International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
February 2019, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
The use of Markov Chain method to determine spare transformer number and location Musa Partahi Marbun1.
Ngapuli Irmea Sinisuka2.
Nanang Hariyanto3 1PT PLN (Perser.
Head Office.
System Planning Division.
Indonesia 2,3School of Electrical Engineering and Informatics.
Bandung Institute of Technology Bandung.
Indonesia
Article Info
ABSTRACT
Article history:
The purpose of this study is to develop a method to determine spare transformer number and location.
Using Markov Chain method, state transition model and steady state probability was used on each 500-kV substation in order to analyze the effect of spare number and location variation with the reliability changes.
To give an actual result of the case study, calculation of spare transformer number and location on 500/150 kV transformers in Java Bali System was analyzed.
The steady state probability results will vary depending on the number of spare transformer, these results can then be used to assess the spare transformer needed.
The variation of spare transformer location can be used to analyze the best possible location of the spare in order to satisfy the reliability required.
The methodology presented shows an integrated calculation for determining the spare transformer number and location.
Received Dec 12, 2017 Revised Jul 12, 2018 Accepted Jul 30, 2018 Keywords:
Markov chain Probability steady state Spare location Spare number Transformer Copyright A 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Musa Partahi Marbun.
PT PLN (Perser.
Head Office.
System Planning Division.
Jakarta.
Indonesia.
Email: musa@pln.
INTRODUCTION
Normal operation of a power system ensures energy flow from generation source to load demand, through its equipment.
If those equipment fails, from either or both causes in random environment, the risk of blackout is increasing.
A method to reduce the risk of blackout is by providing spare equipment.
The effectiveness of spare equipment is determined by its ability to maintain a certain reliability value.
But, maintaining a high reliability value would increase investment cost, therefore a method to determine spare transformer parameters is needed.
Spare part is important aspect in maintaining the system reliability, several methods to determine spare part has been used, some of the method already implemented in actual electrical equipment .
, .
A number of research have been done specifically on spare transformer number calculation, based on these literature, most of them uses Markov Chain method .
However, all of the research did not consider spare location.
Based on an actual condition of a power system, the output should also include spare transformer location.
This paper will show the advantage of the integration of spare transformer number and location calculation.
The concept of this study is reliability calculation.
the reliability definition in Markov Chain Method is a steady state probability in states which is considered as a success conditions.
To obtain the above results, the calculation of reliability is calculated for each 500-kV substation by varying the amount and location of the spare transformer.
In order to give clear implementation of the method, this research uses 500/150 kV transformer in Java-Bali System as the case study.
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RESEARCH METHOD
The main framework used in this research is Markov Chain Method.
Based on the Markov Chain Model .
, .
, the definition of system reliability is the steady probability group of normal condition states .
uccess state.
The first step in Markov Chain Model is by making a state transition model.
This research will use one spare transition state model, as shown on the Figure 1.
Figure 1.
Transition state model of one spare transformer Based on the Figure 1 and referring to the actual condition, the probability group of system reliability will be the steady state probability in state 1 and state 2.
while other states are defining an abnormal operation, the definition of each states are:
State 1 is normal condition with 1 spare available and without any system failure.
State 2 is normal condition with no spare available and without any system failure.
State 3 is N-1 condition with 1 spare available and with system failure.
State 4 is N-1 condition with no spare available and with system failure.
State 5 is N-2 condition with 1 spare available and with 2 transformer disturbance .
ystem failur.
State 6 is N-2 condition with no spare available and with 2 transformer disturbance .
ystem failur.
Based on the Figure 1, there are three rates that will affect the calculation result which are failure rate (), procurement rate (AA), and transport rate (A).
The failure rate () value is derived from A-B-C classification concept.
The procurement rate (AA) is a constant value where there are no constrain in spare The transport rate (A) is derived with spare location variation value.
The failure rate calculation uses A-B-C Classification (Pareto Law Concep.
All of the assets must be classified into AomodelsAo.
The disturbance data which affected the failure rate are only those disturbances occurred on the A component based on the A-B-C classifications.
For asset classification, the method used is inventory management.
Inventory Management is an activity of monitoring and controlling the business and production processes of a company, from the beginning of the booking, storage, using the components, until the production process.
This method has been used to classify different AomodelsAo of any The reason why these classification is necessary is because in this research, each AomodelAo defines the reliability in every 500-kV substations.
