5 unit commitment
TRANSCRIPT
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Unit Commitment:A MCDM case study
Joergen T. HaahrTechnical University of Denmark
Tinkle ChughUniversity of Jyvaskyla, Finland
Viktor SlednevKarlsruhe Institute of Technology, Germany
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Problem definition
Parameters:hourly demand: d(h), Maximum Power, Minimum Power, UpRamp, Down Ramp, Linear Cost, Fix_Cost, Starting Cost, Stopping Cost
Criteria: Cost Reliability Smoothness
To supply power from various units at each hour so that demand can
be meet-In least cost
-In maximum reliability
-In maximum smoothness
if unit i is used to produce power
else
0
1),( hiY
Variables: Power production (MWh): P(i,h)
),(
),(
hiY
hiY
1 If unit i is started in hour h
1 If unit is stopped in hour h
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Model and optimization formulation
Re liability ( , )i h
Y i h
i h
hiY ),(Smoothness
hihiYhiY
hihiYhiY
hiiURhiRhiPhiP
hihiYiURhiR
hSRhdhiR
hihiYhiYhiYhiY
hiiURhiPhiPiDR
hiiMaxPowerhiYhiPiMinPowerhiY
hhdhiP
i
i
,)1,(1),(
,),(),(
,)(),()1,(),(
,),()(),(
*)(),(
,),()1,(),(),(
,)()1,(),()(
,)(),(),()(),(
)(),(
i
),(),(),(),(Cost
h
stopCosthiYstartCosthiYFChiYLChiP
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Payoff matrix
Cost Reliability Smoothness
1162830 83 10
1817475 166 8
1687815 90 4
Cost Reliability Smoothness
1162830 83 10
1355045 166 8
1236925 96 4
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MCDM approaches
Weighted sum method:
Minimize w1*Cost + w2*Reliability + w3*SmoothnessSubject to i
iw 1
() Constraint method:
Minimize Cost
Subject to Reliability 1
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ContdWeighted sum method:
Minimizew
1*Cost +w
2*Reliability +w
3*SmoothnessSubject to i
iw 1
() Constraint method:
Minimize Cost
Subject to Reliability 2
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3 D weighted sum
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3 D epsilon constraint
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Decision maker preferences
1- equally important
3- something more important
5- clearly more important7- much more important
9- exactly more important
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Society weights
w1= 0.151007, w2= 0.184564, w3= 0.66443
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Comparison of weights
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Compromise programming
, ()
=
, max=.
()
min .
()
( 1 , . , )
Cost Reliability Smoothness
1162830 83 10
1355045 166 8
1236925 96 4
w1= 0.151007
w2= 0.184564
w3= 0.66443
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Compromise Programming
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Goal programmingGoal Type Significance Minimise
1 Achieve at most the target level pi
2 Achieve at least the tartget level ni
3 Achieve the target level exactly ni+pi
||1.0 ***
iii zzzGoals
iwi
)3/1(
Cost Reliability Smoothness
1162830 83 10
1355045 166 8
1236925 96 4
+
=
+ 1 , , , 1 , ,
Subject to:
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Goal programming
+ 1 , , , 1 , ,
1
+
=+
d
( 1 , . , )
( 1, . , )
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Concluding Remarks
Model formulation
Basic MCDM approaches: weighted sum and constraintmethod
Payoff Matrix
Role of decision maker
Group decision making
Interactive approach: reference point method
Compromise programming
Goal programming
Heuristic approaches
Metaheuristic approaches
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Thank You