generation system adequacy evaluation

8/12/2019 Generation System Adequacy Evaluation

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Objective : to determine the required amount of system

generating capacity to ensure an adequate supply.

1. Static Capacity Requirement :

Long-term evaluation of the overall system requirement.

Practice : Percentage Reserve method. Issue : comparison

Probabilistic approaches.

2. Operating Capacity Requirement

Short term evaluation of the actual capacity required tomeet a given load.

Fundamental difference: Time period

Generation System Adequacy Evaluation


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Generation System Adequacy Evaluation

The Generation and Load models arecombined to form Risk model


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Binomial Distribution

P(H) + P(T) = [P(H) + P(T)]1

P(H).P(H) + 2P(H).P(T) + P(T).P(T)= P2(H) + 2P.(H)P(T) + P2(T) = [P(H) + P(T)]2

P3

(H) + 3P2

(H)P(T) + 3P(H)P2

(T) + P3

(T)= [P(H) + P(T)]3

Ex. Consider a system with 4 components. Thecomponents are identical with a success

probability of 0.9 and a failure probability of 0.1Obtain the various states in which the components

can exist.


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Since there are 4 components and each one of

them is either available OR unavailable, the

total number of states is

All components working

1 component failed

2 components failed

3 components failed

All components failed


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(S+F)4= S4+4S3F+6S2F2+4SF3+F4

System state Individual Probability

All components working 0.94 = 0.6561

1 component failed 4X0.93X0.1 = 0.2961

2 components failed 6X0.92X0.12 = 0.0486

3 components failed 4X0.9X0.13 =0.0036

All components failed 0.14 = 0.00011.0000


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If at least three components are required for

success then

Success Probability OR Reliability R

R = 0.6561 + 0.2916 = 0.9477

Failure probability of the system Q Q = 0.0486 + 0.0036 + 0.0001 = 0.0523 = 1R


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Case Units out Capacity Individual

Probability

Out available

A 1 X 10 MW

0 0 10 0.98

1 0.02

B 2 X 10 MW

0 0 20 0.9604

1 10 10 0.0392

2 20 0 0.0004

C 3 X 5 MW

0 0 15 0.941192

1 5 10 0.057624

2 10 5 0.001176

3 15 0 0.000008

D 4 X 10/3 MW

0 0 40/3 0.92236816

1 10/3 10 0.07529536

2 20/3 20/3 0.00230496

3 10 10/3 0.00003136

4 40/3 0 0.00000016


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Expected Load Loss


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Case Capacity Out

(MW)

Probability Load loss

(MW)

Expected Load Loss

(MW)

A 1 X 10 MW

0 0.98 0 ---

10 0.02 10 0.2 0.2 MW

B 2 X 10 MW

0 0.9604 0 ---

10 0.0392 0 ---

20 0.0004 10 0.004 0.004 MW

C 3 X 5 MW

0 0.941192 0 ----

5 0.057524 0 -----

10 0.001176 5 0.00588

15 0.000008 10 0.00008 0.00596

MW

D 4 X 10/3 MW

0 0.92236816 0 ------

10/3 0.07529536 0 ------

20/3 0.00230496 10/3 0.00768320

10 0.00003136 20/3 0.00020907

40/3 0.00000016 10 0.00000160 0.0078938

7 MW


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Let the cost per 10 MW unit be 1 unit. The

investment cost for the alternatives is

Investment cost of plant

Expected Load curtailment

System Expected Load Loss (MW) Investment cost p.u.

1 X 10 MW 0.2 1.0

2 X 10 MW 0.004 2.0

3 X 5 MW 0.00596 1.5

4 X 10/3 MW 0.00789387 1.33

System Probability of loss

of load

Expected load

curtailment hr/yr

1 X 10 MW 0.02 175.2

2 X 10 MW 0.0004 3.504

3 X 5 MW 0.001184 10.37814

4 X 10/3 MW 0.00233648 20.46756


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Effect of unavailability

System 1X10 MW 2X10 MW 3X5 MW 4X10/3 MW

Unavailabili

ty %

Expected Load loss, MW

2 0.2 0.004 0.00596 0.007893874 0.4 0.016 0.02368 0.03112407

6 0.6 0.036 0.05292 0.06909417


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Ex. A system consists of three 20 MW units

with a FOR of 4%. Obtain the capacity outage

probability table. (COPT). If a 4th unit of 40MW with an FOR of 4%, is added to the

system, obtain the COPT on a 100 MW

installed capacity.


