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Influence of load diversity exchange on preventive maintenance scheduling in interconnected power systems
Reliability Engineering and System Safety 20 (1988) 287-296
Influence of Load Diversity Exchange on Preventive Maintenance Scheduling in Interconnected Power Systems R. B i l l i n t o n a n d F. A. E1-Sheikhi Power System Research Group, University of Saskatchewan, Saskatoon, Saskatchewan, Canada (Received 2 July 1987) ABSTRACT Preventive maintenance scheduling in a power system can be performed in a number of ways. One approach is to levelize the risk throughout the study period. This paper presents a practical approach to risk levelization. These concepts are extended to maintenance scheduling in two interconnected systems. Power system interconnection can have a significant effect on the maintenance schedules of the connected systems. This effect will depend on the individual system parameters such as generating unit sizes, forced outage rates, and on the interconnection capabilities and availabilities. The individual load characteristics in each system also have a major impact on both the isolated system and interconnected configuration maintenance schedules. This paper illustrates the influence of load diversity exchange on the preventive maintenance schedule in two interconnected systems using the risk levelization approach. The concepts are examined using the I E E E Reliability Test System.
1 INTRODUCTION L o a d diversity between interconnected power utilities is an important factor which will allow the interconnected areas to share generating capacity reserves. The difference in the system loading of a utility between its summer and winter seasons is defined as seasonal diversity. Interconnecting complementary utilities will allow a winter peaking utility to supply a summer peaking system from its surplus during the summer season and a A version of this paper was presented at Reliability'87, 14-16 April 1987, Birmingham,UK, and is reproduced by kind permission of the organisers. 287 Reliability Engineering and System Safety 0951-8320/88/$03"50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
288
R. Billinton, F. A. EI-Sheikhi
summer peaking utility can supply the winter peaking utility from its surplus during the winter time. An exchange of these surpluses is known as a diversity exchange. Each system participating in a diversity exchange can achieve savings through a reduction in generating capacity requirements in its own system. Seasonal diversity exchange also offers opportunities for coordinated generation expansion planning between summer and winter peaking utilities. This paper presents an algorithm based on the moment-cumulant method 1 for performing preventive maintenance scheduling of the generation facilities in interconnected power systems. This technique can be used to investigate the impact of seasonal diversity exchange on the preventive maintenance schedule of each system in the pool. The effects of time capability on the maintenance schedule of each utility involved in load diversity exchange has been studied and illustrated in this paper using the IEEE-Reliability Test System (RTS). 2 This system has a total installed capacity of 3405 MW with generating unit capacities varying from 12 to 400 MW. The system is described in detail in Ref. 2. It was developed by the IEEE Subcommittee on the Application of Probability Methods in 1979 and was intended to provide a consistent set of data that could be used in both generating capacity and composite system reliability evaluation.
2 G E N E R A T I O N SYSTEM M A I N T E N A N C E S C H E D U L I N G IN TWO I N T E R C O N N E C T E D SYSTEMS Interconnection between neighbouring power systems is an important factor in improved system reliability. Factors such as load diversity between the two systems, in the forced outage of generating units and in the required maintenance schedule will allow the interconnected areas to share capacity reserves and to operate on less reserve than would normally be required for isolated operation. Many utilities are now firmly interconnected with neighbouring utilities in order to improve their system reliability and generating capacity planning is conducted on a fully or semi-integrated basis. Maintenance scheduling, therefore, should be conducted in the integrated environment of the interconnected utilities.
3 PREVENTIVE MAINTENANCE SCHEDULING TECHNIQUE Consider two systems, A and B, interconnected through a finite number of tie lines each of which has a given capability and availability. This configuration is shown in Fig. 1.
Load diversity exchange in interconnectedpower systems load
289
loaf J
!
Fig. 1.
T w o i n t e r c o n n e c t e d utilities.
