Failure rates in distribution networks: Estimation methodology and application

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Electric Power Systems Research, Vol. 185, on August 2020, available at: https://doi.org/10.1016/j.epsr.2020.106398 Copyright 2020 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND 1 Failure rates in distribution networks: estimation 1 methodology and application 2 J. A. Clavijo-Blanco 3 Escuela Superior de Ingeniería, Universidad de Cádiz, Avda. Universidad de Cádiz, 10, 4 Campus Universitario de Puerto Real, 11519, Cádiz 5 J. A. Rosendo-Macías * 6 Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los 7 Descubrimientos, s/n, 41092, Sevilla 8 Abstract 9 Electric distribution companies have the responsibility of achieving the 10 standards established by the respective regulating authorities in order to guarantee the 11 highest quality of supply for their customers. To do so, they have to register all the 12 electrical issues produced in the Distribution Network into a database. This paper uses 13 this real database to make a statistical analysis of the failures that occur in distribution 14 networks and identify the interruption causes, in order to estimate failure rates and 15 improve the quality of electrical supply. These failure rates are used to calculate the 16 failure probability of electrical feeders taking into account the different electrical 17 components in them. The expected amount of failures of more than 350 feeders have 18 been calculated and tested with the real database to prove the reliability of the method. 19 This work also shows an application to evaluate the failure probability of alternative 20 network configurations. 21 * Corresponding author. Email address: [email protected] (J. A. Rosendo-Macías) 2 Keywords: 22 Power system reliability, distribution networks, failure rates, electrical failure analysis, 23 breakdowns. 24 List of Abbreviations: 25 FLBS: Fuse load-break switches OPI: Oil-paper insulation IS: Isolation switches SCED: Substation common electrical devices LBS: Load break switch TR: Transformers M&PD: Maneuver and protection devices TTI: Thermoplastic and thermosetting insulated cable OL: Overhead lines UC: Underground cables 26 I. Introduction 27 Due to the liberalization of the electrical sector and the establishment of new 28 regulation systems, distribution network operators have to cope with more liabilities. A 29 large proportion of these systems, have the intention to ensure a reasonable network 30 operation and, at the same time, provide the electrical supply sustainability with the 31 highest quality as far as possible [1] . 32 It is broadly known that the electrical supply is not always available to provide 33 the demand due to technical and economic issues. In fact, the main feature of a power 34 system is to supply the required energy efficiently with acceptable levels of quality and 35 sustainability. The quality supply embraces three important aspects: customer service, 36 electric wave quality and sustainability of supply. The last one is related with the 37 number of power cuts, which affect the service reliability or the ability of the power 38 system to provide a suited and secure electrical supply in any network point at any time, 39 [2]. To quantify these concepts, some international quality indexes are widely used, e.g. 40 in [3], such as ENS, AIT, SAIFI, SAIDI, ASAI, and those in [4] - [5] . Other indexes 41 such as TIEPI and NIEPI [6] are also used in countries as Spain. These indexes allow to 42 3 evaluate the evolution of the continuity of supply and implement proper corrective 43 action plans for the electrical network. Moreover, if these indexes trespass the permitted 44 thresholds, electric power distribution companies could be sanctioned with an economic 45 fine. 46 These indexes depend on the duration of the interruptions and their frequency, 47 which is largely studied in this paper. In order to estimate the number of interruptions in 48 a future period of time, it is necessary to know the expected failure rates of the different 49 components that could cause a power supply cut. Some references, like [7]-[8], estimate 50 the failure rate of an electrical component as: 51 λ = #𝑓𝑎𝑖𝑙𝑢𝑟𝑒𝑠 #𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠∗#𝑦𝑒𝑎𝑟𝑠 =1 ETTF (1) 52 53 where ETTF is the expected time to failure. 