1HL-I Adequacy Evaluation

(Interconnected System Reliability Analysis)

B. Bagen

Section Outline

Concepts E i l t U it A h Equivalent Unit Approach

Multi-Area Reliability Factors Affecting System Resource

Adequacy

2Concepts

S i 1

B

Station 1

Station 2

GenerationLoad

A

Load

Tie LineCapacity:10 MW

FOR=0.01

S t ASystem BGeneration:System A:

Same as the example use LDC

Generation:5x20 MWFOR=0.05Load:75 MW

Equivalent Unit Approach

Develop COPT for the assisted system (System A) Develop COPT for the assisting system (System B) Develop COPT for the assisting system (System B) Develop capacity assistance model Develop equivalent assisting unit model Develop tie line constraint equivalent assisting unit

modelDevelop modified COPT for the assisted system Develop modified COPT for the assisted system

Calculate reliability indices by convolving the modified COPT with appropriate system load model

3Equivalent Unit Approach(COPT for System A)

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

Equivalent Unit Approach(COPT for System B)

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

0 100 0.773781 120 80 0.203627 0.22621940 60 0.021434 0.02259360 40 0.001128 0.00115880 20 2.97E-05 0.000030100 0 3.13E-07 3.13E-07

4Equivalent Unit Approach(Assistance Probability Table from System B)

Assistance Probability(MW)

y

25 0.7737815 0.2036270 0.022592

Equivalent Unit Approach(Equivalent Assisting Unit Model of System B)

Capacity Out (MW)

Capacity In (MW)

Individual Probability

Cumulative Probability

0 25 0.773781 120 5 0.203627 0.22621925 0 0.022592 0.022592

5Equivalent Unit Approach(Tie Line Constraint Equivalent

Assisting Unit Model of System B)

Capacity Out Capacity In IndividualCapacity Out (MW)

Capacity In (MW)

Individual Probability

0 10 0.773781x0.995 5 0.203627x0.99

10 0 0.022592x0.99+1x0.01

Equivalent Unit Approach(Modified COPT of System A)

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

0 190 0.63768289 1

5 185 0.16781164 0.36231710

10 180 0.02694273 0.19450547

25 165 0.05205575 0.16756274 Neglected these 30 160 0.01369891 0.11550699

35 155 0.00219941 0.10180808

40 150 0.06712452 0.09960867

45 145 0.01766438 0.03248416

50 140 0.00442962 0.01481977

55 135 0.00041935 0.01039015

60 130 0.00006373 0.00997080

65 125 0.00547955 0.00990347

gstates with cumulative probabilities less than E-04

70 120 0.00144199 0.00442392

75 115 0.00025320 0.00298192

80 110 0.00177214 0.00272873

85 105 0.00046577 0.00095659

90 100 0.00024238 0.00049082

95 95 0.00004414 0.00024845

100 90 0.00000720 0.00020431

105 85 0.00014423 0.00019711

6Equivalent Unit Approach(Reliability Indices)

System reliability indices can be calculated b l i th difi d COPT f S t

LOLE LOEE EIR

by convolving the modified COPT of System A with appropriate load model. Using the LDC, the following indices can be calculated:

LOLE (h/year)

LOEE (MWh/year)

EIR

22.20 276.19 0.999678

Multi-Area Reliability

7Multi-Area Reliability

G i

MH

GenerationLoad

IESOSASK

GenerationLoad

GenerationLoad

150 MW (W)25MW (E)

200 MW (E)0 MW (W)

2175 MW

(850 M

W (

MISO

GenerationLoad

(S)(N

)

Major Factors Affecting System Resource Adequacy

LOLE (h/year) LOEE (MWh/year)

Original System 33.03 511.54

With Unit deration 21.25 266.70

With LFU 51 43 598 82With LFU 51.43 598.82

With External Assistance 22.20 276.19

8Major Factors Affecting System Resource Adequacy

Generation Type of unit and capacity Type of unit and capacity FOR Unit deration

Load Peak Load level Load models LFU

Interconnection Tie capacity Tie line availability Interconnection agreement