The forced outage rates of generating units and the forecast hourly peak loads of each utility are considered to be independent random variables. The proposed method can be summarized using the following notation: Ui = capacity of unit i CA = installed capacity of system A K~, = j t h cumulant of the generating unit i outage distribution GKAjw = j t h cumulant of the generating system outage distribution in week W of utility A KLA~ = j t h cumulant of hourly peak demand distribution of utility A ELKAjw = j t h cumulant of the equivalent load curve in week W of utility A KASTAjw = j t h cumulant of the equivalent fictitious derated assisting unit in week W from utility A Similar notation can be defined for utility B. The algorithm proceeds as follows: (1) Calculate the maintenance schedule for system A using the method of Ref. 4. (2) Calculate the base case capacity model for system A using the method of the Appendix. (3) In every week W in the year perform the following steps: m
(a)
GKAjw = GKAjw - y , Ki, i=l
wherej = 1, 2 ..... 6, and m is the number of units on maintenance in week W. (b) Calculate a new capacity model for system A using the new cumulants, GKA~w, and the Appendix.
(c)
C A = CA - ~
Ui i=1
290
R. Billinton. F. A. El-Sheikhi
{d) Build the reserve model for system A in week W. (e) Calculate the equivalent assistant unit in week W by convolving the reserve model with the tie lines availability model. (f) Calculate the cumulants KASTRA/w in the week W using the method described in Ref. 5. (4) (5) (6)
(7) (8)
GKBjw = G K B j + KASTRA~w; ./= 1,2 ..... 6; W = 1,2 ..... 52 ELKB~w = K L B j + GKBjw; j = 1,2 ..... 6; W = 1, 2 ..... 52 Repeat steps 1-3 for system B using the 52 equivalent load curve cumulants, ELKB~w, in step 1. Repeat steps 4-6 for system A, excluding step 2. Apply step 7 to system B and then system A in turn and in every pass note the maintenance schedule plan for each system. Continue until the maintenance plan for each utility converges to a fixed plan.
4 LOAD DIVERSITY EXCHANGE: MODEL A N D APPLICATION In order to illustrate the effects on the maintenance schedule of interconnection between the two utilities, the single system maintenance schedules were first constructed. Table 1 shows the results for system A. 2 TABLE 1 Single System Maintenance Schedule PLAN
Week
Level
number 1
1 2 3-5 6, 7 8 9 10
None 76 155 197 197 400 11 400 12, 13 400 14 400 15 400 16, 17 197 18 197 19 None 20 100 21, 22 100 23-25 N o n e
2
155 155 197 197 155 155 197 76
55
3
20 20 155 20
4
12 12 20 Units ( M W )
76 50
1 Week Level number ............................................................. 1 ~ 3 4
26 155 27 155 28 155 29 155 30 76 31, 32 350 33 350 34 350 35 400 36 400 37 400 38,39 400 40 400 41, 42 197 43 197 44 52 None
12 100 100
50 50
12
100 76 20 76 350 155 155 155 197 100 100
50 12 20 76 76
12 Units ( M W )
50
12
50
12
Load diversity exchange in interconnected power systems 0
291
IEEE-RTS ortginal load cycle (System A) Shifted load cycle (System B)
_
0
qP LD
-'.
.
.
N
C
:
~ g g
"i
-:
,,,
o
~o •.
.
.
o
o
-=o
Cz
26
z'8
3[ 4'0
Weeks Number
Fig. 2.
Load diversity model using the IEEE-RTS.
Load diversity has been modelled using two identical IEEE-RTS systems designated as system A and system B. The generation system in both A and B is represented by the original IEEE-RTS generation system as in Ref. 2. The load cycle of system A is the IEEE-RTS original load pattern. For the purpose of modelling the load diversity exchange, the original load cycle of the IEEE-RTS has been time shifted in system B. Week 1 of the shifted load cycle is the same as week 39 of the original load pattern. The system peak loads in both systems were held at 2850 MW. System A peak demand occurs in week 51 and the system B peak demand occurs in week 13. The load cycles are shown in Fig. 2. The two systems A and B are interconnected through a 100% available tie line which has a tie capability of 600 MW. The algorithm outlined in the last section for creating the maintenance schedule in two interconnected systems has been applied to this configuration. Plans 2 and 3 as shown in Tables 2 and 3 respectively illustrate the IEEE-RTS
292
R. Billinton, F. A. El-Sheikhi TABLE 2
IEEE-RTS Load Diversity Analysis--System A PLAN 2: System A maintenance schedule: tie capacity = 600MW: planning expectation in both systems = 0-1 day's yr Week number
Level 1
l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
2
Week number 3
4
No maintenance 76 12 76 12 76 155 155 Units { M W ) 197 155 197 155 20 12 400 197 20 12 400 197 400 100 50 12 400 100 50 12 400 100 400 197 76 197 76 50 197 76 50 12 197 12 No maintenance 100 100 50 100 50
Let;el l
~
3
4
23 25 No maintenance 26 155 20 27 155 100 50 20 28 155 100 50 20 29 155 100 30 76 Units(MW) 31 350 76 50 32 350 76 50 33 350 20 34 350 76 20 35 400 350 76 36 400 155 76 37 400 155 38 400 155 50 39 400 155 50 40 400 197 41 197 155 20 12 42 197 155 20 12 43 197 155 44 155 45-50 No maintenance
m a i n t e n a n c e schedule o f systems A a n d B u n d e r the load diversity e x c h a n g e condition. It s h o u l d be n o t e d in plan 3 o f system B that there are no m a i n t e n a n c e activities d u r i n g the weeks 7 - 1 7 a n d 3 7 - 3 9 as the system load is high in these periods, as s h o w n in Fig. 2.