54 Different authors have studied databases associated with continuity of supply [9] 55 and have shown the difficulty in having enough raw data to get reliable and meaningful 56 results, [7]. In general, failure rates of high voltage transmission lines seem to be based 57 on more representative data than in the case of medium voltage (MV) networks [10], in 58 which the reliability of their devices count only with a limited number of scientific 59 publications, [8]. 60 Preventive maintenance is currently gaining more interest since it is considered 61 as an efficient alternative to improve the quality of supply. For example, references 62 [11]-[12]-[13] show, through real cases, that the study of utility databases are useful to 63 draw up periodic maintenance plans for the electric network or to estimate electrical 64 quality indices [14]. 65 4 The paper presents an analysis of failure causes and a methodology to calculate 66 failure rates of the main equipment in a distribution network using the electrical utility 67 real databases. The so obtained failure rates improve failure predictions, not only 68 because of failure rates of aggregate components are obtained with smaller variation 69 ranges than in the generic bibliography [15], but also, because of a greater typology of 70 components can be considered. Since accuracy on the estimation on quality indices can 71 affect the compensation package for the electric utilities, as in Spain, real cases of 72 aggregate prediction have been tested in the paper, with successful result. 73 II. Description of databases 74 Two databases have been necessary for this paper, an incident database and a 75 network database. Both of them were analyzed during a collaboration scholarship 76 between the University of Seville and a major Spanish distribution company. 77 Spanish utilities are required by law to collect information about incidents 78 produced in their electrical network, which is saved in databases. 79 This paper makes use of unscheduled incidents occurred in the levels of 20 kV 80 and 15 kV in the city of Seville with duration greater than three minutes between years 81 2001 and 2013. These incidents were registered at two different centers: the Customer 82 Center and the Network Control Center, either from the SCADA system or manually 83 introduced. 84 Figure 1 shows the different incident types and the number of incidents 85 registered for each voltage level, in kV. 86 5 87 Figure 1: Record of incidents according to their nature 88 In this figure, the most frequent kinds of incidents are those caused by faults and 89 maneuvers for supply restoration, which together make 83% of the total. However, all 90 of them are explained by the fault incidents, since all the restoration maneuvers are 91 originated by their corresponding faults. 92 Nevertheless, not only it is important to know the number of power outages, but 93 it is also necessary to identify and characterize the faulty elements using the distribution 94 network length, the numbers of MV/LV substations and transformers, and the amount 95 of control and protection devices. These data are obtained from the network database 96 available in 2013. 97 From the later database, the state of the MV electric network in 2013 was easily 98 obtained; but the network status in the previous years was quite uncertain due to the 99 growth and evolution in time of the network from 2001 to 2013. Although the database 100 was upgraded while the network was growing, some data of this process had to be 101 purged for the sake of consistency: contrasting available cartographic data with the city 102 urban growth, and checking project documents, layouts and installations by experienced 103 utility technicians. 104 6 TABLE 1: Medium voltage installation evolution. 2001-2013. 105 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Underground cables (km) 1029 1043 1067 1081 1127 1118 1124 1126 1131 1146 1203 1236 1248 Overhead lines (km) 450 445 447 444 442 433 428 424 420 416 409 408 404 Transformers 3697 3727 3819 3881 3973 4102 4258 4431 4632 4736 4850 4641 4662 Isolating switches 878 867 872 865 861 843 832 826 818 809 796 795 783 Load-break switches 5607 5640 5785 5882 6023 6220 6467 6721 7006 7158 7327 7064 7098 Fuse load-break switches 2519 2533 2599 2642 2706 2795 2907 3020 3147 3214 3290 3176 3191 106 Table I shows the evolution in the amount of the most representative network 107 components over the studied period of time. These data reveal a growing trend of all the 108 components except for overhead lines and their associated switches, which are 109 decreasing due to the gradual substitution by underground cables. 