4 Analysis
4.1 Pre study
4 Analysis
This chapter will give an explanation to the process of analysis and the information that is needed when performing an analysis.
4.1 Pre study
To give a real coupling of the theories to actual distribution systems a pre study has been performed.
The pre study is used as a source of information giving the required input data as well as system structures. It was performed in 2008 at Sandviken Energi AB (SE).
4.1.1 Empirical method
The basic premise for a pre study to be considered reliable is the degree of reliability and validity a pre study investigation meets. In other words critically examine the procedure which has been applied in the data collection.
4.1.2 Trustworthiness of study
The definition of trustworthiness is assessing the degree of repeatability of the study when it is carried out under the same conditions. An important factor to achieve repeatability is by maintaining a careful documentation throughout the whole process. By continuously reviewing the documentation, high reliability is achieved.
Other important factors for high trustworthiness are that measurements are carried out correctly and accurately, so that the same results can be achieved several times.
Deficiencies in the trustworthiness that may arise are mainly due to the subjective assessment of the size and decisiveness on the analyzed risk. This aspect directly affects the accuracy of the index that assesses and describes the distribution system's properties.
4.1.3 Validation of study
The purpose of the validation study is to get an idea of whether the study examines the elements meant to research. The approach in this study to maintaining high validity includes clear clarification on what should be studied and how the pre study proceeds. In addition, the study describes the methods and assessment tools that have been applied so that the study can be repeated. In order to ensure the validity a big effort has been to implement theories that are rooted in the theoretical frame of reference. Furthermore, re‐connection with the operating staff at SE has been a step to strengthen the validity.
4.1.4 Describing the statistical basis
The system analysis included in the reliability calculations requires some type quantity that can represent the behavior of different components. The failure rate is a widely used measure. Failure rate gives an estimate of how often a component fails during a specified period of time. The standard is one year.
Since this measure is based on statistical data the estimated failure rate can in some cases be misleading. This problem is often present due to the substandard in the available information. The credibility of the statistical value increases by the time for which the value corresponds to. However, this requires that the same type of component is studied over the period.
4.1.5 GIS Meldis
The GIS system MELDIS provides an error‐reporting feature that has been used in recent years. A report describing when and where the error occurred is posted for each error. This will in the long run serve as a good source of information for future analyzes. Of course, the creditability would have been better if the statistics had stretched further back in time. Although when comparing the estimated failure rates and those handed by Elforsk the calculated failure rates were deemed as a probable estimates and will be used for the pre studies.
4.2 Handmade calculations
To assess the developed tool, a small distribution system is studied to facilitate an overview of incorporated components. The analyzed test distribution system has been retrieved from RCAM research group at Royal Institute of Technology. The line‐scheme is seen in Figure 20.
Figure 20 shows the line scheme of the test system.
In the line‐scheme the larger components and the components which properties enable the ability to maneuver the system is shown. In addition to the information provided in the line‐scheme, it has been given that faults that occur in one load point do not affect the remaining distribution system.
To satisfy this condition the model could be complemented with a circuit breaker between all load points and power lines. Finally the dotted lines are, in this case, non‐isolated over head lines. The block diagram is illustrated in Figure 21. This example is retrieved from the course TillfE’s, held at KTH, example collection. TRITA‐EE_2007_067.
Figure 21 shows a general block diagram made of the test system.
In the example it has been given how many customers that are connected to each load point and how much the total power consumption per year is at each load point. Information about what kind of cable or power line the distribution is conducted on and the length of them has been provided. To apprehend this information a search in the geographic information system (GIS) could prove to be a satisfying source. Thereafter components as underground cables, lines and load points can be modeled in a block diagram.
When the block diagram has been created, the translation to RACalc is relatively simple. The calculations are conducted and the calculation process is fairly time efficient. Finally, the block diagram in RACalc will look something like Figure 22. Other information that is necessary is failure rates for each component type. The failure rates can be calculated by collecting data from interruption reports.
Figure 22 shows the test system’s block diagram in RACalc.
4.2.1 Manual reliability calculations
The hand‐made reliability calculations are presented in Table 11, Table 12, Table 13 and Table 14
Table 11 shows manual reliability calculations made for load point N2722.
