AGING BASED MAINTENANCE AND REINVESTMENT SCHEDULING OF ELECTRIC DISTRIBUTION NETWORK

Transcription

1 Juha Korpijärvi AGING BASED MAINTENANCE AND REINVESTMENT SCHEDULING OF ELECTRIC DISTRIBUTION NETWORK Thesis for the degree of Doctor of Science (Technology) to be presented with due permission for public examination and criticism in the Auditorium of the Mikkeli University Consortium, Mikkeli, Finland on the 23rd of November, 2012, at noon. Acta Universitatis Lappeenrantaensis 481

2 Supervisor Professor, Dr. Jarmo Partanen Institute of Energy Technology Lappeenranta University of Technology Lappeenranta, Finland Reviewers and opponents Professor, Dr. Pertti Järventausta Departement of Electrical Energy Engineering Tampere University of Technology Tampere, Finland Director, Dr. Juha Lohjala Suur-Savon Sähkö Oy Mikkeli, Finland ISBN ISBN (PDF) ISSN Lappeenrannan teknillinen yliopisto Digipaino 2012

3 To Eeva-Leena

4 Abstract Juha Korpijärvi Aging based maintenance and reinvestment scheduling of electric distribution network Lappeenranta pages Acta Universitatis Lappeenrantaensis 481 Diss. Lappeenranta University of technology ISBN , ISBN (PDF), ISSN The maintenance of electric distribution network is a topical question for distribution system operators because of increasing significance of failure costs. In this dissertation the maintenance practices of the distribution system operators are analyzed and a theory for scheduling maintenance activities and reinvestment of distribution components is created. The scheduling is based on the deterioration of components and the increasing failure rates due to aging. The dynamic programming algorithm is used as a solving method to maintenance problem which is caused by the increasing failure rates of the network. The other impacts of network maintenance like environmental and regulation reasons are not included to the scope of this thesis. Further the tree trimming of the corridors and the major disturbance of the network are not included to the problem optimized in this thesis. For optimizing, four dynamic programming models are presented and the models are tested. Programming is made in VBA-language to the computer. For testing two different kinds of test networks are used. Because electric distribution system operators want to operate with bigger component groups, optimal timing for component groups is also analyzed. A maintenance software package is created to apply the presented theories in practice. An overview of the program is presented. Keywords: maintenance practices, dynamic programming, maintenance scheduling, reinvestment scheduling UDC : :658.58:657.47

5 Acknowledgements The results of this doctoral thesis are mainly based on the research work financed by TEKES, Etelä Savon Energia Oy, Joroisten energialaitos, Joutsenon Energia Oy, Imatran Seudun Sähkönsiirto Oy, Järvi-Suomen Energia Oy, KSS Verkko Oy, Kymenlaakson Sähköverkko Oy, Outokummun Energia Oy, Parikkalan Valo Oy and PKS Sähkönsiirto Oy. The final writing of dissertation was supported by Finnish Cultural Foundation, South Savo Regional fund. I thank all for financial support. I want to thank my employer Mikkeli University of Applied Sciences (MAMK) for working circumstances and organizing the research project. I thank my supervisor Professor Dr. Jarmo Partanen for his guidance and valuable contribution during this work. I express my gratitude to the reviewers of my thesis Professor Dr. Pertti Järventausta and Dr. Juha Lohjala for their critical review of my thesis manuscript and their comments. I want to thank Dr. Jari Kortelainen for the co-operation in developing the optimizing models, Mr Jyri Kivinen for developing the structure and interface of the maintenance software package, Mrs Aija Myyryläinen for collecting the survey material. The SPSS program was used by Mr Mauno Keto and Mr Tero Karjola implemented the test network. Mrs Kirsti Karttunen helped me in literature searching and Mr Jari Hartikainen in the English language. I want to thank them as well. Finally I thank my wife Eeva-Leena for her love during the process and my three beautiful daughters, Helka-Maaria, Helmi-Tuulia and Henni-Riikka for inspirational family atmosphere. Mikkeli, September 14 th, 2012 Juha Korpijärvi

6 Abstract Acknowledgments Nomenclature 1 Introduction Background Network asset management and reliability analysis Maintenance in Finnish system operators The distribution system operators analysed Maintenance policy in the analysed distribution system operators The average interruption time and maintenance Conclusion of the Finnish distribution system operator analysis The scope of the thesis Contributions Maintenance problem Problem description Failure modelling Maintenance activities Maintenance strategies Maintenance directions and cost optimization Objective of maintenance Modelling of cost components Determination of maintenance cost and failure cost Fault risk of the component in electric distribution system Outage cost The maintenance model Overhaul of the component Maintenance problem solving Decision of maintenance and investment actions Example of maintenance and reinvestment timing decision Optimization problem Possible optimization algorithms for maintenance problem solving Line clearance problem Line and generation outage scheduling problem Stochastic transition process Algorithm for sizing, locating and timing of feeder reinforcements Dynamic programming model Example of dynamic programming algorithm Dynamic programming models for maintenance and reinvestment optimization Three-state-model... 60

