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Risk-Based Resource Allocation for Distribution System Maintenance

1. Figure 3 2 Computing contingency probability reductions a Deterioration function The deterioration function denoted by g cj may be an analytical expression if one is available or it may be a set of rules encoded as a program likely consisting of a nested set of if then statements that returns a scalar assessment value For the model of Figure 3 2 the assessment value would be a deterioration level 1 2 3 or 4 This represents a flexible and practical way of connecting our approach to the wealth of existing knowledge and experience contained in the industry relative to interpreting 22 condition monitoring measurements Often such rules depend not only on the measurements c t but also on the rates of change in such measurements These rules together with expertise provided by industry advisors are used to develop the deterioration functions For example a comprehensive compilation of such rules for transformers 23 provides 62 different measurements for characterizing 23 transformer failure modes Examples and some of the failure modes they detect include dissolved gas analysis results on main tank oil indicating insulation deterioration deterioration of cooling system or oil pump failure and load tap changer oil indicating oil dielectric weakening thermography testing indicating magnetic circuit overheating or bushing overheating ultrasonic testing indicating oil pump fa
2. Score 0 1 z Criterion amp Ed Pre Maintenance Age of Oil 20 0 66 Duty Cycle Rate 20 1 Environmental Factor 20 N A Oil Dielectric Strength 15 N A Condition of Contacts 15 N A Age of Recloser 10 0 95 Experience with this Recloser Type 10 0 9 Condition of Tank 5 0 85 Sum 65 55 95 Weighted Average 0 860769231 The estimated failure rate for this recloser is 0 95 861 yy r a 0 95 0 31 0 00351 which is close to 0 0025 the best failure rate previously found on the system A condition score Xes Of 0 30 produces an equation 3 4 score x of 1 015 This score of 0 30 replaces equation 3 6 the previous historical low score of 0 31 and the recloser is assigned the lowest historical failure rate on the system 3 1 5 Summary This methodology allows for quantifiable assessment of a recloser s condition The assessment is designed to be done in the field without removing the recloser from service The assessment score is converted to an estimated failure rate which is based on historical data 21 The assessment criteria are directly related to maintenance tasks that may be performed on the recloser Each maintenance task will increase the score for the associated criteria resulting in a lower calculated failure rate This method can be adapted to other power system components 3 2 Vegetation Another approach to computing failure probabilities is illustrated in Figure
3. Feeder Load Points Load Point Number of Customer Type kW Customers Points 1 1 3 535 210 Residential 1 4 5 566 1 Institution 1 6 7 454 10 Commercial 2 8 1000 1 Industrial 2 9 1150 1 Industrial 3 10 11 535 210 Residential 3 12 450 200 Residential 3 13 14 566 1 Institution 3 15 454 10 Commercial 4 16 454 10 Commercial 4 17 19 450 200 Residential 4 20 21 566 1 Institution 4 22 454 10 Commercial As shown in Table 4 10 the reliability indices computed by the reliability evaluation tool exactly match those provided in 36 Further validation was also performed on two actual distribution feeders using the results obtained from the reliability evaluation software DRIVe developed by EPRI and Iowa State University The reliability indices computed by the reliability tool were found to be in close agreement with those predicted Table 4 9 Lengths of feeder section Length km Feeder Section Numbers 0 60 2 610 1417 21 25 28 30 34 0 75 1479 12 16 19 22 24 27 29 32 35 0 80 35811 13 15 18 20 23 26 31 33 36 by DRIVe Table 4 10 Reliability indices for the ieee reliability test system bus 2 SAIFI SAIDI ENS Feeder customers year customer hours year kWh year Predicted RBTS Predicted RBTS Predicted RBTS 1 0 248 0 248 3 618 3 620 13172 06 13172 2 0 140 0 140 0 523 0 520 1122 06 1122 3 0 250 0 250 3 624 3 620 11203 20 11203 4 0 247 0 247 3 605 3 610 12248 36
4. Figure 3 3 Flow chart of degradation model approach 3 3 2 Degradation Path Model Let Rsg t represent the residual strength in units of N mm at the ground line of wood pole i as a function of time t Because different poles have different initial strengths the residual strength is normalized as Lspi t 1 Rsgi t Rsgi 0 3 8 where Lsp t represents the lost strength percentage for pole i at time t Wood poles decay continuously therefore Lsp t is non decreasing over time If all poles were identical and operated under exactly the same conditions and in exactly the same environment they would have the same degradation path But of course there is a degree of variability in some or all of these factors This variability in turn causes variability in the degradation path While different poles have different degradation paths the general degradation path formed will be quite similar from pole to pole The degradation path model thus represents the degradation path of a particular wood pole over time as Lspi t g t Bi0 fil pin 3 9 where gt 0 and fio pin Bin are the time regression coefficients for pole i In general the form of g may be linear polynomial or exponential in the coefficients Condition data 25 from the field are used to obtain the coefficients of this degradation path model Two kinds of nondestructive measurement data can be used in this model The best kind involves measurements f
5. 0 010473 341 6 44 The best and worst failure rates 1 0 and A 1 respectively are then calculated Each recloser on the system failed either zero times or one time during the six year period This gives failure rates of 0 0 failure 6 44 years 0 00000 1 1 failure 6 44 years 0 15528 These are too low and too high respectively to be practical therefore the following published failure rates 21 are used for the best and worst values A 0 0 0025 A 1 2 0 010478021 A 1 0 060 Next the A B and C coefficients are calculated using equation 3 2 to be A 0 0015321 B 3 6514524 C 0 0009679 The resulting equation 3 3 is 3 6514524 x e A x 0 0015321 0 0009679 and the relationship of assessment score to failure rate is shown in Figure 3 1 18 A x 0 03 0 02 0 01 j 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 X Figure 3 1 Recloser score vs failure rate Best and worst historical scores for reclosers on the system were not available therefore the worst x and best xo scores were assumed to be 0 31 and 0 95 respectively Table 3 2 then shows actual scores for a recloser that failed while in service It was considerably past its expected duty cycle Its condition score Xes was 0 392 Equation 3 4 corrects this to 005 0932 0 95 0 31 x 0 872 which results in a failure rate equation 3 3 of A 0 872 0 038 The low condition score 0 392 as expec
6. To illustrate the variability in SAIFI from maintaining wood poles and vegetation probability plots obtained using this method are shown in Figure 4 1 to Figure 4 4 For this illustration it was assumed that the failure rate of the component is halved after maintenance Similar plots can also be obtained for SAIDI 47 SAIFI variation before maintenance 16 1 8 2 2 2 2 4 2 6 2 8 3 3 2 3 4 SAIFI Figure 4 1 Variation in SAIFI before maintenance of wood pole SAIFI variation after maintenance oL l L L 1 1 l 1 4 1 6 1 8 2 2 2 2 4 2 6 2 8 3 3 2 3 4 SAIFI Figure 4 2 Variation in SAIFI after maintenance of wood pole 48 0 4 FI variation before maintenance 0 35 0 3 0 25 0 2 0 05 1 3 5 5 5 6 I 3 5 4 45 SAIFI Figure 4 3 Variation in SAIFI before tree trimming 0 4 0 5 2 Figure 4 4 Variation in SAIFI after tree trimming SAIFI variation after maintenance Le i i 5 3 3 5 4 4 5 5 2 5 5 6 SAIFI These figures illustrate that maintenance not only improves the expected values of the indices but also reduces the risk of low probability high consequence events For reclosers Section 4 4 shows that the reliability indices are approximately linearly dependent on protection reliability or reclose reliability Unlike the wood pole or vegetation sensitivities which are functions of failure rate the recloser s PR is a probability between zero and one Hence the ris
7. PR A MTTR Lp Circuit breaker fails to clear a fault with failure rate A and repair time MTTR Frequency 1 PR Duration MTTR MTTRp Customers interrupted Downstream of backup next upstream protective device Expected cost of failure 1 PR COF COF p where COFp is cost associated with breaker failure Expected energy interrupted 1 PR MTTR MTTRg Ls 4 3 2 Fuse with No Upstream Recloser A fuse that is not coordinated with an upstream recloser responds like a breaker to a sustained fault Hence the states shown in Table 4 2 apply to a fuse Table 4 2 Protection response of fuse Fuse successfully clears a fault with failure rate A and repair time MTTR Frequency PR A Duration MTTR Customers interrupted Downstream of fuse Expected cost of failure PR COF where COF is cost of outage on faulted line segment Expected energy interrupted PR MTTR Lp Fuse fails to clear a fault with failure rate A and repair time MTTR Frequency 1 PR 2 Duration MTTR MTTRg where MTTRs is average repair time for a fuse Customers interrupted Expected cost of failure Downstream of backup protective device 1 PR A COF COFp where COF is cost associated with fuse failure Expected energy interrupted 1 PR MTTR MTTR Ls 4 3 3 Re
8. Risk Based Resource Allocation for Distribution System Maintenance Final Project Report Power Systems Engineering Research Center A National Science Foundation Industry University Cooperative Research Center since 1996 Power Systems Engineering Research Center Risk Based Resource Allocation for Distribution System Maintenance Final Project Report Project Team Ward Jewell Project Leader Joseph Warner Wichita State University James McCalley Yuan Li Sree Rama Kumar Yeddanapudi Iowa State University PSERC Publication 06 26 August 2006 Information about this Project For information about this project contact Ward Jewell James D McCalley Professor Professor Wichita State University Iowa State University Department of Electrical and Computer Department of Electrical and Computer Engineering Engineering Wichita Kansas 67260 0044 Ames Iowa 50011 Phone 316 978 6240 Phone 515 294 4844 Fax 316 978 5408 Fax 515 294 4263 Email ward jewell wichita edu Email jdm iastate edu Power Systems Engineering Research Center This is a project report from the Power Systems Engineering Research Center PSERC PSERC is a multi university center conducting research on challenges facing the electric power industry and educating the next generation of power engineers More information about PSERC can be found at the Center s website http www pserc org For additional information contact Power Sys
9. Ae E DES a O OO 1G o E OS Os o R m 10 gt OG Ol OO OF a E m 0 1G 2 E 47t 0 0 GO 1 OO Goo Oo tooeaeaece bee 0 0 oO eB Oo eB 2 UO 46 5 0 0 OF 1 O10 0 R OE o t 0 0 00 Se 0 8 r E c OE s OS Br 0 o SE S 39g 0 0 0 12 0 OoOoooOotooeoee ob oboe 8 obo eB oe eB T Dp saree 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 000l ploa gll Ol Oll sitts 0 oO 0 1 0 0 0 0 0 t 0 eB e e eb ee eo eB oa eB TD Figure C 3 Task selection table trim_select m for tree trimming Budget exe creates two files which appear in the directory RDRA DATA One totrisk dat is the total risk reduction vs budget The other split dat is the budget split 96
10. Anthony and J Goodman Nondestructive evaluation of wood utility poles EPRI EL 5063 March 1987 17 G Bhuyan Condition based serviceability and reliability assessment of wood pole structures in Proc Transmission amp Distribution Construction Operation amp Live Line Maintenances ESMO 98 26 30 April 1998 333 339 18 E Ezer Measurement of wood pole strength Polux R a new nondestructive inspection method in Proc Rural Electric Power Conference 29 April 1 May 2001 pp C6 1 C6 7 19 Bureau of Reclamation Bureau of Reclamation Facilities Instructions Standards amp Techniques vols 4 6 Wood Pole Maintenance 20 Cooper Power Systems Type H single phase maintenance instructions Service Information Number 280 10 1 January 1970 p 3 21 Richard E Brown Failure rate modeling using equipment inspection data JEEE Trans Power Systems vol 2 May 2000 pp 782 787 77 22 W F Horton S Goldberg and C A Volkman The failure rates of overhead distribution system components in Proc of Transmission and Distribution Conference IEEE Power Engineering Society 22 27 Sept 1991 pp 713 717 23 Electric Power Research Institute EPRI Integrated monitoring and diagnostics Final Report EPRI Palo Alto CA TE 1000511 2000 24 P Kuntz R Christie and S Venkata A reliability centered optimal visual inspection model for distribution feeders JEEE Trans
11. B A Recloser fails to reclose after clearing a fault with a probability of P BIA 1 RR 4 7 The events described by equations 4 6 and 4 7 depend on the successful opening of a recloser during a fault From the four possible states of a recloser it can be observed that those represented by equations 4 5 and 4 7 correspond to recloser failures Since these are mutually exclusive a recloser can either fail to open or fail to reclose once opened but not both the total probability of recloser failure can be written as PF P A P BO A 4 8 This can be further simplified as PF P A P B A P A 1 PR 1 RR PR 4 9 Assuming the probability a recloser opens in response to a fault is equal to the probability that it recloses after clearing a fault PR RR and rearranging the above 35 expression the values of protection reliability and reclose reliability can be obtained as PR RR 41 PF 4 10 4 2 Models Used in the Program The parameters defined in Section 4 1 are now used in this section to describe the reliability characteristics of distribution system components 4 2 1 Overhead Line and Underground Cable Segments Overhead lines and underground cables are modeled as repairable systems Faults occur on segments that are isolated by protective and switching devices before carrying out repairs The parameters used to describe segments are as follows permanent failure rate per mile p mean time to
12. One approach suggested in the literature is the subgradient method 37 38 but this is computationally intensive and can experience convergence problems Therefore the ELPR s optimal dual solution is used which provides a good estimate of the Lagrange multiplier as indicated in 39 and confirmed by numerical experiments performed in this project This approximate method is a fast and stable way to obtain the Lagrange multiplier Sometimes the Lagrangean solution is infeasible or not good enough e g too many tasks are selected therefore some heuristic methods are used to improve the Lagrange solution For this project a simple heuristic is performed after the solution of the Lagrange relaxation if it is infeasible then the least net benefit decision variable is removed until all the constraints are satisfied If there is residual resource left then the largest net benefit decision variable among the unselected group is chosen until a constraint is violated 5 3 Solution Methods for Budget Planning Subproblem The ELPR LRH algorithm solves the basic integer programming problem which addresses the third question posed in the introduction Section 1 1 to select a set of maintenance projects to be completed within each program constrained by the budget allocation The dynamic programming DP method is used to answer the budget planning subproblem which addresses the first and second problems in Section 1 1 how to identify and just
13. Power Delivery vol 16 issue 4 Oct 2001 pp 718 723 25 G Anders Probability Concepts in Electric Power Systems New York John Wiley amp Sons Inc 1990 26 A Leite da Silva and J Endrenyi Application of first passage times in the Markov representation of electric power systems in Proc 4th Int Conf on Probabilistic Methods Applied to Power Systems Rio de Janeiro Brazil September 1994 27 V Chan and W Meeker Estimation of degradation based reliability in outdoor environments preprint Dept of Statistics Iowa State University 28 W Meeker and L Escobar Statistical methods for reliability data A Wiley Interscience Publication 1998 29 K Kleinbaum and N Muller Applied regression analysis and other multivariable methods Brook Cole Publishing Company 1998 30 Y Jiang Z Zhang T Van Voorhis and J McCalley Risk based maintenance optimization for transmission equipment in Proc 35th North American Power Symposium Rolla MO Oct 2003 31 R Brown Electric Power Distribution Reliability New York Marcel Dekker Inc 2002 32 Theory Manual Distribution Reliability Indices for Vegetation DRIVE Ver 2 0 Electric Power Research Institute 33 J Meeuwsen W Kling and W Ploem The influence of protection system failures and preventive maintenance on protection systems in distribution systems JEEE Trans Power Delivery vol 12 issue 1 Jan 1997 pp 1
14. and repair time MTTR Frequency 1 PRp RRp PRp A Duration MTTR MTTR Customers interrupted Downstream of recloser 1 PRp RRp PRp A COF COFp where COF is cost associated with failed fuse 1 PR RRp PRa A MTTR MTTR Ls where Ls is load downstream of recloser Recloser opens and recloses fuse fails to open and recloser fails to open to clear the fault this event is not modeled due to very low probability Recloser opens but fails to reclose causing outage to all downstream customers Expected cost of failure Expected energy interrupted Frequency 1 RRp PRR A Duration MTTR MTTRp Customers interrupted Downstream of recloser 1 RRp PRR A COF COF p where COFp is cost associated with failed recloser 1 RRp PRR A MTTR MTTRa Ls where Ls is load downstream Expected cost of failure Expected energy interrupted of recloser Recloser fails to open in response to the fault and fuse opens to clear the fault Frequency PRE 1 PRp A Duration MTTR Customers interrupted Downstream of fuse Expected cost of failure PRe 1 PRp A COF Expected energy interrupted PR 1 PRr A MTTR Lp where Lp is load downstream of fuse Recloser fails to open and fuse fails to open this event is not modeled due to very low probability 4 3 5 Sectionalizer with Upstream Recloser Sectionalizers are switches that are coordinated with an upstream recloser
15. downstream switching done after a sustained fault Table 4 7 Switching response for downstream isolation Switching sequence is successful Frequency SReegh Interruption duration for customers upstream of NC switch MTTR Interruption duration for customers restored downstream of NC switch MTTS eq Expected energy restored switching restores some load A SRseq MT TS geq Lewis Where Lswi is interrupted by protective device load restored by switching Switching sequence fails Frequency 1 SRgeq A Interruption duration for customers upstream of NC switch MTTR Interruption duration for customers downstream of NC switch MTTR Expected energy restored None 4 4 Analytical Reliability Evaluation Analytical evaluation of reliability is a predictive method in which each contingency is simulated and its effect on each of component in the system is determined and weighted by the probability of the contingency This gives the expected average values for the frequency and duration of outages caused by each contingency The expected cost of equipment failure and expected energy not served are also computed as required by the formulation for risk reduction of Section 1 3 1 An enumerative analysis algorithm in which the failure consequences of each component are weighted by its failure probability is used to compute system reliability indices The following is a brief description of the a
16. represents the average time taken to restore service to the customers CAIDI Total duration of all customer interruptions A 3 Total number of customers interrupted CAIDI can be improved by reducing the length of interruptions by faster crew response time and repair times 4 Average Service Availability Index ASAI The average service availability index ASAI represents the fraction of time that a customer has received power during the defined reporting period Higher ASAI values reflect higher levels of reliability 31 Customer hours service availability ASAI A 4 Customer hours service demand 80 5 Customer Average Interruption Frequency Index CAIFD The customer average interruption frequency index CAIFI gives the average frequency of sustained interruptions for those customers experiencing interruptions each customer is counted only once regardless of how many interruptions they experienced CAIFI Total number of customer interruptions A 5 Total number of customers interrupted 81 Appendix B User Manual for Reliability Evaluation Tool The following document describes in detail the usage of the reliability evaluation tool discussed in Chapter 4 The spreadsheet was developed in Microsoft Excel To use it macros must be enabled In Excel go to Tools gt Macro gt Security and set the Security Level to low Click OK Close Excel and restart it Then go to Tools gt Cu
17. 12248 System 0 248 0 248 3 613 3 610 37745 68 37746 Reliability indices given in 36 54 5 Optimization This chapter describes a risk reduction optimization problem and its corresponding solution The reliability evaluation tool developed in Chapter 4 first computes the risk reduction introduced by each candidate maintenance task Then the results for each task are combined with the resource consumed resulting in triplets comprised of the candidate task risk reduction financial cost and labor cost These triplets are the inputs to the optimizer The optimization problem is presented in Section 5 1 Possible solution methods are summarized in Section 5 2 Finally Section 5 3 describes the solution method selected and implemented in this project 5 1 Problem Statement In the problem statement the following terms are used P is the number of maintenance categories p 1 P is the index over the set of categories N is the number of candidate components within category p k 1 Np is the index over the set of candidate components within category p Mk is the number of maintenance tasks for component k 1 M is the index over the set of maintenance activities for component k The risk reduction related to each candidate preventive maintenance task is ARisk k 1 Resource requirements for each task are represented by cost Cost k l and labor Labor k l Therefore each task it is associated with a t
18. 51 Figure 4 6 Variation in SAIFI after recloser maintenance ccceceeseeeeeeeeeeeceeeneeeeeees 51 Figure 4 7 Variation in SAIDI before recloser maintenance s sessesssssessssseseesesseseese 52 Figure 4 8 Variation in SAIDI after recloser maintenance 0 00 00 ceceeseeeeeeeeeeeceseeneeeeeees 52 Figure 4 9 IEEE reliability test system 36 bus 2 cccscscsensesscostesscenrssersenedencoseres 53 Figure 5 1 Flowchart of ELPR LRH optimization method 0 0 0 0 ce eseeseeeeeeeeneeeeeeeees 58 Figure 5 2 Reliability benefit vs DUG Set is ssasissevzncsaveniassatiaatesneedennlanuanssugdiastsnbunianseieanles 60 Figure 5 3 Resource splitting curve for different categories 0 0 0 eeeeeeceteceeeneeeeeeeees 60 Figure 6 1 Risk based resource allocation implementation c seceeseeeeeeeceteeneeeneees 62 Figure 6 2 Risk reduction due to maintenance on reclosers sc eeeeeeeeeceteceeeeneeeeeeeeees 69 Figure 6 3 Risk reduction obtained due to wood pole maintenance ceeeeeeeeeeeeees 71 Figure 6 4 Risk reduction due to tree trimming at a feeder level oo eee eeeeeeteeneeeeeees 72 Figure 6 5 Budget vs risk reduction cca acyinca eases ea ies eens 173 Figure 6 6 Budget splitting curve for different tasks ccc cecesseereeeeeeeecesecneeeeeeneeenees 173 Figure G7 Labor Sensitivity denirse eana eo aea ta 74 Figure C 1 Input file of pole candidate tasks cceseeccesecesecseeeneeeseeeeeeecesece
19. Column left blank output of program Column left blank output of program Column left blank output of program Column left blank output of program Column left blank output of program SAIFI of the feeder after maintenance done on segment i output of program SAIDI of the feeder after maintenance done on segment 1 output of program Improvement in SAIFI due to maintenance on segment i output of program Improvement in SAIDI due to maintenance on segment i output of program Improvement in energy not served ENS due to maintenance on segment i column left blank output of program Reduction in cost of failure COF due to maintenance on segment i column left blank output of program Recloser protection reliability after maintenance value between 0 00 and 1 00 only for reclosers Recloser reclose reliability after maintenance value between 0 00 and 1 00 only for reclosers Improvement in SAIFI due to maintenance done on recloser output of program Improvement in SAIDI due to maintenance on recloser output of program Improvement in ENS due to maintenance on recloser column left blank output of program Reduction in COF due to maintenance on recloser column left blank output of program 84 NORMAL MODE OF OPERATION The basic mode of using the reliability evaluation tool is at the feeder level The following macros are available in this mode To assign d