Load point
name: Komponent id
Failure rate
Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000
51 Disconnector 1 0 0 0 0 1 0
Consumption: N2722 0,050000 1,5 1,5 3 1 0,150000
349532 kWh Underground cable 2 0,009816 1 1,5 1 0,818 0,009816
Underground cable 3 0,004140 1 1,5 1 0,345 0,004140
Disconnector 2 0 0 0 1 1 0
Disconnector 3 0 0 0 1 1 0
Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960
Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960
Underground cable 4 0,000096 1 1,5 1 0,008 0,000096
∑ = 0,25657 ∑ =0,37697
Table 12 shows manual reliability calculations made for load point N2789.
Load point
name: Komponent id
Failure rate
Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000
10 Disconnector 1 0 0 0 0 1 0
Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,024540
142837 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,010350
Disconnector 2 0 0 0 0 1 0
Disconnector 3 0 0 0 0 1 0
N2789 0,050000 1,5 1,5 3 1 0,150000
Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960
Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960
Underground cable 4 0,000096 1 1,5 1 0,008 0,000096
∑ = 0,25657 ∑ = 0,39791
Table 13 shows manual reliability calculations made for load point N2783.
Load point
name: Komponent id
Failure rate [int./year]
Repair time [h/int.]
Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,034000
33 Disconnector 1 0 0 0 0 1 0
Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,024540
183009 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,010350
Disconnector 2 0 0 0 0 1 0
Disconnector 3 0 0 0 0 1 0
Over head line 1 0,066960 0,5 0,5 1 0,558 0,066960
N2783 0,050000 1,5 1,5 3 1 0,150000
Over head line 2 0,111960 0,5 0,5 1 0,933 0,111960
Underground cable 4 0,000096 1 1,5 1 0,008 0,000096
∑ = 0,25657 ∑ = 0,39791
Table 14 shows manual reliability calculations made for load point N2791.
Load point
name: Komponent id
Failure rate
Customers: Underground cable 1 0,013600 1 1,5 2,5 0,680 0,03400
13 Disconnector 1 0 0 0 0 1 0
Consumption: Underground cable 2 0,009816 1 1,5 2,5 0,818 0,02454
74220 kWh Underground cable 3 0,004140 1 1,5 2,5 0,345 0,01035
Disconnector 2 0 0 0 0 1 0
Disconnector 3 0 0 0 0 1 0
Over head line 2 0,111960 0,5 0,5 1 1 0,11196
Underground cable 4 0,000096 1 1,5 2,5 0,558 0,00024
N2791 0,05 1,5 1,5 3 0,933 0,15000
Over head line 1 0,066960 0,5 0,5 1
0,008
0,06696
∑ = 0,25657 ∑ = 0,39805
By using the formulas from chapter 2.2 the calculation of the reliability indices were performed. The following values were derived.
These manual calculations will form the basis of quality control of the developed tool. As will be shown in chapter 4.4, the calculations where performed with good accuracy by RACalc.
When the DSO wants to see what component in the example system that provides the desired improvement when maintained, the asset manager can use the “Component sensitivity analysis”
which is one of the available calculation alternatives. By doing this, RACalc will perform the calculation explained in chapter 3.3. The results will be the different reliability indices and presenting new values to these indices based on the “perfect behavior” of the optimized component.
RACalc is based on analytical reliability calculation methods [7].
4.3 Using RACalc to improve asset management
To explain how to use the software RACalc, images taken when using RACalc and a systematic description of the usage will be provided.
First, start the program by clicking the icon. Thereafter should the information specified in chapter 0 be present so that necessary data can be collected and extracted. When this fundamental information is in place, the system can be modeled.
For the system to be realized in the software there must be an infinite bus which represent the strong transmission system. In RACalc, the infinite bus is a perfect component that never fails, and can be found in the component list at the top of the screen. The infinite bus is orange and can be seen in Figure 23. Unfortunatly, the analysis tool cannot handle redundant systems therefore only radial electrical distribution systems are possible to study.
Start by adding an infinite bus on the workspace. Press the orange icon and click on the white area called workspace. The infinite bus can be put anywhere on the workspace.
Figure 23 shows the available components in the upper left corner. From the left there are transformer, ground cable, over head line, disconnector, isolated over head line, fuse, radio-controlled disconnector, infinite bus and breaker.