110 III. Analysis and data pooling 111 To be able to attribute a failure rate to a network sample or element cluster, this 112 sample has to be representative in its population, which affects the way the electrical 113 components can be grouped. This population is considered as the broader group where 114 the statistical analysis results intend to be generalized. A representative sample should 115 be an unbiased representation of what the population is like. For example, there is no 116 sense in trying to assign annual failure rates to those components which are so specific 117 in the whole network that did not have any failure during the study period, which could 118 be considered as a case of data deficiency [16]. The common solution to data deficiency 119 is data pooling, including these components as part of larger groups with more 120 representative information. 121 In order to achieve proper representative samples while coping with population 122 variability [16], it is required to know the relationships between the different 123 7 components to be clustered. For this purpose, this paper considers the functionality and 124 the voltage level. 125 From 2001 to 2013, a total of 2972 failures were registered in 15 and 20 kV. 126 Figure 2 shows the evolution of the number of annual failures in the network for each of 127 the two voltage levels and makes clear that more detailed clustering can be made. The 128 proposed groups are underground cables, overhead lines, MV/LV substations, customer 129 installations, feeder protection and MV substations. Figure 3 shows the same number of 130 failures but classified according to these groups for each voltage. 131 132 Figure 2: Number of faults produced in the network. 2001-2013. 133 134 Figure 3: Number of failures according to electric MV network database groups. 135 8 From figure 3, it is clear that underground cables have most of the failures, 136 63.32% of the total. In this group, 26.87% of them are registered in 15 kV and 73.13%, 137 in 20 kV. 138 This study focusses on the three main groups (underground cables, MV/LV 139 substations and overhead lines) which already cover 90.54% of the failures and are 140 directly related to the electric network, not to the customer installation. 141 Underground cables 142 Failures in underground cables include failures along the cable and joints, and 143 are mainly caused by degradation of the isolation layer and excavation activities. Other 144 failure causes are related with animals, vandalism, maneuver failure, MV customers, 145 lack of maintenance, overvoltage, humidity, fire, rain and overloads. Figure 4 classifies 146 the failures in underground cables according to their causes, where material degradation 147 stands out with 59.78% of all the failures in this group. This percentage is even larger if 148 it is added the second more common cause, those failures made by construction work. 149 150 Figure 4: Underground cables failure groups. 2001 – 2013. 151 15 Data from 2001 to 2012 are used for failure rate calculation, while the data from 238 2013 are used for validation purpose. Depending on the kind of element or aggregation, 239 the generic expression for failure rates in (1) has to be adapted, that is, in the case of 240 lines or cables: 241 𝜆𝑖=#𝑓𝑎𝑢𝑙𝑡𝑠 𝑖𝑛 𝑙𝑖𝑛𝑒𝑠 𝑜𝑟 𝑐𝑎𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ (𝑘𝑚) (failures/km) (2) 242 And in the case of electrical devices: 243 𝜆𝑖=#𝑓𝑎𝑢𝑙𝑡𝑠 𝑖𝑛 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 𝑖 #𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑛 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 𝑖 (failures/cluster) (3) 244 In the case of underground cables, failure rates for each voltage level are obtained 245 taking into account that only failures by material degradation are linked to the 246 respective voltage level. 247 Table II shows, for each element cluster i, the annual average value, 𝜆𝑖 , the annual 248 maximum value, 𝜆𝑚𝑎𝑥, and the annual minimum value, 𝜆𝑚𝑖𝑛, of the failure rates of 249 period 2001-2012. Additionally, Table II includes relevant failure rates from [15] for 250 comparison purposes. But notice that the case of underground cables it not exactly 251 comparable with [15] since our failure rates do include failures in joints and connectors. 252 Also note that variation ranges in [15] are quite larger than those obtained from the 253 electrical utility databases. 