20. Figure 5 3 Resource splitting curve for different categories 5 4 Summary The techniques described in Chapter 5 provide the optimal budget for all assets the allocation of the budget to different maintenance categories and the selection of projects within those categories Different maintenance categories with different characteristics e g some needing scheduled outages and load transfers while others do not can be addressed with new categories with special constraints Additional maintenance 60 categories to account for other types of equipment can also be added If maintenance for a period is to focus on certain categories these can be weighted to bias task selection to those categories If contractors perform certain types of maintenance for a company this strategy can provide guidance to the asset manager on appropriate contractor pricing 61 6 Illustration Data from an actual distribution system is used in this chapter to illustrate the proposed risk based resource allocation strategy developed in the previous chapters The system has 66 feeders each classified as either urban or rural and is divided into three operating regions Figure 6 1 shows the steps to implement this method Historical outage data and network topology including load and customer information obtained from the utility s outage management system OMS are the primary inputs They are used to compute the historical reliability indices and to de
21. Fuse with No Upstream Recloset cccccescccsssceseceeeeeesceceeeceteeeeeeenaees 38 4 3 3 ARCCIOSET iiehs sic eierniie eiaeia EA das E E E MTR 38 4 3 4 Fuse with Upstream Recloser cccccccccssccsseceseceeseeeeeeeeeecsaeceseeseneenaees 39 4 3 5 Sectionalizer with Upstream Recloset ccceesccescceesceesseeeteceseeeeeeensees 40 4 3 6 SWINE canande a ch See a A waelece tater is 42 4 4 Analytical Reliability Evaltationys s0cccsesseacssasssasseazesccadascenssavetasassavssasvenesiiaass 44 4 5 Regulatory Penalty Risk Evaluation ccscte tsecensch di hciaeneeeies 45 4 6 Validation of Reliability Assessment Tool ss snsssnesnesessseessessessresseesresrsssseseess 52 Optima NON e e i E A E A E E ah 55 3 1 Problem St tement in n naaa a a ai i a aa a aai 55 5 2 Possible Solution Methods for Task Selection Subproblem cceeeeee 57 5 2 1 Prioritization Method choc wcseui acto ass dyn nel eames 57 5 2 2 Branch and Bound Method 0 ceccccsscceseeeseceeeeeeseeceaeceeeeeeeeenseeeaeees 57 5 23 ELPR ERH Methoden ao a a ii 58 5 3 Solution Methods for Budget Planning Subproblem sssssessesessssessessesessseesse 59 S O e gs Sols ta a A E A N at 60 Ml sttaton seenak etra a a a E SAREE E EATE teat anna N ERE atA 62 6 1 Historical Reliability Evaluation iceniueunnaiiientu nad ebyeaalant 63 6 2 Predictive A alysis reeni neac ann n e Gea A A oon canna anaes 63 6 2 1 Failure and Repair Parameter Estima
22. In response to a sustained fault they open while the recloser is open to isolate the fault If the sectionalizer fails to open the coordinated recloser opens again locking out to isolate the fault A sectionalizer is described by its protection reliability PRs and repair time MTTRs When a permanent fault with failure rate A and repair time MTTR occurs downstream of the sectionalizer the following mutually exclusive events can happen 40 Recloser opens to clear the fault and sectionalizer opens to isolate the faulted segment The frequency of such an event is PRr PRs RRR A with an outage duration of MTTR to the customers downstream of the sectionalizer Recloser opens but the sectionalizer fails to open The recloser opens and locks out interrupting customers downstream of the recloser The frequency of such an event is PRp 1 PRs with an outage duration of MTTR MTTRs Recloser opens and sectionalizer opens but the recloser fails to reclose causing sustained interruptions to all customers downstream of the recloser The frequency of this event is PRr PRs 1 RRr A with interruption duration of MTTR MTTRg Recloser opens but sectionalizer fails to open The recloser then recloses and fails to open again The fault is interrupted by the backup protection device upstream of the recloser This event has a very low frequency of occurrence 1 PRp 1 PRs PRp A and is neglected in thi
23. SAIDI f SAIDI t k 1 d SAIDI t k nja 1 6 Ax is the failure rate of component k due to a maintainable failure mode 1 At is the time interval under consideration N is the total number of customers served Nk is the number of customers affected due to failure of component k in mode q dj is the duration of the interruption seen by the j th customer due to failure of component k in mode 1 P is the load connected at point j Cost k l is the cost of failure for component k in mode 1 PBR SAIFI is a performance based penalty for a SAIFI violation beyond threshold Tr PBR SAIDI is a performance based penalty for a SAIDI violation beyond threshold Tp f SAIDI t k 1 is a probability distribution of SAIDI obtained by non sequential Monte Carlo simulation for component k in failure mode 1 f SAIFI t k 1 is a probability distribution of SAIFI obtained by non sequential Monte Carlo simulation for component k in failure mode 1 The time interval At is assumed to be one year so it can be removed from equations 1 1 to 1 6 As discussed in Section 1 3 the consequence of a component s failure is assumed to be constant throughout the year Unless the component is maintained the component s failure rate is also assumed to be constant throughout the year This removes scheduling from the optimization problem and leaves allocation of resources t
24. dat files in RDRA data One is the risk reduction vs budget table ptable m and the other is the corresponding task selection table pole_Iselect m for pole etc 95 0 0 0 5128 68931 249 06255 102 65 19511 11885 73384 o o 17914 27853 17914 27853 o 0 0 0 13184 874 o 14238 80502 om 8615152 66377 16002 20306 16793 92338 17509 169 17914 27853 170568 2246 17914 27653 170568 2246 17914 27853 170568 2246 17914 278653 170568 2246 17914 278653 170568 2246 17914 27653 mom 16169 79676 259236 9347 17914 27653 13 18791 77688 259236 9347 74086 0633 Figure C 2 Risk reduction versus budget table ptable m w JaN bf WN Bb l HHH NH O Lat sorte 0 0 OF 1 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 w o 0 Ooa 36 0 300 02 OO e O00 m 68 lh e a m OO m E o R O e O e Ol R e E n E E o ee br iiaa Oo n DO Es O00 e Oo 6 a AS e OF m OF 10 gt e URS o O 0 s A e so OO GT r ge7 t 0 OF 0 tOooGvcooaeageoeHoHeeeoep oOoOoGa oboe ose Oo GG ft OB a9 ee O 0 CO 2 OO Oh OO Oe ee OO Oe OB lo el EE e 407770 OF 0 1 0 0 0 0 00 too Ooo 0 0 a ewe ewe 8B oh Org C ap Ke at ai Aa OO E 20 oO 8 OO tr o O n me o O m E E E e OE E o EE o OSE a DR n O c E o E E E 42t 0 OF OF 1000o 000o toeweebe8 eee owe oe 2 Oo 43 ee 0 0 m tO 30 0 O GO Oo 2 8 8 8 oO fo 8 6 Oo Oo Oo 8 E e E o let E agt 0 0 0 Lt 0 0 0 0 OO 2 o 8 GO ho ob Oo m o o d p O 0o T g 45 ee g 0 OU 17 000 0 DO 0S T G oO Uo oo OU a o 0a a0 a a CO z Ita n R 00
25. failure It is important to note that failure rate and time to failure are population averages The lost strength percentage before maintenance is Lsp t Lspm to gt H to and the lost strength percentage after maintenance is Lsp t Lspm t H t The failure rate reduction 4h is Ah H t H to 3 13 and the increase in time to failure ATTF is ATTF t ti 3 14 This degradation path model can be used to estimate the condition based failure rate failure rate reduction and increase in time to failure This information is highly useful in asset management decision making These procedures are illustrated in Section 3 3 3 together with an application of budget planning and maintenance task selection 3 3 3 Illustration Field data consisting of age initial strength and one residual strength measurement per pole were obtained for a group of wood poles The total pole population includes 13 940 poles ranging in age from 1 to 79 years with a mean age of 30 years Measurements indicated that of the total population 1 163 poles 8 percent had begun to decay These are referred to as the decayed population ranging in age from 5 to 67 years with a mean age of 37 Figure 3 4 shows the distribution of the number of poles at each age for the decayed population eRe it oR cn otee 10 20 30 40 50 60 Age Figure 3 4 Number of poles at every age of the decayed population 27 Obtaining the Degrada
26. failures Region SAIFI 2000 2004 SAIDI 2000 2004 Total 0 620 0 603 Hours Region 1 0 789 0 689 Hours Region 2 0 328 0 337 Hours Region 3 0 476 0 783 Hours 6 2 Predictive Analysis Before predicted indices are used they must correlate with historical indices Predicted indices are calibrated by adjusting component failure rates and repair times 63 6 2 1 Failure and Repair Parameter Estimation for Predictive Analysis To predict the reliability indices of a distribution system the assessment tool must have values for failure rates and mean time to repair for each component modeled overhead lines underground cables fuses reclosers breakers sectionalizers and switches To estimate the failure rate of overhead lines the total number of sustained overhead outages observed during the 2000 04 period was divided by the number of overhead circuit miles and the number of years as shown in equation 6 1 The average repair time is computed from the repair times for each of the sustained faults during the same period as shown in equation 6 2 A similar procedure was followed for under ground cables Table 6 4 summarizes the estimated average failure rates and repair times for overhead lines and underground cables _ Total number of sustained interruptions faults mi yr 6 1 j Total circuit miles number of years Total repair time MTTR 6 2 Total number of sustained interruptions Ta
27. must represent a high failure rate Equation 3 4 will produce values that are negative when a recloser score Xes is greater than the previous best score or greater than one when X s is less that the previous worst score When this occurs Xes replaces the previous best x or worst xo historical score as shown in equations 3 5 and 3 6 Then x for the recloser is recalculated with the new values as follows If x lt 0 then x is the updated xo 3 5 If x gt 1 then x is the updated x 3 6 17 3 1 3 Effects of Maintenance The maintenance tasks associated with each criterion on the score sheet are assumed to bring the score for that criterion to a predetermined value this may be 1 or something less than 1 New post maintenance coefficients equation 3 2 and a new failure rate equation 3 3 are calculated Reliability indices for the system being simulated are then computed using the evaluation tool discussed in Chapter 4 and Appendix B The calculated failure rates should then be calibrated so that the indices correlate with historical indices A least squares approach has been suggested for this 21 using the method of gradient descent 3 1 4 Example Six years of outage data were obtained from a utility and are used to illustrate the recloser assessment method Out of 341 reclosers on the system 23 recloser failures occurred during a 6 44 year period Equation 3 1 produces an average failure rate A 1 2 of 2 202
28. of equation 3 8 and the measurements are used to interpolate or extrapolate the lifetime of the decayed pole population After comparing several different distributions the Weibull distribution is selected giving a hazard function having the form A t B t n B 1 3 18 The parameters are determined using the maximum likelihood method 28 resulting in f 4 6676 and n 50 6090 which is shown in Figure 3 8 To obtain the failure rate the degradation Lsp t of the pole is measured The condition age is the age ta where Lspm t Lspj t and t is the actual age of the pole Lspm t is found from equation 3 15 and substituted into equation 3 18 to get the failure rate Failure rate reduction and time to failure increase can then be calculated using equations 3 5 and 3 6 0 18 r T l I 1 l 1 I 1 l l OG ey oe ae Tete ee E Naat ek POE 1 1 I l l I 1 l 1 18 1 I l l l l I I I 1 o pA 45444 Te pe ages eat E ese Sl co eae eas Len Bs a l I l l I I 1 I 1 I ip dae I A E OAE J D 1 1 I 1 oS 1 I I I i N 0 08 In a In 4 I I 1 I 1 l I 1 I 1 I 0 06 kra a PSS SS Se jee I 1 I 1 1 I I l l l 0 04 gt es Ee l I 1 l l I 1 l l 0 02 l l l l l l I 1 l l 0 L 0 10 20 30 40 50 60 Figure 3 8 Hazard function of decayed poles Wood Pole Asset Management Decision Making Budget Planning The above information can facilitate asset management decisio
29. presented in later sections Storm related extreme weather events are excluded Outages of less than one minute are classified as temporary while those of one minute or longer are classified as sustained Sustained outages are further classified into two categories a Outages caused by overhead or underground line failures including those caused by weather vegetation animals overloads and component failure including switches reclosers fuses sectionalizers and substation breakers b Outages due to other causes including transmission failure public interference failures of lightning arrestors and distribution transformers utility maintenance personnel errors and other events Table 6 1 summarizes the historical reliability indices for all causes of outage Tables 6 2 and 6 3 present the indices by category 1 and 2 Table 6 1 values are the sum of the corresponding indices in Table 6 2 and Table 6 3 Table 6 1 Overall historical reliability indices for distribution system SAIFI 2000 2004 SAIDI 2000 2004 1 489 1 919 Hours Region 1 1 625 2 047 Hours Region 2 1 280 1 676 Hours Region 3 1 315 1 857 Hours Table 6 2 Historical indices overhead underground and device failures Region SAIFI 2000 2004 SAIDI 2000 2004 Total 0 869 1 316 Hours Region 1 0 836 1 358 Hours Region 2 0 952 1 339 Hours Region 3 0 839 1 074 Hours Table 6 3 Historical indices outages caused by miscellaneous
30. project to solve the task selection subproblem combines the enhanced linear programming relaxation method with the Lagrangean relaxation plus heuristic method ELPR ignores the 0 1 integer constraint while introducing a new constraint 0 lt x lt Lagrange relaxation retains the 0 1 integer constraint but relaxes all other resource constraints LRH improves Lagrange relaxation with a heuristic Figure 5 1 illustrates the ELPR LRH algorithm Solve ELPR Is solution integer N Solve LR amp Heuristics LRH Figure 5 1 Flowchart of ELPR LRH optimization method The task selection sub problem is represented in standard integer programming form as Max z cx 5 9 Subject to the following constraints Ax lt b 5 10 xe 0 1 5 11 The ELPR is solved using the general linear programming algorithm If the solution is an integer then the solution is optimal and the algorithm stops If the solution is not an integer the following LRH is solved as follows Max 2 A c AA x Ab c x Ab 5 12 Subject to the following constraint 58 x e 0 1 5 13 In equation 5 12 c is the reliability risk reduction benefit and c is the net benefit after deducting the cost of the resources The optimality criterion for equation 5 12 is simple if the net benefit of a task is positive then select it The difficulty in solving the problem represented by equations 5 12 and 5 13 is obtaining the Lagrange multiplier i
31. repair a fault MTTR average cost per failure COF which is the cost of repair that results from a failure and length of the segment 4 2 2 Fuses Reclosers and Breakers Protective devices are assumed to be located at the upstream node of a segment and are normally closed Fuses reclosers breakers and sectionalizers are modeled using their probability of failure protection reliability reclose reliability and MTTR 4 2 3 Switches Switches are used to reconfigure a system after a fault is interrupted Normally closed NC switches are located at the source or upstream node of a segment Normally open NO switches are located on the load or downstream node of a segment Switches cannot interrupt fault currents so their PR is set to zero Switches are modeled by switching reliability and mean time to switch When a fault occurs the upstream protective device responds to interrupt the fault If there were no switches between the faulted segment and the upstream device the time of outage for all customers downstream of the device is the MTTR of the faulted segment However if there is a switch between the faulted segment and the device it may be beneficial to operate the switch so that the interrupting device can be reset to restore service to some customers Switching in this case requires two operations e Open the upstream switch nearest to the faulted segment with a time of MTTS yi e Close the previously open device with
32. response to a fault 33 4 1 3 Protection Reliability PR Protection reliability PR of a protective device is the conditional probability that the protective device will operate to clear a fault In other words it is the probability of successful operation contingent on a fault occurring Thus it is a quantity between zero and one where the value of one represents 100 percent successful operation upon the occurrence of a fault Failure to operate may arise from mechanical breakdown or improper settings 4 1 4 Reclose Reliability RR Reclosers have the ability to repeat open close actions during a fault These actions allow time for temporary faults to clear thus avoiding long outages and results in reclosers failing in two mutually exclusive modes failure to open and failure to close Both are conditional on a fault occurring downstream of the recloser Reclose reliability RR is the probability that a recloser will successfully reclose after it successfully opens in response to a fault Failure to open and failure to close are the modes of failure on demand Protective devices can also fail due to inadvertent operation 33 when there is no fault but this is not considered here Inadvertent operation is usually due to a problem in device coordination and is comparatively rare 4 1 5 Switching Reliability SR Also called the probability of successful switching the switching reliability SR parameter defines the conditional p
33. ss Snes cs Seca ve ee ncaa ah schon vases aR ee arai erat 54 Table 4 9 Lengths of feeder Section cis cay Gowiad Seiivae steer Gael ie ae 54 Table 4 10 Reliability indices for the ieee reliability test system bus 2 0 54 Table 5 1 Risk reduction vs DUGG et sscichs bac nck nites sass eaee intakes neds cdes or aed eas 56 Table 5 2 Decision variable code table a5 ores wt kane Seana easel aseioaamense aa vadg ed 56 Table 6 1 Overall historical reliability indices for distribution system eeeeeeees 63 Table 6 2 Historical indices overhead underground and device failures 63 Table 6 3 Historical indices outages caused by miscellaneous failures 006 63 Table 6 4 Reliability parameter estimates for overhead lines and underground cables 64 Table 6 5 Reliability parameter estimates for protective and switching devices 65 Table 6 6 Adjusted failure parameters for overhead and underground line segments 66 Table 6 7 Reliability indices using adjusted failure rates and repair times 06 66 Table 6 8 Reliability indices using adjusted failure rates and equivalent component 66 Table 6 9 Failure modes and corresponding maintenance activities eeeeeeeeeeeeee 68 Table B 1 Feeder Topology Spreadsheets aiensacactiausakaneeldtidtsbam cane ede tioicsdea ceanables 82 vi Figure 1 1 List of Figures Reliability benefit obtained from various res
34. the recloser may need maintenance before it is justified by the other factors 3 1 1 1 Scoring Recloser assessment begins with selecting the criteria for a particular recloser as shown in Table 3 1 Different recloser types and models for example will use different criteria Each recloser s score will then be normalized by dividing the score by the maximum possible for the scored criteria For example evaluating contacts and oil dielectric strength for many reclosers requires removal from service These criteria will not be included in the assessment or maximum possible score for those reclosers The score for each item is per unit of the remaining state of the recloser criterion For example if the contacts are 60 percent of their original size their score would be 0 60 A recloser that has completed 75 percent of its recommended duty cycle would have a duty cycle score of 1 00 0 75 0 25 indicating the remaining 25 percent of its duty cycle The resulting condition score between 0 and 1 is denoted as Xes 3 1 1 2 Weighting The weight column in Table 3 1 represents the influence that a particular condition actually has on the failure rate of a recloser Weights will be determined in practice by the combined opinion of manufacturers utility engineers and field personnel Certain items are utility dependent such as the environment factor inspection item 3 1 2 Failure Rate Calculation To relate a recloser s condition score
35. the system Available maintenance tasks are identified and the risk reduction provided by each is computed The risk reduction for each task is based on the condition of the component being serviced the task s effect on improving the component s condition of equipment and the resulting improvement in reliability indices The tasks are prioritized subject to constraints on available resources using an optimization technique combining integer programming Lagrange relaxation and dynamic programming For this initial development work the maintenance tasks incorporated so far are associated with wood poles reclosers and vegetation management of distribution line right of way Actually maintaining these particular assets represents a large percentage of maintenance budgets furthermore outages of these assets can significantly affect system reliability This work can be adapted to most types of distribution equipment The essential elements of the maintenance allocation and scheduling system include 1 Failure mode identification Taxonomies are essential in identifying the effects of maintenance tasks on failure rates We determined the taxonomies of failure modes together with maintenance tasks that address those failure modes 2 Failure rate estimation Failure rate reductions provided by each maintenance task were used to optimize the allocation of maintenance resources Methods were developed for estimating the probabilistic failure ra
36. this the component failure rates and mean time to repair values are adjusted in a two stage process 1 First the failure rates for the urban and rural regions are varied linearly in this case decreased keeping the repair times constant until the predicted SAIFI values matched those from the historical analysis Then the MTTR of the urban and rural regions are varied until the predicted SAIDI values nearly equal those from the historical analysis The adjusted failure rates and the repair times of overhead and underground lines are shown in Table 6 6 In this procedure the protective and switching device parameters in Table 6 5 were held constant for two reasons First the utility personnel involved in the project were confident that the reliability estimates for protective and switching devices were close to 65 the actual values experienced in the system Second it was observed that the predicted indices were not very sensitive to variations in protective and switching parameters as shown in Table 6 5 This is confirmed in a published sensitivity analysis 42 The predicted indices obtained using the adjusted failure rates and repair times are summarized in Table 6 7 These are very close to the historical indices in Table 6 2 Table 6 6 Adjusted failure parameters for overhead and underground line segments Component Category Phase i aie MTTR hours 3 Phase 0 0155 1 25 Urban
37. time period replacements however can lead to sub optimal use of assets and unnecessary maintenance of equipment Such strategies do not compensate for different conditions that identical components may experience on a system 1 2 3 Condition Based Preventive Maintenance Condition based preventive maintenance better allocates resources by using information regarding the current state of equipment to determine when and what kind of maintenance needs to be done These methods require inspection and monitoring to estimate the piece of equipment s condition and its remaining useful life before maintenance Examples include dissolved gas tests for transformer oil recloser operation counters and visual inspection of feeders for vegetation growth Condition information is used to predict the probability of component failure and the maintenance that is needed to prevent failure Relative to time based maintenance condition based methods typically extend the interval between successive maintenances and therefore reduce maintenance costs 2 This method is restricted however to equipment whose cost of failure outweighs the inspection and monitoring costs incurred Improved testing monitoring inspection and data collection methods are needed to accurately predict the state of many power system components Condition based maintenance uses information from equipment inspection and monitoring to estimate the condition of the equipment and schedule mai
38. to be completed within each program constrained by the secondary budgetary allocation A solution to this problem allows the asset manager to compare the benefits of the different maintenance tasks available within a program and choose the best options depending on the resources available Apart from the above three issues there may be a situation where certain parts of the system need to be maintained due to safety or regulatory requirements regardless of the reliability benefit obtained Such obligatory tasks also have to be addressed In order to find a comprehensive solution to each of the above problems asset managers need tools to assess the benefit obtained from each maintenance task Once that is determined the corresponding cost and labor requirements can be used to judge the usefulness of the activity and prioritize accordingly 1 2 State of the Art in Power System Maintenance Before proposing a solution to the asset management problem presented in Section 1 1 a brief review of the state of the art in power system maintenance will be presented Maintenance of a component reduces its failure rate and thereby the frequency and duration of interruptions experienced by customers Utilities follow different procedures 1 or strategies to maintain different kinds of equipment These maintenance practices can be broadly classified into two categories corrective maintenance and preventive maintenance 1 2 1 Corrective Maintenance Al