Each AomodelAo has its own failure rate, therefore to calculate this failure rate, the disturbance data needs to be classified by using Pareto Law.
The Pareto principle, also known as the 80/20 rule, is a theory which says that 80 percent of the output from any given situation or system is determined by 20 percent of the input.
The next step is determining the AA value and A value.
Based on an ideal repair and preventive maintenance .
, .
concept, these values have uniform probability density based on the following yce = 1/ycN .
ce Int J Elec & Comp Eng.
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The difference is, the AA value will be constant for every variation but the A value will have variation value based on the spare transformer location.
The one spare transition state has six possibilities of states.
therefore, the calculation of the transition matrix is as shown in Figure 2.
FROM
TRANSITION MATRIX
1-A-
Figure 2.
One Spare Matrix Transition By definition, this research calculates the steady state probability.
Mathematically, steady state probability is a condition where any initial state when multiplied with the transition matrix will have the same output as the initial state.
[Intial Stat.
x [Transition Matri.
= [Initial Stat.
Calculating the above formula by using the principle of matrix calculation will give the steady state probability results.
The required output is the probability group values of all states which has normal Based on the above simple example, the output is the sum of steady state probability of state 1 and state 2.
METHODOLOGIES
This paper will determine the spare transformer number and location by reliability of each 500-kV The main framework used is Markov Chain Model therefore the reliability is the steady state probability of Markov Chain Calculations.
General description of the proposed model In order to have comprehensive effect, every 500-kV substation have its state transition model, therefore it have its own failure rate based on the disturbance data of each substation and different transportation rate based on the location variation.
Location variation The idea of transportation rate variation is based on the different range between 500-kV substation.
This assumption regarding the spare transformer, is located in the 500-kV substation, not in a special spare The visualization of location variation based on Table 1.
Table 1.
Substation Range Table From In order to utilize the reliability value of each 500-kV substation, every substation has its own Markov Chain model and its own calculation results, while every model is linked to each other by the installation rate (A).
Based on this definition, the location determination is the effect of component reliability when the installation rate (A) changes.
This installation rate value changes based on the distance changes between substations.
The mathematical formula of the ideal rate .
, .
is, yce = 1/ycN .
The use of markov chain method to determine spare transformer number and .
(Musa Partahi Marbu.
A ISSN: 2088-8708 Therefore, the distance calculated from Table 1 will be converted into period (TM) by rough assumption of a distance per time constant factor.
These assumptions were based on several actual spare transformer transportations between the substations.
The installation rate will be different for every componentAos reliability even though each substation will have the same Markov Chain model but different installation rate and different failure rate.
Value of lost load The Markov Chain calculation will produce the probability steady state of success states or Based on the results, the economical calculation should give exact number and location based on the cost/benefit analysis of spare provision.
The cost component is spare price or cost, but the benefit instead of production cost or tariff, this research uses value of lost load.
The first step of coming up with the benefit component is calculating the outage cost.
Outage Cost=.
-reliabilit.
x capacity x LF x VoLLxtime .
And the Value of Lost Load calculation is:
ycOycuyaya = ycu VoLL calculation assume that any electricity outages will affect the economic condition .
RESULTS & DISCUSSION
500/150 kV transformer of Java Bali System was used as case study.
These transformers had several conditions that needed to be classified in order to have logical calculations of spare amount number and Classification 1 phase per banks or 3 phase per bank.
2 kinds of impedance.
Locations throughout Java Failure rate calculation Inventory management was used to classify the above conditions into several AumodelsAy.
These models had their own failure rates, which would be derived from Pareto LawAeABC Classifications.
The next step was steady state probability calculation for every failure rates and each variation of spare Java Bali 500/150 kV transformer model 500/150 kV Transformer or Inter Bus Transformer (IBT) in Java Bali System has two types, which are the single phase per bank transformer and the 3 phase per bank transformer.
The majority of the IBT in Java Bali system are single phase per banks transformer.
The advantages of single phase per banks transformers are the flexibility of the spare transformer, where if there is a failure in one of the transformer, the spare will replace only one unit instead of all three.
Moreover, it is lighter than 3 phase per bank transformer, where the advantage will be on transportation method aspect.
The type of the transformer used for this calculation is shown in the transformer type graphical recap in Figure 3.
