3 hli single area

8/12/2019 3 HLI Single Area

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HL-I Adequacy Evaluation(Single Area Reliabil ity Analysis)

B. Bagen

Section Outl ine

Example System

Calculating LOLE Using DPLVC

Calculating LOLE, LOEE and EIR Using LDC

Expected Energy Supplied by Each Unit

Unit Derated States

oa orecas ncer a n y Capacity Expansion Planning



Example System

1 2Station 1:

4X25 MW H dro

Station 2:

2X40 MW (Thermal)

= 2 f/year

= 98 r/year

= 3 f/year

= 57 r/year

•Scenario 1: Annual DPLVC is straight line from 100% to 50% point

•Scenario 2: Annual LDC is straight line from 100% to 40% point•Scenario 3: Annual LDC is straight line with a 70% load factor

•Scenario 4: Constant Load for a year at peak

ea oa :

Development of Generation Model

Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

COPT with 1x25 MW unit

0 25 0.98 1

25 0 0.02 0.02

Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

COPT with 2x25 MW units

0 50 0.9604 1

25 25 0.0392 0.0396

50 0 0.0004 0.0004





Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

0 75 0.941192 1

25 50 0.057624 0.058808

. .

75 0 0.000008 0.000008

Development of Generation ModelCOPT with 4x25 MW units

Capacity Out Capacity In Individual Cumulative

0 100 0.92236816 1

25 75 0.07529536 0.07763184

50 50 0.00230496 0.00233648

75 25 0.00003136 0.00003152

. .

If all units are the same, it is easy to develop a COPT

using the binominal distribution





Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

0 80 0.9025 1

40 40 0.0950 0.0975

80 0 0.0025 0.0025

Development of Generation ModelCOPT with 4x25 MW and 1x40 MW units

Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

.

25 115 0.0715305920 0.1237502480

40 100 0.0461184080 0.0522196560

50 90 0.0021897120 0.0061012480

65 75 0.0037647680 0.0039115360

75 65 0.0000297920 0.0001467680

90 50 0.0001152480 0.0001169760100 40 0.0000001520 0.0000017280

115 25 0.0000015680 0.0000015760

140 0 0.0000000080 0.0000000080



Development of Generation ModelCOPT with 4x25 MW and 2x40 MW units

Capacity Out ( MW) Capacity In ( MW) Individual Probability Cumulative Probability

0 180 0.8324372644 1

25 155 0.0679540624 0.1675627356

40 140 0.0876249752 0.0996086732

50 130 0.0020802264 0.0119836980

65 115 0.0071530592 0.0099034716

75 105 0.0000283024 0.0027504124

80 100 0.0023059204 0.0027221100

90 90 0.0002189712 0.0004161896

100 80 0.0000001444 0.0001972184

105 75 0.0001882384 0.0001970740

115 65 0.0000029792 0.0000088356

130 50 0.0000057624 0.0000058564

140 40 0.0000000152 0.0000000940

155 25 0.0000000784 0.0000000788

180 0 4E-10 4E-10

Calculating LOLE Using DPLVCIf the DPLVC is simply represented by a straight line

T L L

Cin Lt *

minmax

max

t

T

max L

min L

Cin



Calculating LOLE, LOEE and EIR

Using LDCCapacity In

(MW)

Individual

Probability

Time

(p.u.)

LOLP Energy

Curtailed(MWh)

Col 2*Col 5

(MWh)

180 0.8324372644 0 0 0 0

.

140 0.0876249752 0 0 0 0

130 0.0020802264 0.119050 0.000248 5214.2861 10.8469

115 0.0071530592 0.297620 0.002129 32589.2852 233.1131

105 0.0000283024 0.416667 0.000012 63875.0000 1.8078

100 0.0023059204 0.476190 0.001098 83428.5781 192.3797

90 0.0002189712 0.595240 0.000130 130357.1406 28.5445

80 0.0000001444 0.714290 0.000000 187714.2969 0.027106

75 0.0001882384 0.773810 0.000146 220303.5625 41.4696

65 0.0000029792 0.892860 0.000003 293303.5625 0.873810

50 0.0000057624 1 0.000006 420480.0000 2.4230

40 0.0000000152 1 0.000000 508080.0000 0.007723

25 0.0000000784 1 0.000000 639480.0000 0.050135

0 4E-10 1 0.000000 858480.0000 0.000343

Total 0.003772 511.54

Calculating LOLE, LOEE and EIR

Using LDC

LOLE=0.003772x8760=33.03 h/year

.

E

=Total Energy Required by the system

=Area under the LDC

=858480 MWh/year

EIR=1-LOEE/E=0.999404




(Load Factor)

For a given load factor of 70%:

Average Load=(Lmax+Lmin)/2

LF=Average Load/Peak load

Lmin=0.4 p.u.

Straight line from 100% to 40% point

Capacity In

(MW)

Individual

Probability

Time

(p.u.)

LOLP LOLE

(h/year)

LOEE

(MWh/year)

180 0.8324372644 0 0 0 0

155 0.0679540624 0 0 0 0


(Constant Load at Peak)

.