39. to its numerical failure rate historical failure rate data from a number of systems were compiled for various power system components including reclosers 21 From this data the best worst and average failure rates for each component were calculated The resulting values for reclosers are as follows A 0 0 0025 Best A 1 2 0 015 Average A 1 0 060 Worst If no historical data exists for the system to be modeled then these values can be used If however historical data is available for the system then that data can and should be used to determine recloser failure rate statistics for that system Equation 3 1 22 demonstrates how a system wide average recloser failure rate is calculated fi 2 Total number of recloser JUNTE Gi Number of reclosers x Time period Ideally the number of reclosers should be constant over the time period a failure rate should be calculated for each such period and then the failure rate for the entire period calculated from these values The calculations are complicated by the inherent reliability and low failure rates of reclosers The accuracy of the calculation thus depends on the 16 availability of such data and the time period over which it is available Some utilities already have systems in place to collect data that can be used to track component reliability Those that do not must use the best available data while gathering the needed information Also from the availa
40. trees that are likely to fail and determine the maintenance needed including reinforcement or replacement to avoid failures 2 2 4 Factors Influencing Failure Rates A feeder s vegetation related failure rates are influenced by the following factors 13 Length of overhead lines Local density of vegetation measured in number of trees per mile Growth and regrowth rates of different species of vegetation Climate weather and other environmental factors Since these factors may vary significantly among feeders it is appropriate to model each individual feeder s failure rate if data is available aoc 2 2 5 Vegetation Condition and Modeling Overhead feeders are repairable systems and vegetation related failures are a recurring process When failures occur repairs restore the system to a working state Repair or maintenance decreases the failure rate of the system However the system tends to deteriorate as vegetation regrows and clearances decrease This causes the number of tree related outages to increase with time thereby increasing the failure rate Vegetation management decreases but does not totally eliminate vegetation related failures The number of tree related outages occurring in a unit of time may be used as a measure to estimate the state of the system If this value is higher than a specified limit the feeder may inspected to identify areas of maintenance A low value indicates that no maintenance is required Thi
41. with failure probability that tends to increase with time Maintenance improves the condition of equipment and thus reduces its likelihood of failure In defining risk the following effects of equipment failure will be considered a Customer satisfaction in terms of the expected number and duration of outages b Revenue lost by the utility due to energy not served c Cost to replace or repair failed equipment d Regulatory or contractual penalties paid by the utility due to missed reliability targets Repair and switching times for each component are assumed to be constant and the distribution network configuration is considered fixed This allows the reliability effects of each component to be expressed as linear contributions to the overall system indices 4 These effects are expressed 4 5 as follows 1 3 1 1 Effect on customer satisfaction SAIFI the system average interruption frequency index is defined as SAIFI total number of customer interruptions total number of customers served for a given time period For time period Af as a function of failure rate Ax for failure mode of component k the contribution of failure mode of component k to the system SAIFI is SAIFI t k 1 Ay At a 1 1 with units of average number of interruptions per customer in time period At The system SAIFI is the sum of these individual SAIFI contributions over all components k and failure modes SAIDI the system average i
42. 0 0 1 A Ag Ha 0 0 l fy 3 7 In addition to failure probability this model provides the ability to predict maintenance induced probability reduction and expected time to failure metrics that are important for a number of decision problems If a particular maintenance task results in renewing a component to deterioration level 1 for example then if the component is in deterioration level 3 the probability reduction for maintenance task m Ap m k is given by the last element of the 1x4 row vector resulting from the calculation 1 0 0 OJP 0 0 1 OJP 1 0 1 OJP The expected time to failure is captured by computing first passage times First passage time is the expected value of the time a process will take to transition from a given state j to another state i under the assumption that the process begins in state j The remaining life of the component is estimated from this computation The method of computing first passage times is provided in 25 26 discusses this issue from a power system reliability perspective 3 3 Wood Poles Wood poles form the backbone of most overhead distribution circuits Their purpose is to keep conductors and equipment away from the public and the ground and to maintain separation between conductors Poles also serve as a support platform for equipment such as regulators and reclosers 14 For most utilities the wood pole is one of the most ubiquitous assets and different maintenance strategies f
43. 2 Phase 0 2010 1 25 1 Phase 0 5317 1 50 Openia Dine 3 Phase 0 1180 1 00 Rural 2 Phase 0 1590 1 75 1 Phase 0 5450 1 25 3 Phase 0 0168 2 15 Underground Cable Urban 2 Phase 1 6923 0 50 1 Phase 0 0980 3 25 3 Phase 0 0140 1 50 Rural 2 Phase 0 0000 0 00 1 Phase 0 4990 2 75 To include the miscellaneous failures of Table 6 3 the failure rate and repair time of the equivalent component at the sending end of every feeder is adjusted until the predicted indices are nearly equal to total indices in Table 6 1 For the test feeder equivalent component failure rates of 0 4 faults year for urban and 0 7 faults year for rural and repair times of 1 25 hours for urban and 1 00 hours for rural provide the indices in Table 6 7 which are in close agreement with those in Table 6 1 Table 6 7 Reliability indices using adjusted failure rates and repair times Region SA IPI SAIDI Predicted Historical Predicted Historical Total 0 901 0 869 1 337 1 316 Region 1 0 892 0 836 1 409 1 358 Region 2 0 910 0 952 1 231 1 339 Region 3 0 917 0 839 1 318 1 074 Table 6 8 Reliability indices using adjusted fai lure rates and equivalent component Region Salal SAIDI Predicted Historical Predicted Historical Total 1 428 1 489 1 930 1 919 Region 1 1 534 1 625 2 082 2 047 Region 2 1 298 1 280 1 723 1 676 Region 3 1 305 1 315 1 810 1 857 6 2 3 Discussion
44. 25 133 34 S Yeddanapudi Y Li J McCalley A Chowdhury and W Jewell Development of a predictive reliability assessment tool for distribution systems presented at the Northern American Power Symposium NAPS conference Ames Iowa 2005 35 Z Shi H Zhu and B Farhang Boroujeny Markov chain Monte Carlo techniques in iterative detectors A novel approach based on Monte Carlo integration in Proc IEEE Global Telecommunications Conference GLOBECOM 04 vol 1 29 Nov 3 Dec 2004 pp 325 329 36 R Allan R Billinton I Sjarief L and Goel K So Areliability test system for educational purposes basic distribution system data and results JEEE Trans Power Systems vol 6 issue 2 May 1991 pp 813 820 37 L Wolsey Integer Programming New York John Wiley amp Sons Inc 1998 38 M Guignard Lagrangean relaxation Sociedad de Estadistica e Investigacion Operativa Top vol 11 no 2 2003 pp 151 228 39 S Martello and P Toth Knapsack Problems Algorithms and Computer Implementations New York John Wiley amp Sons Inc 1990 40 A Wood and B Wollenberg Power Generation Operation and Control New York John Wiley amp Sons Inc 1996 41 R Billinton Distribution system reliability evaluation JEEE Tutorial Course Power System Reliability Evaluation Course Text 82 EHO 195 8 PWR c1982 42 R Brown and J Ochoa Distribution system reliability Default data and m
45. 3 2 based on a multi state Markov probability model where each of the J states is represented as a deterioration level Boundary conditions separating J states of deterioration in component k are defined in terms of the measurements c t using the deterioration function g c t The deterioration function returns a deterioration level j identified by dj lt g ci t lt d where the last state j J represents the failed state State J need not represent the relatively rare catastrophic failure for which very little data is typically available Rather state J represents a set of measurement values for which engineering judgment indicates the component should be removed from service The particular representation in Figure 3 2 shows J 4 deterioration levels and deterioration level j can be reached only from deterioration level j 7 However the model is flexible so that any number of deterioration levels can be represented and if data indicates that transitions occur between non consecutive states e g state 1 to state 3 then the model can accommodate this easily The transition from level 4 to level 1 stochastically represents the effects of maintenance and if the decision problem is whether to maintain or not a deterministic result of the problem then we would set 4 0 The steps to implementing this approach are described as follows Level 1An Level 2 423 Level 3 434 Level 4 Statistical new minor major failed
46. 39 pea mae I a a 4 el g O etasan RE en 30 mann 6 au a A 10 MIN REPLACEMENT j MAJOR MAINTENANCE OR MAINTENANCE Figure 6 2 Risk reduction due to maintenance on reclosers 6 3 2 Wood Pole Maintenance The risk reduction computation for wood poles is done for each pole Data was not available for the example system however so pole maintenance was computed by line segment and segments needing maintenance were chosen randomly Degradation in a pole s mechanical strength on each segment was drawn from a uniform random generator that produces values between 0 and 0 3 A 0 3 value or 30 percent degradation represents pole failure Regression expressions 43 estimate failure rates before maintenance 69 con_age On years 6 8 a h 2 con _ age 6 9 a where e con is the degradation in pole mechanical strength e con_age is the conditional age estimate for the pole based on its condition e a and a are linear regression coefficients 43 that determine the relationship between the degradation level con and the condition age as follows o a 0 014418 o a 0 10683 e h is the pole failure rate derived from the Weibull hazard function shown in equation 6 9 with these parameters 43 o a 50 6090 o b 4 6676 As indicated in 43 two separate maintenance activities are considered for wood poles Pole reinforcement is assumed to reduce a pole s failure rate to 1 4th its va
47. AEE a a a 10 Ded Maintenance PLAC HGS ara a aan tia aa eee eee 10 DD SIV SACL OINS cfc nessa vat oh a Seats a aa besactec os Scents ae gtestan Vans es Ha eee oa ates wa we SONNE 11 2 2 1 Failure Modesovsccnac taiii ren R R E a a a ates 11 2 2 2 Maimtenance Actions sis he tes cht en Seed tvntee eel reas wees 11 2 255 Inspection Methods sissectsnesenis le atakdsuade adie Gupaadaiataahis E E a nena 12 2 2 4 Factors Influencing Failure Rates sec 2s ae kivtia eosin ieahaseastess 12 2 2 5 Vegetation Condition and Modeling ss ssssessssessesesseessesesssresseserssesse 12 2 3 Wood Poles s naraenia ees A AEAEE E tase A A A AESA RA AANER 13 2 3 4 Decay of Wood Polesia ieciiinesiinenireiaa i 13 2 3 2 Detection and Measurement of Decay eceecceessceesceeseeesteceteeeeeeensees 13 2 3 3 Maintenance Practices asnapa n en R A aa ii 13 Patlire Rate E S O a AA AA S 14 Deh O a EEE T EA 14 ILI Condition Assessment soen inocuo a a a a a i 14 3 12 Failure Rate Calculati satina a a aaa a n 16 3 1 3 Effects of Maintenance ir ntaa e i E A it 18 S A Example eara E E E ee ee E Mie ea 18 3A SUMMA Yoe occas e e cede a0 asin och here oh ne Satins sa oasis ac cade e at 21 D2 Vegetati oDe ete cas eu eee e E Nhy Mena eeaiaue nanan 22 3 3 Wood POLES iraniane a A Eni a a A RN 24 3 3 1 Degradation Path Model Approach Basis ccccesceeeseeeseeesseeeteeeeeeees 24 3 3 2 Degradation Path Model nsssseseesessseessesessseessessrssesseesresessreseesersse
48. AIDI and SAIFI A risk based approach has been developed to address this issue 30 32 4 Reliability Evaluation for Distribution Systems The objective of this chapter is to describe the development of a predictive reliability assessment tool that computes the reliability indices of a system and estimates the risk reduction associated with maintaining each component in the system The tool whose user manual in Appendix B is used to determine the relative importance of each component and prioritize maintenance resource allocation Section 4 1 defines the various parameters used to describe the reliability of distribution system equipment A description of the various components modeled in the analysis is provided in Section 4 2 Section 4 3 describes the different states associated with protective and switching equipment in response to a sustained or permanent fault while Section 4 4 describes the algorithm used for analytical reliability evaluation Section 4 5 describes a Monte Carlo integration method to compute the risk associated with regulatory penalties imposed due to violations of SAIFI and SAIDI limits 4 1 Parameters Used in Reliability Modeling of Distribution System Equipment The various components modeled in the distribution system include overhead and underground line segments protective devices fuses reclosers circuit breakers sectionalizers that operate when a fault occurs and switching devices that are used to reconfigu
49. AIFI k gt 4 13 g gt PBR SAIFI x i i l A similar expression can be developed for SAIDI These expressions are evaluated for each component before and after maintenance to determine the reduction in regulatory penalty risk obtained by maintaining each component To draw a comparison between the curve fitting method proposed in the literature 11 and this Monte Carlo integration the lognormal distribution is used as suggested in 11 However the distributions were highly skewed and the lognormal fit does not accurately represent the risk of events with low probability and high consequences especially for equipment with very low failure rates The fit improves for higher failure rates but variability in the reliability indices also increases This provides erroneous estimates for the risk of penalties associated with component failure Because the Monte Carlo integration method does not make an assumption about the distribution of variability in the indices it represents low probability events with greater accuracy The Monte Carlo integration method was also found to take about 30 to 40 percent less computation time than the conventional curve fitting method The drawback of the Monte Carlo technique however is that the accuracy of solution depends on the length of the simulation period and it requires a very large sample to achieve significant accuracy The method to compute the regulatory penalty risk reduction for wood poles a
50. Calibration of failure rates and repair time for lines and cables is a multidimensional problem since each component has two adjustable parameters Because only two system indices per region SAIFI and SAIDI are computed the problem is under constrained 66 therefore more than one set of parameter values can yield historical indices Reference 1 suggests a least squares approach using the method of gradient descent to determine one or more such values Combining such an approach with the experience and judgment of utility engineers may be most effective The extent of adjustment needed to the input data is influenced by various factors An important one is the accuracy of the initial estimates For the example system the adjustment to the estimates for the urban regions is higher than for the rural regions Because the estimated average failure rate and repair times for the rural region are determined over a large area with about 1 400 miles of conductors they tend to better represent the actual observed indices In contrast the urban regions are estimated over a much smaller region about 170 conductor miles and hence are less accurate Similar conclusions can also be drawn from the initial estimated failure rates in Table 5 4 The estimated failure rate for urban two phase underground cables is unusually high The initial estimate in this case is influenced by the short cable length rather than the number of outages The 0 03 mile cable h
51. Figure 3 7 and equation 3 16 that the percentage of decayed poles grows with time indicating that the time at which a pole actually begins to decay is a random variable We call this random variable the penetration age and represent it as b The reason the penetration age almost always exceeds ten years is due to the chemical treatment applied to each pole prior to installation This treatment resists decay very well until it is penetrated at which time the degradation process begins and continues from then on By inspecting the number of poles having a minimal but non zero level of strength loss in Figure 2 5 it can be seen that the penetration time ranges from 10 years to about 55 years This variability is due to the quality of the pretreatment and the pole location and environment From Figure 3 6 and equation 3 15 the mean strength loss rate is calculated as a 0 014418 From Figure 3 7 and equation 3 16 the penetration age b is identified as a random variable Therefore for a given value of b the mean lost strength percentage is expressed as a function of pole age as Lspm t a t b 3 17 29 Because there is only one measurement per pole and the population degradation rate is used to predict the degradation of each pole a is fixed and b is a random variable Implied is that while the age at which decay begins is unknown once it begins the pole will decay at the rate of a7 Estimation of Failure Rate The transformation
52. M E 1 13 Ya ss d ASAIDI k SAIDI k SAIDI OE 29 44 ETE J 1 14 AENS k A k ALP M Pid 1 15 ADevRisk k A k ee eee 1 16 APBRF k f PBR SAIFI f SAIFI k d SAIFI k PBR SAIFI f SAIFI k d SAIFI k Tp Ti 1 17 APBRD k PBR SAIDI f SAIDI k d SAIDI k PBR SAIDI f SAIDI k d SAIDI k 1 18 The subscripts B and A used in equations 1 13 to 1 18 correspond to the state of the component before and after maintenance respectively Thus the overall risk reduction obtained from maintaining a component k can be written as a linear combination of each of factors as shown in equation 1 19 Customer satisfaction Lost revenue ARisk k a ASAIFI k a ASAIDI k 1 AENS k Cost of component failure Re gulatory penalties p as a ADevRisk k a APBRF k a APBRD k 1 19 The coefficients aj in equation 1 19 correspond to weights that an asset manager assigns to the different factors based on their relative importance or confidence in their accuracy By choosing the units appropriately for the coefficients aj the overall risk reduction associated with a component s failure can be represented by a single monetary value 2 Maintenance Practices This chapter reviews common maintenance practices for the following distribution components included in the methodology developed in this project reclosers vege
53. Thus a device s probably of PF may be defined as 34 E Number of device failures 4 1 Total number of device operations l The total number of device operations in equation 4 1 includes the number of times the device successfully operated and the number of times it failed Using this failure probability the reliability metrics for various protective and switching devices can be estimated In the case of fuses sectionalizers and substation breakers whose primary mode of failure is failure to open PR is simply the complement of PF as shown in equation 4 2 A similar expression can be used compute the switching reliability of switches as shown in equation 4 3 PR 1 PF 4 2 SR 1 PF 4 3 Special consideration needs to be given to reclosers Since these devices have more than one mode of failure both the protection reliability and reclose reliability must be computed If data distinguishing the failure modes is not available PR and RR can be estimated by using PF If A is the event that the recloser fails to open in the event of a fault and B is the event that the recloser fails to reclose then a recloser has four different states of operation A Recloser opens when a fault occurs with a probability of P A PR 4 4 A Recloser fails to open when a fault occurs with a probability of P A 1 PR 4 5 B a Recloser successfully recloses after opening on a fault with a probability of P B A RR 4 6
54. a 0 014418 and a2 0 10683 28 Equation 3 15 characterizes well the lost strength percentage for a pole once it is known that the pole has begun to decay However as indicated previously the number of decayed poles is only eight percent of the total population For very new poles the percentage of decayed poles is expected to be significantly less than eight percent and for very old poles it is expected to be significantly more than eight percent Figure 3 7 shows a plot of the percentage of decayed poles in the total population as a function of age l l phenn n EE EE l l Cee ce eee Ree PSE BES eee eed osp Oe lh Percentage of the Decayed Poles Oto cso sl oo alge eM eo eto dosed Figure 3 7 Percentage of decayed pole at every age Figure 3 7 indicates that the percentage of decayed poles increases almost linearly with age beginning at about ten years Therefore after removing several outliers linear regression is again used to obtain a linear model of the percentage of decayed poles as a function of pole age Per t 0 004 t 0 04 3 16 Per t can also be interpreted as the probability of decay at age t This information is useful for predicting the number of decayed poles in a system as a function of time Figure 3 4 confirms the observation from Figure 3 7 that very few poles begin deteriorating until about ten years old We also observe from
55. a feeder SAIDI value exceeds 3 5 h customer year Coefficients for the various contributing factors are assumed to be as follows e Customer satisfaction 100 00 e Lost Revenue 10 00 e Cost of component failure 1 00 e Regulator penalties 0 01 Each utility will specify these coefficients to represent the relative importance or the relative confidence in the values computed for each The total risk reduction obtained from maintaining a component is given by equation 6 7 Customer satisfaction Lost revenue ARisk k 100 ASAIFI k ASAIDI k 10 AENS k ee d ae 6 7 ost of component failure Regulatory penalties ADevRisk k 0 01 APBRF k APBRD k 6 3 1 Recloser Maintenance No statistical failure models were found for reclosers so a simpler deterministic approach is used for risk reduction calculations As shown in Table 6 9 three different activities are considered for recloser maintenance minor maintenance oil change major maintenance recalibration and replacement Reclosers are modeled by their protection reliability and reclose reliability As discussed previously these are assumed to be equal which gives a linear relationship between reliability indices and PR In this example recloser reliability before maintenance is assumed to be the average value estimated by the predictive analysis developed in Section 6 2 1 In reality however each recloser will have its own PR These differences can be modeled us
56. a time of MTTSaev for that device The total time to complete this sequence is estimated as MTTS MTTS i MTTS i MTTS goy 4 11 This equation assumes that all switch and device MTTS values represent base to station travel time so MTTSswi MTTSaev is the travel time between the switch and the protective device The switching reliability of the protective device represents the probability that the device will actually be reset when desired A value other than 1 means overloading and mechanical failures 36 4 2 4 Sectionalizers Sectionalizers are used in conjunction with an upstream recloser in cases where fast switching to restore load is required When a fault occurs the upstream recloser opens and recloses allowing sufficient time for the fault to clear After a predefined number of such operations the recloser remains open long enough for the sectionalizer to open and then reclose again This allows customers between the sectionalizer and recloser to avoid a sustained outage Sectionalizers are modeled using PR MTTR MTTS and SR 4 2 5 Equivalent Component In addition to the failures of overhead lines underground cables and protective equipment outages also occur for many other reasons including the following a Transmission outages b Public acts such as accidents vandalism and accidental dig ins c Failure of other equipment including lightning arrestors capacitor banks transformers and m