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Table A

Table B

Sl. No CapacityAvailable

Capacity out Probability

1 60 0 0.884736

2 40 20 0.110592

3 20 40 0.004608

4 0 60 0.000064

Sl No Capacity

available

Capacity out Probability

1 40 0 0.96

2 0 40 0.04


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Table C

State Capacityavailable

Capacityout

Howobtained

Probability

a 100 0 1(a),1(b) 0.8493465

b 60 40 1(A), 2(B) 0.0353894

c 80 20 2(A), 1(B) 0.1061683

d 40 60 2(A), 2(B) 0.0044236

e 60 40 3(A), 1(B) 0.0044236

f 20 80 3(A),2(B) 0.0001843

g 40 60 4(A),1(B) 0.0000614

h 0 100 4(A), 2(B) 0.0000025


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Table D

State Capacityavailabl

e

Capoacity out

Howobtain

ed

Probability(state)

Cumulative

probability

i 100 0 a 0.8493465 1.00

ii 80 20 c 0.10616863 0.1506534

iii 60 40 b+e 0.039813 0.0444851

iv 40 60 d+g 0.004485 0.004672

v 20 80 f 0.0001843 0.0001868

vi 0 100 h 0.0000025 0.0000025


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Ex. A system consists of two 3 MW units with

a FOR of 2%. Obtain the capacity outageprobability table. (COPT). If a 3rdunit of 5 MW

with an FOR of 2%, is added to the system,

obtain the COPT.

Also obtain the COPT in the increments of 5

MW


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Table 1. COPT for two units

Table 2. COPT with 5 MW unit in service

Capacity Out Probability

0 0.9604

3 0.0392

6 0.0004


0+0 = 0 MW (0.9604) X (0.98) = 0.941192

3 + 0 = 3 MW (0.0392) X (0.98) = 0.038416

6 + 0 = 6 MW (0.0004) X (0.98) = 0.000392

= 0.980000


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Table 3. COPT with 5 MW out of service

Table 4. COPT with all the units


0+5 = 5MW (0.9604) X (0.02) = 0.019208

3 + 5 = 8 MW (0.0392) X (0.02) = 0.000784

6 + 5 = 11 MW (0.0004) X (0.02) = 0.000008

= 0.020000

Capacity Out Probability Cumulative Probability

0 0.941192 1.000000

3 0.038416 0.058808

5 0.019208 0.020392

6 0.000392 0.001184

8 0.000784 0.000792

11 0.000008 0.000008


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Table 5. Rounded table

Capacity Out Probability0 0.9565584

5 0.0428848

10 0.0005552

15 0.0000016


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Comparison of percentage reserve margin and

largest unit reserve criteria


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system 1, 24 x 10 MW units each having a FOR of 0.01

system 2. 12 x 20 MW units each having a FOR of 0.01

system 3, 12 x 20 MW units each having a FOR of 0.03

system 4,22 x 10 MW units each having a FOR of 0.01


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Loss of Load Indices

The generation system model is convolvedwith an appropriate load model to produce a

system risk index. The risk indices depends

upon the nature of load model.


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Sample types of load models

Daily peak load variation curve.

Each day is represented by its daily peak load.

Individual peak loads arranged in descending manner

forming a cumulative modeldaily peak load variation

curve.

Load duration curve.

Individual hourly loads are used.

Area under the curve represents the energy required in

the given period.


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Loss of Load Expectation (LOLE)

The expected number of days in the specified

period in which the daily peak load will exceedthe available capacity.

Capacity Outageloss of generation which may or may notresult in a loss of load. This depends on the generatingcapacity reserve margin.

Loss of loadoccur only when the capability of thegenerating capacity remaining in service is exceeded by thesystem load.

The applicable system capacity outage probability

table is combined with the system loadcharacteristics to give an expected risk of loss ofload.


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Where

Ci= available capacity on day I LI = forecast peak load on day I

Pi(CiLi) = probability of loss of load on day i.( obtained from the capacity outage cumulative probability table)


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Ex. A system consists of two units of 25 MW each and one unit of 50

MW with a FOR 0.02.Obtain LOLE with the load data given in table 1below.