5 TIE LINE CAPABILITY IMPACT ON THE SYSTEM MAINTENANCE SCHEDULE WITH LOAD DIVERSITY EXCHANGE T h e effect o f tie line c a p a b i l i t y o n the g e n e r a t i o n system m a i n t e n a n c e schedule including the seasonal diversity e x c h a n g e has been e x a m i n e d using the I E E E - R T S .
Load diversity exchange in interconnected power systems
293
TABLE 3 IEEE-RTS Load Diversity Analysis--System B PLAN 3: System B maintenance schedule; tie capacity = 600MW; planning expectation in both systems = 0-1 days yr- 1
Week number
Level 1
1 2 3 4 5 6 7-17 18 19 20 21 22 23 24 25 26 27 28 29 30
Week
Level
number
2
3
4
5
197 155 50 20 12 197 155 155 50 20 197 155 155 197 155 155 155 50 50 Units ( M W ) No maintenance 76 76 76 100 197 I00 20 12 197 100 50 20 12 400 197 50 400 197 76 400 100 76 400 100 76 400 100 400 100 76 197 76 50
6
12
1
2
3
4
5
31 197 76 50 12 32 197 12 33 No maintenance 34 100 35 100 50 36 100 50 Units ( M W ) 37-39 No maintenance 40 350 20 12 41 350 20 12 42 350 43 350 44 350 45 350 155 76 20 46 155 76 20 12 47 400 155 76 48 400 155 49 400 155 50 400 155 51 400 155 50 52 400 155 50
The tie line capability has been increased to 900 MW and the same load cycles shown in Fig. 2 used for systems A and B. The IEEE-RTS system A and system B maintenance schedules in this case are shown in plans 4 and 5, respectively (see Tables 4 and 5). An examination of plans 2 and 4 for system A indicates that the maintenance activities are different in 19 weeks due to an increase in the tie capacity of 300 MW. The weeks which have different maintenance activity are 3, 4, 11-14, 17, 18, 26, 27, 30-32, 38, 39 and 41-44. One of the bigger units, which is a 155 MW unit, has been shifted by the computer program for weeks 41-44, when the capacity was 600 MW, to weeks 11-14 after increasing the tie capacity to 900 MW. An investigation of plans 3 and 5 for system B reveals that the maintenance schedule is different in every week in the year except weeks 29, 30, 34, 42--44, 47 and 48. The maintenance activity is, therefore, changed in 31 weeks, which is a large difference. Plans 4 and 5 illustrate that tie capability is an important factor in the system maintenance schedule.