57. ad one outage during the five year period resulting in a failure rate estimate of 6 7692 failures mile year Also the number of outages on the three phase system was lower than the one phase and two phase outages which explains the lower three phase failure rates The predictive analysis estimates steady state long term reliability indices while the historical indices reflect recent performance which may not be representative of the steady state values Hence the predicted reliability indices tend to be closer to those from the historical analysis when a longer period of outage data is used The granularity or extent of modeling also influences the predicted indices Predictive analysis using individual failure rates for three phase two phase single phase lines resulted in estimates much closer to historical values than when one failure rate was used for all lines regardless of phase In summary predicted indices are closer to historical indices when the system is modeled at a sufficient level of granularity and the input failure estimates accurately reflect each component s tendency to fail Thus it is important to first validate input data with historical indices as described here 6 3 Computation of Risk Reduction In the previous section the predictive reliability algorithm was implemented on the example system and estimated failure parameters were adjusted to ensure that the predicted indices match historical indices The predic
58. again Duty cycle is a combination of the number of interruptions the recloser has performed and either the percent of rated interrupting current or the circuit X R value NEMA has defined a standard duty cycle for distribution class reclosers 20 Constant monitoring of every recloser s duty cycle is impractical so an alternate criterion duty cycle rate is defined To calculate the duty cycle rate the number of faults a recloser will see per year in a certain location is determined from the historical data used to calculate the utility s SAIFI index The value of system X R at the recloser location is determined from system data Then the NEMA standard duty cycle definitions give the number of operations per duty cycle for that location Dividing the operations cycle by the expected operations year gives the duty cycle in years cycle for a recloser at that location Duty cycle is then compared to expected oil life whereby duty cycle rate equals the expected duty cycle divided by the expected oil life This score is high for a high expected remaining duty cycle If the score is greater than one then the expected duty cycle is longer than the expected oil life and the score is entered as one This score is a function of recloser location on the system and not of the actual recloser condition Environment Factor This criterion is for reclosers in locations that require more frequent maintenance It consists of a combination of recloser placem
59. ain the system to achieve the appropriate reliability level Operations and maintenance O amp M budgets can be reduced through improved efficiency However of concern is the effect of such budget reductions on a distribution business ability to keep its system operating at the desired reliability level To meet customer needs for affordable and reliable service while complying with regulatory requirements with limited budgets it is necessary to find tools and techniques that when coupled with a sound asset management policy can be used to optimally maintain distribution systems Such a policy also extends equipment life to avoid or defer costly capital investments resulting from poor equipment maintenance In this project we have developed a comprehensive and cost effective maintenance allocation and scheduling system and have implemented it in software tools These tools assist in answering three concerns commonly faced by an asset manager 1 How to identify and justify the resources needed for managing the assets of the entire system 2 How to allocate the available resources to different maintenance programs 3 How to select a set of maintenance tasks to be performed within each maintenance program Our system allocates resources and schedules maintenance tasks to optimize system reliability by maximizing risk reduction achieved from those tasks It uses information obtained from inspection and monitoring to determine the state of
60. alues_rural default values urban Macros in All Open Workbooks Description Macro recorded 12 25 2004 by sreerama Default Failure rate assignment to the Urban feeders To compute the reliability of the entire system Go to Tools gt Macro gt Macros select automate and press Run Alternatively press Ctrl a This requires the user to input the value of 1 if reliability evaluation for the entire system is desired and 0 if not 93 Macro name default_values_rural default_values_urban Macros in All Open Workbooks Description Computes reliability of the entire system If 0 is entered the program execution is terminated and is followed by the message below Microsoft Excel You have chosen manual mode hence the procedure is terminating 94 Appendix C User Manual for the Optimizer The optimizer is written in Matlab and compiled into executable file The following files are contained in a compressed file RDRA zip which contains the following RDRA root directory RDRA DATA recl dat recloser candidate triplets RDRA DATA stree dat tree trimming candidate triplets RDRA DATA pole dat wood pole candidate triplets RDRA optconFiguredat user configuration file RDRA task exe solves the task selection subproblem RDRA budget exe solves the budget planning subproblem In the optconFiguredat the user can set the availa
61. an B Tree Trimming t 2 Resource allocation mw S amp 3 500 1000 1500 Budget Thousand Figure 6 6 Budget splitting curve for different tasks 73 6 4 2 Labor Sensitivity Analysis Labor constraints are included in Figure 6 5 and Figure 6 6 It is also useful to modify the labor constraints to see if increased or decreased labor spending results in different spending decisions This information provides the basis for increasing or decreasing the number of maintenance crews Figure 6 7 shows the results of this analysis The lower curve is the same as Figure 6 5 with existing labor constraints The middle curve reflects the addition of one new recloser maintenance crew The upper curve represents no labor constraints at all The curves show that additional labor resources provide no significant improvement until a budget of about 300k is reached If a desired ARisk reduction Abudget occurs at a budget level below 300k then labor reduction may be in order Likewise if a desired ARisk_reduction Abudget occurs for a higher budget level then increased labor should be considered Complementary information may be obtained by plotting risk reduction against labor for a fixed monetary budget x 10 3 5 N a N oa wo T T T T Risk reduction T 0 5 0 500 1000 1500 budget Thousand Figure 6 7 Labor sensitivity 74 7 Conclusions 7 1 Summary Distribution system reliabilit
62. and the recloser is described by its protection reliability PRp reclose reliability RRR and repair time MTTRar For a permanent fault downstream from the fuse with fault failure rate and repair time MTTR the following mutually exclusive events can occur a Recloser opens and recloses and the fuse opens causing an outage to customers downstream of the fuse The frequency of such a situation is given by PRr RRr PRe A and the duration of interruption is MTTR Recloser opens and recloses but the fuse fails to open The recloser locks out interrupting customers downstream of the recloser The frequency of such a situation is given by 1 PRF RRg PRe A and the duration of the interruption is MTTR MTTRg Recloser opens and recloses the fuse fails to open and the recloser fails to open causing the fault to be interrupted by the next device upstream of the recloser and interruptions to all customers downstream of that device The frequency of occurrence of this event is 1 PRr 1 PRr RRr PRr and the duration of interruption is MTTR MTTRrp MTTRg The probability of this event however is very low and will be neglected in this analysis Recloser opens but fails to reclose causing interruptions to customers downstream of the recloser The frequency of this event is 1 RRr PRr A with an outage duration of MTTR MTTR Recloser fails to open and the fuse opens interrupting custome
63. any others d Utility errors Since it would be inappropriate to attribute such outages to any of the equipment listed in subsections 4 2 1 to 4 2 4 they are represented as a separate component with characteristics equivalent to the components and failure modes that are not modeled This equivalent component will be included at the beginning of every feeder It represents the combined effects of all other outage causes Similar to an overhead or underground line segment the equivalent component is modeled using permanent failure rate A and MTTR 4 3 System Response to Outages When an outage occurs in a distribution system the system transitions into one or more states based on events that happen after the outage This begins with the nearest upstream protective device sensing a fault and operating to isolate it After a crew is dispatched to repair the fault the nearest switch upstream of the fault is opened by the crew This isolates the fewest possible customers while the rest are restored by reclosing the protective device Further restoration is possible by opening switches downstream of the fault and closing tie switches to connect the isolated region to another feeder or another region of the same feeder Once the failed equipment is repaired the system returns to its original state and remains there until the next fault In this section the response of protective and switching devices to a sustained fault are described along with th
64. ariability in the degradation level across a pole population at a particular age f is best described by a distribution This distribution is denoted as Lspd t dist Lspm t Lspe t 3 10 where Lspd t is the degradation distribution at age t Lspm t is the mean of the distribution at age t Lspe t is the standard deviation of the distribution at age t At each age t the mean Lspm t is mapped to the hazard function H t for the decayed population that is if the lost strength percentage of pole i at an age t Lsp t equals the lost strength percentage population mean at some age t Lspm t then the pole i failure rate equals H t This ensures that the condition based failure rate can be estimated After the mean at every age is fit the following expression is obtained for Lspm t Lspm t t a0 al an 3 11 where gt 0 and ao a Ay are the time regression coefficients The failure probability for any pole of age defined as P T lt t is given by the probability that the random variable Lspd t exceeds fp according to F t P T lt t P Lspd t gt fp 3 12 26 Effect of Preventive Maintenance A maintenance activity on a component subject to degradation may renew the component to a less degraded state slow the future rate of degradation or both For example a wood pole may be treated by chemical material to slow decay The effect on degradation can be quantified in the failure rate and time to
65. be evaluated while the recloser is in service or from prior maintenance records A large part of the cost of recloser maintenance is removing it from service and removing a recloser from service to assess it without performing maintenance is never cost effective Components that can never be assessed in service are therefore omitted from Table 3 1 Table 3 1 Recloser score sheet Score 0 1 Criteria 161EM Pre Maintenance Age of Oil Duty Cycle Rate Environmental Factor Oil Dielectric Strength Condition of Contacts Age of Recloser Experience with this Recloser Type Condition of Tank Sum Weighted Average 14 Scoring criteria are as follows Age of Oil The oil in a recloser is the most important dielectric in the unit especially if the contacts are not in a vacuum The oil helps extinguish arcs as contacts open and close keeps arcs from occurring between other electrical conductors within the recloser lubricates most of the moving parts and is used to raise the trip piston after operation The average expected life of oil is three years Oil age thus provides a rough estimate of the oil s dielectric strength without removing the recloser from service Duty Cycle Rate Duty cycle is a measure of the use a recloser has experienced since its last maintenance and is one of the most important criteria for determining when maintenance should be performed
66. bility Indices The most common reliability indices used by utilities are SAIDI SAIFI CAIDI and ASAI 31 Most of them are based on averages of customer reliability that weight each customer equally The following are five of the most common reliability indices used for 79 distribution systems as defined in the IEEE Guide for Electric Power Distribution Reliability Indices IEEE 1366 2003 1 System Average Interruption Frequency Index SAIFI The system average interruption frequency index SAIFI indicates how often the average customer experiences a sustained interruption over a predefined period of time for a given area in the system SAIFI Total number of customers interrupted A 1 Total number of customers served For a fixed number of customers the only way to improve SAIFI is to reduce the number of sustained interruptions 2 System Average Interruption Duration Index SAIDI System average interruption duration index SAIDI indicates the total duration of interruption for the average customer during a predefined period of time commonly measured in customer minutes or customer hours of interruption Total duration of all customer interruptions SAIDI A 2 Total number of customers served SAIDI can be improved by reducing the number of interruptions or the duration of the interruptions 3 Customer Average Interruption Duration Index CAIDD The customer average interruption duration index CAIDIJ
67. ble 6 4 Reliability parameter estimates for overhead lines and underground cables Component Category Phase ee MTTR hours 3 Phase 0 0632 1 75 Urban 2 Phase 0 8043 1 75 1 Phase 2 1268 2 00 Ovetieed Ling 3 Phase 0 0983 175 Rural 2 Phase 0 1323 2 50 1 Phase 0 4543 2 00 3 Phase 0 0672 3 25 Underground Cable Urban 2 Phase 6 7692 0 50 1 Phase 0 3922 3 75 3 Phase 0 0116 2 15 Rural 2 Phase 0 0000 0 00 1 Phase 0 4156 3 50 The reliability parameters for protective and switching devices is ideally computed from the average number of times the device is expected to operate and the number of times it is successful However these were not available in the outage database Instead the failure probability was estimated from available data using equation 6 3 Number of device failures 6 3 Total number of device operations ee Reliability metrics for protective and switching devices can be estimated from PF For fuses sectionalizers and substation breakers whose primary mode of failure is fail to open during a fault protection reliability is the complement of PF as described in Section 4 1 7 and shown in equation 6 4 64 PR 1 PF 6 4 Similarly a switch s switching reliability is estimated by equation 6 5 SR 1 PF 6 5 For reclosers two failure modes are possible failure to open and failure to reclose Protection reliability and reclose reliability are estimat
68. ble data the lowest and highest failure rates for reclosers on the system become the best A 0 and worst A 1 historical failure rates If the calculated values are not judged to be accurate then the published 21 values should be used From the historical failure rates coefficients A B and C are calculated using equation 3 2 21 __ Ad 2 A f A 1 2A 1 2 0 A 1 2 A A 0 a B 2In 3 2 C A1 0 A These coefficients are recalculated periodically as data becomes available Equation 3 3 then estimates the failure rate for an individual recloser based on the coefficients and its condition 21 A x Ae C 3 3 where A x is the recloser s failure rate and x is a modified condition score that is calculated from the check sheet score Xes using equation 3 4 Xes 7 A es AOS Al 7 3 4 x 1 If Xcs is used directly then a recloser would need a score of Xes 1 to be assigned the best failure rate on the system and a score of Xes 0 to be assigned the worst A recloser with Xcs 0 would have completely failed every condition with a score of zero which is not practical Instead the best and worst scores on the system should relate to the best and worst historical failure rates Thus x 1s the worst recloser condition score recorded on the system and xo is the best The resulting value is subtracted from 1 because a high Xes indicates a low failure rate and a high x in equation 3 3
69. ble resource budget step size and maximum budget for the study An example of this file is as follows unit 1000 UNIT 10008 maxbudget 2000 so the total budget maxbudget unit pole_labor 16000 person hour for wood pole category recl_labor 1600 Y person hour for recloser category trim_labor 9600 person hour for tree trimming category In the recloser recl dat tree tree dat and pole pole dat data files the inputs are the candidate triplets risk reduction money cost labor cost pole 1 T E N 6 65 4188 3000 0 24 0 16 35472 200 0 16 40943 3000 0 24 0 4 10236 200 0 190 98087 3000 0 240 47 81504 _ 200 0 51 39968 3000 0 24 0 12 84992 200 0 302 15175 3000 0 24 0 75 53794 200 0 36 16557 3000 0 24 0 9 54139 200 0 17 76203 3000 0 24o 444051 200 0 177 27813 _ 3000 0 24 0 44 31953 200 0 128 68019 3000 0 24 0 32 17005 200 0 21 50145 3000 0 24 0 5 37536 200 0 51 37194 3000 0 24 0 12 64299 200 0 1658348 3000 0 240 414587 2000 __110 37174 3000 0 240 ar 5774 2000 11 52335 3000 0 24 0 2 68084 200 0 Figure C 1 Input file of pole candidate tasks Each line of data has two triplets corresponding to two levels of maintenance activities for each device The two executable files task exe and budget exe solve the task selection and budget planning subproblems After running the task exe file there will appear two new
70. ce 2 75 2 8 2 85 29 2 95 SAIFI 51 SAIDI variation before maintenance 3 4 3 5 3 6 3 7 3 8 3 9 4 4 1 4 2 SAIDI Figure 4 7 Variation in SAIDI before recloser maintenance 0 45 04 SAIDI variation after maintenance 0 35 03 0 25 0 2 0 15 0 1 0 05 a 3 5 3 6 3 7 3 8 3 9 4 4 1 4 2 SAIDI Figure 4 8 Variation in SAIDI after recloser maintenance 4 6 Validation of Reliability Assessment Tool The reliability evaluation tools developed in Sections 4 2 to 4 6 are validated using the IEEE test system 36 Figure 4 9 shows the test system of four radial distribution feeders The number of customers and corresponding loads connected to each load point are shown in Table 4 8 Table 4 9 provides the lengths of each feeder section The 52 overhead line failure rate is 0 065 failures km yr and the average repair time is five hours The transformers in the system are modeled as lines with a failure rate of 0 015 failures year and average repair time of 200 hours Switching time MTTS is assumed to be one hour All protective and switching devices are assumed to operate with 100 percent reliability Transformers and corresponding line segments are reduced to a single equivalent component using the failure rate and repair time expressions for series connected components 31 20 LP12 Tiz Figure 4 9 JEEE reliability test system 36 bus 2 53 Table 4 8 Customer data
71. ced or new one is installed in its place Since removal is costly most utilities perform a standard maintenance procedure on each recloser that comes into the shop The procedure returns the recloser to a serviced condition and reduces its failure rate During service of reclosers oil is replaced or filtered Mechanical parts bushings and stringers are inspected and replaced if they are damaged or excessively worn Contacts are inspected for wear and replaced if needed Insulation is tested to reduce the likelihood of internal or external recloser faults Structural maintenance includes removing rust and repainting the tank can to a specified thickness of paint to reduce the effects of weather When maintenance is complete the recloser is tested to ensure that it is operating in accordance with its specified time curves It is then returned to the warehouse for installation when needed 10 2 2 Vegetation Vegetation related failures are a large contributor to distribution system interruptions Utilities spend sizeable portions of their maintenance budgets controlling vegetation Because of the high cost utilities must assess the effectiveness of their vegetation maintenance programs 2 2 1 Failure Modes Tree growth into power distribution lines is less of a factor in distribution outages that it is in transmission Most utility tree trimming programs are effective in keeping growing vegetation away from distribution lines Tree growth cause
72. closer As a primary protective device a recloser s response to a sustained fault is similar to that of a breaker In the event of a permanent fault the recloser is expected to open and lockout Recloser failure occurs when the recloser fails to open during a fault For a 38 downstream fault with failure rate A and repair time MTTR the states shown in Table 4 3 occur for a recloser with protection reliability PR and repair time MTTRp Table 4 3 Protection response of recloser Recloser successfully clears a fault with failure rate A and repair time MTTR Frequency PR A Duration MTTR Customers interrupted Downstream of recloser Expected cost of failure PR COF where COF is cost of outage on faulted line segment Expected energy interrupted PR A MTTR Lp Recloser fails to clear a fault with failure rate and repair time MTTR Frequency 1 PR A Duration MTTR MTTRg Customers interrupted Downstream of backup protective device Expected cost of failure 1 PR COF COF p where COF is cost associated with recloser failure Expected energy interrupted 1 PR A MTTR MTTRg Ls 4 3 4 Fuse with Upstream Recloser Fuses are coordinated with upstream reclosers to allow temporary faults to clear by opening and reclosing thus saving the fuse The fuse is described by its protection reliability PRr and repair time MTTRg
73. d and the dirt around the pole is replaced A decayed pole can be stubbed whereby the decayed section is simply cut off if the remaining portion is long enough strong enough and in good enough condition Stubbing costs one third to one half the cost of replacing a pole If stubbing is not possible the pole must be replaced when its residual strength is below applicable standards 13 3 Failure Rate Estimation This chapter presents models that estimate the failure rates of components as well as the failure rate reduction achieved by preventive maintenance tasks 3 1 Recloser This section discusses the methodology for determining the condition of a recloser while in service This condition data is then used to estimate the recloser s failure rate 3 1 1 Condition Assessment The methodology begins by assessing the condition of the recloser A scoring sheet that itemizes relevant failure causes is shown in Table 3 1 Each of the criteria on the score sheet contributes to the reliability of a recloser and most can be improved by preventive maintenance Those that cannot be improved are still relevant in determining the recloser s condition These include the age of the recloser which can only be improved by replacing the recloser and the duty cycle rate and environmental factor both of which are a function of placement on the distribution system rather than any maintenance performed For some reclosers each of the criteria can
74. d after Opening AFER MAINTENANCE Enter the probability of Recloser Failure to 8 78861992 Open on demand Enter the probability of Recloser Failure to 8 78861992 Reclose on demand after Opening Enter the MTTR 1 75 Enter the Cost of Failure S 1000 Reset Cancel NOTE Use this option to enter recloser failure information that classfies modes of failure a Failure to Open when a fault occurs Demand and b Failure to Reclose after successful Opening of the Recloser To enter data for reclosers the user has two options Option 1 requires the user to input the probability that a recloser fails to open in the event of a fault and the probability that a recloser fails to reclose once it has cleared a fault Also required are the probabilities of failure after maintenance and the recloser s MTTR and COF If information characterizing individual failure modes is not available i e failures cannot be classified as failure to open or reclose Option 2 can be used to enter the overall failure probability of the recloser 88 RECLOSER x OPTION 1 OPTION 2 BEFORE MAINTENANCE Enter the probability of Recloser Failure on 0 05 demand AFTER MAINTENANCE Enter the probability of Recloser Failure on 0 0175 demand Enter the MTTR 1 75 Enter the Cost of Failure 1000 Reset Cancel NOTE Use this option to enter recloser failure information that doesn t classify between failure modes of recloser
75. d the resulting failure rate estimates should be verified The problem formulation should be further enhanced by considering scheduling issues involved in equipment maintenance The result will provide a schedule of planned maintenance for a budget period The optimal resource allocation strategy sacrifices some accuracy to solve the large scale problem Further research involving other optimization techniques will help improve the accuracy of the solution ill Table of Contents TNtPOCUECHON 5 35 cei cette ait Satine Rie desde age nic Ae as l 14 Asset Management Probletitcka s tweactcasck ustsanduietedacdsthet a A E 1 1 2 State of the Art in Power System Maintenance 0 0 ceccceecceeseeesseeeeceteeeeseeeeees 2 1 2 1 Corrective Maintenance cscs iiss gasses saaceess te ances asades a receer noes ees 2 1 2 2 Time Based Preventive Maintenance sisi ssccs4sii4sa2sad 9ansarsvsaasaqescasheantacvose 2 1 2 3 Condition Based Preventive Maintenance ccccccccessecesseceeeseeeeseees 3 1 2 4 Reliability Centered Maintenance RCM ccccescceseceeseeeteeeeteeeteeeees 3 1 2 5 Risk Based Preventive Maintenance cccccescccesscecesececsseceesseeeesseeees 3 1 3 Risk Based Allocation of Distribution System Maintenance Resources 4 13 Definition of RAS Ke a Er ra AAA E EA AAA RENS 5 Maintenance Practices enin i En E A E A E E 10 PA ORECIOSETS eea e a e aE ath saws aca tues ous 10 211 Faire Mod s mererien d e