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Capacity Out Cumulative Probability

0 1.00000025 0.058808

50 0.020392

75 0.000792

100 0.000008

Table 2


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LOLE from daily peak load variation curve.

Qk- magnitude of kth outage in the system COPT

tknumber of time units in the study interval that an outage of magnitude Qkwould result in a loss of load.

The load model is a represented by a continuous curve for 365 days.


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Pkcumulative outage probability for capacitystate Qk


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Ex. Consider a system containing five 40 MW units each with a FOR of 0.01. theCOPT for the system is given in the table 3. The system load model is representedby the daily peak load variation curve shown in the figure. Obtain LOLE if theforecast peak load is 160 MW


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100 % means 365 days on the x - axis and 160 MW on the

y - axis.


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LOLE using individual probability

The LOLE is 0.0412413 % of the time baseunit. With 365 days year, the LOLE will be

0.150410 days.


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LOLE using Cumulative Probability

Capacity out Capacity In Cumulative

Probability

Time interval

Tk

LOLE

0 200 1.000000 0 ----------

40 160 0.049009 0 ----------

80 120 0.000980 41.7 0.0408660

120 80 0.000009 41.7 0.0003753

0.0412413 %

Table 4. The LOLE obtained is identical to the value obtained with

the value obtained with individual probability.


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Examples A power system contains the following generating capacity.

3 X 40 MW hydro units FOR = 0.005

1 X 50 MW thermal units FOR = 0.02

1 X 60 MW thermal unit FOR = 0.02

The annual daily peak load variation curve is given by astraight line from the 100 % to the 40% point. Calculate the

loss of load expectation for the following peak load values.a. 150 MW

b. 160 MW

c. 170 MW

d. 180 MWe. 190 MW

f. 200 MW.

S i i i S di


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Table 5. Variation in risk as a function of peak load

Sensitivity Studies


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Fig 1. Variation in risk with system peak load, drawn on a semi log sheet


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Table 6 . Effect of FOR and System Peak Load


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The system used is very small hence the effect ofgenerating unit unavailability is quitepronounced. The effect for a big system with

large units having high FORs is shown in the fig. 2

The total installed capacity of the system is 10100MW

The largest units have 300 MW and 500 MWcapacity with FOR varying from 4 % to 13%.

The risk profile is almost a straight line.

This is because, a large system with a wide range

of unit sizes has a more continuous COPTresulting in a smoother risk profile.


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Fig 2. LOLE as a function of FOR


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The system peak load carrying capability (PLCC)

The PLCC at a risk level of 0.1 day/year is 9006 MW for FOR of 0.04. Table

7 shows the change in PLCC for FOR values from 0.04 to 0.13. the decrease

in PLCC is 815 MW.

FOR % PLCC (MW) Difference (MW) Cumulative difference MW

4 9006 ------ ------

5 8895 111 111

6 8793 102 213

7 8693 100 313

8 8602 91 404

9 8513 89 493

10 8427 86 57911 8345 82 661

12 8267 78 739

13 8191 76 815

Table 7 . Changes in PLCC


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If the forecast peak load is 9000 MW and the

FOR of the large units are 0.13, an additional

capacity of approximately 1000 MW has to beinstalled.

The investment has to be therefore increased

to meet the new demand. This clearly shows the consequences of the

unit unavailability in terms of additional

capacity.


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Capacity Expansion Analysis

Time required for designing, construct and commissioning a

large power station takes normally 510 years.

Consider a plant with five 40 MW units whose COPT is shown

in table 8

Table 8


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It is decided to add additional 50 MW units

with FOR 0.01, to meet a projected load

growth of 10 %.

The question- In what years must the units be

committed in order to meet the accepted

system risk level? Table 9 shows the change in risk level for with

the sequential addition of 50 MW units.

