3 and Case 4 is analyzed.
Table 4 Comparison between Case 3 and Case 4 for different Load Point
Load Point, LP Case 3 Case 4 Percentage error (%)
LP 1-14 0.4064 0.22995 43.41
LP 15-28 0.4004 0.3117 22.15
LP 29-42 0.5048 0.4650 7.88
LP 43 -56 0.2697 0.3015 10.54
The model accuracy based on the calculation of the value outside the control limits, as calculated in Table 4.
The root cause analysis model has high accuracy in detecting the anomalies by using Shewhart Control Chart. The detection accuracy is around 95-100%
when the abnormal data operation in range 1-80 tested. However, the accuracy of detection slightly decreased to 60% when the data condition is bad real demand power due to unscheduled time operation when the operator turns on or off the power, and there is the warm-up value of power after turning on the power. For the case of normal data operation, a false alarm rate also implemented to identify how many alarms are being triggered in the data range 101-200. It is only 88% accuracy, which means 12 out of 100 normal data are being declared as bad data and are not shown consecutively. Therefore, no potential alarm is trigger during the operation, and the model is safe to be applied. Table 4 shows the percentage error of SAIDI between (Case 3) and (Case 4). The value of SAIDI for 14 customers in Case 3 is compared with the equivalent customer in Case 4. From Table 3 above, we can see that the percentage error of SAIDI between these two cases is the highest compared to the others. Thus, Table 4 shows the percentage error of SAIDI for each load point between these two cases.
LP 1-14 contributes to the highest percentage error compared to the others. Hence, LP 1-14 and LP 15- 28 were analysed to observe the value of SAIDI for each load point in both cases.
Figure 7 below shows the comparison of SAIDI for Network 1 between Case 3 and Case 4. The average of SAIDI for 14 customers in Case 1 is 0.4064, while an average of SAIDI in Case 4 is 0.22995. From Figure 7, the value of SAIDI for each customer in Case 3 varies among each other. Since there is no interruption experienced by C1, C2 and C5 thus none of the values of SAIDI are recorded. This is because the overhead lines connected to these customers do not interrupt at the same time. Hence, the electrical route combinations from source to load increased the level of security for these customers. In this network, the transformer is located at Buses 4, 5, 7 and 9. Hence, the repair of the time of these customers is 5 hours/
failure while other customers are 6.44 hours/failures.
C7 and C9 consist have the same value of CAIDI. This is because they have the same total of interruptions and repair time. The value of SAIDI in C8 and C10 have the highest value of SAIDI compared to others. This value exceeds the average of SAIDI in Case 3. C8 and C10 experienced the most interruptions compared to others. Hence, this total of interruptions will affect the value of SAIDI.
Figure 7 Comparison of SAIDI between Case 3 and Case 4 at Lp 1-14
Figure 8 Comparison of SAIDI between Case 3 and Case 4 in LP 15-28
Figure 8 shows the comparison of SAIDI in LP 15-28 between Case 3 and Case 4. The average of SAIDI in Case 3 and Case 4 is 0.4004 hours/faults and 0.3117 hours/faults, respectively. The percentage error between these two contributes to the second largest percentage error compared to others, as shown in Table 4. From figure 1 above, the value of SAIDI is varied among each other. C16 and C19 do not experience at all; hence there is not recorded reliability indices. From the graph above, we can see that most of the SAIDI in each LP 15 to 28 in Case 3 exceeds the average SAIDI in Case 3. This is due to a large amount of interruption experienced by these customers. Thus, it can say that the value of SAIDI depends on the interruptions and repair time of the component.
Detailed Network
The detailed network (Case 3) is a combination of MV and LV detailed network. As mentioned, MV and LV networks are represented by IEEE Case 14 and IEEE Case4gs, respectively. In Case 3, the detailing network model took more time to design the network and a higher time to simulate than in Case 4. One of the advantages in Case 3 is it will give more details information, especially on the particular location/
component of interruption and the duration of the interruption.
Figure 9 shows the reliability indices for each of 56 customers in the detailed network. This graph shows that the reliability indices for every customer are varied among them. The reliability indices SAIFI always related to the occurrence of faults in the system. Every customer will experience a different total number of interruptions. Hence, the value of SAIFI always varies among them. From the graph above, Customers 1, 2, 5,16 and 19 do not have any recorded reliability indices, which means they do not experience interruptions at all. This is due to many combinations of the electrical path from source to load, which increases the security level for these customers. Since the length of the lines will give effect to its failure rate, thus increasing in the length of the line will increase the failure rate. As for the value of CAIDI, most customers will have a reading of CAIDI, which is 6.44 customer hours /customers failures.
