Again about reliability characteristics of electrical power grids elements

The reliability characteristics of the (auto)transformers and overhead transmission lines of the unified national electric grid are subjected to statistical analysis. It is shown that their scheduled outages for scheduled or unscheduled repairs, as well as maintenance, weaken the network layout much more than emergency repairs. At the same time, there was a noticeable deterioration in the (auto)transformers and overhead transmission line reliability indexes over the last 30 years, which requires the development and adoption of appropriate organizational and technical solutions.


Problem description
Problem of power systems reliability performance existed before and continue to be relevant. One of its aspects is traditionally a research of reliability indexes of electrical grids. The most important are: failure intensity (preciselymean failure intensity or failure rate); mean restoration time; medium frequency µ and duration Т rep of scheduled repairs.
Reliability characteristics of (auto)transformers ((A)T) and overhead power transmission lines (OHL) were analyzed in many published papers [1][2][3][4][5][6]. On it may be concluded that their fault characteristics are roughly the same, despite different time periods of monitoring: from 1980s-era till the beginning of 2000s. It is to be supposed that the reason is that equipment failures are investigated thoroughly followed by development of organizational-technical measures of their prevention.
In its turn the information about reliability characteristics of scheduled repairs is less presented and it's often controversial. Published data about characteristics of (A)T scheduled outages and singlecircuit and double-circuit OHL is shown in the Table 1; Metal OHL supports are taken as a basis, as the most commonly used. Thus, frequency of (A)T scheduled repairs in [1] and [2] is defined as 1 1/year. It clearly says in [2], that it's periodicity of only current repairs. Therefore, medium and major repairs are left out of consideration. In [3] µ values are defined at a level of 6,3 1/year with reference to [4]. However, in [4] there was talk of scheduled commutations, i.e. total bringing into and withdrawal from operation count, from where frequency of scheduled repairs µ=6,3/2≈3,2 1/year. As one can see, inconsistent information about (A)T scheduled outages is presented in considered sources.  [4], which equals 10,0-14,8 1/year, i.e. sum of their switching on/off; it is clear, that frequency of OHL scheduled repairs from [4] will be twice as little, i.e 5,0-7,4 1/year. It can be assumed, that such significant spread in presented characteristics can't give an estimate of real reliability characteristics of overhead lines in terms of scheduled outages.  [4], which equals 10,0-14,8 1/year, i.e. sum of their switching on/off; it is clear, that frequency of OHL scheduled repairs from [4] will be twice as little, i.e 5,0-7,4 1/year. It can be assumed, that such significant spread in presented characteristics can't give an estimate of real reliability characteristics of overhead lines in terms of scheduled outages.
Only in works [2,5] there were undertaken a studies of scheduled outages of double-circuit OHL. But these works refer to period of late 1970sbeginning of the 1980s.
Thus, authors set themselves the task of throwing light on reliability characteristics of (A)T and OHL in main electrical grids from the perspective of real values of frequency and duration of scheduled repairs.

2
Reliability characteristics of (auto)transformers  Classification of scheduled outages of grid elements was proposed in [6]. (A)T outages were considered by analogy with: for carrying out scheduled or unscheduled repairs or maintenance of (A)T (group 1); for carrying out scheduled or unscheduled repairs, maintenance or reconstruction of allied equipment (group 2); Make notice that 'unscheduled repair' term was due to the fact that equipment is taken out from the service by an unscheduled dispatching form, but fundamentally it's scheduled outage. Whereby a common feature of scheduled outage is availability of certain period of time between making decision about outage and the moment of outage [6].
Number and duration of scheduled outages from table 4 is presented in table 5. As shown in table 5, scheduled outages connected with scheduled or unscheduled works on (A)T (group 1) constitute the major portion of outages (75-90%). There were calculated medium frequency and duration of scheduled repairs of (A)T according to table 5 datasee table 6.
Annually, (A)T 220-500 kV is scheduled taken out from the service more than twice (table 6). Thus, frequency of scheduled repairs (A)T from table 6 is close to values given in [4] about 50 years ago. But it should be noted, that actual medium durations and annual average durations of (A)T repairs turn out to be much greater than values published before. Thus, medium duration of a scheduled outage for (A)T 220 kV is 153 hours facing 30 hours shown in [1], for example. According to [1] failure rate of (A)T 220 kV is 0,014 1/year with mean restoration time of 250 hrs. Hereof an annual average downtime of (A)T for emergency and restoration repair 0,014•250=3,5 hrs8, i.e. is in 100 times lesser than 357 hrs, shown in table 6.  There were defied following fault groups for OHL (see [6]): for carrying out scheduled or unscheduled repairs or maintenance of OHL (group 1); for carrying out scheduled or unscheduled repairs, maintenance or reconstruction of allied equipment (group 2); for carrying out OHL reconstruction (group 3); for performing construction and installation and other works in fenced-off area of OHL on requests of outside organizations (group 4).  Unscheduled outages connected with works, carried out on OHL (group 1), are equal 75-80% of total number of outages. Medium frequency and duration of scheduled repairs of OHL were determined based on data from tables 7-10see tables 11-12.
From the table 11 following that each of OHL 220-750 kV is taken out from the service from 2,6 to 3,2 1/year. This is a bit more than it was in 1980s: 1,5-2,9 1/yearsee [5]. However, average duration of scheduled repair of OHL 220-500 kV was grown from 12-17 (see [5]) to 98-159 hrs, approximately by an order of magnitude, during the same period. According to [3] nonrecoverable failure for OHL 500 kV is 0,3-0,4 1/year for 100 km for mean restoration time of about 10 hrs. For average length of OHL 500 kV in Russia at a level of 200 km, its emergency and restoration downtime is 0,4(200/100)•10≈8 hrs. Whereby annual average duration of scheduled repair of OHL 500 kV is (table 11) 3,2•127=406 hrs, that almost 50 times higher its annual average emergency and restoration downtime.