294
R. Billinton, F. A. EI-Sheikhi
TABLE 4 I E E E - R T S Load Diversity Analysis--System A I'LAN 4: System A maintenance schedule; tie capacity = 900 M W ; planning expectation in b o t h systems = 0.1 days y r 1 Week Level number . . . . . . . . . . 1 ~ 3
1-2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
76 76 76 155 155 Units ( M W ) 197 155 197 155 20 400 197 20 400 197 155 400 155 50 400 155 50 400 155 400 197 76 197 76 50 197 76 50 197
No maintenance 100 100 100
50 50
4
12 12
Week nttmhet . . . . . . l 2
23-25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44-52
Let'e/ 3
4
No maintenance 155 12 155 100 50 12 155 100 50 155 100 76 12 Units ( M W ) 350 76 20 20 350 76 20 20 350 20 350 76 20 400 350 76 400 155 76 400 155 400 155 50 12 400 155 50 12 400 197 197 100 50 12 197 100 50 12 197 100 No m a i n t c n a n c c
5
12
6 CONCLUSION Seasonal diversity exchange offers opportunity for coordinated generation expansion planning between summer and winter peaking utilities. The coordination of generating unit maintenance is an important task. The single system may have a weekly levelized risk maintenance schedule, but when it is connected with another system its weekly risk will be affected by the parameters of the other system as well as the capability and availability associated with the tie lines. Consequently, its weekly risk will no longer be levelized. This paper has presented a technique for generating unit maintenance scheduling in two interconnected systems based on the moment-cumulant method. The risk is levelized throughout the year in the two systems using an iterative procedure. This paper illustrates that the maintenance schedule in a system can be affected by the transfer capability between the connected utilities.
Load diversity exchange in interconnectedpower systems
295
TABLE 5
IEEE-RTS Load Diversity Analysis--System B PLAN 5: System B maintenance schedule; tie capacity = 900 MW; planning expectation in both systems = 0"1 days yr-
Week number
Level 1
1
2 3 4 5 6 7 8-16 17 18 19 20 21 22 23 24 25 26 27 28 29
2
3
Week number 4
Level 1
197 155 50 12 197 155 50 12 197 155 100 197 155 100 100 76 76 76 No maintenance 50 12 Units (MW) 50 12 50 50 100 76 197 100 76 197 100 76 400 197 400 197 155 400 155 20 400 155 20 400 155 400 197 76
2
3
4
5
30 197 76 50 31 197 76 50 32 197 33 No maintenance 100 34 100 20 20 35 100 20 20 36 37-39 No maintenance 40 12 Uni~ (MW) 41 350 12 42 350 43 350 44 350 45 350 76 50 46 155 76 50 400 155 76 47 48 400 155 49 400 155 155 20 12 400 155 20 12 50 51 400 155 50 12 52 400 155 50 12
REFERENCES 1. Kendal, M, G. and Stuart, A. The Advanced Theory of Statistics, Vol. I. Distribution Theory, 2nd Edition, Griffin, High Wycombe, UK. 2. IEEE Reliability Test System, A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee, IEEE Trans. PAS, PAS-98(6) (1979), pp. 2047-54. 3. Billinton, R. and Allan, R. N. Reliability Evaluation of Power Systems, Longman, London/Plenum Publishers, New York, 1984. 4. EI-Sheikhi, F. A. and Biilinton, R. Probabilistic simulation of power system operation for maintenance scheduling of generating facilities, AFRICON'83, 1st IEEE Conference in Africa, 7-9 December 1983, Nairobi, Kenya. 5. Billinton, R. and EI-Sheikhi, F. A. Preventive maintenance scheduling in power generation systems using a quantitative risk criterion, Can. Electr. Engn. J., January 1983. 6. Rau, N. and Schenk, K. Application of Fourier methods for the evaluation of capacity outage probabilities, IEEE/PES Paper No. A 79 103-3, Winter Meeting, 1979.