7 4.2.2 Three-state-plus-model Total-cost-model Annual-cost-model Conclusion of the presented models Fundamental improvement and dynamic programming Group optimization The analysis methods and the test networks Test network The analysis of components Separately optimized components Maintenance years The effect of maintenance on the reinvestment timing Results of the maintenance model three Component groups Test network The description of the network Failure rate levels and initial values in the network Results of the dynamic programming algorithm Sensitivity analysis Interrupted power The age of the component Interest rate Failure cost level Investment price Scale-factor λ Shape-factor β Conclusion of the sensitivity analysis Maintenance software package Discussion Conclusions References

8 Nomenclature Roman Letters a A 0 A 1 A 2 A02 A01 A11 A12 A22 A[] B[] c kw c kwh C C C clr (t) C comp (t) C dar C energy (t) C F (t) C F1 (t) C F (t,a) C F (a m (t),n) Chsar C ins (t) C I (t) C L (t) C ljtp C Mi C out (t) C ovh (t) C uitp C per C rep (t) C Ri C M (t) variable, which express the reference year after the maintenance action discounted failure costs to the end of the design period, if investment is not realized discounted failure costs to the end of the design period, if maintenance action is realized discounted failure costs to the end of the design period if investment is realized additional cost when transferring from no-state to investment state additional cost when transferring from no-state to maintenance state additional cost when transferring in maintenance state additional cost when transferring from maintenance state to investment state additional cost when transferring in the investment state additional cost in total-cost model the cost function to find the optimal route in annual cost model outage cost of power [ /kw] outage cost of no delivered energy [ /kwh] cost associated with the maintenance task total cost costs of clearing the corridors compensation costs including the costs not reaching the target level of the criteria cost of delayed automatic reclosing for the customer marginal profit of the undelivered energy failure costs in year t failure rate of the component in year t without maintenance action failure rate of the component a years after the maintenance action in year t outage cost per year when state alternative n is realized for component in age a m (t) cost of high speed automatic reclosing for the customer costs of inspection and costs of eliminating minor faults costs of investments in year t operational costs in year t maintenance cost of line j at time t at interval p maintenance cost for line i in interval j costs experienced by the customer costs of capital overhauls maintenance cost of unit i at time t at interval p. For instance t could be an hour and p could be a week long cost of permanent interruption for the customer repairing costs of the failure average repair cost for line i maintenance costs in year t

9 e Euler s number E cost-effectiveness of a maintenance task E i state of the process ( I = 1,2,,n) F objective function F ij (t) distribution function of the one-step transition time f failure rate f(t) density function F(t) probability of failure up to time t G(t,n) minimum costs up to state (t,n) I component I m the state the system enters at time t m j consumer l length of the conductor [km] M total number of lines in the system N the number of possible strategies N 1 total scheduling time intervals N 2 the number of components in one component group p rate of interest P power of interrupted load [kw] P[] probability function P={p ij } time homogeneous transition probabilities r(t) failure rate at time t r ij (σ i (k)) cost/reward of a transition (from E i to E j ) controlled by the strategy σ i (k) selected at t k R ij ( ) function which denotes the cost of transition of the system when it goes from state E i to E j t age of the component or reference year t ij length of interruption [h] t 1 step year t 2 year of the action (t,n) state T length of the design period T p utilization time of the investment V[1,2] transfer costs from state 1 to state 2 w i (σ i (k)) expected cost of the step k+1 if the system is in state E i at t k, and controlled by σ i (k) wn the weighting factor in group optimizing X ij maintenance decision variable for line i in j th time interval (0-no maintenance, 1-maintenance) X itp maintenance status of unit i at time t at interval p, 0 if unit is offline for maintenance, otherwise 1 Y jtp maintenance status of line I at time t at interval p, 0 if unit is offline for maintenance, otherwise 1 Z(t,n) the cumulative costs in year t in node n, when the minimum route is chosen

10 Greek Letters α α 1 β β 1 ε λ λ ij σ() σ j (k) ω discount factor parameter, which express the relation of the failure rate shape factor in Weibull distribution parameter, which express the annual increase of the failure rate after the maintenance action annuity factor scale factor in Weibull distribution failure rate of line i in j th time interval maintenance strategy maintenance action selected when arriving to state E j at time t k weighting factor Abbreviations DP INV INV RES MAIFI NG NL NP NT RNA/AM SAIDI SAIFI WASRI dynamic programming cost of reinvestment residual value of the previous investment of the component momentary event average interruption frequency number of units number of transmission lines number of intervals under study number of times at each interval reliability based network analysis tool system average interruption duration index system average interruption frequency index system average reliability index