130 0.0020802264 1 0.0020802264 18.2228 182.2280

115 0.0071530592 1 0.0071530592 62.6608 1566.5200

105 0.0000283024 1 0.0000283024 0.247929 8.6775

100 0.0023059204 1 0.0023059204 20.1999 807.9944

90 0.0002189712 1 0.0002189712 1.9182 95.9094

80 0.0000001444 1 0.0000001444 0.001265 0.075896

75 0.0001882384 1 0.0001882384 1.6490 107.1830

65 0.0000029792 1 0.0000029792 0.026098 1.9573

50 0.0000057624 1 0.0000057624 0.050479 4.5431

40 0.0000000152 1 0.0000000152 0.000133 0.013315

25 0.0000000784 1 0.0000000784 0.000687 0.078980

0 4E-10 1 4E-10 0.000004 0.0004906

Total 0.011984 104.98 2775.18



Summary of Calculated Indices

LOLP LOLE LOEE

Constant Load

(Annualized)

0.011984 104.98 2775.18

LDC

(Annual)

0.003772 33.03 511.54

LOLP LOLE

(Days/year)

DPLVC 0.004524 1.65

Expected Energy Supplied by Each UnitEENS0=The total energy needed by the system

=858480 MWh/year

Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

0 25 0.98 1

25 0 0.02 0.02

1. Loading the first 25 MW hydro unit

1= year Expected Energy Supplied by Unit 1 (EES1)

=EENS0 -EENS1

=858480-643860=214620 MWh/year



2. Loading 2x25 MW hydro units


(MW)

(MW)

Probability

Probability

0 50 0.9604 1

25 25 0.0392 0.0396

50 0 0.0004 0.0004

2

EES2=EENS1 –EENS2

=643860-429240=214620 MWh/year



EENS =232337 MWh/ ear

EES3=EENS2 –EENS3

=429240-232337=196903 MWh/year


EENS4=94529 MWh/year

=4 3 – 4

=232337-94529=137808 MWh/year




5. Loading 4x25 MW hydro and the first thermal units

EENS5=7351 MWh/year

EES5=EENS4 –EENS5

=94529-7351=87178 MWh/year

6. Loading 4x25 MW hydro unit and two thermal units

EENS6=512 MWh/year

EES6=EENS5 –EENS6

=7351-512=6839 MWh/year


Summary

Loading

Sequence

Unit Capacity

(MW)

EENS

(MWh/year)

EES

(MWh/year)

1 25 643860 214620

2 25 429240 214620

3 25 232337 196903

5 40 7351 87178

6 40 512 6839



Unit Derated States

Assume that one of the two-state 40 MW thermal unit in

-

shown in the following

State Capacity Out

(MW)

Probability

1 0 0.96

2 20 0.03

3 40 0.01

Unit Derated StatesCOPT with 1x40 MW unit represented by a 3-state unit

Capacity Out

(MW)

Capacity In

(MW)

Individual

Probability

Cumulative

Probability

0 180 0.84119976 1

20 160 0.02628749 0.15880024

25 155 0.06866937 0.13251275

40 140 0.05303617 0.06384338

45 135 0.00214592 0.01080721

50 130 0.00210212 0.00866129

60 120 0.00138355 0.00655917

65 115 0.00432948 0.00517561

70 110 0.00006570 0.00084613

75 105 0.00002860 0.00078044

Neglected these

states with

cumulative

probabilities less

than E-05

80 100 0.00046118 0.00075184

85 95 0.00011294 0.00029066

90 90 0.00013254 0.00017771

95 85 0.00000089 0.00004520

100 80 0.00000015 0.00004430

105 75 0.00000038 0.00004410



Unit Derated States

LOLE=0.002426x8760=21.25 h/year

.

EIR=0.999689

LOLP LOLE

(h/year)

LOEE

(MWh/year)

EIR

derated state

. . . .

Withderated state

0.002426 21.25 266.70 0.999689

Load Forecast Uncertainty

0.383

0.36

0.4

0.0062

0.0606

0.2417 0.2417

0.0606

0.00620.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

P r o b a b i l i t y

01.12 1.08 1.04 1 0.96 0.92 0.88

Peak Load Multiplier



Load Forecast Uncertainty

STD Load Probability LOLE (h/year) LOEE (MWh/year) LOLE LOEE

Load

in Col 2

in Col 2 Col 3xCol 4 Col 3xCol 5

1.12 156.8 0.006 196.70 2271.38 1.18 13.63

1.08 151.2 0.061 138.31 1419.50 8.44 86.59

1.04 145.6 0.242 87.70 826.37 21.22 199.98

1 140.0 0.382 33.03 511.54 12.65 195.92

0.96 134.4 0.242 27.12 360.56 6.56 87.26

. . . . . . .

0.88 123.2 0.006 15.36 145.30 0.0922 0.8718

Weighted Average 51.43 598.82

Capacity Expansion Planning Annual load growth forecast is 5% with no LFU

Year Peak Load LOLE

(MW) (days/year)

1 140 1.65

2 147 5.03

3 154.40 8.28

4 162.07 13.49

System LOLE should be kept no grater than 2

days/year

Perform a 5-year adequacy evaluation

. .



Capacity Expansion Planning

Year Unit Added

(MW)

System Capacity

(MW)

Peak Load

(MW)

LOLE

(days/year)

1 180 140 1.65

2 180 147 5.03

25 205 147 0.6737

3 205 154.40 1.05

4 205 162.07 1.51

5 205 170.17 3.87

25 230 170.17 0.5577

year f /2 year r /98

New unit to be added are 25 MW unit with t he followin g reliability data:

Capacity Expansion Planning(Cri teria of 0.1 days/year)

Year Unit Added System Capacity Peak Load LOLE

1 180 140 1.65

2x25 230 140 0.026

2 230 147 0.054

3 230 154.40 0.126

. .

4 255 162.07 0.023

5 255 170.17 0.05



Capacity Expansion Planning(Criteria of 0.1 days/year)

0.3

0.1

0.15

0.2

.

L O L E

( d a y s / y e a r ) 0.1 days/year

System LOLE

0

.

0 1 2 3 4 5 6

Planning Year

3 hli single area

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