Looking at Figure 3, the single phase per bank transformer has two type of impedance.
For this study the impedance difference will be neglected.
The effect will be the loading differences, therefore in order to have good results of spare number and location, the loading differences when there is different impedance will be neglected.
The next logical way to classify the IBT was dividing substation location in Java-Bali System by its This logic is based on the transportation constrain in order to have spare location and economical There are 7 provinces in Java Bali System but only 5 provinces have the 500 kV Substation.
The IBT data by provinces is shown in Figure 4.
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Figure 3.
500/150 kV Transformer Type Figure 4.
500/150 kV Transformer by Provinces Next step is determining the transformer failure classification, in order to have failure rate of each AomodelsAo.
Classification of disturbances type was recorded and compiled by maintenance engineer on Extra High Voltage Substation.
The data type of this failure was taken from disturbance data from 2008 up to 2013.
In order to get the failure rate, the disturbance data needs to be defined into major disturbance and minor Pareto Law-ABC classification .
has become a commonly used method, where the classification of A only has 20% volume of the total equipment but have the interference effect of 80%.
In a transformer, this principle means, the small component of a whole equipment, could disturb the whole Based on A-B-C classification method, the transformer failure data was divided into failure/disturbance on component A, component B, and component C of the whole transformer.
A-B-C
classification analysis simplified the component disturbance data based on the Pareto Law where the definition of component A in this study is a component where its disturbance has major effect on the entire transformer and this component is unique.
Component B is defined as components that has a high investment value but does not affect the entire transformer in maintenance or replacements phase.
Component C is defined as supporting components.
Based on the definition of the classification of A-B-C above, it can be summarized that:
Disturbance of component A were Bushing & Insulators, and OLTC, by 19 %.
Interference Protection System of Component B by 31 %.
Impaired Support Tools of Component C which.
Outer Party, and system conditions, by 49 %.
Due to data limitations and monitoring equipment.
Figure 5 is showing the different classification types of disturbance per IBT 500/150 kV components in Java-Bali system for major disturbance.
According to Pareto LawAeA-B-C Classification, the Component A failure will have major effect to the entire transformer and also to the entire power system.
Based on the classification of location and impedance, the failure rate from the disturbance data has been simplified into its average number.
The failure rate calculation was using three units of transformer as one.
This condition occurred because Java Bali System uses 1 phase per bank transformer, therefore one disturbance in one unit will fail all of the three units.
Component Name
Bucholz Relay
Bushing Power Supply Current Transformer Insulator Power Cable Trip Control
Marshailling Kiosk
OLTC
Protection System Reactor Switch Wiring A-B-C Classifications Figure 5.
Component Disturbance & A-B-C Classifications The use of markov chain method to determine spare transformer number and .
(Musa Partahi Marbu.
A ISSN: 2088-8708 Failure rate Based on Section i, the first step is detailing the failure rate() into every 500-kV substation.
The results are shown in Figure 6 The results of the above figures were using statistical data for every IBT in Java Bali System.
The calculation of failure rates of each substation was based on A-B-C classification.
Figure 6.
500 kV Substation failure rate Transportation rate The next step is modeling the range data between 500 kV substations, the transportation model is shown in the Table 2 Based on the above data assumption, there will be a significant installation rate value.
The one-spare Markov Chain model on each substation is linked to each other by the installation rate value.
Table 2.
Range Between Each 500-kV Substation Spare number and location results The steps are putting the spare transformer at Cilegon Substation, by using the data in Table 2.
The installation rate on Markov Chain model at Cilegon Substation, and another different substation.
Thus, the steady state probability group at each Substation will be different.
The second scenario and so on is done by changing the spare transformer location.
The location optimization is the steady state probability group calculation result that changes as the installation rate changes as well.
The results calculation of probability steady state of each 500-kV substation with spare IBT location variation is shown in Table 3.
Based on the results above, each provinces should have a spare, because the significant increase of reliability occur from 0 spare to 1 spare.
Based on the reliability calculation, the spare number should be 5 .
in every provinc.
and the optimum locations are Cilegon.
Gandul.
Cibatu.
Ungaran, and Krian (Green The next calculation is by comparing these with the economic criteria.
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Table 3.