11 11 1 Introduction 1.1 Background Ten Eastern-Finnish distribution system operators decided to develop their maintenance activities in the year All the companies had the same future challenges. The personnel have shorter careers so the maintenance and reinvestment decisions can no longer be based only on the opinion of the network designers. Secondly the capital tied to the network is increasing and money can be saved through the proper timing of maintenance actions and reinvestments. The third reason is the compensation which the distribution system operator has to pay for disturbances in electric distribution. For these reasons the operators decided to begin a project to study the maintenance practices. They decided to compare their practices to the those of the other fields and to improve their own maintenance system to have savings in failure and investment costs. The project took two and a half years. The content of this dissertation was produced in this project. The main idea of the project was to model the deterioration of distribution components depending on their age. The deterioration of components accounts for the failure costs of the components. When the failure costs of the components are modelled, it is possible to find the optimal maintenance and reinvestment moments for the distribution components. The analysis concentrates not only on single distribution components but on component groups as well. The objective of this dissertation is to develop methodology for the maintenance of electric distribution systems. The scope of this thesis is restricted to the deterioration due to aging. The trimming of the corridors, major disturbances, regulations and capacity of the network are ruled out of the scope of the thesis. The strategy of the distribution system operator is developed from the condition and time based strategy to the reliability centred maintenance strategy. Further it is proved that the reliability and likely failure costs of the electric distribution network can be a basis for modelling maintenance and investment scheduling of the network. 1.2 Network asset management and reliability analysis According to Lakervi and Partanen (Lakervi, Partanen, 2008) the network asset can be divided into three categories: the operating functions, maintenance functions and building functions. These three main functions are presented in Figure 1.1. The main objective of network asset management is to minimize the total costs of the network in design period and at the same time maximize the productivity of the invested capital.

12 12 Figure 1.1 The main functions of network asset management (Lakervi, Partanen, 2008) In further analysis the main interest is in network renovations and construction of new network. According to Jukka Lassila the most important reasons for large-scale renovation are environmental factors, the age of the network, poor reliability, changes in the objectives of network owners and the development of the needs of the society or changes in legislation (Jukka Lassila, 2009). Figure 1.2 sums up the most essential reasons for network renovation.

13 13 Figure 1.2 Drivers for network renovation according to Jukka Lassila (Jukka Lassila, 2009) In this thesis, the focus is in network age and condition. However this is seldom the only reason for renovation. The tightened reliability requirements, major disturbances and regulation, lead to the new operating, maintenance and construction functions of the electric distribution network. In the near future main focus is on the environmental reasons why network operators are transforming the open overhead lines beside the roads or to the underground cabling network. When talking about network age and condition the main interest is in the reliability of the network. The design process is started by analyzing the basic structure of the network by using traditional network criteria. After the construction of the basic network alternative plans are created. The reliability analyses are then made for the network alternatives. (Orvassaari et al., 2005). The reliability analysis can be made for the network with a suitable tool. In (Pylvänäinen et al., 2009) the reliability based network analysis and life cycle cost functionality (later RNA/AM) is used for analyzing the reliability of the network. The RNA/AM utilization in network planning is presented in Figure 1.3.

14 14 Figure 1.3 RNA/AM utilization in network planning according to Pylvänäinen et al. (Pylvänäinen et al., 2009) Figure 1.4 presents the process description of the maintenance problem presented in this thesis. In the figure the capacitive, environmental and regulation reasons are not included in the problem analyzing. These can be called external reasons. The internal reasons are aging and deterioration of the network which is the scope of this thesis. The aging and deterioration of the network is analyzed by age depending failure rates. According to these rates three possibilities are analyzed: no action, maintenance action and reinvestment. Also the fourth possibility, fundamental improvement, is presented. Two different analyses are made: the other for single components and the other for component groups. For optimizing the dynamic programming (DP) models are presented. The main focus in the modeling are the poles, overhead lines and transformers. Figure 1.4 Problem solving of the maintenance modelling in dissertation