The value of CAIDI for each customer will have the same reading as its repair time. As mentioned above, the repair time used for the transformer is 5 hours/
failures while for overhead line in LV and MV are 6.44 hours/failures and 5 hours/failures, respectively. In this detailed network, MV network is located at Buses 1,15,29 and 43 while transformers are located at Buses 7,9,18,19,23,32,33,37,46,47 and 51 as shown in Figure 4. Thus, the value of CAIDI at these customers are 5 hours/failures.
Figure 9 Detailed Reliability Indices for Case 3
Interruptions in Case 3
Figure 10 Interruptions experienced by each customer in Case 3 Figure 10 shows the total interruptions experienced by
each customer in 1000 years. In this research, the total simulation is set until 1000 years, starting from year 1 to the year 1000. From this graph, each customer will experience a different total number of interruptions.
At Customers 1, 2,5,16 and 19, they do not experience interruptions. This is due to many electrical path combinations from source to load that improve the level of safety for customers. For example, at customer 1, C1, there are no interruptions at all. This is because they are continuously supplied at C1 as the generator is on Bus 1. So C1 will not be disrupted under any circumstance and any year unless the backup supply is a failure. One of the contributions against interruptions in the network is the failure of the overhead line. Line failures may probably occur as a result of network overload, overvoltage, etc. The overhead line factor, which is exposed to external conditions like lightning, may also cause the line to fail. This failure will, therefore, impact reliability quality. The total of interruptions depends on the length of the overhead line, which will give effects to the failure rate of component. Thus, the increase in the length of the line will increase the failure rate, thus increasing the total of interruptions.
Equivalent Network
The complexity of the network in Case 3 will be simplified into an equivalent network. In this Case 4, each equivalent customer will represent every 14 customers in Case 3. Thus, 4 equivalent customers will represent a total of 56 customers in this detailed network. This representation will not change the parameter of the components in the network because the total of the same parameter will represent with one equivalent value. The reliability index (SAIFI, SAIDI, CAIDI) will be used in this case to justify the detailed network (Case 3) representation by an equivalent network (Case 4). The reliability indices between Case 3 and Case 4 will have a closed reading to each other.
This is because the equivalent representation (Case 4) will not change the parameter of the components in the network because the total of the same parameter is represented with one equivalent value. Sometimes, the reliability index calculation using this equivalent network may not be accurate if the failure rates and repair times of all components in the LV/MV network aggregate are not used to assess the supply quality of a bus where the bulk load is connected. Although this
equivalent network has advantages, particularly in reducing the simulation time, the interruption occurs in the network is difficult to detect. This is because of one equivalent value represents a numerous value of components and configuration in the LV network.
Based on Figure 11, the value of SAIFI in Customer 1 is the lowest compared to the others. This is because the line connected to Customer 1 is the shortest than the others. Since the failure rate of the line depends on its length, a decrease in the length will decrease the failure rate at the component. Thus, Customer 1 will experience the least interruption compared to others while Customer 3 experience the most interruptions because the lines connected to it has the longest length.
have the same value or close to each other depends on the number of simulations. The percentage error of reliability indices can be reduced by increasing the number of simulations (years). Since the basic input of reliability indices are fault rate and repair time, hence the reliability indices depend on these two parameters. As for SAIFI, increase the interruptions will increase the value of SAIFI. While for SAIDI, higher the number of interruptions and repair time will increase the value of SAIDI. In this project, although the equivalent of a network can simplify the network and reduce simulation time, the disadvantage of this network is the difficulty of determining the location of the fault and faulty component.
Figure 11 Detailed reliability indices for Case 4
CONCLUSION
This paper has introduced the methodology of reducing large/complex networks into a single equivalent network. The complexity of the network is represented by one equivalent network in which the parameter of reliability indices of these networks will
ACKNOWLEDGEMENTS
This research is supported by the Ministry of Education (FRGS/1/2018/TK04/UMP/02/16) and Universiti Malaysia Pahang under grant number RDU190186.
The authors would also like to thank the Faculty of Electrical & Electronics Engineering Universiti
Malaysia Pahang for providing facilities to conduct this research and financial support throughout the process.
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