R. Billinton, F. A. EI-Sheikhi
296
APPENDIX The capacity outage probability model in any week can be found using the Gram-Charlier expansion of a distribution. The probability of having capacity on outage of X or greater is given by: 6
G(z) dz +
Prob [capacity on outage > A"] = 1
where the Gram-Charlier expansion of a distribution G(z) = N(z) -
~K3A~3)(z) +
~K4~4~(z)
G(z) dz 2
-
G(z) is given
by:
~-~-6Ks~5~(z)
1 -k-7~-~K6 -k- 10K~U~6~(z)- 5-~0K7 + 35K4K3)A~7~Iz) 1 + 4-O~T6(K8 + 56K3K 5 + 35K])N~8)(z)
(A.I)
with
Kj = GKjw/aJ where GKiwis thejth cumulant of the generating system outage distribution in week W, and p l
GKjw=~Kji; i=1
j = 1,2 ..... 8; W = 1,2 ..... 52
Influence of Load Diversity Exchange on Preventive Maintenance Scheduling in Interconnected Power Systems R. B i l l i n t o n a n d F. A. E1-Sheikhi Power System Research Group, University of Saskatchewan, Saskatoon, Saskatchewan, Canada (Received 2 July 1987) ABSTRACT Preventive maintenance scheduling in a power system can be performed in a number of ways. One approach is to levelize the risk throughout the study period. This paper presents a practical approach to risk levelization. These concepts are extended to maintenance scheduling in two interconnected systems. Power system interconnection can have a significant effect on the maintenance schedules of the connected systems. This effect will depend on the individual system parameters such as generating unit sizes, forced outage rates, and on the interconnection capabilities and availabilities. The individual load characteristics in each system also have a major impact on both the isolated system and interconnected configuration maintenance schedules. This paper illustrates the influence of load diversity exchange on the preventive maintenance schedule in two interconnected systems using the risk levelization approach. The concepts are examined using the I E E E Reliability Test System.
1 INTRODUCTION L o a d diversity between interconnected power utilities is an important factor which will allow the interconnected areas to share generating capacity reserves. The difference in the system loading of a utility between its summer and winter seasons is defined as seasonal diversity. Interconnecting complementary utilities will allow a winter peaking utility to supply a summer peaking system from its surplus during the summer season and a A version of this paper was presented at Reliability'87, 14-16 April 1987, Birmingham,UK, and is reproduced by kind permission of the organisers. 287 Reliability Engineering and System Safety 0951-8320/88/$03"50 © 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain
288
R. Billinton, F. A. EI-Sheikhi
summer peaking utility can supply the winter peaking utility from its surplus during the winter time. An exchange of these surpluses is known as a diversity exchange. Each system participating in a diversity exchange can achieve savings through a reduction in generating capacity requirements in its own system. Seasonal diversity exchange also offers opportunities for coordinated generation expansion planning between summer and winter peaking utilities. This paper presents an algorithm based on the moment-cumulant method 1 for performing preventive maintenance scheduling of the generation facilities in interconnected power systems. This technique can be used to investigate the impact of seasonal diversity exchange on the preventive maintenance schedule of each system in the pool. The effects of time capability on the maintenance schedule of each utility involved in load diversity exchange has been studied and illustrated in this paper using the IEEE-Reliability Test System (RTS). 2 This system has a total installed capacity of 3405 MW with generating unit capacities varying from 12 to 400 MW. The system is described in detail in Ref. 2. It was developed by the IEEE Subcommittee on the Application of Probability Methods in 1979 and was intended to provide a consistent set of data that could be used in both generating capacity and composite system reliability evaluation.
2 G E N E R A T I O N SYSTEM M A I N T E N A N C E S C H E D U L I N G IN TWO I N T E R C O N N E C T E D SYSTEMS Interconnection between neighbouring power systems is an important factor in improved system reliability. Factors such as load diversity between the two systems, in the forced outage of generating units and in the required maintenance schedule will allow the interconnected areas to share capacity reserves and to operate on less reserve than would normally be required for isolated operation. Many utilities are now firmly interconnected with neighbouring utilities in order to improve their system reliability and generating capacity planning is conducted on a fully or semi-integrated basis. Maintenance scheduling, therefore, should be conducted in the integrated environment of the interconnected utilities.
3 PREVENTIVE MAINTENANCE SCHEDULING TECHNIQUE Consider two systems, A and B, interconnected through a finite number of tie lines each of which has a given capability and availability. This configuration is shown in Fig. 1.
Load diversity exchange in interconnectedpower systems load
289
loaf J
!
Fig. 1.
T w o i n t e r c o n n e c t e d utilities.