15 Maintenance in Finnish system operators To understand the maintenance practices and policies in electric distribution system operators, the representatives of the distribution system operators were interviewed. First ten Eastern-Finnish companies financing the study were interviewed. After that the other Finnish distribution companies were asked if they were interested in answering the question sheet by mail. There were seventeen interested companies. The inquiry sheet is presented in Appendix 1 (In Finnish). The comparison of maintenance practices between different distribution system operators is quite difficult. The practices are not commensurable. However the maintenance level of the operators is compared by giving points to the operator depending on the maintenance practices. The correlation of points and the average interruption time of the distribution system operators are also studied The distribution system operators analysed Three of the 27 companies distribute electricity in big cities. They have more than customers and the electricity transmission is more than 1000 GWh per year. Three companies represent very big provincial companies, which operate in the very large area and they have over customers each. The distributed energy is over 1000 GWh in a year. Six companies represent medium size city companies. They have customers and the electricity transmission is GWh in year. Five companies are medium size provincial companies. They have customers and the energy transmission is GWh per year. The rest 10 companies are small companies. They have less than customers and the electricity transmission is less than 250 GWh per year. (Korpijärvi, 2009) The classified number of customers and the energy transmission is presented in Appendix 2. The 20 kv cable length, and the 20 kv cable length per customer is presented in Appendix 2 as well Maintenance policy in the analysed distribution system operators The maintenance policy of the distribution companies was evaluated based on eleven maintenance practises. These practises are checking interval of 0,4 kv network, checking interval of 20 kv network, checking interval of transformer substations, checking interval of disconnectors, checking interval of remote-controlled disconnectors, trimming interval of vegetation, helicopter checking, thermographic survey and checking the rate of decay of wooden poles. Further it was asked whether the company has used long term investment planning and if it would use a maintenance program. The frequencies of the practices are presented in Appendix 2 The distribution system operators are nearly at the same level with regard to some practices. Most of the companies have maintenance program in use and most of the companies make long term investment planning. In one company the maintenance

16 16 program was used only for the documentation of the poles, but the faults and problems were repaired immediately when they were detected but they were not documented. In one company the maintenance program was not very advanced and manual cards and Excel files were still in use. In the companies where a maintenance program is used, the program is based on predefined activities carried out at regular intervals (scheduled maintenance). In all companies including the companies where the program is not used, the 0,4 kv and 20 kv installations are checked every 5 10 years. The most common interval is 6 years. The remote controlled disconnectors are checked mostly every 3 and 5 years. The vegetation maintenance involving trimming and removing trees is made every 3 6 years excluding one company. In 11 companies the network is checked with the helicopter. This is done in addition to field checking. The checking interval in the companies where helicopter checking was used, was two to eight years. In most companies (21 of 27 companies) the 20 / 0,4 kv transformer stations were checked by an infrared camera. In some companies where infrared camera checking was used, this was done only for critical transformer stations. The critical component, where aging has a powerful effect, is the pole for an overhead line. Because wood is the used material, rot is a normal phenomenon. The rot inspection is made in 23 of 27 companies. The interval of the checking varies. In one company the checking is only made for poles over 40 years. In most companies the checking interval for poles varies from checking every pole every 5 years to checking poles every 6 years but only older poles are checked. In 20 companies of 27 the long-term investment plan is used. When there is the investment plan it is possible to decide whether to make an investment or to carry out a smaller or larger overhauling or maintenance action instead. The most typical criteria for investment are the age, reliability and availability. In some cases the city construction office gives boundary condition for the investment. To study the level of the maintenance policy of the company, all the maintenance practices are evaluated with points 1 3. If the maintenance is at the best level, the company receives 3 points and when it is at the lowest level company receives 1 point. The points of maintenance activities and the total points for the companies are presented in Appendix 2. The difference of the points between the highest and the lowest maintenance level is not very big. This is because the maintenance level is partly regulated by safety norms. However the difference exists and the highest frequency is in the middle of the highest and lowest value The average interruption time and maintenance The impact of the maintenance policy was analyzed by the interruption time of the company. The interruption time is energy weighted and is reported to the Energy Market Authority of Finland (year 2008). The interruption time is given for unexpected faults in 1 70 kv network for one customer. The classified average interruption time is given in Appendix 2.

17 17 The hypothesis is that the maintenance policy of the distribution company has a strong effect on the interruption time of the company. The further hypothesis is that the high amount of cable network has an effect on the interruption time of the company so that a higher rate of cable network decreases the interruption time of the company. Also it was assumed that a modern network has lower interruption time than an old network. So the value ratio of the network to the replacement value of the network was studied. The cabling level of the 20 kv network and the current value of the network to the replacement value are presented in Appendix 2. The correlation matrix is presented in Table 1.1. The values are based on the statistics from (EMV, 2008) Table 1.1 The correlation matrix of the factors. We can notice a very high correlation (significant level under 0,01) in the relation of annual energy transmission and number of customers, which is obvious. Further there is a very high correlation between the current value of network and average time of interruption. The main reason is that the new conductor has a lower failure rate than the old conductor which has already deteriorated. We can also notice a correlation (significant level 0,01 0,05) between the total points of maintenance activities and average time of interruption. This correlation should be obvious but it is not so high as it could be assumed. Also a correlation between cabling level of 20 kv network and average time of interruption exists but it is lower than assumed. Furthermore there is a correlation between total points of maintenance activities and current value of the network. The reason for this is probably the fact that the distribution companies which invest more money in the network also maintain the network more intensively. Also the correlation between 1-70 kv conductor length (including overhead lines and underground cables) per customer and average time of interruption was studied. The correlation coefficient is 0,465 at the 0,05 significant level which is high enough to confirm the correlation between these two factors.