Then the components that are part of the system are to be modeled. This is done, by looking at the information of the system, the line‐scheme or the data found in the GIS. In this example, the first component is a ground cable with a length of 300 meters. The underground cable is red in RACalc. It can be found at the same place as the infinite bus. Deploy it in the system the same way as with the infinite bus. First press the red icon and click somewhere close to the infinite bus. When the underground cable has been placed on the workspace, one wants to change its properties. To alter the properties of a component, right‐click on the placed underground cable and choose “Ändra komponentegenskaper”. This is shown in Figure 24. What happens next is that a window will appear and show that specific components properties. This underground cable has a failure rate of 0,02 faults per year and a total fault time of 4 hours.
Name of the component can be chosen freely, in this case the name has been chosen to Underground cable 1. When the correct values are set, press “Ok” and the settings will be saved. This window is shown in Figure 25.
Figure 24 shows the workspace and two components. The user is in this case about to change the properties of a ground cable.
Connected to the first Underground cable there is a load point called N2722. Given in the example specification is that faults that occur in one load point does not affect other load points. This implies that a breaker is added in front of the load point. A breaker is in line‐schemes usually described as a cross, which it also is in RACalc. This component is found in the list among the rest of the components. To connect two components, the user must press the “c”‐button. To easier remember this, c can stand for connect. First press “c” then click at the two components that are supposed to be connected.
A load point has in data such as name, failure rate, fault location time, repair time, number of customers and yearly consumption. A load point is yellow in RACalc.
After that, there is supposed to be a disconnector. It has been given that the disconnectors are maneuvered in one hour. In the same fashion as described earlier, the user choose a disconnector to be placed, the blue icon, places it on the workspace, alter the properties and connects it to the other modeled components.
Hereafter it is just to model the remaining system in the same way as earlier described.
When the user considers him or her to be finished with the model, it is recommended to save the system. This is done by clicking at the file‐menu and choosing the “Spara som” alternative. By doing this, RACalc will save a survey picture of the modeled system and of course all the incorporated components coordinates, component types, properties etcetera.
Figure 25 shows the window for component information input.
Finally, when the model is finished; all wanted components are incorporated and their properties are set, the user can press the “Action”‐menu and choose calculate. A window will appear, see Figure 26, and show different calculation options. First option is the ordinary reliability calculation. These calculations are the ones described in chapter 4.2.1.
Next is the component sensitivity analysis, which is described in chapter 0. Finally there are different scenarios which can be simulated. The ones chosen is a representation over a 12 month period, based on Patrik Hilber’s research [3], “Storm” and “Extreme cold” based on discussions with Sandviken Energi Elnät AB and supervisors on Royal Institute of Technology.
Figure 26 shows the window where the user chooses what calculations are to be made.
Figure 27 shows the window in RACalc that displays the output-data.
When desired calculations have been chosen, the user press ”Ok”‐button and RACalc will start analyzing the system with algorithms described in chapter 3.2 and in the end a window with results will be shown, Figure 27.
4.3.1 Results from RACalc
The result of the example will according to RACalc be as presented in Table 15.
Table 15 shows the output from RACalc for test system, transferred to an Excel-table.
Komponentnamn
Felfrekvens
Lastpunkts namn: N2722 Infinite bus 0 0 0 0 0 0
Antal kunder: 51 st
Underground
cable 1 0,0136 1 1,5 2,5 0,68 0,034
Effektförbrukning: 349532 kWh Disconnector 1 0 0 0 0 1 0
Avbrottskostnad (12<t<24 [h]):
45900 kr N2722 0,05 1,5 1,5 3 1 0,15
Avbrottskostnad (24<t<48 [h]):
91800 kr
Underground
cable 2 0,009816 1 1,5 1 0,818 0,009816
Avbrottskostnad (48<t<72 [h]):
137700 kr
Underground
cable 3 0,00414 1 1,5 1 0,345 0,00414
ENS i lastpunkten: 15,04 Disconnector 2 0 0 0 1 1 0
Del‐SAIFI: 13,085172 Disconnector 3 0 0 0 1 1 0
Del‐SAIDI: 19,225572
Over head line
1 0,06696 0,5 0,5 1 0,558 0,06696
h(p(i)):
0,9999927397348887637872438023
Over head line
2 0,11196 0,5 0,5 1 0,933 0,11196
Underground
cable 4 0,000096 1 1,5 1 0,008 0,000096
Table 16 shows the output from RACalc for test system, transferred to an Excel-table.
