Calculation of SAIDI indicator for the distribution line, equipped with a device search accelerate fault location

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Calculation of SAIDI indicator for the distribution line, equipped with a device search accelerate fault location

One of the most important indicator of reliability of the reporting power to grid companies is the average frequency of interruptions index (SAIFI) [1, 2]. Consider index SAIDI more. SAIDI index is the average duration of an abnormality in which serves to measure the average time during which the user is not served. Mathematical index entry:

(1)

where Tсум,i - annual downtime of the consumer in the i-th place, Ni - the number of customers in the i-th place, NT - the total number of customers served.

Early in Russia and the former Soviet Union instead of SAIDI indicator used the concept of the average time of recovery of power supply:

(2)

where pi - the likelihood of short-circuit on the i-th site, tв,i - time power is restored to the i-th section of the line.

Powerline organizations are responsible for the number and duration of interruptions in the supply of electrical energy. When designing a new distribution line and its reconstruction is often a problem of estimation of SAIDI indicator for future line when there is no more exploitation of statistical data.

Using a special device for detecting fault location (sc) - one of the radical ways to improve the reliability of power supply. With a relatively small capital costs (the price of 300 euros. short circuit indicator and 1,000 euros. for remote meter) can be a significant effect on reducing the time power is restored. Therefore SAIDI index calculation for the distribution line, equipped with a device search accelerate fault location, is an urgent task.

In developing the SAIDI index calculation methodology, we took as a basis the methodology for calculating the recovery of power supply time, [3] and the methodology for calculating the time search space sc using fault location detection devices in distribution networks for agricultural purposes 6-10 kV [4].

Estimated time for restoration of power supply to consumers of i-site and those that may not be included, in case of damage of i-section

(3)

where tнач, i - the time from the start line to disable search damage,

tпоиск, i - while searching the damaged area, tлок, i - while the damaged site localization, tвкл, i - ON time of the loads that may be included in the circuit in the absence of the damaged area, tобх, i - while bypassing the damaged area, tрем, i - time to repair the damaged area and enable loads to the top of the disconnected repair.

Time from the start line to disable search damage

(4)

where tинф - time from line to disable the receipt of this information, tожид - waiting time operational readiness visiting team (EOD) to travel to the damaged line, tдост - time spent on the move.

Consider how you can find the search space during short circuit When using the device short-circuit detection space These devices include:

1) Remote Meter (CI), the distance to the short circuit, which is set at the beginning of the line in the circuit breaker box;

2) Short-circuit indicator with telecontrol functions (ECI TM);

3) Short-circuit indicator without telemechanical functions (ECI without TM).

Below are the calculation formulas for the first 2 options. LED short circuit without telemechanical functions should not be used during reconstruction or new construction line. Therefore, the formula for option 3 is not present. If necessary, the formula can be taken from [4].

Option №1 - CI.

Figure 1 - Replacement scheme for the calculation of short-circuit time search space for the simplest plot

Search time places sc for the simple plot (Figure 1) using CI

(5)

where p1 the likelihood of short-circuit 1 section of the line; tд delivery time up to 1 EOD area, the average delivery time from the beginning of EOD 1st section to the site of sc



Figure 2 - The replacement scheme for the calculation of short-circuit time search space for 2 sites (option 1)

Search time places sc 2 possible sites (Figure 2) can be found by the formula

(6)

Search time places sc for 3 sections with remote meter.

(7)

Variant №2 - ECI TM

If the substation is installed ECI TM, it significantly reduces the search time as manager immediately know whether the short-circuit occurred in the line section of the ECI with TM.

For the general case, when n sections of lines installed ECI TM search time space sc



(8)

Figure 3 - The equivalent circuit for the calculation of short-circuit time search space for 2 sections with ECI with telecontrol functions

For example, in Figure 3 the search space during short circuit is given by

Time bypassing the damaged area of the simplest:

(9)

where Li complete (with the blind branches) the length of the considered line section; LМi length of the line section of the line under consideration; coefficient taking into account the increase in the speed of the bypass line operational fielding team (EOD) when returning from a branch.

Time to recovery of the remaining power consumers which can be incorporated, if damaged i-th section

(10)



When designing a new dispensing line or index SAIDI its reconstruction, with (1) and (2) can be calculated by the formula

(11)

where tв. расч, i - the estimated time of recovery of power consumers in the i- th place. Look at an example to confirm the procedure.

Figure 4 - Diagram of distribution line

Example 1. Find the SAIDI indicator for the distribution line, equipped with a device search accelerate fault location (Figure 4). Accept that the substation has a remote control switch or a substation electrician on duty there, which performs switching switch. Long stretches of line are given in kilometers.

When calculating the reliability of the switch at the beginning of the line is considered ideal. The average number of failures in stable 1 km line of 0.25 per year. The average number of failures KTP 0.07 per year. The average number of failures of the linear disconnectors for outdoor installation 0.01 per year.

The average speed of an electrician bypass line 4 km/h. Coefficient =1,25. Average speed of movement of the machine along the line EOD 40 km/h. Time shift switching device tперекл=3 min.