254 An important issue is to know if annual failure rates are constant or show any trend in 255 the period studied. For this reason, a Laplace test has been applied according to [17] to 256 the elements in Table II. Results show that failure rates cannot be assumed as constant, 257 having, in some cases, a confidence for an upward or downward trend greater than 95%. 258 According with [15], a possible cause is the maintenance action planning, which can 259 16 vary the distribution of failures along the period of time. For this reason, authors have 260 assumed the sample means in this table as appropriate estimators for predictions. Lower 261 and upper bounds 𝝀𝑳 and 𝝀𝑼 for the 95% c.i. of E(𝜆) are also included in this Table. 262 TABLE II. Analysis of annual failure rates 263 Failure rates 2001-2012 Benchmarking [15] 𝝀𝒎𝒊𝒏 𝝀𝑳 𝝀  𝝀𝑼 𝝀𝒎𝒂𝒙 𝝀𝒎𝒊𝒏 𝝀 𝝀𝒎𝒂𝒙 Underground cables 15/20 kV 0.0777 0.1148 0.1335 0.1523 0.1902 0.0019 0.0435 0.3647 -/km TTI 15 kV 0.0235 0.0779 0.1026 0.1273 0.1670 - - - -/km TTI 20 kV 0.0919 0.1254 0.1444 0.1635 0.1853 - - - -/km OPI 15 kV 0.0469 0.0788 0.1218 0.1647 0.2823 - - - -/km OPI 20 kV 0.0360 0.0800 0.1312 0.1824 0.2921 - - - -/km Overhead Lines 15/20 kV 0.0244 0.0419 0.0514 0.0609 0.0744 0.0124 0.0621 0.1864 -/km Substation Common Electrical Devices 15/20 kV 0.0006 0.0020 0.0030 0.0040 0.0065 - - - -/unit 15 kV 0.0006 0.0017 0.0026 0.0034 0.0056 - - - -/unit 20 kV 0.0006 0.0021 0.0033 0.0045 0.0074 - - - -/unit Transformers 15/20 kV 0.0013 0.0023 0.0038 0.0053 0.0085 0.0010 0.0100 0.0500 -/unit 15 kV 0.0011 0.0024 0.0038 0.0053 0.0079 - - - -/unit 20 kV 0.0013 0.0022 0.0038 0.0055 0.0100 - - - -/unit Load-Break Switches 15/20 kV 0.0002 0.0007 0.0011 0.0015 0.0023 0.0010 0.0030 0.0050 -/unit 15 kV 0.0000 0.0005 0.0011 0.0016 0.0030 - - - -/unit 20 kV 0.0000 0.0006 0.0011 0.0017 0.0025 - - - -/unit Isolating Switches 15/20 kV 0.0023 0.0055 0.0079 0.0103 0.0138 0.0040 0.0140 0.1400 -/unit 15 kV 0.0012 0.0054 0.0078 0.0103 0.0139 - - - -/unit 20 kV 0.0000 0.0000 0.0094 0.0200 0.0572 - - - -/unit Fuse Load-Break Switches 15/20 kV 0.0000 0.0003 0.0009 0.0015 0.0028 0.0010 0.0030 0.0050 -/unit 15 kV 0.0000 0.0002 0.0006 0.0010 0.0021 - - - -/unit 20 kV 0.0000 0.0004 0.0011 0.0018 0.0032 - - - -/unit 264 Note that, failure rates of underground cables reported in [15] cover a wide range of 265 values with an average slightly lower than that of overhead lines. However, those 266 reported in this work, which include failures in cable elements such as joints, elbow 267 connectors and cable terminations, result in considerably higher averages but in a 268 narrower range. 269 According to this table, failure rate of TTI underground cables is very sensitive to the 270 voltage, having the highest value for 20 kV and the lowest value for 15 kV. Among the 271 failure rates of single units the isolating switches, commonly used in overhead lines, 272 have the highest failure rates due to their exposure to atmospheric agents. 273 17 V. Validation of results 274 An important use of failure rates in Table II is to estimate the expected number 275 of failures in MV networks. This estimation can be made for each MV feeder and later 276 grouped to obtain the expected number of failures in the network fed by a single 277 distribution substation, or even the whole electric network of a region. 278 To validate the usability of these failure rates, the MV network in 2013 will be 279 used to compare the real number of failures with the estimated one using failure rates in 280 Table II. 281 The considered network is designed as weakly meshed, with typical urban rings, 282 but operated radially, with a circuit breaker at the head of each MV feeder. So, in each 283 feeder, the expected number of interruptions in a year can be estimated by 284 𝑁𝐼 = ∑𝜆LINE_i ∙Li+𝑁𝑇𝑅 ∙ 𝜆TR +𝑁𝑆 ∙ 𝜆SCED +𝑁 𝐼𝑆 ∙ 𝜆IS +𝑁 𝐿𝐵𝑆 ∙ 𝜆𝐿𝐵𝑆 +𝑁 𝐹𝐿𝐵𝑆 ∙𝜆𝐹𝐿𝐵𝑆 𝑖 (4) 285 Where: 286  𝑖 is an index of the different line sections in the feeder 287  𝐿𝑖 is the length of section i 288  𝑁𝑇𝑅, 𝑁𝑆 , 𝑁𝐼𝑆, 𝑁𝐿𝐵𝑆 and 𝑁𝐹𝐿𝐵𝑆 are the corresponding number of transformers 289 (TR), MV/LV substations (S), isolating switches (IS), load-break switches 290 (LBS) and fuse load-break switches (FLBS). 291 Using the average failure rates from 2001 to 2012, the expected number of failures 292 in 2013 has been estimated for a total of 383 feeders. Figure 15 shows these estimations 293 together with the real number of failures in each feeder in 2013, where feeder labels 294 have been chosen according, first, to the ranking of real data, and in case of a draw, to 295 the ranking of estimations. 