76. delete or move this file from the folder Table B 1 Feeder Topology Spreadsheets One line of data for each feeder segment Col No Column Description Unique identifier for each segment of feeder first segment for A Segment each feeder is the equivalent component discussed in section 4 2 5 B From node Node number that marks beginning of segment 82 x lt GC H lt AB To node Upstream segment Protection zone Switching zone Ht above the ground Over under flag Length Load A Load B Load C No of customers Permanent failure rate before Permanent failure rate after Cost of failure MTTR Phase Protective device Segment Type Upstream segment PR RR MTTS SR Status Close to node Node number that marks end of segment Upstream segment of segment Column left blank output of program Column left blank output of program Column left blank output of program 999 Takes values Over or Under or for overhead line segments underground cables and equivalent segment respectively Length of line segment in kft 1000 ft Load connected to Phase A in kWh Load connected to Phase B in kWh Load connected to Phase C in kWh Customers connected to segment Failure rate of segment before maintenance failures mile year Failure rate of segment after maintenance failures mile year Cost of failure on segment Average repair time of segmen
77. distributed random numbers either zero or one for parameter PR to represent recloser failure or operation for each of the fault 3 Keep in the mind that the average number of times the recloser operates is the PR for the specified year e For the estimated PR calculate the annual reliability indices SAIFI and SAIDI using their straight line equations f Express the annual variability in SAIFI and SAIDI as probability distribution functions g Using equation 4 14 calculate the risk of penalty before maintenance Repeat for the risk of penalty after maintenance h Remember that risk reduction is the difference in risk before and after maintenance To illustrate the variability in SAIFI and SAIDI from maintaining reclosers probability plots obtained using this method are shown in figures 4 5 through 4 8 The method developed for wood poles and vegetation related failures can also be applied to failures of overhead and underground conductors The method for reclosers can be similarly extended to other protective equipment such as circuit breakers and fuses oS 50 0 35 SAIFI variation before maintenance 0 3 0 25 0 2 0 15 0 1 0 05 37 2 75 2 8 2 85 29 2 95 SAIFI Figure 4 5 Variation in SAIFI before recloser maintenance 0 45 SAIFI variation after maintenance 0 47 0 35 0 3 F 0 25 0 2 0 15 0 1 0 05 2 Figure 4 6 Variation in SAIFI after recloser maintenan
78. ective area of the cross section at the wood pole ground line A number of approaches for doing this vary in accuracy and implementation cost Some approaches described in the literature include acoustic 16 resistance force 17 and combining measurements of resistance force and humidity 18 Another simple but cost effective approach is to remove external decay and assess the internal decay pocket by drilling This method is assumed here Figure 3 3 provides a flow chart of the degradation path model approach to convert such condition measurements into probabilistic failure indicators After obtaining the condition history 1 the component degradation path model 2 is determined and the lifetime analysis 3 is performed using the actual failure data or the extrapolated failure data from the degradation path model These two procedures provide the population degradation path model 4 and the age based hazard function 5 which are then mapped point by point to get the condition based failure rate 6 and then the time to failure and the effect of maintenance are estimated This model is data driven more data and better data result in better models and ultimately better decision making Condition Obtain component Lifetime History degradation path analysis D Obtain population Hazard degradation path function Map condition to the failure rate amp O estimate the effect of preventive maintenance activity
79. ects in order to maximize risk reduction For transmission systems risk is defined as the time dependent product of the probability of equipment failure and the consequence of its failure 2 The consequence of failure is the quantified effect of equipment outage such as overload of equipment cascading failures and low voltage Risk based maintenance is thus a form of RCM with the following specific attributes when applied to transmission systems 2 a Condition information is used to estimate equipment failure probability b Failure consequences are estimated and used in prioritizing maintenance tasks c Equipment failure probability and consequence at any particular time are combined into a single metric called risk d Equipment risk may be accumulated over a time interval e g a year or several years on an hour by hour basis to provide a cumulative risk associated with each piece of equipment e The prioritization and thus selection of maintenance tasks is based on the amount of reduction in cumulative risk achieved by each task Selection and scheduling of maintenance tasks are performed at the same time using optimization algorithms since the amount of reduction in cumulative risk depends on the time when a maintenance task is implemented 1 3 Risk Based Allocation of Distribution System Maintenance Resources The objective of this work is to develop a similar risk based strategy to allocate maintenance resourc
80. ed as described in Section 4 1 7 and shown in equation 6 6 PR RR 41 PF 6 6 The calculated reliability measures for protective and switching devices are tabulated in Table 6 5 The mean time to switch for each is assumed to be one hour based on the field experience of the switching personnel Because the switching times of the protective devices are not known it is assumed that the MTTSgey is one hour the same as the MTTS i For this example it is assumed that all switching failures are due to a switch failing to do the intended operation Protective device reliability is then 100 percent and the probability for the switching sequence is SR of the switch alone Table 6 5 Reliability parameter estimates for protective and switching devices Component Category Proteevon MTIR Ss Syel ching Reliability PR hours RR Reliability SR Fuse Urban 0 970 1 13 0 000 1 00 Rural 0 950 1 50 0 000 1 00 Recloser Urban 1 000 1 75 1 000 1 00 Rural 0 975 1 75 0 975 1 00 Switch Urban 0 000 2 00 0 000 0 60 Rural 0 000 1 50 0 000 0 73 ee ee Urban 1 000 1 75 0 000 1 00 Rural 0 950 1 75 0 000 1 00 Urban 0 988 1 75 0 000 1 00 Pupp On E Ra 0 985 2 00 0 000 1 00 6 2 2 Results Using the values listed in Table 6 4 and Table 6 5 predictive analysis was performed However the indices predicted did not agree with those from the historical analysis as shown in Table 6 2 To correct
81. eeeeeeneeeeees 95 Figure C 2 Risk reduction versus budget table ptable m ec eecceeseeeseeeeeeeteeeeseees 96 Figure C 3 Task selection table trim_select m for tree trimming 0 0 eeeeeeeeeeees 96 vil 1 Introduction Both inspection and maintenance of equipment are a critical part of utility expenditures It is important to ensure that every dollar spent helps improve the reliability and performance of the system As illustrated in Figure 1 1 the ideal budgetary allocation results when the greatest benefit is obtained for every dollar spent In this case the benefit is reliability improvement indicated by relevant reliability indices From the asset manager s point of view a resource allocation within the indicated region in Figure 1 1 is desirable because it is the resource allocation for which the ratio of benefit to allocation is greatest For larger resource allocations this ratio falls off and within the organization the strength of the argument for obtaining such resource allocations diminishes This chapter describes in detail the challenge that asset managers face in maintaining their different distribution system assets A brief review of common utility maintenance practices and their impact on reliability is discussed A risk based method of allocating maintenance resources is then proposed Because of the limited resources available to this project the methodology developed is limited to reclosers vegetation a
82. efault failure and repair parameters for each feeder Go to Tools gt Macro gt Macros select rate_assign and press Run Alternatively press Ctrl d rate assign reliability_evaluation Macros in All Open Workbooks Description Macro recorded 06 27 2005 by sreerama Default Failure rate assignment to the feeder Upon execution failure and repair parameters are assigned to various distribution system components as shown in the following figures The default values that appear are drawn from the Master File xls They can be changed in the interfaces shown Parameters for individual components and segments are changed directly in the spreadsheet 85 OVERHEAD LINE SEGMENT 3 Phase Over head line Segment Failure Rate Before Maintenance Failures Mile year Failure Rate After Maintenance Failures Mile year MTTR Hours repair Enter the Cost of Failure 2 Phase Over head line Segment Failure Rate Before Maintenance Failures Mile year 0 159 Failure Rate After Maintenance Failures Mile year 0 1 MTTR Hours repair 1 75 Enter the Cost of Failure 1 Phase Over head line Segment Failure Rate Before Maintenance Failures Mile year 0 545 Failure Rate After Maintenance Failures Mile year 0 25 MTTR Hours repair 1 25 Enter the Cost of Failure Using the line and cable interfaces shown failure rates before and after ma
83. eir equivalent models 4 3 1 Circuit Breaker A circuit breaker is described by its protection reliability mean time to repair MTTRg switching reliability and mean time to switch For a fault with failure rate A occurring downstream of the breaker its probability of operating successfully and clearing the fault is PR The repair time of the faulted segment is MTTR so all the customers downstream of the breaker experience an outage with frequency PR and duration of MTTR 37 If the breaker fails to operate the next upstream protective device is expected to operate and clear the fault The number of customers interrupted is determined by the upstream device The frequency of such events is given by 1 PR A and the duration of interruption is MTTR MTTRg The probability of the upstream device failing will be neglected in this analysis because the probability of multiple breaker failures is very low If Lp and Ls refer to the load interrupted when the primary and the secondary backup protection device operate the outcomes of the two states are shown in Table 4 1 Table 4 1 Protection response of circuit breaker Circuit breaker successfully clears a fault with failure rate and repair time MTTR Frequency PR A Duration MTTR Customers interrupted Downstream of breaker Expected energy interrupted Expected cost of failure PR COF where COF is cost of outage on faulted line segment
84. ent and environmental effects on the physical condition of the recloser For example a recloser bank protecting a feeder along a coastline will experience air with a much higher salt content than one located farther inland The salt may cause the dielectric strength of the recloser oil to fall below standards much sooner than normal This criterion addresses such conditions Oil Dielectric Strength This score is important if the utility s recloser maintenance includes filtering the oil instead of replacing it The score should be given as the difference between the post maintenance oil dielectric strength which is measured as part of maintenance and the minimum allowable oil dielectric strength divided by the difference between the new and minimum oil dielectric strengths Condition of Contacts This score is given as a percentage of remaining useful contact life Age of Recloser This is important because as with all machines reclosers become less reliable and fail with age However reclosers have proven to last for many years and age has not been shown to be a reliable predictor of failure Recloser age should still be monitored though as one indicator of condition 15 e Experience with this Recloser Type This criterion is used to differentiate among failure rates for different manufacturers or models types and sizes of reclosers e Condition of Tank If a tank has excessive damage either from nature or handling
85. es and prioritize maintenance projects for distribution system assets The work will also provide a solution to the asset management problem discussed in Section 1 1 To do this certain important differences between transmission and distribution need to be understood before extending the method to distribution systems First unlike transmission systems which are highly networked most distribution systems are radial Hence the effects of an outage are localized and the chance of cascading outages is very small Furthermore maintenance scheduled in one area can be assumed to be independent of the conditions in another region of the system This is not the case in transmission systems where maintenance of a component in one transmission region may restrict a task in another region due to stability constraints Second distribution systems have a much larger number of components than transmission systems The consequence of failure in most distribution components is thus lower than that in transmission components This implies a large number of decision variables candidate maintenance tasks from which to choose and hence the need for optimization techniques that can suitably handle them Furthermore the conditions in a distribution system are relatively constant or predictable compared to those in a transmission network which can be highly dependent on such variables as network topology loading and equipment outages due to maintenance and envi
86. f Maintenance Strategy on Reliability of the Reliability Risk and Probability Applications Subcommittee The present status of maintenance strategies and the impact of maintenance on reliability IEEE Trans Power Systems vol 16 issue 4 Nov 2001 pp 638 646 2 J McCalley T Voorhis Yong Jiang and A P Meliopoulos Risk based maintenance allocation and scheduling for bulk transmission system equipment Final Project Report PSERC Publication 03 26 Oct 2003 3 J Goodfellow Applying reliability centered maintenance RCM to overhead electric utility distribution systems JEEE Trans Power Engineering Society Summer Meeting vol 1 16 20 July 2000 pp 566 569 4 R Brown H Nguyen and J Burke A systematic and cost effective method to improve distribution system reliability JEEE Trans Power Engineering Society Summer Meeting vol 2 18 22 July 1999 pp 1037 1042 5 F Li and R Brown A cost effective approach of prioritizing distribution maintenance based on system reliability JEEE Trans Power Delivery vol 19 issue 1 Jan 2004 pp 439 441 6 S Kostyal T Vismor and R Billinton Distribution system reliability handbook Final Report EPRI EL 81 16 LD Project 136 1 Electric Power Research Institute Sept 1981 7 R Billinton and P Wang Network equivalent approach to distribution system reliability evaluation JEEE Trans Generation Transmission and Distribution
87. failure rate Maintenance changes the recloser s condition and thus its failure rate Similar techniques can be applied to other distribution system components Research grade software from this research includes 1 Reliability evaluation tool A predictive reliability evaluation tool was developed in Excel It is used to compute system reliability levels This software tool also computes sensitivities of reliability metrics to maintenance tasks When combined with estimates of failure rate reduction obtained from maintenance tasks the tool computes the risk reduction associated with maintenance The output of this tool is one input to an optimizer tool that selects and prioritizes maintenance tasks 2 Optimizer tool An optimizer processes the inputs of 1 candidate maintenance tasks 2 effect of each task on reliability i e risk reduction 3 financial and labor resources needed for each maintenance task and 4 available resources The program selects and prioritizes maintenance tasks for the budget cycle Follow on work to this project is needed The reliability and inspection models developed should be further expanded verified and then adapted to other distribution equipment Specifically the wood pole degradation path model should be validated for other components with complex failure processes such as switches and transformers Similarly the inspection methods developed for reclosers should be applied to other components an
88. failures in each of the n years can be determined by solving equation 4 12 where x i is the number of failures in year 1 BO e7 x i By using the number of times the component fails in a particular year instead of its failure rate SAIFI and SAIDI can be computed using the linear relationships between the indices and the failure rate of the component Thus for a set of random numbers drawn for a component the number of times it fails each year and the corresponding SAIFI k and SAIDI k indices for each of the years can be determined Since the numbers drawn are random SAIFI k and SAIDI k are also random Similarly random variations of SAIFI k and SAIDI k can be determined using the failure rate of the component after maintenance Since SAIFI k and SAIDI k are randomly distributed with unknown distributions statistical methods can be used to suitably fit parametric equations that represent their distributions But this is a cumbersome process and not an attractive solution especially if the number of components is very large If there are m components in a system 4m curve fitting procedures for SAIFI and SAIDI before and after maintenance would be needed to evaluate the expected risk Using the Monte Carlo integration 35 instead the complex integral defined in equation 3 11 can be reduced to a more convenient summation as shown in equation 4 13 u i 4 12 PBRF k PBR SAIFT f SAIFI k d S
89. formation obtained from inspection and monitoring of distribution system assets with their failure characteristics to estimate failure rates The failure rate combined with the consequences of failure determines risk Computing the risk reduction provided by each maintenance task allows the asset manager to weigh the benefits against the cost This method combines maintenance activities into a single objective of maximizing system performance with minimal allocation of resources It is a comprehensive strategy that results in optimal utilization of resources and enhanced system performance A reliability evaluation tool was developed in Chapter 4 It is deliverable in the form of a spreadsheet that can be used to estimate the reliability of a feeder and the benefits of reliability improvement schemes such as automation introduction of reclosers or sectionalizing devices and feeder reconfiguration The User Manual for the spreadsheet is included as Appendix B to this report To include all distribution maintenance activities both failure models and inspection methods are needed for each component under consideration This method is highly data intensive and requires detailed information about the equipment s condition obtained from inspection monitoring and maintenance records Some of the data is available in a utility database but these are usually designed for bookkeeping and inventory and are not readily accessible for failure analysis The pr
90. he risk reduction for every recloser and wood pole on the feeder Vegetation maintenance is assumed to be done on an entire feeder so the risk reduction for vegetation growth is computed for the entire feeder Maintenance performed on a pole influences the failure rate of the overhead line segment it supports Hence the risk reduction due to maintenance on a particular pole is determined by the sensitivity of the reliability indices to maintenance on the corresponding segment Reliability indices are linearly dependent on the failure rate of the pole so sensitivities can be computed using the difference in indices before and after maintenance It can also be shown that the reliability indices of a feeder change linearly with respect to the vegetation related failure rate of the feeder If the failure rate of all overhead line segments is changed by the same proportion which corresponds to the failure rate reduction due to vegetation maintenance then the change in reliability indices can be predicted using a linear relationship For a recloser however two parameters quantify its reliability 34 protection reliability and reclose reliability Furthermore a recloser may have to function in one or more of the following ways during a sustained fault a As a primary protective device in the event of a fault occurring directly downstream In conjunction with a downstream fuse for a fault downstream of the fuse c In conjunction with a sectionali
91. hose customers between the switch and interrupting device If there is no upstream switch or if it is not opened all customers downstream of the interrupting device will experience an outage duration equal to the time taken to repair 42 the fault If SRp and SRs are the switching reliabilities of the device that interrupted the fault and the upstream switch operated to isolate the faulted area respectively then SRseg SRp SRs represents the switching reliability of the switching sequence The equivalent switching time required to open the switch and close the protective device is as follows MTTS MTTS M7TS MTTS jo swi The customers that are restored by switching experience an equivalent outage duration given by MOT SR MTTS 1 SR MTTR hours seq where MTTR is the time taken to repair the fault Table 4 6 describes the states associated with upstream switching done after a sustained fault Table 4 6 Switching response for upstream isolation Switching sequence is successful Frequency SRseg Interruption duration for customers downstream of switch MTTR Interruption duration for customers downstream of protective device and upstream of switch MITA a Expected energy restored switching restores some of A SRseq MTT Sseq Lswis Where Lswi is load load that was interrupted by the protective device restored by switching Switching sequence fails Frequency 1 SRseq In
92. ify the resources needed for asset management and how to allocate the available resources to the different maintenance programs DP is chosen because it provides not only the optimal policy but also the optimal policies of the subproblems 40 Illustrations of typical results obtained from these algorithms are given in Figures 5 2 and 5 3 The curve in Figure 5 2 provides the asset manager with a direct view of the relationship between the reliability risk reduction benefit and the maintenance budget It allows a solution to the first problem regarding the total maintenance budget The DP solution also gives the optimal allocation of the budget among different categories as shown in Figure 5 3 For example with a total budget of 12 000 the manager can allocate 3 000 to the recloser category 4 000 to the wood pole category and 5 000 to the tree trimming category This addresses the second problem Finally using the information in Table 5 2 the manager decides which tasks should be performed to solve the third problem 59 50 T 1 40 d 35 4 30 4 oe ar 10 15 20 25 30 Budget Thousand Figure 5 2 Reliability benefit vs budget Risk reduction fo ob N Wood Pole L Recloser Tree Trimming J oO a A p pee L Resource allocation Thousand 0 5 10 15 20 25 30 Budget Thousand
93. ilure partial discharge testing indicating magnetic circuit overheating and winding and oil temperature measurements indicating deterioration of the transformer cooling system Little has been published on correlating equipment deterioration with operating histories a fact that stems from the difficulty in obtaining and merging operating and condition data in ways that properly characterize deterioration Statistical modeling and analysis can be used to capture such trends however For vegetation probabilistic vegetation failure rate models developed in 13 24 are used to capture deterioration in this failure mode b Transition intensities Transition intensities between the various states of the model can be obtained from life histories of multiple units of the same manufacturer and model In the case of Figure 3 2 A12 A23 and A34 are needed Consider a set of condition measurements c t ci t c2 t cx for K similar components taken over an extended period of time 0 7 For component i the deterioration function is used to compute the deterioration level indicated by each measurement This gives the time the component spent in deterioration level j The mean of the durations for all components is then used as the estimated time spent in state j Reasonable estimates of the desired transition intensities are obtained by inverting these mean duration times Transition intensities computed in this way capture deterioration
94. in the state of the equipment but they do not capture variations in equipment failure propensity as a function of loading or environmental conditions To do this one needs to model the dependency of the transition intensities on these parameters However component loading and environmental histories typically reside in database systems such as control center historians distinct from component condition histories This requires a significant effort in data integration c Desired failure probability For a particular set of transition intensities the transition probability matrix for the case represented by Figure 3 2 is given by equation 3 7 The state probability vector gives the probability that a component is in any particular deterioration level at a given time and is denoted by p hT pl hT p2 hT p3 hT p4 hT where h 1 2 3 and T is the time step If at time t 0 the component resides in deterioration level 1 then the initial state probability vector is p 0 1 0 0 0 The probability of finding the component in any deterioration level at time hT is then given by p hT p 0 Ph Given that at time t 0 the component s deterioration level is known this provides the probability of residing in the failed state in any future time interval We denote this failure probability for component k as pk c This probability is a function of the time dependent physical condition of the equipment c t 23 l gt Ab 0 0 p 0 1 A Ay 0 at