Calculation Results GITET Suralaya Suralaya Baru Cilegon Balaraja Kembangan Cawang Gandul Depok Bekasi Cibinong Cibatu Cirata Bandung Selatan Mandirancan Tasikmalaya Pedan Ungaran Tanjung Jati Kediri Ngimbang Krian Grati Gresik Paiton 0 Spare 1 Spare 2 Spare 3 Spare 4 Spare Spare number and location by economical criteria The economic criteria are comparing the cost and benefit.
The cost component is spare transformer price, with the assumption of Rp 3.
24 B .
000,- USD) The benefit component is the outage cost with value of lost load, whereas the value of lost load in each province is shown in Table 4.
Based on the above calculation results and the calculation result of spare cost, the outage cost with spare number and location variation are calculated and analyzed.
The results for 500-kV Substation in Banten in Figure 7.
Table 4.
Value of Lost Load Provinces Banten Jakarta West Java Central Java East Java Value of Lost Load Rp 4,247 /kwh Rp 8,888 /kwh Rp 4,906 /kwh Rp 4, 481 /kwh Rp 7, 300 /kwh Figure 7.
Cilegon 500-kV substation results Based on the above results, the spare number is 1 referring to the crosspath between spare cost and avoided cost, and spare location in Cilegon Substation .
o other 500 kV substatio.
The next results for 500-kV Substation in DKI Jakarta in Figures 8-12.
The use of markov chain method to determine spare transformer number and .
(Musa Partahi Marbu.
A ISSN: 2088-8708 Figure 8.
Kembangan 500-kV substation results Figure 9.
Cawang 500-kV substation results Figure 10.
Gandul 500-kV substation results Int J Elec & Comp Eng.
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Figure 11.
Bekasi 500-kV substation results Figure 12.
Cibinong 500-kV substation results Based on the above results, the spare number is 2 .
orresponding to the Kembangan and Bekasi result.
and the location of each spare is in Cawang and Cibinong .
orresponding to the small effect of Bekasi and Gandul reliability on spare location variatio.
The Cawang and Cibinong must have a follow up on reducing the disturbance, because its problem cannot be solved with spare provision.
The next results for 500-kV Substation in West Java in Figures 13-16.
Figure 13.
Cibatu 500-kV substation results The use of markov chain method to determine spare transformer number and .
(Musa Partahi Marbu.
A ISSN: 2088-8708 Figure 14.
Cirata 500-kV substation results Figure 15.
Bandung Selatan 500-kV substation results Figure 16.
Mandirancan 500-kV substation results Based on the above results, the spare number is 2 .
orresponding to the Mandirancan result.
and the location of each is in Mandirancan .
orresponding to location variation .
, and Cirata .
orresponding to the small effect of Cibatu reliability on spare location variatio.
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reducing the disturbance, because its problem cannot be solved with spare provision.
The next results for 500-kV Substation in Central Java in Figures 17-18.
Based on the above results, the spare number is 2 and the location of each is in Ungaran and Pedan.
Based on the Pedan results, both spares should be located in Pedan, but the effect on Ungaran will be greater if the location of each is in Pedan and Ungaran.
The 3 spares provision will be too high and redundant.
The next results for East Java in Figure 19.
Figure 17.
Pedan 500-kV substation results Figure 18.
Ungaran 500-kV substation results Figure 19.
Krian 500-kV substation results The use of markov chain method to determine spare transformer number and .
(Musa Partahi Marbu.
A ISSN: 2088-8708 Discussion These results give two major revelation regarding transformer spare, especially in Java-Bali system.
First revelation is optimal number of spare transformer number, the idea of increasing spare transformer number will not increase significant reliability, and there are certain limit of spare transformer number.
Therefore, some investment cost could be saved if the spare transformer number is limited.
Second revelation is the effect of location variation to maintain reliability of each substation show that with the optimum way of putting the spare transformer could maintain reliability of overall system reliability, these aspects currently overlooked by other research.
CONCLUSION
Markov chain gives the best calculation to determine the number and location of spare transformer by varying every possible combination.
Markov Chain model in every 500 kV substations gives clear reliability results based on the variation above.
Most of the current studies have not clearly consider the spare location output, on the other hand this research finds the opportunity to maintain the system reliability by changing the installation rate.
This installation rate defines the location of spare transformer.
Based on the calculation results, there are significant effect on system reliability if the spare number and location could be determined by this method.
Economic criteria give better determination of spare number and location, instead of reliability measure standalone as the criteria.
REFERENCES