The forced outage rates of generating units and the forecast hourly peak loads of each utility are considered to be independent random variables. The proposed method can be summarized using the following notation: Ui = capacity of unit i CA = installed capacity of system A K~, = j t h cumulant of the generating unit i outage distribution GKAjw = j t h cumulant of the generating system outage distribution in week W of utility A KLA~ = j t h cumulant of hourly peak demand distribution of utility A ELKAjw = j t h cumulant of the equivalent load curve in week W of utility A KASTAjw = j t h cumulant of the equivalent fictitious derated assisting unit in week W from utility A Similar notation can be defined for utility B. The algorithm proceeds as follows: (1) Calculate the maintenance schedule for system A using the method of Ref. 4. (2) Calculate the base case capacity model for system A using the method of the Appendix. (3) In every week W in the year perform the following steps: m
(a)
GKAjw = GKAjw - y , Ki, i=l
wherej = 1, 2 ..... 6, and m is the number of units on maintenance in week W. (b) Calculate a new capacity model for system A using the new cumulants, GKA~w, and the Appendix.
(c)
C A = CA - ~
Ui i=1
290
R. Billinton. F. A. El-Sheikhi
{d) Build the reserve model for system A in week W. (e) Calculate the equivalent assistant unit in week W by convolving the reserve model with the tie lines availability model. (f) Calculate the cumulants KASTRA/w in the week W using the method described in Ref. 5. (4) (5) (6)
(7) (8)
GKBjw = G K B j + KASTRA~w; ./= 1,2 ..... 6; W = 1,2 ..... 52 ELKB~w = K L B j + GKBjw; j = 1,2 ..... 6; W = 1, 2 ..... 52 Repeat steps 1-3 for system B using the 52 equivalent load curve cumulants, ELKB~w, in step 1. Repeat steps 4-6 for system A, excluding step 2. Apply step 7 to system B and then system A in turn and in every pass note the maintenance schedule plan for each system. Continue until the maintenance plan for each utility converges to a fixed plan.
4 LOAD DIVERSITY EXCHANGE: MODEL A N D APPLICATION In order to illustrate the effects on the maintenance schedule of interconnection between the two utilities, the single system maintenance schedules were first constructed. Table 1 shows the results for system A. 2 TABLE 1 Single System Maintenance Schedule PLAN
Week
Level
number 1
1 2 3-5 6, 7 8 9 10
None 76 155 197 197 400 11 400 12, 13 400 14 400 15 400 16, 17 197 18 197 19 None 20 100 21, 22 100 23-25 N o n e
2
155 155 197 197 155 155 197 76
55
3
20 20 155 20
4
12 12 20 Units ( M W )
76 50
1 Week Level number ............................................................. 1 ~ 3 4
26 155 27 155 28 155 29 155 30 76 31, 32 350 33 350 34 350 35 400 36 400 37 400 38,39 400 40 400 41, 42 197 43 197 44 52 None
12 100 100
50 50
12
100 76 20 76 350 155 155 155 197 100 100
50 12 20 76 76
12 Units ( M W )
50
12
50
12
Load diversity exchange in interconnected power systems 0
291
IEEE-RTS ortginal load cycle (System A) Shifted load cycle (System B)
_
0
qP LD
-'.
.
.
N
C
:
~ g g
"i
-:
,,,
o
~o •.
.
.
o
o
-=o
Cz
26
z'8
3[ 4'0
Weeks Number
Fig. 2.
Load diversity model using the IEEE-RTS.
Load diversity has been modelled using two identical IEEE-RTS systems designated as system A and system B. The generation system in both A and B is represented by the original IEEE-RTS generation system as in Ref. 2. The load cycle of system A is the IEEE-RTS original load pattern. For the purpose of modelling the load diversity exchange, the original load cycle of the IEEE-RTS has been time shifted in system B. Week 1 of the shifted load cycle is the same as week 39 of the original load pattern. The system peak loads in both systems were held at 2850 MW. System A peak demand occurs in week 51 and the system B peak demand occurs in week 13. The load cycles are shown in Fig. 2. The two systems A and B are interconnected through a 100% available tie line which has a tie capability of 600 MW. The algorithm outlined in the last section for creating the maintenance schedule in two interconnected systems has been applied to this configuration. Plans 2 and 3 as shown in Tables 2 and 3 respectively illustrate the IEEE-RTS
292
R. Billinton, F. A. El-Sheikhi TABLE 2
IEEE-RTS Load Diversity Analysis--System A PLAN 2: System A maintenance schedule: tie capacity = 600MW: planning expectation in both systems = 0-1 day's yr Week number
Level 1
l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
2
Week number 3
4
No maintenance 76 12 76 12 76 155 155 Units { M W ) 197 155 197 155 20 12 400 197 20 12 400 197 400 100 50 12 400 100 50 12 400 100 400 197 76 197 76 50 197 76 50 12 197 12 No maintenance 100 100 50 100 50
Let;el l
~
3
4
23 25 No maintenance 26 155 20 27 155 100 50 20 28 155 100 50 20 29 155 100 30 76 Units(MW) 31 350 76 50 32 350 76 50 33 350 20 34 350 76 20 35 400 350 76 36 400 155 76 37 400 155 38 400 155 50 39 400 155 50 40 400 197 41 197 155 20 12 42 197 155 20 12 43 197 155 44 155 45-50 No maintenance
m a i n t e n a n c e schedule o f systems A a n d B u n d e r the load diversity e x c h a n g e condition. It s h o u l d be n o t e d in plan 3 o f system B that there are no m a i n t e n a n c e activities d u r i n g the weeks 7 - 1 7 a n d 3 7 - 3 9 as the system load is high in these periods, as s h o w n in Fig. 2.