296 18 As can be seen in such figure, there is a disagreement between estimated and 297 real failures, which is even more clear in those feeders that have no real accidents in 298 2013 but have an expected number of failures. 299 300 Figure 15. Comparison between expected and real numbers of faults in each feeder in 2013. 301 However, if feeders are grouped by departing substation, a considerable 302 improvement of the prediction is noticed. Feeders have been clustered in a total of 29 303 substations, where the aggregated results are shown in figure 16. 304 305 Figure 16. Comparison between estimated and real failures grouped by substations. 306 Although there is still a small difference between estimated and real data, it can 307 be seen that these predictions are closer to real data than feeder predictions showed 308 19 before. Moreover, if all estimated predictions are added, the number of total failures 309 estimated in 2013 is 211 and the real one is 177, which shows good accuracy. 310 To achive higher reliability in the estimations, beyond the average failure rates 311 applied before, maximum and minimum failure rates, 𝜆𝑖 𝑚𝑎𝑥 and 𝜆𝑖 𝑚𝑖𝑛, are obtained to 312 estimate an interval where the number of real failures should be found. Using these 313 failure rates our worst-case and best-case scenarios for 2013 are 339 and 91 failures 314 respectively. 315 Figure 17 shows a comparison between real and estimated failures in 2013 based 316 on 𝜆𝑖  , 𝜆𝑖 𝑚𝑎𝑥 and 𝜆𝑖 𝑚𝑖𝑛. It can be observed that in the majority of substations the real 317 values are between the maximum and minimum estimated values. 318 319 Figure 17. Comparison of different estimated failure amounts in 2013 320 VI. Application case 321 As a practical application, the failure rates obtained above are used in a case with two 322 feeders, F1 and F2, fed by a substation in a ring arrangement. Both feeders are radially 323 operated and share an open load-break switch as electrical border point. Figure 18 324 shows the default operation configuration in which feeder F1 consists of underground 325 20 cable with cross-linked polyethylene cable (XLPE), and F2 is mostly an overhead 326 feeder. 327 328 Figure 18. Application case: feeders F1 and F2 329 The expected number of faults in each feeder has been estimated by clustering 330 all the electrical feeder components according to Table II and using their respective 331 failures rates λi , resulting in 2.849 and 0.772 failures/year respectively. If a lower 332 number of expected faults in F1 is required, the proposed alternative border point 333 location could be used to shorten feeder F1 at the cost of worsening F2, resulting in 334 1.909 and 1.712 failures/year respectively. With this methodology, the expected 335 number of faults of a whole distribution network can be obtained and used to assess its 336 quality of supply by estimating the System Average Interruption Frequency Index 337 (SAIFI) during a period of time [3], [14]. 338 VII. Conclusions 339 This paper reports the analysis of incident and network databases of 383 feeders 340 from an electrical distribution company in order to estimate element failure rates 341 adapted to the components in the databases, obtaining narrower variation ranges than in 342 the bibliography. Data deficiency has been faced using data pooling, by adopting up to 343 21 18 electrical component clusters with enough representativeness. Annual failure rates 344 of these clusters have been estimated and validated through their ability to predict the 345 aggregated number of failures of the studied network. 346 Finally, the estimated failure rates have been used in a case with two feeders in a 347 ring arrangement to illustrate the estimation of their numbers of faults and the 348 optimization of the electrical border point location. 349 The knowledge of detailed failure rates as presented in this paper allows the 350 distribution companies for better planning and operation when the quality of supply is 351 considered. 352 Acknowledgment 353 The authors want to thank the financial and technical support of ENDESA RED in the 354 framework of the chair ENDESA RED-University of Seville and the cooperation of 355 Luis Pérez-Morla Berrocal, as manager of the operation department of ENDESA. 356 References 357 [1] F. 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