18 18 It is also interesting to see a correlation in two different groups - city operators (cabling level of 20 kv network over 15 %, 9 operators) and rural operators (cabling level under 15 %, 18 operators). The correlations are presented in Table 1.2 The energy and interruption data is according (EMV, 2008) Table 1.2 The correlation matrix for rural and city operators We can notice that the correlations between total points of maintenance activities and average time of interruption are in both groups lower if city and rural operators are analysed separately. Actually the correlation is very low for city operators. The correlation between current value of network and interruption time is high only for rural operators. The cabling level and interruption time has correlation only in city operators Conclusion of the Finnish distribution system operator analysis There are differences between maintenance actions in the distribution system operators analysed. The differences are between checking intervals and the use of checking methods. Of course the safety regulations set the minimum level to the maintenance policy.

19 19 There are meaningful correlations when all the electricity system operators are analysed together. The correlations are between the maintenance level and average time of interruption, between the maintenance level and the current value of the network, cabling level and the time of interruption and the cabling level and the maintenance level. When the operators are divided into two groups according to the cabling level, the meaningful correlations are between the network value and average interruption time for rural operators and current value of network and total points of maintenance activities for rural operators. There is also meaningful negative correlation between total points of maintenance activities and current value of network for city operators but this result is opposite to the result where city operators and rural operators are together. This result is not logical and could be coincidental. The biggest weakness of the study is the commensurability of the different maintenance parameters. It would have been possible to use weighting between different maintenance practises. However the value of the weighting parameters would have been questionable and so the weighting is not used. 1.4 The scope of the thesis The main objective of this thesis was to use deterioration curves of the distribution components as a base for maintaining and reinvesting the distribution components. This area is studied and further development is presented. The whole problem includes however not only deterioration but also other initial data. The initial data, calculation process and results are presented in Figure 1.5 The starting points, which are not included to the thesis are in the white boxes.

20 20 Figure 1.5 The maintenance problem Chapter 2 describes the maintenance problem, the objective function and the basis for calculating the objective function including the costs and failure rates of the electric distribution system. Chapter 3 describes the basic functions for solving maintenance and reinvestment time of the system. It describes the optimization problem and algorithms for problem solving in literature. The dynamic programming model for solving the optimization problem is described in chapter 4. The dynamic programming model includes four different kinds of algorithms presented in this chapter. Testing the presented optimization algorithms is carried out in chapter 5. Two different kinds of test networks are used. The first test network is imaginary and simple enough to test the models. The second test network is real to test the algorithms in real circumstances. The sensitivity analysis of the described models is presented in chapter 6. The maintenance software package is presented in chapter 7. The discussion and conclusion of the thesis are presented in chapters 8 and 9. The focus in this thesis is in aging and the deterioration of the network. So the environmental reasons are not included to the scope of this thesis.

21 Contributions In this thesis a methodology is created for scheduling the maintenance and reinvestment of the electric distribution components. The analyses include the network deterioration due to aging. For this scheduling four dynamic programming algorithms are created and tested. The four created models are so called three-state-model, three-state-plus-model, total-cost-model and annual-cost-model. The characteristic of these methods is described in this thesis. The experimental analysis is also made for comparing the results of the four presented dynamic programming models. Because it is economical for the distribution system operator to maintain or reinvest in components at the same time in one location, the component groups are studied in this thesis. A method to find the optimized time for maintenance action and reinvestment of component groups is created and tested. The environmental, capacitive and regulation reasons are not included to the analysis. However these point of view can be taken in account in weighting operations of component groups, which is presented in the thesis. To test the dynamic programming models in practice a maintenance software package is created. A short description of the maintenance software package is presented. The usability of the program would be however much better if the automatic data transmission between the network information system and the maintenance software package were developed. The maintenance strategies and policies of the distribution system operators are also analysed in this thesis. The study shows that the maintenance level of the operator has an effect on the interruption time of the operator but the effect is lower than was assumed. One reason can be the sample of the operators studied, the other reason can be the large scale interruptions caused by storms where the maintenance level and the modernity of the network have lower impact.