5 TIE LINE CAPABILITY IMPACT ON THE SYSTEM MAINTENANCE SCHEDULE WITH LOAD DIVERSITY EXCHANGE T h e effect o f tie line c a p a b i l i t y o n the g e n e r a t i o n system m a i n t e n a n c e schedule including the seasonal diversity e x c h a n g e has been e x a m i n e d using the I E E E - R T S .
Load diversity exchange in interconnected power systems
293
TABLE 3 IEEE-RTS Load Diversity Analysis--System B PLAN 3: System B maintenance schedule; tie capacity = 600MW; planning expectation in both systems = 0-1 days yr- 1
Week number
Level 1
1 2 3 4 5 6 7-17 18 19 20 21 22 23 24 25 26 27 28 29 30
Week
Level
number
2
3
4
5
197 155 50 20 12 197 155 155 50 20 197 155 155 197 155 155 155 50 50 Units ( M W ) No maintenance 76 76 76 100 197 I00 20 12 197 100 50 20 12 400 197 50 400 197 76 400 100 76 400 100 76 400 100 400 100 76 197 76 50
6
12
1
2
3
4
5
31 197 76 50 12 32 197 12 33 No maintenance 34 100 35 100 50 36 100 50 Units ( M W ) 37-39 No maintenance 40 350 20 12 41 350 20 12 42 350 43 350 44 350 45 350 155 76 20 46 155 76 20 12 47 400 155 76 48 400 155 49 400 155 50 400 155 51 400 155 50 52 400 155 50
The tie line capability has been increased to 900 MW and the same load cycles shown in Fig. 2 used for systems A and B. The IEEE-RTS system A and system B maintenance schedules in this case are shown in plans 4 and 5, respectively (see Tables 4 and 5). An examination of plans 2 and 4 for system A indicates that the maintenance activities are different in 19 weeks due to an increase in the tie capacity of 300 MW. The weeks which have different maintenance activity are 3, 4, 11-14, 17, 18, 26, 27, 30-32, 38, 39 and 41-44. One of the bigger units, which is a 155 MW unit, has been shifted by the computer program for weeks 41-44, when the capacity was 600 MW, to weeks 11-14 after increasing the tie capacity to 900 MW. An investigation of plans 3 and 5 for system B reveals that the maintenance schedule is different in every week in the year except weeks 29, 30, 34, 42--44, 47 and 48. The maintenance activity is, therefore, changed in 31 weeks, which is a large difference. Plans 4 and 5 illustrate that tie capability is an important factor in the system maintenance schedule.
