1. INTERCONNECTED SYSTEM GENERATING CAPACITY RELIABILITY EVALUATION
Presented by
S.PRABAKARAN( )
K.MOHAN( )

2. INTRODUCTION Interconnections between systems
– to improve the overall level of system reliability
Installed capacity benefits due to interconnection depend mainly upon
Operating reserves in the individual systems
Interconnection limitations
Type of agreement between the two systems regarding emergency help

3. PROBABILITY ARRAY FOR TWO SYSTEMS
Frequency and Duration method
Loss of Load approach
-more physically significant criterion
-possibly extended into transmission system
Assumption made in Loss of Load approach:
No transmission limitation – each system will share the difficulties equally
The total generated capacity can be used to create a single capacity outage probability table

4. GENERATION AND LOAD DATA OF SYSTEMS
NO. OF UNITS
UNIT CAPACITY IN MW
FORCED OUTAGE RATE
SYSTEM CAPACITY IN MW
PEAK LOAD IN MW A 5 10
0.02 75 50 1 25 B 4 60 40 20
Assume that the interconnection between the two systems has a firm capacity of 10 MW and a negligible probability of outage.
Assume that each system has a thirty day peak load model represented by a straight line from 100 % to 40 % of the peak.

5. PROBABILITY FORMULA
The capacity outage probability is obtained from the Binomial Distribution Approach using the formula
where
q= forced outage rate
p= 1-q
n=number of trials
r=number of success

6. DEVELOPMENT OF CAPACITY OUTAGE PROBABILITY TABLE
5-10 MW UNITS
CAPACITY OUT IN MW
PROBABILITY 10 20 30 40 50
1-25 MW UNITS
CAPACITY OUT IN MW
PROBABILITY
0.98 25
0.02

7. INDIVIDUAL SYSTEM CAPACITY OUTAGE PROBABILITY
SYSTEM A
Capacity out in MW
Probability 10 20 25 30 35 40 45 55 65
SYSTEM B
Capacity out in MW
Probability 10 20 30 40 50

8. PROBABILITY OF SIMULTANEOUS OUTAGES IN SYSTEMS A & B
SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 35 45 55 65 75

9. LOSS OF LOAD APPROACH
The above probability array does not provide a useful risk index until it is combined with the load model
The following table assumes System B will assist A up to the point at which B suffers load curtailment
The maximum assistance is limited by the tie capacity
The probability of any loss of load in the given day for System A is the sum of the values in the corresponding table and similarly for System B
The Expected Load Loss (in MW) can be calculated by multiplying the probabilities and the corresponding load losses and then summed

10. LOSS OF LOAD IN SYSTEM A SYSTEM B S Y T E M A MW OUT 10 20 30 40 50 6010 20 30 40 50 60 25 5 35 15 45 55 65 75

11. LOSS OF LOAD IN SYSTEM B SYSTEM B S Y T E M A MW OUT 10 20 30 40 50 6010 20 30 40 50 60 5 15 25 35 45 55 65 75

12. LOAD LOSS PROBABILITIES IN SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 35 45 55 65 75

13. LOAD LOSS PROBABILITIES IN SYSTEM B
SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 35 45 55 65 75

14. EXPECTED LOSS OF LOAD IN DAYS
SYSTEM
INDIVIDUAL SYSTEM
INTERCONNECTED SYSTEM A B
The system expectancy on a one day basis for each system considered on a non-interconnected basis can be obtained by the individual capacity outage probability values.

15. SYSTEM EXPECTANCY FOR A MONTH
The values for a longer period can be found by finding the expectancy for each day and summing the values
(50) 40 MW
(20)
100 % 30
days
Fig. Load Duration Curve

16. THE TIME IN DAYS FOR WHICH LOAD LOSS CAN OCCUR IN SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 5 35 15 45 55 65 75

17. THE TIME IN DAYS FOR WHICH LOAD LOSS CAN OCCUR IN SYSTEM B
MW OUT 10 20 30 40 50 60
12.5 25
6.25
18.75 35 45 55 65
12. 5 75

18. EXPECTED LOSS OF LOAD IN DAYS FOR SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 35 45 55 65 75

19. EXPECTED LOSS OF LOAD IN DAYS FOR SYSTEM B
SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 60 25 35 45 55 65 75

20. SYSTEM RISK LEVEL FOR THE 30 DAY PERIOD
METHOD
TIE CAPACITY = 0 MW
TIE CAPACITY = 10 MW
USING THE PEAK LOAD AND THE MONTHLY PEAK LOAD VARIATION CURVE FOR 30 DAYS
SYSTEM A
SYSTEM B
Limitation to the assistance:
Tie line capacity relative to the reserve
The slope of the daily peak load variation curve
The degree of correlation between the system daily peak loads

21. LOAD FORECAST UNCERTAINTY
The uncertainty associated with a System load forecast can be incorporated in the two area interconnected study
The number of load combinations should be kept to a minimum in a large practical system and it may be necessary to reduce the number of steps in the load uncertainty model to a smaller value
The following curve shows the effect of varying the interconnection capacities between the two systems