22 22 2 Maintenance problem 2.1 Problem description The main components in a distribution system include overhead lines (lines, poles and related items), cables (cables, junctions and related items), breakers, transformers, disconnectors, load disconnectors, fuses and bus bars (Bertling 2002). The further analysis concentrates on lines (including disconnectors) and transformers. The underground cables are not included to the test networks. The reason is that it was possible to collect failure rate data and the main interest of the distribution system operators is focused on these components. Furthermore there are established maintenance programs to transformer stations. There are four different kinds of maintenance impulses for distribution network. The environment, for example vegetation is the first impulse. The second impulse is deterioration or aging of the components which is the view of point in this dissertation. The third impulse is regulation. To achieve the desired return of investment according regulation the desired investments have to be done and interruption level has to be reached. The failures can also be random failures, which are not caused by environment or aging but may be impulse to maintenance action. (Endrenyi et al., 2001) According to Lina Bertling there are two major impacts on system reliability of overhead lines, trees and aging (wear) (Bertling 2002). Trees are included to the further analysis as location dependent initial values for failure rate data in the further model presented in this dissertation. The most interesting phenomenon is aging or deterioration because it gives impulse for maintenance activities of distribution equipment and also for the reinvestment of the equipment. The deterioration is modelled in the further analysis using age dependent failure rate curves. These failure rates can be found in literature. However the real failure rates depend on the producer of the component and on the environment where the component is used. Thus the used failure rate data gives only one possible basis for the analysis. Because the deterioration curves of the distribution components are used, the outage cost level of the component can be found. It is possible to decrease this cost level by maintenance or reinvestment action of the component. So it is possible to find the optimal moment for maintenance action or reinvestment for the distribution components. It is economical for the distribution system operator to maintain not only single components but whole component groups. This matter is analysed as well. There are different strategies for the design period. The first possibility is to do nothing, when the costs increase according to aging for the whole design period. The second possibility is to make a component reinvestment without maintenance and the third possibility is to have first maintenance and then reinvestment. There are still other strategies. The maintenance can be carried out several times during design period and also the reinvestment can be made twice. The objective of the chosen strategy is the high availability of the system or total cost (including investment, maintenance and failure costs) minimization during the design period.

23 23 The analysed distribution network consists of 20 kv cables and overhead lines and 20/0,4 kv transformers. Because the failure costs of 0,4 kv network are not in the level to carry out reinvestment or capital overhaul, they are not included to the analysis. A typical analysed network is presented in Figure 2.1 Industry Household Services Public Farming 8 Disconnector FOREST ROAD 7 Disconnector 5 3 Remotecontrolled disconnector 110/20 kv 1 Disconnector 2 Disconnector Disconnector 6 FIELD 4 8 Disconnector 110/20 kv 1 3 Disconnector 2 Remotecontrolled disconnector 5 7 Disconnector Disconnector Disconnector 4 Disconnector 6 Figure 2.1 Example of analysed network

24 Failure modelling The reliability of the system is calculated as the sum of individual failure rates that affect the reliability of the system (Janjic, Popovic, 2007) The transmission and distribution system is composed of different components such as transmission lines, transformers, circuit breakers and transmission feeders. Each component has a failure rate. The failure rates of the component rise over time until maintenance is performed, which lowers the failure rate (Dai, Christie, 1994) The other way of decreasing the failure rate is reinvestment which decreases the failure rate to the initial value. According to (Sittithumwat et al., 2004) ( Chow, Taylor, 1995) the distribution outage causes can be divided into the following categories: equipment 14 %, trees 19 %, animals 18 %, lightning 9 % and others 40 %. In (Horton et al., 1991) the component failures accounted for 15 % of the total permanent outages. For the remaining 85 % of the outages, 75 % were due to external factors such as lightning strikes, trees, car-pole accidents and third party contacts and 10 % were attributed to substation or transmission outages. According to the outage statistics of Finnish Energy Industry the environmental reasons for interruptions account for 76 % of the outages, technical problems account for 10 % of the outages and others 14 % of the outages. This result is for open conductors without planned interruptions. For underground cables the share of natural reasons is 14% of the interruptions, the share of technical reasons 46 % and others 40 %. (Energy Industry, 2010) Sensitivity studies indicate that the cables have a significant impact on the system reliability and are therefore the critical component. The causes of failures which have significant impact on cables are a) damage 16 %; b) personnel 12 %; c) material and method 59 %. To material and method the main contributions to this failure are a) fabric and material 14 %; b) lack of maintenance 5 %; c) wrong method or instruction 15 % These can be divided into two categories deterioration and non-deterioration (random). (Bertling et al., 2001). The age dependent deterioration can be divided in to different kind of performance. In (Komonen, 2005) there are six types of patterns representing most kinds of aging and deterioration situations. These curves represent different failure models used in air traffic and ships. K.Harker (Harker, 1998) has the same figures presented in Figure 2.2