294
R. Billinton, F. A. EI-Sheikhi
TABLE 4 I E E E - R T S Load Diversity Analysis--System A I'LAN 4: System A maintenance schedule; tie capacity = 900 M W ; planning expectation in b o t h systems = 0.1 days y r 1 Week Level number . . . . . . . . . . 1 ~ 3
1-2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
76 76 76 155 155 Units ( M W ) 197 155 197 155 20 400 197 20 400 197 155 400 155 50 400 155 50 400 155 400 197 76 197 76 50 197 76 50 197
No maintenance 100 100 100
50 50
4
12 12
Week nttmhet . . . . . . l 2
23-25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44-52
Let'e/ 3
4
No maintenance 155 12 155 100 50 12 155 100 50 155 100 76 12 Units ( M W ) 350 76 20 20 350 76 20 20 350 20 350 76 20 400 350 76 400 155 76 400 155 400 155 50 12 400 155 50 12 400 197 197 100 50 12 197 100 50 12 197 100 No m a i n t c n a n c c
5
12
6 CONCLUSION Seasonal diversity exchange offers opportunity for coordinated generation expansion planning between summer and winter peaking utilities. The coordination of generating unit maintenance is an important task. The single system may have a weekly levelized risk maintenance schedule, but when it is connected with another system its weekly risk will be affected by the parameters of the other system as well as the capability and availability associated with the tie lines. Consequently, its weekly risk will no longer be levelized. This paper has presented a technique for generating unit maintenance scheduling in two interconnected systems based on the moment-cumulant method. The risk is levelized throughout the year in the two systems using an iterative procedure. This paper illustrates that the maintenance schedule in a system can be affected by the transfer capability between the connected utilities.
Load diversity exchange in interconnectedpower systems
295
TABLE 5
IEEE-RTS Load Diversity Analysis--System B PLAN 5: System B maintenance schedule; tie capacity = 900 MW; planning expectation in both systems = 0"1 days yr-
Week number
Level 1
1
2 3 4 5 6 7 8-16 17 18 19 20 21 22 23 24 25 26 27 28 29
2
3
Week number 4
Level 1
197 155 50 12 197 155 50 12 197 155 100 197 155 100 100 76 76 76 No maintenance 50 12 Units (MW) 50 12 50 50 100 76 197 100 76 197 100 76 400 197 400 197 155 400 155 20 400 155 20 400 155 400 197 76
2
3
4
5
30 197 76 50 31 197 76 50 32 197 33 No maintenance 100 34 100 20 20 35 100 20 20 36 37-39 No maintenance 40 12 Uni~ (MW) 41 350 12 42 350 43 350 44 350 45 350 76 50 46 155 76 50 400 155 76 47 48 400 155 49 400 155 155 20 12 400 155 20 12 50 51 400 155 50 12 52 400 155 50 12
REFERENCES 1. Kendal, M, G. and Stuart, A. The Advanced Theory of Statistics, Vol. I. Distribution Theory, 2nd Edition, Griffin, High Wycombe, UK. 2. IEEE Reliability Test System, A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee, IEEE Trans. PAS, PAS-98(6) (1979), pp. 2047-54. 3. Billinton, R. and Allan, R. N. Reliability Evaluation of Power Systems, Longman, London/Plenum Publishers, New York, 1984. 4. EI-Sheikhi, F. A. and Biilinton, R. Probabilistic simulation of power system operation for maintenance scheduling of generating facilities, AFRICON'83, 1st IEEE Conference in Africa, 7-9 December 1983, Nairobi, Kenya. 5. Billinton, R. and EI-Sheikhi, F. A. Preventive maintenance scheduling in power generation systems using a quantitative risk criterion, Can. Electr. Engn. J., January 1983. 6. Rau, N. and Schenk, K. Application of Fourier methods for the evaluation of capacity outage probabilities, IEEE/PES Paper No. A 79 103-3, Winter Meeting, 1979.
R. Billinton, F. A. EI-Sheikhi
296
APPENDIX The capacity outage probability model in any week can be found using the Gram-Charlier expansion of a distribution. The probability of having capacity on outage of X or greater is given by: 6
G(z) dz +
Prob [capacity on outage > A"] = 1
where the Gram-Charlier expansion of a distribution G(z) = N(z) -
~K3A~3)(z) +
~K4~4~(z)
G(z) dz 2
-
G(z) is given
by:
~-~-6Ks~5~(z)
1 -k-7~-~K6 -k- 10K~U~6~(z)- 5-~0K7 + 35K4K3)A~7~Iz) 1 + 4-O~T6(K8 + 56K3K 5 + 35K])N~8)(z)
(A.I)
with
Kj = GKjw/aJ where GKiwis thejth cumulant of the generating system outage distribution in week W, and p l
GKjw=~Kji; i=1
j = 1,2 ..... 8; W = 1,2 ..... 52