Table 9 The change in risk level with sequential addition of 50 MW units


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Table 9. The change in risk level with sequential addition of 50 MW units

System Peak

Load (MW)

LOLE (days/year)

200 MW 250 MW 300 MW 350 MW

100 0.001210 ---- ---- ----

120 0.002005 ---- ---- ----

140 0.08686 0.001301 ---- ----

160 0.1506 0.002625 ---- ----

180 3.447 0.06858 ---- ----

200 6.083 0.1505 0.002996 ----

220 ---- 2.058 0.03615 ----

240 ---- 4.853 0.1361 0.002980

250 ---- 6.083 0.1800 0.004034

260 ---- ---- 0.6610 0.01175280 ---- ---- 3.566 0.1075

300 ---- ---- 6.082 0.2904

320 ---- ---- ---- 2.248

340 ---- ---- ---- 4.880

350 ---- ---- ---- 6.083


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Year number Forecast peak load (MW)

1 160

2 176

3 193.6

4 213.0

5 234.3

6 257.5

7 283.1

8 311.4

Table 10. Load growth at 10 %

Fig 3. Variation in risk with unit additions.


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If it i t d th t i t ll d it f


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If it is accepted that an installed capacity of

200 MW is adequate for a system peak load of

160 MW, the risk criterion is 0.15 days/year.

Choosing this risk criterion, the timing of unit

additions can be obtained.

The actual choice of the risk value is amanagement decision.

In the present case, 50 MW additions can be

made in the years 2,4 and 6 The expansion is shown in the table 11.

T bl 11 G ti i lt


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Table 11. Generation expansion results

Year Unit added (MW) System capacity

(MW)

Peak Load

(MW)

LOLE

(days/year)1 ----- 200 160 0.15

2 ----- 200 176 2.9

50 250 176 0.058

3 ----- 250 193.6 0.11

4 ----- 250 213 0.73

50 300 213 0.011

5 ----- 300 234.3 0.11

6 ----- 300 257.4 0.55

50 350 257.4 0.009

7 ----- 350 283.1 0.125

8 ----- 350 311.4 0.96

b i ff


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Perturbation Effects

Large units have relatively low cost per KW installed.

Large units have better heat rates than the smaller units.

However, the impact on the system reliability by adding a

large unit should be considered when carrying out economic

evaluation of alternate sizes.

This effect is considered in Increased Peak Load CarryingCapacity due to unit additions. (IPLCC)

The IPLCC values with each 50 MW unit at a system risk level

of 0.1 is shown in table 12.

Table 12 IPLCC for five unit system


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Table 12. IPLCC for five unit system.

System Capacity

(MW)

Available peak load

(MW)

Increase in PLCC (MW)

Individual Cumulative

200 144 0 0

250 186 42 42300 232 46 88

350 279 47 135


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Consider a large system with 2010 MW

units. The total installed capacity = 200 MW

With the criterion of loss of largest unit , thissystem can carry a 190 peak load.

The initial load carrying capability is different

than the 5 unit system The addition of each 50 MW unit has a

different IPLCC

Initial PLCC penalty


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Table 13. IPLCC for 20 unit system.

System Capacity

(MW)

Available peak load

(MW)

Increase in PLCC (MW)

Individual Cumulative

200 184 0 0250 202 18 18

300 250 48 66

350 298 48 114

S h d l d O t


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Scheduled Outages

If the units are removed from the service for periodic

inspection/maintenance, the capacity availableduring this period is not the same as that during the

other period.

Hence a single COPT is not applicable.

The year is divided into several periods and the LOLE

is calculated for each period.

The annual risk index is obtained as

Modified capacity model is obtained by creating new

COPT for each capacity condition.


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If a new unit is added to the system, the same can be

added to the capacity model also.

If the actual in-service date of the new unit isuncertain, it can be represented by a probability

distribution function and LOLE is obtained as


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Alternate method

A th lt t th d


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Another alternate method

Most realistic approach is to obtain the COPT by considering the


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Most realistic approach is to obtain the COPT by considering theunits actually available in a given period.

Other methods give a higher risk value which increases withincreased maintenance capacity.

Maintenance Scheduling.

While scheduling the maintenance, the important point to be

considered is that, the reliability of a system becomes poorer if aunit with low FOR is removed from service.

Approaches for maintenance scheduling:

1. To reduce the total installed capacity by the expected capacity lossrather than by the actual unit capacity and then schedulemaintenance on a constant reserve base.

2. Determine the decrease of PLCC at the appropriate risk level foreach individual unit on maintenance and then using these values,schedule is prepared on a constant reserve basis.