95. ing statistical models of Section 3 1 to determine each recloser s failure rate PR after maintenance is also assumed to be deterministic After minor maintenance PR is assumed to be improved by 0 005 Similarly major maintenance improves PR by 0 0125 and replacement improves it by 0 025 Full implementation of the recloser model of Section 3 1 will require incorporation of the model into the software which is beyond the scope of this project 68 Figure 6 2 illustrates the risk reduction obtained from recloser maintenance Three levels of maintenance minor major and replacement of five reclosers were chosen to demonstrate the benefits of maintenance versus their cost and labor resource requirements To simplify the example reclosers were assumed to be in identical condition before maintenance This figure shows that despite identical initial conditions the risk and corresponding risk reduction obtained from maintenance vary significantly for the five reclosers and thus should be included when prioritizing maintenance tasks The figure also shows that the risk reduction obtained from a lower level maintenance task can be greater than that obtained from a higher level more expensive maintenance task on another recloser This demonstrates the importance of using these decision making methods to optimize the use of available resources 5 Ecco tid ee aa E E eal F Labor 10 Hours BB Risk Reduction 1000 MM
96. intenance mean time to repair MTTR and cost of failure COF can be input for three phase two phase and one phase line segments The failure rates are the average number of sustained or permanent failures expected in a unit mile length Values for failure probabilities should be between 0 00 and 1 00 MTTR is entered in h and COF has the units of US Once all values are entered they are applied to the feeder by clicking OK Clicking Reset restores the default parameters stored in the Master_File xls Cancel sets all parameters to zero 86 UNDERGROUND CABLE SEGMENT 3 Phase Underground Cable Segment Failure Rate Before Maintenance Failures Mile year 0 014 Failure Rate After Maintenance Failures Mile year 0 01 MTTR Hours repair 15 Enter the Cost of Failure 2 Phase Underground Cable Segment Failure Rate Before Maintenance Failures Mile year 0 Failure Rate After Maintenance Failures Mile year 0 MTTR Hours repair 0 Enter the Cost of Failure 1 Phase Underground Cable Segment Failure Rate Before Maintenance Failures Mile year 0 499 Failure Rate After Maintenance Failures Mile year 0 1 MTTR Hours repair 2 75 Enter the Cost of Failure 87 RECLOSER OPTION 1 OPTION 2 BEFORE MAINTENANCE Enter the me of Redoser Failure to 7 i 0 025 Enter the probability of Recloser Failure to 0 025 Redose on deman
97. ion This plot addresses the Level 1 question of how much to spend on all maintenance activities The key to answering this question is the amount of risk reduction obtained for each increment of maintenance spending which is the slope of the Figure 6 5 curve ARisk_reduction Abudget at a given budget level As spending increases the slope decreases The asset manager can identify a ratio below which no further maintenance spending is justified For example Figure 6 5 indicates that the reliability benefit per additional dollar spent is low when the total budget increases beyond 1 000k The ratio is much better for maintenance budgets up to about 500k 72 2 5 Risk reduction 0 5 500 1000 1500 budget Thousand Figure 6 5 Budget vs risk reduction Figure 6 6 displays resource allocation vs total budget which is the result of solving the Level 1 problem for various values of total budget This identifies the optimal budget split among maintenance categories For example the figure indicates that for a budget of 500k maximum risk reduction is achieved by allocating about 240k each to recloser maintenance and tree trimming and only about 20k to wood pole maintenance Wood pole maintenance spending should remain relatively small for budgets below about 850k Then wood pole spending increases for budgets exceeding 850k when risk reduction from additional spending on recloser maintenance or tree trimming is minimal Recloser
98. ion and maintenance Wood pole failures usually occur as a result of physical stress such as wind ice or vehicle impact The tendency of a pole to fail under such stress is related to the strength of the pole at ground level where almost 90 percent of pole failures occur 15 2 3 2 Detection and Measurement of Decay Nondestructive evaluation methods estimate the effective area of the pole cross section at the ground line Visual inspection is ineffective since it will not reveal internal decay or decay below this point Other approaches vary in accuracy and cost These include acoustic 16 and resistance force 17 sometimes combined with measurements of humidity 18 Another simple but cost effective approach is to remove external decay and assess the internal decay by drilling into the pole This project assumes measurements based on this approach 2 3 3 Maintenance Practice The primary maintenance on wood poles is ground line treatment 19 which can provide an economical extension of a pole s physical life Ground line treatment is recommended under the following conditions e Whenever a pole is inspected and the decay is not so far advanced that the pole must be replaced e Whenever a pole over five years old is reset e Whenever a used pole is installed as a replacement Ground line treatment consists of removing the external decay followed by application of a preservative paste or grease Then the treated section is wrappe
99. k of penalties associated with recloser 49 failure can be simulated using a Bernoulli distribution of parameter PR For each year simulated PR is determined in the following manner a Either assume a fixed number of faults per year Or if the distribution of the number of faults occurring downstream of the recloser is known randomly generate the number of faults per year b Generate Bernoulli distributed random numbers either zero or one for parameter PR to represent recloser failure or operation for each of the fault c Remember that the average number of times the recloser operates is the PR for the specified year Using the estimated PR for each simulated year and the straight line equations for SAIFI and SAIDI as functions of PR the reliability indices are computed Using the Monte Carlo integration of equation 4 13 the corresponding risks of penalties before and after maintenance are computed This method is summarized as follows a Input PR before and after maintenance and the resulting reliability indices SAIFI and SAIDI before and after maintenance Determine the straight line equations for SAIFI and SAIDI as functions of PR Specify the number of years to simulate d Determine recloser PR for each year 1 Assume a fixed number of faults per year Or if the distribution of the number of faults occurring downstream of the recloser is known randomly generate the number of faults per year 2 Generate Bernoulli
100. lgorithm a For a feeder determine the protective and switching device locations and the number of customers and load interrupted when each operates in response to a fault Select a contingency and evaluate its outage effects number of customers interrupted duration of interruption energy not served and cost of the failure on the feeder by determining the following 1 The device that interrupts the fault 2 Switching actions that reconfigure the feeder and restore some customers Weight the outage effects of the contingency by the probability of its occurrence and update the outage effects on the feeder If the component failed is an overhead line segment or a recloser determine its sensitivity to maintenance by the following 1 Fora line segment recompute the number of customers affected customer hours interrupted energy not served and cost of failure using the failure rate of the overhead line segment under consideration after maintenance 2 For a recloser determine the same quantities for reduced failure probabilities or improved PR and RR due to maintenance 44 The difference in the outage effects before and after maintenance can then be used to determine the risk reduction associated with maintenance e Repeat steps 2 to 4 until all contingencies have been simulated In step 4 the change in reliability indices for reclosers and wood poles is performed for every component on the system thus identifying t
101. lls but rather as defined in Section 3 1 that the strength loss reduction percentage exceeds 33 percent Maintenance Tasks Selection Budget constraints often require asset managers to prioritize maintenance tasks Useful indicators in this process for poles are the lost strength percentage condition age and failure rate of each pole Table 3 6 provides this information together with the actual age for four selected poles It is interesting that poles 3 and 4 although nearly the same age have significantly different condition ages and corresponding failure rates Table 3 6 Estimate of failure rate pie ae o O e 1 10 0 0 0 2 17 0 1025 14 5 0 001 3 39 0 0615 11 7 0 0004 4 42 0 2929 27 7 0 01 Similarly the effect of maintenance can be estimated Replacement is assumed to entirely renew the pole whereas treatment delays further decay by five years but does not improve the condition of the pole Therefore both actions result in an increase in time to failure but the effects on failure rate of the two actions are different while replacement causes immediate failure rate reduction the failure rate reduction from treatment is not incurred until the next and following years when the treated pole s failure rate remains fixed but the untreated pole s failure rate continues to increase For poles without decay in the current year equation 3 9 is used to estimate the probability of decay in the next
102. lue before maintenance Pole replacement reduces the pole s failure rate to that of a new pole The risk reduction associated with pole reinforcement and replacement is then calculated as described in Section 4 4 Figure 6 3 illustrates the risk reduction obtained from maintaining wood poles considering reinforcement and replacement It may seem surprising that the risk reduction associated with maintaining wood poles is lower that the expenses involved in maintaining them However it may be noted that the average life span of a typical wood pole extends typically in tens of years while that of a recloser is only a few years Since the formulation of risk looks at the potential benefits of maintenance over the next year it is unable to capture the benefits of maintenance done on wood poles 70 ia GB Risk Reduction 1000 Labor 100 Hours B cost 1000 0 Wood Pole Replacement Wood Pole Reinforcement J Figure 6 3 Risk reduction obtained due to wood pole maintenance 6 3 3 Tree Trimming Maintenance When data such as tree density and precipitation are available existing models 13 can estimate the vegetation related failure rate for each feeder These were not available for the example system Instead it was assumed that 35 percent of overhead failures were caused by vegetation Thus the total overhead failure rate of each feeder is multiplied by 0 35 to obtain the vegetation rela
103. med at restoring service to customers in the shortest possible time Preventive vegetation maintenance is done before a failure actually occurs and may include the following e Tree trimming which is the most common vegetation maintenance activity Most utilities follow a three to six year cycle of trimming whereby a specialized crew identifies vegetation overgrowth and trims to prescribed standards e Tree growth regulators These are chemical agents used to slow vegetation growth rates and are typically used after trimming to slow regrowth e Tree removal Utilities also remove trees that threaten the system sometimes replacing them with shorter slower growing species e Spacer and tree cables Insulated overhead conductors are used in areas requiring higher reliability and in regions where accessing the right of way is difficult These cables allow vegetation to grow closer to the conductors and reduce the number of outages 11 2 2 3 Inspection Methods To identify areas where tree related outages are likely to occur and to determine the proximity of trees to conductors utilities have inspection programs to assess vegetation near their circuits Vegetation is inspected visually often midway between two tree trimming cycles Remote sensing and laser imagery e g light detection and ranging LiDAR are also used Some utilities also have inspection activities that extend beyond the right of way These hazard tree programs identify
104. n problem for a specific category p of maintenance tasks Its results are used in a higher level problem Task selection is solved repeatedly increasing the budget each time by a specified increment until all candidate tasks in each category are selected or available resources are exhausted Task selection is repeated for each category p P resulting in a risk reduction vs budget table for each category as illustrated with example data in Table 5 1 Tasks are selected as illustrated by the binary strings in Table 5 2 where element k of a string indicates whether task k is performed 1 or not 0 Each cell in Table 5 2 corresponds to the cell in the same position in Table 5 1 Table 5 1 Risk reduction vs budget Risk Reduction from Different Budget Categories 91000 Wood Pole Recloser ee Trimming 0 0 0 0 1 4 2 3 75 2 25 9 19 8 13 5 14 4 10 20 7 13 5 15 Table 5 2 Decision variable code table Budget Profit from Different ategories 1 000 Wood Pole Recloser oe Trimming 0 000 000 000 000 000 000 1 010 100 101 001 100 010 9 100 110 110 101 010 101 10 110 011 111 100 110 110 Cells in the risk reduction table are denoted by Cat_ARisk i x corresponding to category i with budget allocation x To obtain the maximum risk reduction within the total budget constraint the budget planning subproblem is solved This
105. nd vegetation related outages is summarized as follows 46 a Input the failure rate of the component before and after maintenance and the resulting SAIFI and SAIDI values before and after maintenance b Determine the straight line equations for SAIFI and SAIDI as functions of the failure rate of the component c Specify the number of years to simulate d Determine the number of times the component fails each year by drawing uniform random numbers for each of the simulated years as in equation 4 12 e Determine SAIFI and SAIDI for each of the simulated years by using the linear relationship between the failure rate and the reliability index replacing the failure rate with the number of times the component fails during each year f Express the variability in SAIFI or SAIDI indices due to the variability in the component s failure each year as a probability distribution g Compute risk as an expectation of the probability distribution and the penalty curve PBR SAIFI as in equation 4 14 where PBR SAIFI is a piecewise linear function that describes the penalty as a function of the SAIFI for the year PBRF k PBR SAIFI f SAIFI k d SAIFI k 4 14 Tp h Keep in mind that equation 4 14 gives the risk of penalty before maintenance Repeating the computation using the failure rate after maintenance provides the risk of penalty after maintenance Risk reduction is the difference in risk before and after maintenance
106. nd wood poles The methods developed for these can be adapted to other distribution equipment Reliability Benefit Abenefit Abenefit Desirable Region Tentative Resource Allocation Figure 1 1 Reliability benefit obtained from various resource allocation levels 1 1 Asset Management Problem Asset managers allocate resources among various maintenance activities They are constrained by limited monetary and labor resources available for a broad array of maintenance activities This presents a set of challenges to the asset manager that can be broadly classified into three categories The first is how to identify and justify the resources needed for asset management Usually once a year each asset manager must make a case for the financial and human resources required to manage equipment for which he she is responsible His her argument is best made in terms of the benefit obtained from the resources allocated This establishes the total resources available to each asset manager Each manager must then decide how to allocate the available resources to different maintenance programs This secondary resource allocation distributes available resources from the first allocation to the different asset management programs For this the asset manager must understand how the total benefit from all programs changes as resources are shifted from one program to another The third problem is to select a set of maintenance projects
107. nitiation of an interruption to a customer until service has been restored to that customer Momentary Interruption A single operation of an interrupting device that results in a voltage zero Momentary Interruption Event An interruption of duration limited to the period required to restore service by an interrupting device Switching operations must be completed within a specified time of 5 minutes or less If a reclosing device operates multiple times within 5 minutes of the first operation then all of the momentary interruptions are classified as a momentary interruption event Outage The state of a component when it is not available to perform its intended function due to some event directly associated with that component An outage may or may not cause an interruption of service to customers depending on system configuration Planned Interruption Loss of electric power that results when a component is deliberately taken out of service at a selected time usually for the purposes of construction preventative maintenance or repair If it is possible to avoid the interruption then it is classified as a planned interruption Planned Outage The state of a component when it is not available to perform its intended function due to a planned event directly associated with that component Sustained Interruption Any interruption not classified as a part of a momentary event which would be any interruption lasting more than five minutes Relia
108. ns for wood poles An asset manager in planning financial resources for the next year must answer the following two questions How many poles need to be replaced How many poles need to be treated To predict the failed number of poles and thus the number of poles to replace the strength loss rate a is used to estimate the degradation level of the decayed pole in the future For example if a pole i has Lsp 0 3 it is estimated to reach a strength loss reduction of 0 33 and therefore fail within 0 33 0 3 0 014418 2 08 years 30 To predict failure times for poles not yet decaying the randomness at which healthy poles join the decayed population must be accounted for Equation 3 16 predicts the number of decayed poles The age distribution of the poles moves forward along the age axis in the next year meaning more poles are decaying at that time Table 3 5 presented the decayed pole percentage expected number of failed poles expected number of poles needing chemical treatment for future years 2006 and 2015 and the condition history of 2005 the current year This data together with replacement and treatment costs facilitate development of condition driven budgets by the asset manager Table 3 5 Population predictions Year Decayed Pole Percentage Failed Number of Poles Poles Need Treatment 2005 8 156 541 622 2006 8 479 549 633 2015 12 012 644 1030 Failure does not imply that the pole fa
109. ntenance The method does not however consider the effects of component failure or quantify the benefits of preventing failures Decisions are made solely based on equipment condition not its relative importance 1 2 4 Reliability Centered Maintenance RCM Reliability centered maintenance RCM is a preventive strategy that is being used increasingly by utilities In this method condition based measurements are used to determine the various components that require maintenance Maintenance projects are then ranked according to their effect on improving selected criteria One or more reliability indices are usually chosen as the criterion and maintenance projects are carried out to achieve desired target levels While traditional maintenance programs such as vegetation management recloser maintenance and maintenance of sectionalizing devices are considered as discrete and unrelated programs RCM provides a method to integrate a variety of programs and tasks with a single global objective of improving system performance 3 1 2 5 Risk Based Preventive Maintenance Risk based preventive maintenance methods further advance RCM 2 Failure probabilities estimated by condition monitoring methods along with the failure effects quantified by RCM methods are used to determine the risk associated with failure of a particular piece of equipment This risk is combined with the financial and human resource requirements to prioritize maintenance proj
110. nterruption duration frequency index is defined as SAIDI sum of customer interruption durations total number of customers served for a given time period The contribution of failure mode of component k to the system SAIDI is Nk 2 d SAIDI t k 1 4 At a 1 2 with units of average hours of interruptions per customer in time At The system SAIDI is the sum of the individual SAIDI contributions over all components amp and failure modes 1 3 1 2 Revenue lost by the utility ENS t k 1 4At Pad 1 3 j l 1 3 1 3 Cost of equipment failure DevRisk t k 1 A At Cost k 1 1 4 1 3 1 4 Regulatory penalties due to violation of regulatory limits The effects expressed by equations 1 1 to 1 4 can be directly computed using standard analytical methods 6 9 However due to increased regulatory monitoring of reliability indices it may be necessary for utilities to also estimate the risk of paying penalties that might arise from missed reliability targets In such scenarios it becomes necessary to estimate not only the average reliability indices for the system but also the variability in the indices 11 due to events that have low probability of occurrence with substantially high penalties The risk of penalties associated with each component may be defined as shown in equations 1 5 and 1 6 where PBRF t k l PBR SAIF1 f SAIFI t k 1 d SAIFI t k oa 1 5 PBRD t k l PBR
111. o programs and selection of maintenance tasks for the year Furthermore the subscript 1 indicating the maintainable failure mode can also be dropped without loss of generality assuming that each of the equations 1 1 to 1 6 represents the consequences of equipment failure due to a single maintainable failure mode Thus the simplified expressions for the risk associated with each component can be correspondingly written as shown in equations 1 7 to 1 12 SAIFI k Atk TE 1 7 i z SAIDI k AEE 1 8 ENS k a k S Pd 1 9 DevRisk k A k Cost k 1 10 PBRF k PBR SAIFI f SAIFI k jd SAIFI k r 1 11 PBRD k PBR SAIDD f SAIDI k d SAIDI k T 1 12 The consequence of equipment failure may be expressed as the sum of the quantities defined by equations 1 7 to 1 12 This sum comprises the risk associated with a component s failure The risk associated with a component varies with its failure probability If during the time period under consideration the failure rate of the component remains constant and is sufficiently low the failure probability in equations 1 7 to 1 12 can be replaced with the failure rate of the component Maintenance reduces the failure rate of a component and thus the risk associated with its failure The following expressions then can be used to define the effect of maintenance on a component ASAIFI k SAIFI k SAIFI k Ag k 20 A
112. oblem may be compounded by insufficient or inaccurate data or significant changes to the network configuration Because risk reduction computations depend on accurate component failure rate estimations the accuracy of the entire method depends on the quality of condition and historical data available But with the correct data even though the number of devices in a distribution system is very large the strategy can be effectively used to solve the resource allocation problem in a reasonable time and with sufficient accuracy 7 3 Further Work The reliability and inspection models developed should be further expanded verified and then adapted to other distribution equipment Specifically the wood pole degradation path model should be validated for other components with complex failure processes such as switches and transformers Similarly the inspection methods developed for reclosers should be applied to other components and the resulting failure rate estimates should be verified The problem formulation should be further enhanced by considering scheduling issues involved in equipment maintenance The result will provide a schedule of planned maintenance for a budget period The optimal resource allocation strategy sacrifices some accuracy to solve the large scale problem Further research involving other optimization techniques will help improve the accuracy of the solution obtained 76 References 1 IEEE PES Task Force on Impact o