Decision. We divide the source schema to 6 independent stations, which can be obtained by disconnecting (Figure 2). 1 set up a table for the calculation of the probability of failure of i-site.

Table 1 - Calculation of the number of trips

N area	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
1	9,86	9	4	3,14	0,31
2	4,13	4	0	1,31	0,13
3	0,20	1	0	0,12	0,01
4	8,18	5	0	2,40	0,24
5	5,94	7	1	1,99	0,20
6	4,30	1	0	1,15	0,11
Total:	32,61	27	5	10,09	1

Example of calculation for line 1:

the number of trips



probability on the site of the accident

We form the equivalent circuit for the calculation of short-circuit time search space for the first part of the 1st section (Figure 5) and perform the calculation (Table 2-4).

Figure 5 - The equivalent circuit for the calculation of short-circuit time search space for the 1st section

Table 2 - Calculation of the probability of outages for the 1st section

N	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
11	1,94	1	1	0,57	0,06
12	0,6	1	0	0,22	0,02
13	2,63	0	0	0,66	0,07
14	0,5	1	0	0,20	0,02
15	1,32	0	2	0,35	0,03
16	0,3	2	0	0,22	0,02
17	0,3	1	0	0,15	0,01
18	0,44	1	0	0,18	0,02
19	0,78	0	1	0,21	0,02
Total:	8,81	7,00	4,00	2,73	0,27



Table 3 - Timing inspections sections 1st section EOD

N	L, km	t, h
11	1,94	0,024
12	0,3	0,004
13	2,63	0,033
14	0,25	0,003
15	1,32	0,017
16	0,1	0,001
17	0,3	0,004
18	0,22	0,003
19	0,78	0,010

Example of calculation for line 1:

Table 4 - Calculation of the time of delivery EOD from the substation to the beginning of the sections for the 1st section

N area	Lд, km	tд, h
11	0	0
12	1,94	0,024
13	2,24	0,028
14	4,87	0,061
15	5,12	0,064
16	6,44	0,081
17	6,54	0,082
18	6,84	0,086
19	7,06	0,088

Example of calculation for line 1:



Calculation of short-circuit time search space EOD for the sections of the 1st site

We form the equivalent circuit for the calculation of short-circuit time search space for the 2nd part of the 1st section (Figure 6) and perform the calculation (Table 5-7).

Figure 6 - Replacement scheme for the calculation of short-circuit time search space for the 1st section

Table 5 - Calculating the probability of outages for the 1st section

N area	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
11	0,4	0	0	0,10	0,01
12	0,3	1	0	0,15	0,01
13	0,35	1	0	0,16	0,02
Total:	1,05	2,00	0,00	0,40	0,04



Table 6 - Timing inspections sections 1st section EOD

N area	L, km	t, h
11	0,4	0,005
12	0,15	0,002
13	0,35	0,004

Table 7 - Calculation of the time of delivery EOD from the substation to the beginning of the sections for the 1st section

N area	Lд, km	tд, h
11	1,60	0,020
12	2,00	0,025
13	2,15	0,027

Calculation of short-circuit time search space EOD for the sections of the 1st site

By analogy we make up the equivalent circuit for the calculation of short-circuit time search space for other areas, and perform the calculation.



Figure 7 - The equivalent circuit for the calculation of short-circuit time search space for the 2nd section

Table 8 - Calculation of the probability of outages for the 2nd section

N area	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
21	0,05	0	0	0,02	0,002
22	0,5	0	0	0,13	0,01
23	0,24	1	0	0,13	0,01
24	2,44	2	0	0,75	0,07
25	0,9	1	0	0,30	0,03
Total:	4,13	4,00	1,00	1,32	0,13

Table 9 - Timing inspection sections of the 2nd section of EOD

N area	L, km	t, h
21	0,05	0,001
22	0,25	0,003
23	0,08	0,001
24	1,22	0,015
25	0,9	0,011

Table 10 - Timing EOD delivery from the substation to the beginning of the sections for the 2nd section

N area	Lд, km	tд, h
21	0,90	0,011
22	0,95	0,012
23	1,20	0,015
24	1,28	0,016
25	2,50	0,031

Table 11 - Calculation of time moving between the lines EOD section for 2nd site

N section	N line	L, km	tл, h
23	31	0,58	0,015
24	41	1,38	0,035

Calculation of short-circuit time search space EOD for the sections of the 2nd section

Figure 8 - Replacement scheme for the calculation of short-circuit time search space for 3rd section



Table 12 - Calculation of the probability of tripping for 3rd section

N section	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
31	0,05	1	0	0,08	0,008
Total:	0,05	1,00	0,00	0,08	0,008

Figure 9 - The equivalent circuit for the calculation of short-circuit time search space for the 4th section

Table 13 - Calculation of outage probability for the 4th section

N section	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
41	4,9	1	0	1,30	0,13
42	0,32	0	0	0,08	0,01
43	0,24	1	0	0,13	0,01
44	0,16	0	0	0,04	0,004
45	0,72	1	0	0,25	0,02
46	0,16	1	0	0,11	0,01
47	1,68	1	0	0,49	0,05
Total:	8,18	5,00	0,00	2,40	0,24