25 25 Figure 2.2 Failure models (failure rates) in air traffic and ships (Komonen, 2005) The first curve is the so called bathtub curve. It begins with a high failure rate followed by a constant failure rate. In the end of the bathtub curve the failure rate increases. The second curve shows constant or slowly increasing failure probability, ending with a slowly or exponentially growing failure rate. This model represents the classical failure rate model but it is valid only for certain types of simple equipment, and for some complex items with dominant failure modes. (Moubray, 1997). The third curve shows steadily increasing failure probability, but there is no identifiable wear-out age. The fourth curve represents the case when the beginning of the failure rate is low but increases rapidly to the constant level. The fifth curve represents the constant failure rate at all ages. The last pattern represents slowly increasing failure rate when the beginning of the curve is exponentially decreasing. It is debatable if it is possible to use the same failure models in electric distribution as is used in air traffic. The reason is that electric distribution is different from air traffic and the risks in air traffic are very high. The components in air industry are replaced well before aging. There are many stresses which occur during the service life of the component. They are associated with fatigue, corrosion, oxidation and evaporation (Moubray, 1997). The point at which the failure occurs is not very predictable. It can be said that there is useful life of the item, where the failure rate is very low and then a wear-out zone where the failure rate grows rapidly. The question is if it is possible to lengthen the useful life by maintenance or predict the moment when the failures occurs. Richard E. Brown (Brown, 2004) suggests that the failure rate of the power distribution component depends on the inspection outcome. The components are divided into three groups according to inspection: a) the best inspection outcome, b) the average inspection outcome and c) the worst inspection outcome. The failure rate per year varies between failure rate 0,001 for case (a) up to 1,0 for case (c) for the studied primary

26 26 trunk cable. For the other components studied the variation between the best and worst inspection level is not so high Maintenance activities Alexandar D. Janjic and Dragan S. Popovic present (Janjic, Popovic, 2007) that the failure rate of the component depends on the maintenance activities of the distribution company. They divide the preventive actions to a) inspection and minor repairs to solve minor damages, b) larger overhauls to solve major damages and c) trimming to solve the influence of vegetation. For overhead conductors the inspection means visiting the conductor along a corridor in order to check correct condition of insulation, lines, joints, sag control, determining necessary trimming, noticing all adjacent installations, thermo vision recording, grounding measurements, inspection and cleaning of insulators and climbing the poles for the purpose of control. The minor repairs mean straightening poles, replacing insulation, tightening conductors, replacing voltage arresters and replacing line disconnectors. Trimming means partial or total trimming of the feeder corridor. In addition to minor repairs also major repairs can be carried out for overhead lines. For example backing the pole is this kind of major repair. It also has to be determined if it is economical to make a reinvestment of the overhead conductor to the existing location or to a new location. Richard E Brown presents the maintenance for transformers to decrease the failure rate. For that purpose the inspections are used. The items to be inspected are the condition of internal solid insulation, oil type, condition of core, condition of tank, cooling system, tap changer, the inspection of the noise level, core and winding losses and oil analysis (Brown R., 2004). Endrenyi et al. divide the maintenance operations to minor maintenance, minor overhaul and major overhaul (Endrenyi et al., 2001). Minor maintenance means maintenance of limited effort and effect. Minor overhaul means an overhaul of substantial effort involving only a limited number of parts, whose effect is a considerable improvement of the equipment s condition. Major overhaul means an overhaul of extensive effort and duration which involves most or all parts of the equipment Maintenance strategies There are two main approaches in maintenance strategies: corrective approach and preventive maintenance.(nakagawa, 2005),(Hilber et al., 2007). Corrective maintenance (CM) can also be called run to failure and it is the most primitive maintenance strategy. This strategy is based on restoring operation by fixing or replacing the component in the case of failure and does not include any additional maintenance activities.(lehtonen, 2006),(Janjic, Popovic, 2007) Preventive maintenance (PM) can