113. od This technique is a mature and robust algorithm capable of solving integer programming problems to optimality In the general case the algorithm begins with a linear program identical to the original integer program except that all variables are relaxed to be real The problem is solved and then one variable is selected Two additional problems are formed one with the selected variable constrained to be zero and the other with the selected variable constrained to be one The two problems are solved and the one with the best objective value is selected as the next branching point From this point a new variable is selected and two new problems are again formed one with the selected variable constrained to be zero and the other with the selected variable constrained to be one At this stage then the two new problems have two variables that are constrained to be integers The process continues until a branching point is reached where there are no more real valued variables The algorithm terminates at this point 57 Computation time for the branch and bound method increases exponentially with problem size and it will not solve a large scale problem like the task selection problem in a reasonable time Sometimes stop criteria are introduced such as errors between upper and lower bounds or maximum number of nodes searched But it is still a time consuming method for large scale problems 5 2 3 ELPR LRH Method The method used in this
114. odel validation IEEE Trans Power Systems vol 13 issue 2 May 1998 pp 704 709 43 Y Li S Yeddanapudi J McCalley A Chowdhury and M Moorehead Degradation path model for wood pole asset management presented at the North American Power Symposium NAPS Ames Iowa 2005 44 IEEE guide for electric power distribution reliability indices IEEE Standard 1366 2003 edition 78 Appendix A Distribution Reliability Metrics A brief review of some of the standard definitions and indices used in distribution reliability evaluation are provided in this appendix The definitions provided here are found in the current Draft Guide for Electric Power Distribution Reliability Indices IEEE P 1366 2003 44 Definitions 10 Connected Load The connected transformer kVA peak load or metered demand on the circuit or portion of circuit that is interrupted Interrupting Device An interrupting device interrupts the flow of power usually in response to a fault Restoration of service or disconnection of loads can be accomplished by manual automatic or motor operated methods Some interrupting devices include transmission circuit breakers feeder breakers line reclosers fuses sectionalizers and motor operated switches Interruption The loss of service to one or more customers connected to the distribution portion of the system as the result of one or more component outages Interruption Duration The time period from the i
115. or multiple poles taken over multiple time instances Such measurements provide the ability to obtain pole specific degradation functions More common though is the kind that involves measurements for multiple poles taken at approximately the same time resulting in a single measurement per pole Although such data are inferior multiple measurements they may still be used to characterize degradation functions and from those to extract probabilistic failure indicators 27 28 29 Degradation Leading to Failure Loading on a wood pole varies with time as weather conditions mainly wind and ice change so the model should include these conditions 27 It is possible to use force analysis based on weather modeling to obtain a statistical load model 17 but in this report a simpler model is used The National Electric Safety Code requires that a pole be rejected when 33 percent of its strength is lost 18 Based on this requirement a pole is assumed to fail when its strength falls below a given percentage of its initial strength denoted by fp failure percentage to which a value of 33 percent is assigned After obtaining a group of Lsp t curves interpolation when the poles have lost more than 33 percent of their original strength or extrapolation is used to obtain the random variable lifetime LT The lifetime distribution cumulative function F t and the hazard function H t can be obtained by standard statistical methods 28 V
116. or them can result in significant cost differences Maintenance planning can be more cost effective if pole degradation can be predicted Such predictive capabilities provide the ability to estimate the number of required replacements in the next budget cycle Pole specific prediction provides the ability to determine which poles are most likely to need replacement If degradation information can be transformed to probabilistic failure indicators e g probability of failure and time to failure then the effect of wood pole maintenance on these indices can be evaluated These failure indicators can then be used in system level decision tools such as reliability evaluation programs to compare different maintenance related resource allocations among regions components and types of maintenance This section describes conversion of wood pole condition data gathered from the field into predictive functions and illustrates the use of these functions in developing probabilistic failure indicators 3 3 1 Degradation Path Model Approach Basis Wood pole failures occur as a result of physical stresses such as wind ice and vehicle impact The tendency of a pole to fail under such stress is usually related to the strength of the pole at the ground line where almost 90 percent of pole failures occur 15 Therefore the most useful indicator of wood pole condition is its residual strength at the ground line 24 This strength is usually measured as the eff
117. ource allocation levels 1 Figure 1 2 Risk based resource allocation for distribution systems csceeseeeeeeeeees 5 Figure 3 1 Recloser score vs failure Tate sires cds io sent is vteteauunt meas aaa iaa aetna 19 Figure 3 2 Computing contingency probability reductions 0 00 0 ceeeeeseeeeeeeeeeneeeneeeeees 22 Figure 3 3 Flow chart of degradation model approach eeceseeseeneceeeeeteceeeeneeeneeerees 25 Figure 3 4 Number of poles at every age of the decayed population 0 0 0 eeeeeeeees 27 Figure 3 5 Decayed population Lspi t plot ccscccosscrsccsssssrsssecsassrscenteencscncesseosetes 28 Figure 3 6 The average degradation level at every age sssesssesesssssssessessersesseseesesseseese 28 Figure 3 7 Percentage of decayed pole at every age isc ci tsencsteiviadssossstecaesateviviniss 29 Figure 3 8 Hazard function of decayed poles cecccecssccsseceseceeeeeeeeceseceeeeeseeeeseeesaeenes 30 Figure 4 1 Variation in SAIFI before maintenance of Wood pole ceceeeeeeseereeeeees 48 Figure 4 2 Variation in SAIFI after maintenance of Wood pole eseeeeceeteeneereeeeees 48 Figure 4 3 Variation in SAIFI before tree trimming 00 0 eee eseeeeeeeeeeecesecneeeeeeneeeees 49 Figure 4 4 Variation in SAIFI after tree trimming 00 0 0 eeceeceseeeeeeneeeeeeeeecneeeeeeneeeeees 49 Figure 4 5 Variation in SAIFI before recloser maintenance ceceecceeeceseceeeteeeeeeeeees
118. ponding sensitivities due to maintenance Outputs appear in the spreadsheet as indicated in Table B 1 Macro name reliability_evaluation rate _assi gn N reliability evaluation Macros in All Open Workbooks 7 Description Perform reliability evaluation on the feeder l AUTOMATED MODE OF OPERATION In the automated mode failure and repair parameters can be assigned to feeders grouped as rural or urban feeders Reliability evaluation can also be performed on the entire system These functions can be performed using the Automate Control xls spreadsheet provided Open the file Automate Control xls To assign default failure and repair parameters for all rural feeders Go to Tools gt Macro gt Macros select default values rural and press Run Alternatively press Ctrl r Enter the reliability parameters as they were entered in the rate_assign macro 92 default_values_rural automate default values rural default_values_urban Macros in All Open Workbooks Description Macro recorded 12 25 2004 by sreerama Default Failure rate assignment to the Rural feeders To assign default failure and repair parameters for all urban feeders Go to Tools gt Macro gt Macros select default values urban and press Run Alternatively press Ctrl u Enter the reliability parameters as they were entered in the rate_assign macro Macro name default_values_urban automate default_v
119. r score sheet aiaia iiias 14 Table 3 2 Condition of typical failed recloser c xetiue scasceusdeedithemaradacdiacooiecaiemeeatates 20 Table 3 3 Score for recloser in average condition 0 00 eeeceesseceteceteeeeeeeeeeceeseeceaeeneenees 20 Table 3 4 Score for recently maintained reclOser eeceesceeecceeseeeeeceeeeeeeeeeseecsaeeneenees 21 Table 3 5 Population predictions vcsasgehgcesdvscies sav dcastsnsaranentacendaeatiatansarananiadenhatssecaaeinacsts 31 Table 3 6 Estimate of failure 2ate jscccs 3cciysisaccasisidccsiahsevasssedactvcaseserisnes ceded Wsaveneapetneanta 31 Table 3 7 Estimate of miaititenance GT Ct six checeseecssiegsu tes aasuccad sites ceepvared tea voee sta seqeentawnense 32 Table 4 1 Protection response of circuit breaker ec ceeeeseeseeeeteceteeeeeeeeseecsseenteeeaes 38 Table 4 2 Protection response of fuse sa cceicstscccetiadeeesaclsactesavevireeti cases aunts todieteenicedee 38 Table 4 3 Protection response Of reClOSer eeeceecseceseceseceeseeeseeceaeceeceeeeeeseecsseecsaeeneenaes 39 Table 4 4 Protection response of fuse with upstream reclOser 00 0 eeeeseeeseeeeceneceeeeeeees 40 Table 4 5 Protection response of sectionalizer with upstream recloser ceeeeeeeeees 42 Table 4 6 Switching response for upstream isolation cceccceseeeteceeeeeeeeeeseeeeseeeteeeees 43 Table 4 7 Switching response for downstream isolation eceeceeesceeseceeteeeeteceteeeees 44 Table4 8 C stomer d ta mers
120. re the system after the fault is cleared In order to develop a predictive reliability analysis method mathematical equivalents for each component in the system are required to represent their failure and repair characteristics Since the indices used to compute the risk reduction are associated with the effects of sustained or permanent faults temporary faults are excluded from the analysis The following is a list of parameters used to describe the reliability of distribution system equipment 1 32 4 1 1 Permanent Failure Rate p The permanent failure rate is a measure of the expected number of sustained or permanent outages of a component in a fixed duration of time usually one year Permanent faults require operating protective devices to clear them Customers downstream of the protective devices are interrupted and experience an outage duration equivalent to the time taken to repair the fault or determined by the switching and sectionalizing actions done after the fault is interrupted 4 1 2 Mean Time to Repair MTTR The mean time to repair MTTR a component is the expected time required to repair a permanent fault occurring on the component It includes the time it takes to identify the failed component travel to the fault location isolate the fault and carry out repairs before service is restored The MTTR for protective and switching devices however is the expected duration of repair for a component that fails to operate in
121. riplet ARisk k Cost k and Labor k l For every task variable select k l reflects whether the task is selected 1 or not 0 The triplets are input to the optimizer which identifies the values of select k 1 for all tasks that maximize the risk reduction subject to the resource constraints Budget p is the budget assigned to maintenance category p TotLabor p is the available labor in person hours in maintenance category p Totbudget is the total budget for all categories The optimization formulation has two steps The first is the task selection subproblem selecting tasks within resource constraints in each maintenance category The second is the budget planning subproblem allocating budgeted resources to the maintenance tasks The formulation of the task selection subproblem is as follows Max ye ARisk k l Iselect k 1 5 1 Subject to the following constraints E J Sel k Cost k 1 lt Budget p 5 2 gt Sellk I Labor k 1 lt TotLabor p 5 3 Iselect k 1 lt 1 k 1 2 N 5 4 55 The objective equation 5 1 is to maximize the total risk reduction The constraint equation 5 2 represents the budget constraint and equation 5 3 represents the available labor resource constraint The constraint represented by equation 5 4 indicates that each component is maintained at most once during the time frame This task selection subproblem is a low level formulation of the maintenance optimizatio
122. robability that a switching action takes place successfully as a part of the fault isolation scheme Switching actions may not occur because of mechanical failures inability to locate a switch failure of a crew to operate a switch or conditions such as overloading of feeders Thus SR is the probability that switching is performed based on the occurrence of a fault whose MTTR is greater than the time taken to perform the switching operations 4 1 6 Mean Time to Switch MTTS Mean time to switch MTTS represents the average time to operate a switch and isolate a faulted area This includes both the time to identify the faulted area and the time to operate the switch In the case of manually operated switches it also includes the time taken to travel to the switch s location 4 1 7 Probability of Failure PF In order to compute the reliability metrics for protective and switching devices like fuses reclosers and switches the average number of times the device was expected to operate and the number of times it was successful are required Since such data may not be available because such records often are not maintained device parameters like protection reliability reclose reliability and switching reliability may be approximated from the available data An approximate value for a devices probability of failure PF is estimated by using the ratio of the number of failures of a particular type of device to its number of operations
123. ronmental conditions This results in an important distinction in the nature of failure consequences The consequence of failure of a specific transmission component is time varying and influences the short term hourly as well as long term yearly reliability indices The failure consequence of a distribution component tends to be constant and thus can be well represented using the long term or yearly indices Figure 1 2 provides an outline of steps involved in the risk based resource allocation strategy as it applies to distribution systems Historical outage data and condition measurements are used to develop models that can predict equipment failure rates The failure models are used to estimate how much each maintenance task will reduce a component s failure rate The effects of a failure are then related to changes in reliability indices Failure rate reduction and the associated change in indices are used to compute the risk reduction associated with each maintenance task Finally tasks are selected and scheduled to maximize risk reduction subject to the resources available DATA ACQUISITION Develop failure models for individual components Evaluate failure rate reduction for each maintenance activity Compute risk reduction for each maintenance task Figure 1 2 Risk based resource allocation for distribution systems 1 3 1 Definition of Risk Every piece of equipment in the distribution system has a finite life
124. rs downstream of the fuse The frequency of the event is given by PR 1 PRr A while the duration of outage experienced by the customers downstream of the fuse is MTTR This is an event when the failure of the recloser goes unnoticed since the fuse successfully operates to clear the fault It must be included in the analysis however to completely describe the coordinated fuse recloser combination 39 f Recloser fails to open and the fuse fails to open resulting in the fault being cleared by the next device upstream of the recloser The frequency of this occurrence is given by 1 PRp 1 PRr A which is a very low and will be neglected in this analysis The interruption duration is MTTR MTTR MTTRa These six states completely describe a fuse coordinated with a recloser when a sustained fault occurs downstream of the fuse These events are summarized in Table 4 4 Table 4 4 Protection response of fuse with upstream recloser Recloser opens and recloses and fuse clears the fault with failure rate A and repair time MTTR Frequency PRa RRR PRp A Duration MTTR Customers interrupted Downstream of fuse Expected cost of failure PRe RRpr PRe A COF COF is cost of outage on faulted line segment Expected energy interrupted PRp RRr PRr A MTTR Lp Lp is load downstream of fuse Recloser opens and recloses fuse fails to clear the fault and recloser opens to clear the fault with failure rate A
125. s Thus the failure probability entered in this option includes failure to Open and failure to Reclose that are assumed to be equally likely A simplification The interface for fuses circuit breakers and sectionalizers is similar to that for reclosers These components have only one failure mode failure to open in response to a fault 89 CIRCUIT BREAKER 90 SECTIONALIZER Enter the Failure Probability Before Maintenance Enter the Failure Probability After Maintenance Enter the MTTR 1 75 Enter the Cost of Failure 400 SWITCH Enter the Failure Probability before Maintenance Enter the Failure Probability after Maintenance Enter the MTTR switch Enter the MTTS Enter the Cost of Failure In the switch interface shown switch failure probability is the probability that a switch fails to switch when needed The MTTR and mean time to switch MTTS represent the average repair and switching times in h The switching characteristics of protective devices are not included in the rate_assign macro The values MTTS and switching reliability SR the probability that a device is switched when required are entered in the spreadsheet in columns 25 and 26 respectively 91 To compute the reliability of the feeder Go to Tools gt Macro gt Macros select reliability evaluation and press Run Alternatively press Ctrl r This computes the reliability indices of the feeder and the corres
126. s about 20 percent of sustained distribution outages most of which are of short duration Growth related failures are maintainable and can be effectively controlled through regular tree trimming 11 Tree failures occur when branches or entire trees break and come into contact with the power carrying conductors resulting in short circuited or downed conductors Trees outside the actual right of way may fail and cause outages which makes maintenance more difficult because utilities have limited authority outside of this area Tree failure causes about 40 percent of all sustained distribution outages These faults are often more severe and take longer to repair Some tree failures are preventable and thus maintainable that is if the tree shows external signs of decay or degradation If identified these failures can be corrected by providing structural support or removing dead or weak branches Other tree failures such as those caused by severe weather may cause extensive damage to the distribution network Such failures which account for about 40 percent of all tree related outages 12 are not maintainable 2 2 2 Maintenance Actions Corrective maintenance refers to repair activities done to restore the system after a fault Crews are dispatched to locate the fault and remove the branch or tree from the circuit They should also clear any overhang that may come in contact with the lines in the near future Such maintenance is local and is ai
127. s analysis The duration of interruption for this event is MTTR MTTRs MTTRa Recloser fails to open so the fault is cleared by the backup protective device All customers downstream of the backup device are interrupted The frequency of this event is 1 PRr 4 while the duration of interruption is MTTR MTTRe 41 Table 4 5 Protection response of sectionalizer with upstream recloser Recloser opens sectionalizer opens to isolate the fault and recloser recloses Frequency PRp PRs RRp A Duration MTTR Customers interrupted Downstream of sectionalizer PRr PRs RRp A COF COF is cost of outage on faulted line Expected cost of failure segment Expected energy interrupted PRr PRs RRr A MTTR L gt L is load downstream of sectionalizer Recloser opens sectionalizer fails to open and recloser opens again and locks out to clear the fault Frequency 1 PRs PRp A Duration MTTR MTTRs Customers interrupted Downstream of recloser 1 PRs PRp A COF COF p where COFp is cost associated with failed sectionalizer 1 PRs PRp A MTTR MTTRs Ls where Ls is load downstream of recloser Recloser opens sectionalizer fails to open and recloser fails to open again to clear the fault This event is not modeled due to very low probability Recloser opens sectionalizer opens to isolate the fault but recloser fails to reclose causing outage to all downstream customers Expected co
128. s method can also be used to determine if the current trimming cycle is adequate Information that utilities maintain about tree related outages is generally obtained from an outage management system Such information may include the location date and time when the outage occurred the time it took to repair the problem the number of customers interrupted and the time when service was restored There is often however no information about the failure mode or maintenance performed Parametric failure rate models require information on each of these factors for individual feeders Because such information is often not available the use of non parametric models may be necessary Non parametric models only require historical outage information and information about when the feeder was trimmed 12 2 3 Wood Poles Wood poles keep energized conductors and equipment away from the public and the ground and maintain separation between conductors Poles also serve as a support platform for equipment such as capacitors regulators and reclosers 14 2 3 1 Decay of Wood Poles Wood poles decay both internally and externally Most decay is just below ground level where moisture temperature air and absence of direct sunlight are most favorable to the growth of fungi This portion of the pole is also hidden from view and is close to its natural breaking point under strain Thus it is the most critical part of the pole and warrants special inspect
129. so known as the run to failure strategy corrective maintenance involves no maintenance of equipment until it fails Once a component fails it is replaced with a new or repaired component This strategy can be disastrous in terms of reliability and can result in costly regulatory penalties Most utilities have evolved from this method and use one or more of the following preventive maintenance strategies 1 2 2 Time Based Preventive Maintenance Unlike corrective maintenance preventive maintenance is done on equipment before a failure occurs thus improving its condition and increasing the time before its next failure In time based preventive maintenance a fixed time period is associated with each piece of equipment after which it is replaced or maintained This period is based on Program A budgetary category within the asset management group Programs are typically identified by a geographical region or type of equipment e g tree trimming recloser maintenance wood pole maintenance for a city or county etc Projects A set of tasks within a particular program e g tree trimming for three feeders in a city wood pole maintenance that may comprise of reinforcement or replacement for ten segments etc analysis of failure statistics and may use trial and error methods expert judgment or more analytical methods to estimate the optimal frequency of maintenance that is both economical and reliable at acceptable levels The use of fixed
130. sse 2 3 3 3 MMOS HA OM cas do cnccen e aa erent ane AT rates 27 Reliability Evaluation for Distribution Systems sessesessseseesesseseesesseserssssersessesee 33 4 1 Parameters Used in Reliability Modeling of Distribution System Equipment 33 4 1 1 Permanent Failure Rate p eseeeessessssseseesesesrssrseserrertsrsseseseererrnreesesesreee 33 4 1 2 Mean Time to Repair MTTR esssssesessssessssessssessessesseessesrrsseessesersseesse 33 4 1 3 Protection Reliability PR i x seccsiase cs Bavmstsdtee tere diate ncaetviies teers 34 4 1 4 Reclose Reliability RR is caivacssecssustsncosase coadnaanviavas ise atucssootenn teusieatsees 34 4 1 5 Switching Reliability SR e ui igaacvccBecstaecsisybatieetaatinnesaantettew 34 4 1 6 Mean Time to Switch METS ssscctsticcsetiisstscci tees liakscerse ee heen 34 iv 4 1 7 Probability of Failure PP cs ccaconeecactuacaae quscskee detente 34 4 2 Models Used inthe Programserie iaria i i ait 36 4 2 1 Overhead Line and Underground Cable Segments sssssessesseese0ss000 36 4 2 2 Fuses Reclosers and Breakers cccceccccscsscsccccessesssssessceseeseesssseesess 36 4 23 SWEDES Daaa ites u a a aaa a tae A a a aN a ace 36 ADA SECHOMAHZETS seii en e a i eaters ween aa aaia 37 4 2 5 Equivalent Component s ssesseesseeseeseesseeseseesseeseesresseesesersseeseesersseesse 37 4 3 System Response 10 Outat CS aA e ntl a aa A Wha at 37 MSN AZTEC Breaker onen e E E a E a a eae ho Deve 37 4 3 2