Evaluation methods on period basis


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Evaluation methods on period basis. Annual risk index can be obtained by using any of the three

methods

1. Monthly (or period) basis considering maintenance2. Annual basis neglecting maintenance

3. Worst period basis.

Monthly approach : Constant capacity for the period is assumed.

Appropriate COPT is combined with the load model. The annual risk is the sum of the 12 monthly risks.

If the capacity on maintenance is not constant during the month,the month is divided into several intervals during which thecapacity is constant.

The COPT, modified by removing the units on maintenance foreach separate interval, is combined with monthly peak and loadcharacteristic using the interval as its time base.

A l h l ti i t


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Annual approach neglecting maintenance:

The annual forecast peak load and the systemload characteristics are combined with thesystem COPT.

Basic assumption: a constant capacity exists forthe entire period.

Justification: The year can be divided into a peak load season and a

light load season.

The planned maintenance can be scheduled entirely

during the light load season. The contribution of light load season to the annual

risk is quite low and hence a constant capacity can beassumed.

Worst Period Basis


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Worst Period Basis:

The load level in a particular season or month

may be so high that the same may dominatethe annual figure.

The risk value for that month is calculated.

The annual risk level is obtained bymultiplying this risk value by 12.

Usually the worst period is December.

12 December Basis.

Load Forecast Uncertainty


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Load Forecast Uncertainty

Assumption that the actual peak load will

differ from the forecast peak load with zeroprobability, is extremely unlikely to happen in

the actual practice, as the forecast is actually

predicted on past experience.

Method 1: This uncertainty can be described

by a probability distribution, whose

parameters can be determined from past

experience, future load modeling.

The load forecast probability is divided into


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The load forecast probability is divided into

several class intervals.

LOLE is computed for each load by multiplying

the class interval and the probability of the load

existing.

The uncertainty is well described by a normal

distribution.

The distribution mean is the forecast peak load.

The distribution is divided into a discrete number

of class intervals.

The load representing the class interval mid point

is taken as the probability for that class interval.

E A t i t f t l 5 MW it


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Ex. A system consists of twelve 5 MW units,

each with a FOR of 0.01. the forecast peak

load is 50 MW. The COPT can be obtained

The uncertainty is normally distributed using a

seven step approximation.


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Period = 1 month = 30 days = 720 hours.

Standard deviation is 2% of the forecast peak

load = 1 MW. Monthly load-duration curve is represented by a

straight line .

The LOLE is obtained as

Probability of load X LOLE (hours/month for the load)

Method 2


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Method 2

Conditional Load Duration Curves


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Conditional Load Duration Curves

Modified Load Duration Curve


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LOLE


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In general

LOLE is affected by

Generation unit unavailability (FOR)

Load Forecast uncertainty.

Hence the calculated value is only approximate.

The actual distribution of LOLE can be obtained by Monte

Carlo simulation

Loss of Energy Indices


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Loss of Energy Indices

The area under the load duration curve

represents the energy utilized during thespecified period and can be used to

determine the expected energy not supplied

due to insufficient installed capacity.


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The normalized LOEE is obtained as

Where E is the total energy under load duration curve.

The energy index of Reliability EIR is

EIR = 1LOEE pu


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Consider the LDC for a period of 100 hours and the generating unit capacity

shown in the table


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The total energy in the period is 4575 MWh.If there were no units, the Expected Energy Not Supplied

(EENS) is 4575 MWH. If the system contained only unit 1, the

EENS is obtained as


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EENS with units 1 & 2


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EENS with units 1,2 & 3


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The expected energy produced by unit 3 is 401.764.08 = 337.6 MWh

Summary of EENS


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Summary of EENS

The expected energy not supplied is therefore 64.08

MWh. The energy index of reliability EIR is obtained asEIR = 1(64.08/4575) = 0.985993

A generating contains three 25 MW


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A generating contains three 25 MW

generating units each with a 4 % FOR and one

30 MW unit with 5 % FOR. If the peak load fora 100 day period is 75 MW, what is the LOLE

and EIR for this period? Assume that

appropriate load characteristics is a straight

line from the 100 % point to 60 % point.

generation system adequacy evaluation

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