Analysis of scheduled repairs duration during a year
Additionally there were plotted distributions of scheduled repairs duration of (A)T and OHL by year of period under review, i.e. proportions of the total number of repairs of given duration on time axis with accepted bin of 10 hrs. Obtained results are shown on fig. 1 and 2 as an example as applied to North-West region.    (table 4). It is commonly known that correlational relationship is high for R≥0,7 and very high for R≥0,9. Thus, it is to be supposed that for accepted maintenance and repair of OHLs system for a period under review a choice of a certain year of observation is not general contributing factor.
It is commonly assumed that in reliability evaluations scheduled repairs are carried out on 'summer' periods. With that a decreasing correction factor, that is approximately K=0,5-0,6, is introduced for calculation period. Therefore, scheduled outages from table 5 and 7 were classified by months. The result is shown on fig. 3 and 4. Frequency and duration of scheduled repairs are constantly increasing from March till November; in the winter period a number of scheduled repairs is lower, than in summer period, however, they shouldn't be neglected. For example, 4-6% of annual number of repairs accrue to December, while the annual maximum is about 11-13% for both (A)T and OHL. From fig. 2 also following that histogram of total number of repairs is lower than histogram of total duration of repairs, but it's vice versa for the winter period. The reason is obvious -it's necessary to carry out more labor and time consuming repairs in warm seasons.
The maximum value of proportion of total duration of scheduled repairs of (A)T accrues to June and equals about 16%, and to July for OHL (14%). Therefore, 100/16=6,3 and 100/14=7,1 are minimum necessary number of months to carry out scheduled repairs of (A)T and OHL by an analogy with maximum load utilization time in a power system.

Analysis of medium frequency of scheduled repairs of OHL dependence on their length
It was shown in [6] that frequency of scheduled outages has small dependence on a length of lines. This was explained for a variety of causes. In particular, when it's necessary to performance greater quantity of work it's accepted to increase a number of personnel (teams), but not duration of outage.
According to processed statistical data (table 9) there was analyzed dependence medium frequency of scheduled repairs on their duration: Line length, km to 100 100-200 200-300 Above 300 Frequency of repairs, 1/year 3,0 3,9 3,7 4,5 As we can see, some association between frequency of repairs and length appears at line lengths above 100 km. Thus, for OHL length above 300 km frequency of scheduled outages increases of 1.5 times more than short lines.
As for rather short OHLs 330 kV, which are located only in European part of the country -there's no association between given characteristics at all: Therefore, it's confirmed once more that association between OHL length and frequency of its repairs in reliability evaluations of electric circuit schemes isn't general contributing factor and could be taken into account only for extremely long lines.

Conclusion
1. According to processed representative statistical data there were obtained reliability characteristics of (A)T and OHL in main electrical grids of power systems. It's found that from the perspective of medium frequency and duration of scheduled repairs they are way below than values obtained in the last century.
2. Average duration of scheduled repairs of (A)T increased of 5 times upon the average for last 30 years and annual duration of their scheduled downtimesmore than ten times. Applied in the last century normative approach to planning a periodicity of scheduled repairs of (A)T included their annual current repair and major repair once in 8-12 years. Technically, it could have been seemed more progressive than the modern approach, based on evaluation of current state of equipment, because it provided shorter periods of weakening of grid scheme during operation.
For the last 30 years average duration of scheduled repair of OHL 220-500 kV was grown from 12-17 to 98-159 hrs, i.e. almost in ten times. Upon that the main part of scheduled outages connects with repairs or maintenance of OHL itself, but not its reconstruction or other external reasons.
These facts require to be carefully thought.
3. It is found that annual duration of scheduled downtimes of (A)T and OHL exceed their annual duration of emergency and restoration repairs more than ten times. Thus, reduction of duration of repair conditions of electric grid elements could be significant reserve of power systems reliability improvement.