131. st of failure Expected energy interrupted Frequency 1 RRp PRs PRR A Duration MTTR MTTRe Customers interrupted Downstream of recloser 1 RRp PRs PRpR A COF COF p where COF is cost associated with failed recloser 1 RRp PRs PRR A MTTR MTTRag Ls where Ls is load downstream of recloser Expected cost of failure Expected energy interrupted Recloser fails to open Frequency 1 PRp A Duration MTTR MTTRag where MTTRg is recloser s expected repair time Customers interrupted Downstream of backup protection device 1 PRp A COF COF where COFp is failure cost associated with failed recloser 1 PRp A MTTR MTTRp L z where Ly is load downstream of backup device Expected cost of failure Expected energy interrupted 4 3 6 Switching After these devices operate distribution circuits are switched to isolate the faulted portion of the system and restore power to as many customers as possible in the shortest possible time In the previous sections protective devices and their fault responses were modeled In this section two such switching modes are modeled upstream isolation and backfeeding or downstream isolation 4 3 6 1 Upstream Isolation In an upstream isolation scheme the upstream switch nearest to the fault is opened after the fault is interrupted The interrupting device is then reset closed This reduces the outage duration to t
132. stomize gt Toolbars and check the box for Visual Basic Then add the resulting VBA toolbar to the tools The reliability evaluation software comes as a zip file that contains the following files 1 A folder named Backup with the updated Visual Basic macros and user forms 2 Spreadsheets for six individual feeders Feederl Feeder2 Feeder6 Each describes the topology of one feeder in the distribution system being analyzed Table B 1 describes the layout of these spreadsheets To create or add new feeders to the existing system of six feeders copies of any of the feeder files can be used 3 Special function files a Automate Control xls provides the interface and platform for performing reliability evaluation on the entire distribution system It can also be used to assign failure and repair parameters to various feeders urban or rural Please do not rename delete or move this file from the folder b Master_file xls Contains the default values of failure and repair parameters of various distribution components Sheet 1 stores all the default values for the rural feeders Sheet 2 stores the values for urban feeders Please do not rename delete or move this file from the folder c Results summary xls Updates the results obtained from a reliability evaluation done on the entire system It also computes the sensitivities of the various reliability indices when maintenance is done on a particular component Please do not rename
133. subproblem is formulated as follows Max 2 Cat _ ARist i x 5 5 56 Subject to the following constraints yg lt TotBudget 5 6 x 0 1 Vi 1 5 7 5 2 Possible Solution Methods for Task Selection Subproblem The task selection subproblem is an integer programming problem that is known for its difficulty Three different solution methods were tried prioritization branch and bound and enhanced linear programming relaxation ELPR with the Lagrangean relaxation plus heuristic method LRH All three are summarized here and the ELPR LRH method is selected because it provides a better solution without a significant increase in computation time 5 2 1 Prioritization Method For optimization using prioritization the cost effectiveness ratio index is defined as p ARisk k 1 Cost k 1 5 8 The prioritization algorithm is as follows a Obtain R for each candidate task b Rank all candidate tasks by R c For maintenance tasks on the same component select the task with the highest ranking and eliminate all others from the list d Select tasks from the top of the ranking list until the cost limit is reached available labor resources are used up or the reliability target is reached This algorithm is very fast and easy to perform but there is no elegant way to apply constraints 5 3 and 5 4 5 2 2 Branch and Bound Method Most integer programming optimizations are solved with the branch and bound meth
134. sulting improvement in reliability indices The tasks are prioritized subject to the constraints on available resources using an optimization technique combining integer programming Lagrange relaxation and dynamic programming The method is demonstrated in Section 6 using data from an actual distribution system This method assists in answering the three concerns commonly faced by an asset manager 1 How to identify and justify the resources needed for managing the assets of the entire system 2 How to allocate the available resources to different maintenance programs 3 How to select a set of maintenance tasks to be performed within each maintenance program A degradation path model to estimate failure probability and probability reduction was developed This model was applied to wood poles to predict individual pole failure probability based on condition measurements that represent degradation in the pole s residual strength A condition assessment technique was developed for reclosers A check sheet for evaluating a recloser s condition either in the field or in the shop is provided The condition score is then correlated with historical data to provide an estimate of the recloser s failure rate Maintenance changes the recloser s condition and thus its failure rate Similar techniques can be applied to other distribution system components 75 7 2 Conclusions The risk based approach to maintenance scheduling integrates in
135. t hours Phase configuration of segment For segments with protective device contains unique identifier for protective device Same as column A BRK FUS REC SWI SZL For a CLOSED device same as column D for an OPEN switch same as column A Value between 0 00 and 1 00 Value between 0 00 and 1 00 Average time to perform switching hours Value between 0 00 and 1 00 CLOSED OPEN For a CLOSED device same as column B for an OPEN switch same as column C 83 AC AD AE AF AG AH Al AJ AK AL AM AN AO AP AQ AR AS AT AU AV AW MTTR of device Cost of device failure Expected number of customers affected before maintenance Expected number of customers hours interrupted before maintenance Expected energy interrupted before maintenance Expected cost of failure before maintenance Expected number of customers affected after maintenance Expected number of customers hours interrupted after maintenance Expected energy interrupted after maintenance Expected cost of failure after maintenance SAIFI i SAIDI i Delta SAIFI i Delta SAIDI Delta ENS i Delta COF i PRa Recloser RRa Recloser Delta SAIFI i Delta SAIDI Delta ENS i Delta COF i Average repair time of device hours Cost of failure of device Column left blank output of program Column left blank output of program Column left blank output of program
136. tation and wood poles 2 1 Reclosers Reclosers are very reliable devices that seldom fail When failures do occur however they can lead to widespread outages and damage that significantly affect reliability indices and costs Thus many utilities use time based preventive maintenance for reclosers scheduling maintenance for all reclosers on the system every three to five years Reducing the frequency of maintenance by using a risk based methodology may significantly reduce recloser maintenance costs 2 1 1 Failure Modes Failure of reclosers can occur in four different modes a Failure to open b Failure to close reclose c False trip d Failure to lockout Most failures are caused by improper settings Causes of recloser failure fit within these four modes and most can result in more than one type of failure mode Causes of recloser failure can be classified as follows Mechanical moving parts including linkage plunger and contacts Electrical insulation including bushings stringers and oil Structural which addresses the integrity of the tank Improper setting or placement of a recloser e Electronic for electronic reclosers Preventive maintenance is performed to reduce the probability that these will occur aor 2 1 2 Maintenance Practices All but the very simplest recloser maintenance must be done in a shop therefore the recloser must be removed from service When a recloser is removed another recently servi
137. te for wood poles and il reclosers using condition measurements obtained from either continuous monitoring or from periodic inspection and testing These methods also estimate the reduction in failure rate by maintenance task for each component 3 Risk reduction due to maintenance Using information on failure rate and its reduction by maintenance task risk reduction was estimated with a reliability assessment tool developed in this project 4 Maintenance task selection and prioritization Risk reduction estimates form a pool of candidate maintenance tasks along with their resource requirements The system selects and prioritizes maintenance tasks based on the risk reduction obtained Constraints on the optimization include the maintenance budget and level of labor resources An integer programming optimization technique was developed for the selection and prioritization of candidate maintenance tasks A degradation path model to estimate failure probability and probability reduction was developed This model was applied to wood poles to predict individual pole failure probability based on condition measurements that represent degradation in the pole s residual strength A condition assessment technique was developed for reclosers A check sheet for evaluating a recloser s condition either in the field or in the shop is provided The condition score is then correlated with historical data to provide an estimate of the recloser s
138. ted produced a higher than average failure rate 19 Table 3 2 Condition of typical failed recloser 2 Score 0 1 Criteria Pre Maintenance Age of Oil 20 0 Duty Cycle Rate 20 0 5 Environmental Factor 20 N A Oil Dielectric Strength 15 N A Condition of Contacts 15 N A Age of Recloser 10 0 65 Experience with this Recloser Type 10 0 7 Condition of Tank 5 0 4 Sum 65 25 5 Weighted Average 0 392307692 Next a recloser in near average condition was scored as shown in Table 3 3 Table 3 3 Score for recloser in average condition z Score 0 1 Criteria 3 Pre Maintenance Age of Oil 20 0 33 Duty Cycle Rate 20 0 9 Environmental Factor 20 N A Oil Dielectric Strength 15 N A Condition of Contacts 15 N A Age of Recloser 10 0 65 Experience with this Recloser Type 10 0 9 Condition of Tank 5 0 65 Sum 65 43 35 Weighted Average 0 666923077 This score produced the estimated failure rate of 20 Hh 0 95 0 667 0 95 0 31 0 00867 which is close to the system average failure rate of 0 01048 Finally Table 3 4 shows scores for a relatively new recloser that underwent scheduled maintenance about a year before it was scored This is indicated by the age of the oil in the recloser The recloser is not expected to complete a duty cycle before the oil is due to be changed again Table 3 4 Score for recently maintained recloser
139. ted failure rate before maintenance This failure rate is then reduced to 40 percent of its original value to get the failure rate after maintenance Figure 6 4 illustrates the potential benefits obtained by implementing tree trimming programs on distribution feeders It may be noted that the cost of maintenance in this case is proportional to the length of the feeder The cost of performing tree trimming in the case of Feeder 2 is nearly twice that of Feeder 3 even while the risk reduction obtained may be comparable 71 So Jo B cos caooo o l Labor 100Hours aa Si BB Risk Reduction 10008 Feeder6 Feeder7 Feeder 8 Feeder Feeder2 Feeder 3 Feeder 4 Feeder 5 Figure 6 4 Risk reduction due to tree trimming at a feeder level 6 4 Optimization 6 4 1 Three Level Questions The optimization procedure solves the task selection problem first and then the budget planning problem It is common practice in industry however to first set the total maintenance budget and then distribute that budget to the maintenance categories The solution for the example system is presented in that order More examples are presented in the Optimizer User Manual in Appendix C Figure 6 5 displays the calculated risk reduction for the example system versus the total maintenance budget which is the solution to the budget planning problem Each increment of the budget is allocated to the activities that produce maximum risk reduct
140. tems Engineering Research Center Arizona State University 577 Engineering Research Center Box 878606 Tempe AZ 85287 8606 Phone 480 965 1643 FAX 480 965 0745 Notice Concerning Copyright Material PSERC members are given permission to copy without fee all or part of this publication for internal use if appropriate attribution is given to this document as the source material This report is available for downloading from the PSERC website 2006 Wichita State University and Iowa State University All rights reserved Acknowledgements This is the final report for the Power Systems Engineering Research Center PSERC research project titled Risk Based Maintenance Resource Allocation for Distribution System Reliability Enhancement PSERC project T 24 We express our appreciation for the support provided by PSERC s industrial members and by the National Science Foundation s Industry University Cooperative Research Center program We are particularly grateful to MidAmerican Energy the National Rural Electric Cooperative Association and the Minnesota Valley Cooperative Light and Power Association for supplying data used in some parts of this project Executive Summary Distribution systems are maintenance intensive so maintenance budgets are a substantial share of costs for distribution businesses Maintenance budgets are high in part due to the size of the systems and the number of people that it takes to properly maint
141. terruption duration for customers downstream of switch MTTR Interruption duration for customers downstream of MTTR protective device and upstream of switch Expected energy restored None 4 3 6 2 Backfeeding Another method of reducing the outage duration experienced by customers during a sustained interruption is through backfeeding Normally open switches are closed while normally closed switches are opened to provide alternative paths for service to customers Thus when a sustained outage occurs the nearest NC switch downstream of the fault is opened and an NO switch located further downstream of the circuit is closed restoring power to the segments in between the switch pair NO switches may connect to other parts of the faulted feeder or to an adjacent feeder when closed The expressions for the expected outage duration and energy restored are similar to those for upstream switching If SRyo and SRnc are the switching reliabilities of the NO switch that is closed and the NC switch that is opened respectively then SRseg SRnc SRno represents the switching reliability of the sequence to restore service to customers downstream of the NC switch The equivalent switching time is MTTS a MTTS xe MTTS ye MTTS yo The outage duration for restored customers is 43 MOT SR MTTS 1 SR MTTR hours seq where MTTR is the time to repair the fault Table 4 7 describes the states associated with
142. tion Path Model Figure 3 5 plots the lost strength percentage for each pole as a function of pole age t represents a specific pole s degradation level at its for the decayed population Each point given age 1 0 9 0 8 0 7 0 6 0 5 0 4 H 0 3 Strength Loss Percentage 0 2 Pe Ta 0 1 oe 0 T 7 bd T qt K TEA e g So 20eg o ees wf ee sh te 33095988 52338 bet Ss eae gt Fiddi bid Ftit ta ia fy en Soconebeptedbfoigfense os 1 1 0 10 20 1 30 60 Age 40 50 70 Figure 3 5 Decayed population Lspi t plot From the data illustrated in Figure 3 5 for each age the average lost strength percentage was computed using the lost strength percentages for all poles of the given age The resulting averages are plotted against pole age in Figure 3 6 0 9 0 8 0 7 OG OSacosts seats 0 4 Strength Loss Percentage 0 3 0 2 0 1 Figure 3 6 The average degradation level at every age Figure 3 6 indicates that the average degradation trend of the population is nearly a straight line Therefore as shown in equation 3 4 the degradation path for the decayed model of the lost strength percentage mean population is represented using a linear 70 Age Lspm t a t a2 where the random variable a is calle d the mean strength loss rate After removal of several outliers regression is used to obtain
143. tion for Predictive Analysis 64 6 2 2 Results nra aaa a a ae aaa a ii ia 65 0 2 3 DISCUSSION sit csc e aa a e a vas AEE vi Senco uaceo aR aoe 66 6 3 Computation of Risk Reduction w 2 ccnvnunascigeeaucee eee aes 67 6 3 1 Recloser Maintenances 3 33 8csesarisastccarchsesaategacteaevariemineaseceaci ances 68 6 3 2 Wood Pole Maintenance 25 54 essaktiesccdaendechiwntannentenreainad ween 69 6 3 3 Tree Trimming Maintenance ast pica yes ted cues code tanta etal ora ceune ed atta ends colar 71 GA NATTA ALN at oa erick cede coe cates acl ys detec wastes os bose Saati voce de vac A E 72 G4 Three Level Quests sireisas A AA REE ai 72 6 4 2 Labor Sensitivity Analysis i 0 sceisszccuxesstcaavdssgeceessevacresueccaneusecwussbarccies 74 CONIC IIS TOT Siete vast n a e aero tune ea banca atealuades aad cen ao wees aS 75 are SURVEY aah n a a Sea he alain San ales es a At Sale uaa ak hoe ad Seah Pale ota 75 T2 Conclusions anand i a a a a aA 76 13t F rther Work ja ceavsseselanatinassanlinasd ans aiaa icanhandtnabaantassaustaanlaateatoamaeants 76 References i gach a ae Oa ee las eae Teh aces 71 Appendix A Distribution Reliability Metrics ss snssseessesesseessesseseesseesreseesseessesressesse 79 Appendix B User Manual for Reliability Evaluation Tool essesssesseeseesesseseesesseseese 82 Appendix C User Manual for the Optimizer 0 cc ceccescceeseceeeceeeceeseeceeeceeeneeeeeseeeaeens 95 List of Tables Table 3 1 Reclose
144. tions thus correlate well with the actual system reliability and can be used to calculate the benefits of maintenance and associated risk reduction In this section risk reduction computations are performed for the example system The results are then provided to an optimizer to allocate resources as discussed in Section 1 1 Table 6 9 lists the available maintenance tasks Three categories are considered wood poles reclosers and tree trimming Each category has its own labor pools There are 5 026 wood poles on the system so there are 5 026 candidate tasks in the wood pole category There are 252 candidate tasks in the recloser category and 66 candidate tree trimming tasks This produces a total of 5 344 triplets The risk reduction introduced by each is calculated and the financial and labor costs are obtained These are input to the optimizer 67 Table 6 9 Failure modes and corresponding maintenance activities Contingency Failure Modes Maintenance Activity Maintenance Level Cost of Failure Distribution Tree contact Tree trimming Feeder based 500 outage line outage Pole failure Pole treatment and Segment based 200 replacement Recloser Failure to open Minor maintenance Component based 25 000 failure and failure to major maintenance and reclose replacement Regulatory penalties are assumed to be as follows e 25 000 if a feeder SAIFI exceeds 3 0 sustained outages customer year e 75 000 if
145. velop the statistical models to predict the failure characteristics of distribution equipment and evaluate the effects of maintenance They also provide the basis for modeling various distribution components for the predictive reliability evaluation and a reference or benchmark for the predictive reliability evaluation method The predictive reliability evaluation is followed by the computation of risk reductions for various maintenance tasks which are then optimized to provide the asset manager with solutions to resource allocation problems This chapter describes the results obtained from the historical analysis predictive analysis and risk reduction computation shaded boxes in Figure 6 1 for the example feeder Develop Statistical Failure Models for Individual Components Historical Outage and Maintenance Data Historical Reliability Network Topology including Evaluation Load and Customer Data Predictive Reliability Evaluation and Failure Rate Adiustment Compute Risk Reduction for Each Maintenance Task Figure 6 1 Risk based resource allocation implementation 62 6 1 Historical Reliability Evaluation Outage history is used to calculate SAIFI and SAIDI 41 for a five year period from 2000 to 2004 They provide a reference to compare with those obtained from the predictive analysis The outage history analysis also forms the basis for the average failure rate and outage duration estimation used in the predictive analysis
146. vol 145 issue 2 Mar 1998 pp 149 153 8 D Koval Zone branch reliability methodology for analyzing industrial power systems IEEE Trans Industry Applications vol 36 issue 5 Sept Oct 2000 pp 1212 1218 9 T Gonen Electric Power Distribution System Engineering New York McGraw Hill 1986 10 R Brown and J Burke Managing the risk of performance based rates JEEE Trans Power Systems vol 15 issue 2 May 2000 pp 893 898 11 S Cieslewicz and R Novembri Utility vegetation management Trends issues and practices CN Utility Consulting LLC August 2004 12 S Guggenmoos Effects of tree mortality on power line security J Arboriculture vol 29 no 4 July 2003 13 D Radmer P Kuntz R Christie S Venkata and R Fletcher Predicting vegetation related failure rates for overhead distribution feeders IEEE Trans Power Delivery vol 17 issue 4 Oct 2002 pp 1170 1175 14 E Hill C Schwan and D Reny Doing a better job on maintenance Application of reliability centered maintenance to distribution systems Cooperative Research Network National Rural Electric Cooperative Association Report 98 11 2001 15 J Sandoz and O Vanackere Wood poles aging and non destructive testing tool 4th International Conference and Exhibition on Electricity Distribution Part 1 Contributions TEE Conf Publ no 438 vol 3 2 5 June 1997 pp 26 1 26 6 16 J Bodig R
147. y and asset management are assuming greater importance as utilities try to control costs while maintaining service quality Equipment maintenance and associated reliability improvements are important not only to ensure that equipment lasts as long as it should but also to ensure customer satisfaction and retention manage operating costs and comply with relevant service quality regulations Advanced strategies like reliability centered maintenance are being adopted by utilities to manage their vast amounts of assets Preventive maintenance reduces the failure probability of a component and hence reduces the risk due to failure of the component Each preventive maintenance task has both financial and labor costs The objective of this project is to maximize risk reduction obtained from maintenance within the available budget and labor constraints In the work presented in this report the following applies e Available reliability evaluation techniques are reviewed e Utility maintenance strategies are reviewed e A risk based resource allocation method is developed The proposed method uses information obtained from inspection and monitoring to determine the state of the system Available maintenance tasks are identified and the risk reduction provided by each is computed The risk reduction for each task is based on the condition of the component being serviced the task s effect on improving the component s condition of equipment and the re
148. year For example for pole 1 which is ten years old without decay the next year s failure rate is Per I 1 H 1 0 004 5 2 10 2 10 and its time to failure increase is Per 1 5 0 004 5 0 02 For this pole replacement and treatment have the same effect because this pole is in good condition to start For decayed poles such as pole 2 replacement will renew the pole so the failure rate reduction is H 4 5 0 01 and the increase in time to failure is its condition age of 14 5 31 years Treatment will stop the decay and the failure rate reduction seen in the next year is H 15 5 H 14 5 0 000 the increase in time to failure is 5 These procedures were applied to poles 1 through 4 with results summarized in Table 3 7 The results are reasonable maintenance activities on healthy poles have almost no effect but result in significant benefit on the most decayed poles Table 3 7 Estimate of maintenance effect Failure Rate Reduction Time to Failure Increase Pole Age failures year years replace treatment replace treatment P per year P 1 10 2 10 2 10 0 02 0 02 2 17 0 01 0 0003 14 5 5 3 39 0 0004 0 00015 11 7 5 4 42 0 01 0 0014 277 5 In selecting maintenance tasks an asset manager should consider not only the effect on failure rate and time to failure but also the consequences of failure in terms of the effect of each candidate maintenance task on system reliability indices such as S
149. zer interrupting the fault and then reclosing after the sectionalizer opens The reliability indices are not linearly related to PR and RR and can be deduced from expressions in Table 4 3 Table 4 4 and Table 4 5 The reliability indices however can be approximated with less than 5 percent error as varying linearly by assuming that the recloser s PR and RR are equal If reliability indices vary linearly with failure rates the risk reduction associated with maintaining each component can be obtained by computing the reliability indices before and after maintenance 4 5 Regulatory Penalty Risk Evaluation The definition of risk in Section 1 3 1 includes regulatory penalties A method to determine the regulatory penalty risk associated with the failure of a component is described here The computation of regulatory risk uses information obtained from the analytical evaluation The reliability indices SAIDI and SAIFI and the failure rates computed before and after maintenance of a component are used as inputs Because the indices are assumed to be linear the equations of the straight lines for SAIFI and SAIDI as a function of the component failure rate can be determined For wood poles and vegetation a vector of random numbers un is created in which n represents the number of years the simulation is carried out Assuming a Poisson distribution for the number of times a component fails in a given year the number of 45

Risk-Based Resource Allocation for Distribution System Maintenance

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