27 27 further be divided to time-based maintenance (TBM) and condition-based maintenance (CBM) (Li, Brown, 2004) TBM is based on regular and scheduled intervals and on the service history of the component. CBM is based on the condition and state of equipment and maintenance activity is formulated when the condition falls below acceptable standard. Reliability-centered maintenance (RCM) is an improvement over TBM and CBM (Li, Brown, 2004) In RCM the maintenance is activated when the theoretical reliability of the component falls below standard. The overhaul or reinvestment can be activated when the failure costs rise over the maintenance or investment costs. The comparison between the maintenance action and reinvestment as well as the timing of the operations is possible using optimization algorithms. Lina Bertling et al. define reliability centered maintenance as a systematic method for achieving a cost-effective preventive maintenance strategy by balancing between corrective and preventive maintenance. (Bertling et al., 2003) In (Lehtonen, 2006) the role of RCM is to balance the spending in maintenance activities with their effect on the system performance. A general RCM process could include the following stages (Endrenyi et al, 2001) - listing of critical sub-components and their functions - failure mode and effect analysis for each chosen sub-component, determination of failure history and calculation of mean time between failures - categorization of failure effects and determination of possible maintenance tasks - maintenance task assignment - program evaluation, including cost analysis In Sweden, the RCM process has been presented as follows (Bertling et al., 2001) - choosing and defining the system to be analyzed - defining and collecting necessary input data - performing a reliability analysis on the chosen system - identifying the critical components - identifying the benefit of maintenance on the critical components from the knowledge of either their functions (for example transfer of energy), their failure modes (for example short circuit), their failure events ( for example insulation failure) or their failure causes ( for example matrial and method) (Yatomi et al., 2004) present Life-Cycle Maintenance (LCM) as a solution of preventive maintenance strategy, the. In this strategy the risk and maintenance costs of the plant are minimized during the life time of the plant. Risk Based Maintenance (RBM) is included in the LCM to assess the risk of the components in the plant. According to (Harker, 1998) there are still two more maintenance strategies apart from corrective and preventive maintenance. These two strategies are opportunity maintenance and statutory maintenance. Opportunity maintenance is carried out when a higher priority item of equipment is out of service. For example, generator-circuitbreaker maintenance is carried out only when the generator is out of service. Statutory maintenance is carried out to facilitate statutory timescales and requirements usually associated with health and safety.

28 28 Key areas within the maintenance management problems are a) determining the time intervals or the equipment age for optimal maintenance, b) determining the frequency of inspections and condition based optimal maintenance, c) determining the optimal resources to meet maintenance requirements and d) finding the economic life cycle of an equipment studying the repair versus replace problem. (Marquez, Hequedas, 2002) The first step in drawing up an effective maintenance plan is to decide which parts of the system to maintain and how to perform the maintenance activities. To achieve this a sensitivity analysis is performed for the system with the aim of identifying the critical components, i.e. the components which have the largest influence on the system reliability. (Bertling et al., 2001) The life of power-system equipment is long, typically years for high-voltage equipment and years for protection and control equipment (Harker, 1998). In this life-cycle many maintenance actions can be activated: - periodic exercising of equipment - visual inspections - cleaning, dusting and painting - lubrication and periodic replacement of parts - monitoring and examination of interrupting and insulating mediums - equipment performance tests - removal of foliage to maintain clearances In addition to maintenance activities presented by Janjic and Popovic (Janjic, Popovic, 2007) and Harker, the reinvestment of the component is added to the activities modelled in this dissertation. Maintenance activities are carried out according to the following periodicity (Harker, 1998) - regular intervals according recommendations and experience - increased maintenance of older equipment - statutory maintenance activities - opportunity maintenance - targeted sampling of a population of equipment - no maintenance As to overhead lines and transformers, the preventive maintenance actions can be used. This means periodic checks and minor or larger overhauls of the components Maintenance directions and cost optimization In a maintenance model there are four possible directions: 1) maintenance costs minimization, 2) reliability maximization, 3) overall costs minimization and 4) overall risk minimization. (Janic, Popovic, 2007) The maintenance cost minimization doesn t take into account the straight failure costs and outage costs caused by the low maintenance level. So this strategy does not give the most economical life-time cost for

29 29 the system. This strategy is reasonable only if maintenance action doesn t decrease the failure level of the system. In this approach reliability is defined as a limit, or minimal requested level. Reliability maximization is not an economical solution. It is possible to increase the reliability level by investing more in maintenance, clearance of corridors and new components. However the marginal benefit of maintenance action decreases with a higher level of maintenance. Zhang et al. present that the security index of a traditional power system no more exists independently but together with the economic point of view. (Zhang et al., 2005) In the reliability maximization the effectiveness of maintenance can be modelled by using a weighted average system reliability index (WASRI) (Li, Brown, 2004). The WASRI index is modelled by using an index of system average interruption, an index of average interruption duration and an average temporary interruption index. If costs are not included to the examination of WASRI index the strategy is straight reliability maximization. (2.1) where WASRI SAIFI SAIDI MAIFI ω i system average reliability index system average interruption frequency index system average interruption duration index momentary event average interruption frequency weighting factor Using effectiveness index it is possible to achieve the most effective operations and maintenance tasks for system reliability. The goal is to minimize the WASRI index. The cost-effectiveness of minimizing the WASRI index can be taken account into by calculating relation (2.2). (2.2) where E ΔWASRI C cost-effectiveness of a maintenance task is the change of WASRI index is the cost associated with the maintenance task. In the model presented in this thesis SAIFI is the sum of the failure rates of all components in one feeder. The SAIDI index is found out by calculating the average failure length of the customers per one transformer area. The MAIFI index depends on the environment of the conductor and is the function of the number of re-closings. Because MAIFI doesn t depend on deterioration it is not included in the presented model (automatic reclosing is not included). In the fundamental improvement of the