Komponentnamn
Felfrekvens
Lastpunkts namn: N2789 Infinite bus 0 0 0 0 0 0
Antal kunder: 10 st
Underground
cable 1 0,0136 1 1,5 2,5 0,68 0,034
Effektförbrukning: 142837 kWh Disconnector 1 0 0 0 0 1 0
Avbrottskostnad (12<t<24 [h]): 9000 kr
Underground
cable 2 0,009816 1 1,5 2,5 0,818 0,02454
Avbrottskostnad (24<t<48 [h]):
18000 kr
Underground
cable 3 0,00414 1 1,5 2,5 0,345 0,01035
Avbrottskostnad (48<t<72 [h]):
27000 kr Disconnector 2 0 0 0 0 1 0
ENS i lastpunkten: 6,48 Disconnector 3 0 0 0 0 1 0
Del‐SAIFI: 2,565720 N2789 0,05 1,5 1,5 3 1 0,15
Del‐SAIDI: 3,9790600
Over head line
1 0,06696 0,5 0,5 1 0,558 0,06696
h(p(i)):
0,9999911465963000987991954165
Over head line
2 0,11196 0,5 0,5 1 0,933 0,11196
Underground
cable 4 0,000096 1 1,5 1 0,008 0,000096
Table 17 shows the output from RACalc for test system, transferred to an Excel-table.
Komponentnamn Felfrekvens
[fel/år,km]
Lastpunkts namn: N2783 Infinite bus 0 0 0 0 0 0
Antal kunder: 33 st Underground
cable 1 0,0136 1 1,5 2,5 0,68 0,034
Effektförbrukning: 183009 kWh Disconnector 1 0 0 0 0 1 0
Avbrottskostnad (12<t<24 [h]):
29700 kr
Underground
cable 2 0,009816 1 1,5 2,5 0,818 0,02454
Avbrottskostnad (24<t<48 [h]):
59400 kr
Underground
cable 3 0,00414 1 1,5 2,5 0,345 0,01035
Avbrottskostnad (48<t<72 [h]):
89100 kr Disconnector 2 0 0 0 0 1 0
ENS i lastpunkten: 8,46 Disconnector 3 0 0 0 0 1 0
Del‐SAIFI: 8,466876 Over head line
1 0,06696 0,5 0,5 1 0,558 0,06696
Del‐SAIDI: 13,1308980 N2783 0,05 1,5 1,5 3 1 0,15
h(p(i)):
0,9999835028283576229710429514
Over head line
2 0,11196 0,5 0,5 1 0,933 0,11196
Underground
cable 4 0,000096 1 1,5 1 0,008 0,000096
Table 18 shows the output from RACalc for test system, transferred to an Excel-table.
Komponentnamn
Felfrekvens
Lastpunkts namn: N2791 Infinite bus 0 0 0 0 0 0
Antal kunder: 13 st
Underground
cable 1 0,0136 1 1,5 2,5 0,68 0,034
Effektförbrukning: 74220 kWh Disconnector 1 0 0 0 0 1 0
Avbrottskostnad (12<t<24 [h]):
11700 kr
Underground
cable 2 0,009816 1 1,5 2,5 0,818 0,02454
Avbrottskostnad (24<t<48 [h]):
23400 kr
Underground
cable 3 0,00414 1 1,5 2,5 0,345 0,01035
Avbrottskostnad (48<t<72 [h]):
35100 kr Disconnector 2 0 0 0 0 1 0
ENS i lastpunkten: 3,37 Disconnector 3 0 0 0 0 1 0
Del‐SAIFI: 3,335436
Over head line
2 0,11196 0,5 0,5 1 0,933 0,11196
Del‐SAIDI: 5,1746500
Underground
cable 4 0,000096 1 1,5 2,5 0,008 0,00024
h(p(i)):
0,9999783549288690432098661979 N2791 0,05 1,5 1,5 3 1 0,15
Over head line
1 0,06696 0,5 0,5 1 0,558 0,06696
As can be seen, the values presented in Table 15,
Table 16,
Table 17 and
Table 18 is a perfect match of the handmade calculations made in chapter 4.2.1.