Table 14 - Timing inspection sections of the 4th section of EOD

N area	L, km	t, h
41	4,9	0,061
42	0,16	0,002
43	0,08	0,001
44	0,08	0,001
45	0,24	0,003
46	0,08	0,001
47	1,68	0,021

Table 15 - Timing EOD delivery from the substation to the beginning of the sections for the 4th section

N area	Lд, km	tд, h
41	6,44	0,081
42	11,34	0,142
43	11,50	0,144
44	11,58	0,145
45	11,66	0,146
46	11,90	0,149
47	11,98	0,150

Table 16 - Calculation of time moving between the lines EOD section for 4th section

N section	N линий	L, km	tл, h
43	31	0,4	0,01
44	41	0,24	0,004
45	51	0,56	0,034
46	61	0,56	0,021

Example of calculation for one moving line of AXO between section lines

Calculation of short-circuit time search space EOD for the sections of the 4th section



\

Figure 10 - The equivalent circuit for the calculation of short-circuit time search space for the 5th section

Table 17 - Calculation of outage probability for the 5th section

N section	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
51	0,8	1	0	0,27	0,03
52	0,17	1	0	0,11	0,01
53	2,72	2	0	0,82	0,08
54	0,85	2	1	0,29	0,029
Total:	4,54	6	1,00	1,50	0,15



Table 18 - Timing inspection sections of the 5th section of EOD

N area	L, km	t, h
51	0,4	0,005
52	0,17	0,002
53	1,36	0,017
54	0,85	0,011

Table 19 - Calculation of the time of delivery EOD from the substation to the beginning of the sections for the 5th section

N area	Lд, km	tд, h
51	6,74	0,084
52	7,14	0,089
53	7,31	0,091
54	8,67	0,108

Calculation of short-circuit time search space EOD for the sections of the 5th section

Figure 11 - The equivalent circuit for the calculation of short-circuit time search space for the 5th section



Table 20 - Calculation of outage probability for the 5th section

N section	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
51	0,3	0	0	0,08	0,01
52	0,14	1	0	0,11	0,01
53	0,88	1	0	0,29	0,03
Total:	1,32	2,00	0,00	0,47	0,05

Table 21 - Timing inspection sections of the 5th section of EOD

N area	L, km	t, h
51	0,3	0,004
52	0,07	0,001
53	0,88	0,011

Table 22 - Timing EOD delivery from the substation to the beginning of the sections for the 5th section

N area	Lд, km	tд, h
51	7,74	0,097
52	8,04	0,101
53	8,11	0,101

Calculation of short-circuit time search space EOD for the sections of the 5th section



Figure 12 - The equivalent circuit for the calculation of short-circuit time search space for the 6th section

Table 23 - Calculation of the probability of outages for the 6th section

N section	lуч, km	NКТП, psc	NЛР, psc	Nоткл	p
61	4,3	1	0	1,15	0,11
Total:	4,30	1,00	0,00	1,15	0,11

calculation plot space

Figure 13 - Scheme of control process of finding places sc line



Here is the formula to calculate the time power is restored to the line for a variety of sites.

The accident at the site 1

The accident at the site 2

The accident at the site 3

The accident at the site 4

The accident at the site 5

The accident at the site 6

We reduce the calculation results in Table 24 and find the index SAIDI

Table 24 - Calculation of the index SAIDI

№ area	p	tв.осн	Nосн	tв.ост	Nост			Nпотр	SAIDI
1	0,31	3,51	27			29,44	59,60	27	2,21
2	0,13	3,13	4	1,12	23	4,98
3	0,01	3,24	1	1,24	26	0,42
4	0,24	3,31	5	1,26	22	10,50
5	0,20	3,29	8	1,27	19	9,92
6	0,11	3,36	1	1,34	26	4,33

The problem is solved. SAIDI indicator for the distribution line was 2.21 hours.



Conclusion

The article first proposed method of theoretical calculation of SAIDI indicator for distribution lines for agricultural purposes, is equipped with a device search accelerate fault location. The methodology can be used the design of grid organizations in the design of a new line or its reconstruction. For power grid organizations technique may be useful for establishing the planned SAIDI indicator values for specific distribution lines.



Literature

1. http://www.thegreenmechanics.com/2012/05/how-do-you-calculate-saidi.html?m=1

2. http://www.l2eng.com/Reliability_Indices_for_Utilities.pdf

3. V.L. Pruss, V.V. Tislenko Improving the reliability of village electric networks. - L. Energoatomisdat. Leningrad. Dep, 1989 -. 208.

4. I.I. Bandurin, O.A. Sadchenkova. Reducing the time power is restored by the use of detection devices fault location in distribution networks for agricultural purposes, methodical and practical problems of reliability of liberalized energy systems: Sat. Art. / Hole. Ed. N.I. Voropai, M.A. Karatkevich, A.A. Mikhalevich. - Minsk: Belarusian National Technical University, 2015. - P. 323-329

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