22. RISK VARIATION IN SYSTEM A
0.01
0.04
0.001
0.0004 25 20 5 10 15
Uncertainty
Tie Capacity in MW
Risk for
30 days

23. RISK VARIATION IN SYSTEM B
0.01
0.04
0.001
0.0004 25 20 5 10 15
Uncertainty
Tie Capacity in MW
Risk for
30 days

24. INFERENCE
As the tie capacity increases, the risk in each system decreases until it reaches a point at which any increase in tie capacity has no further effect
This point is a function of
- the operating reserve in the two systems
- load models
- generating capacity composition
This point is designated as ‘infinite tie capacity’

25. RELIABILITY EVALUATION IN MORE THAN TWO SYSTEMS
The method of evaluating risk levels in two interconnected systems can be extended to find the risk levels when a third system is added
An assistance probability table of the third system can be obtained which contains the different capacity assistance levels each of which has a probability of availability
The assistance is equal to the difference between the operating reserve and the capacity on outage or the tie capacity whichever is less

26. GIVEN SYSTEMS SYSTEM NO. OF UNITS UNIT CAPACITY IN MW
FORCED OUTAGE RATE
SYSTEM CAPACITY IN MW
PEAK LOAD IN MW A 4 10
0.02 60 40 1 20 B 5 75 50 25 C
130 90 30
SYSTEM C
130 MW
SYSTEM A
60 MW
SYSTEM B
75 MW
Tie Capacity
15 MW
30 MW
Assume that each system has a thirty day peak load model represented by a straight line from 100 % to 75 % of the peak.

27. INDIVIDUAL SYSTEM CAPACITY OUTAGE PROBABILITY
SYSTEM B
Capacity out in MW
Probability 10 20 25 30 35 40 45 55 65
SYSTEM C
Capacity out in MW
Probability 20 30 40 50 60 70 80 90
110
SYSTEM A
Capacity out in MW
Probability 10 20 30 40 50

28. PROBABILITY OF SIMULTANEOUS OUTAGES IN SYSTEMS A & B
SYSTEM A
SYSTEM B
MW OUT 10 20 30 40 50 25 35 45 55 65

29. ASSISTANCE PROBABILITY FROM SYSTEM C
ASSISTANCE IN MW
PROBABILITY 30 20 10
When there is no outage in System C, the capacity available for assistance
is equal to the reserve of 40 MW but due to the tie capacity limitation the assistance
is only 30 MW.

30. LOSS OF LOAD IN SYSTEM A SYSTEM A S Y T E M B MW OUT 10 20 30 40 50 6010 20 30 40 50 60 5 15 25 35 45 55 65

31. LOSS OF LOAD EXPECTATION IN SYSTEM A
ASSISTANCE FROM SYSTEM C IN MW
RISK IN SYSTEM A
PROBABILITY 30
0.0 20 10
TOTAL RISK IN SYSTEM A = days/month
The risk level in System A is obtained using the combined capacity model of System A
& B, adding the capacity assistance from C to System A directly and multiplying the
Expected loss of load by the probability of the assistance from System C
The sum of the products obtained for all the levels in the assistance probability table
of System C is the risk in System A

32. ASSISTANCE PROBABILITY FROM SYSTEM B & C
SYSTEM C
ASSISTANCE IN MW
PROBABILITY 30 20 10
SYSTEM B
ASSISTANCE IN MW
PROBABILITY 15 5

33. ASSISTANCE PROBABILITY FROM SYSTEM B & C
SYSTEM C
CAPACITY OUTAGE IN MW
PROBABILITY 10 20 30
SYSTEM B
CAPACITY OUTAGE IN MW
PROBABILITY 10 15

34. INTERCONNECTION BENEFITS
The interconnection benefit to a system can be defined as the corresponding increase in load carrying capability at a specified risk level
The load carrying capability can be obtained by studying the variation in risk with peak loads for the system
If the load carrying capability of System A at a risk level of days for the 30 day period = MW

35. Case 1,2 &3 were obtained by the method developed for two interconnected systems. Case 4 were obtained by developing a capacity model for systems A & B and using the assistance probability table of System C. Case 5, the firm purchase of 10 MW was added to the capacity in System A as a 10 MW unit of zero forced outage rate in obtaining the risk level.

36. Case 6, the firm purchase of 10 MW from System B was added to the capacity in System A and subtracted from that of System B. It was assumed that additional assistance between the systems is possible over the remaining tie capacity of 15-10=5MW.
Case 7, the sale is tied to the 25MW unit in System B. If the unit is out of service, the sale capacity is not available. The risk in System A is the sum of the expected risk contributions with and without the 10 MW addition.

37. INTERCONNECTIONS BENEFITS TO SYSTEM A
CASE NUMBER
INTERCONNECTION DETAILS
BENEFIT TO SYSTEM A
IN MW 1
Connected to System B with tie capacity: 15 MW
12.35 2
Connected to System C with tie capacity: 30 MW
17.32 3
Sum of the benefits obtained from System B & C separately
29.67 4
Connected to System B & C simultaneously
31.92 5
Firm purchase of 10 MW
12.15 6
Firm purchase of 10 MW with 15 MW tie to System B
17.02 7
Firm purchase of 10 MW with 25 MW unit in System B
9.20
INTERPRETATION FROM TABLE
The table shows that, due to the larger size units in System C, the benefits are less than those from System B, even though System C has a higher operating reserve.

38. THANK YOU