The reliability indices acquired from the test distribution system are according to RACalc shown in Table 19.
Table 19 shows the reliability indices for test system, calculated by RACalc.
SAIFI [int./y] SAIDI [h/y] CAIDI [h/int.] ASAI ENS [kWh] AENS [kWh]
0,25657 0,38794 1,51203 0,999955 33,21 0,31042
If the user copies the values given from RACalc to a table managing software, for example Microsoft Excel, graphs can be created to easier grasp the results.
Here are examples of results extracted from RACalc. Interruption costs for each load point during different time intervals t, shown in Graph 1.
Graph 1 shows the most significant components affecting SAIFI for test system.
Component importance results
In this chapter the results of the component importance analysis will be presented. In this small system all components are shown in the graphs which lead to the fact that some components do not contribute to a better reliability of the system, when they are optimized. This is due to the fact that they, from the beginning, are considered to never fail.
Graph 2 shows the most significant components affecting SAIFI for test system.
From Graph 2 it can be seen that the components affecting SAIFI are the over head lines in the system. By securing these components the number of faults will decrease dramatically leading to a better availability of the system.
Graph 3 shows the most significant components affecting SAIDI for test system.
In Graph 3 it is evident that the component affecting SAIDI the most is one of the over head lines.
When studying Graph 4 it is also giving an indication for the importance of maintaining the over head line.
Graph 4 shows the most significant components affecting CAIDI for test system.
CAIDI is a measure depending on the earlier mentioned measures SAIFI and SAIDI. Even if the reliability of the system generally has been better, it is not obvious that this measure is lower. CAIDI is a measure that reflects how long each outage lasts. Even if there are fewer faults, the faults occurring may last longer. As seen in Graph 4 all reliability measures are not comparable. This is
easiest explained by a small example. If a system consist of two components were both components fail one time each year. The first component, C1, has a total time of one hour while the other component, C2, has a total time of 100 hours. The mathematical explanation is that if a load point with one customer is connected to these components and C1 becomes optimized the new CAIDI will increase with almost 100 %, despite a total improvement of the system reliability.
The resemblance can be seen in Table 20.
Table 20 shows an example of the CAIDI index and how an outcome can be if a component is set to be perfect.
With explained, it is realized that CAIDI is not a measure that necessary describes the reliability of the system as SAIFI and SAIDI, only how long a fault is averaged to last when it occurs.
Graph 5 shows the most significant components affecting ASAI for test system.
To improve the ASAI index at a big scale is difficult when dealing with single components. In this measure, components with high failure rate and long total time stand out if there is a bigger change.
In Graph 5 one can see that the over head line has biggest impact on the ASAI index.
Graph 6 shows the most significant components affecting AENS for test system.
Another of measures that can be extracted from RACalc is AENS. This measure declares the delivering quality of the system and the components affecting it. For this distribution system, once again it is the over head line that clearly has biggest impact on the AENS index.
By studying these graphs, the DSO can allocate the maintenance depending on what reliability measure that is needed to be improved.
12‐month simulation results
One of the simulation alternatives is the 12‐months simulation. This calculation takes in consideration an altered failure rate for each month of the year.
The scale factors are based on Patrik Hilber’s research of time based failure rates and how they are distributed over a year. The distribution can be seen in Graph 7. [3].
Graph 7 shows the 12-month distribution of the different reliability indices for the test system.
4.4 Validation of RACalc
To be able to guarantee the correctness of the reliability indices and other results that RACalc produces a comparison with results that have been calculated by hand has been performed. The distribution system that will be evaluated is illustrated in Figure 28.
Figure 28 illustrates the distribution system used for validation.
To validate the results acquired from RACalc, this chapter will present a comparison between the hand‐made calculations performed in chapter 4.2.1 and the output from RACalc presented in chapter 4.3.1. The results are presented in Table 21, Table 22.
To validate the results acquired from RACalc, this chapter will present a comparison between the hand‐made calculations performed in chapter 4.2.1 and the output from RACalc presented in chapter 4.3.1. The results are presented in Table 21, Table 22.