Ever experienced problems with congestion pricing using LMPs - - PowerPoint PPT Presentation

Ever experienced problems with congestion pricing using LMPs (byproduct of optimal dispatch)?

MW

$ Dual space shows “the other side

• f the coin”!

A dual space approach for pricing congestion in electricity markets

Ricardo Rios-Zalapa, Jie Wan, Kwok Cheung

11/04/2010

GRID

Purpose: Show you some ideas for Congestion Management (pricing) based on dual formulation of the dispatch problem

Transmission congestion pricing cost causation – cost recovery

− “Traditional” approach: electricity markets are, still, rather “primal”

• Single interval dispatch
• Dispatch instructions & $ (with the same tool)
• heuristic methods: iterative dispatch re-runs, tuning

penalties for transmission congestion violations, tuning transmission limits, tuning minimum dispatch limits of generating units, so the nodal balance equations’ LaGrange Multipliers are “good” $

• With multi-interval (dynamic) dispatch such fine

tuning of parameters becomes a very intricate task.

Transmission congestion pricing cost causation – cost recovery

− “Alternative” approach

• Multi-interval dispatch: dispatch instructions ONLY
• Prices:

− minimize side-payments necessary to guarantee cost recovery, and that are as close as possible to the profit maximizing perspective of market participants, minimizing the incentives to deviate from the dispatch instructions (i.e. the dispatch is also optimal from such profit maximizing perspective, with respect to such prices) − Modified Dual − Other ?

• No load and Start up costs covered in UC

• Transmission perspective of the market
• A common trick to price congestion
• Dual pricing (example)
• Economic sensitivities

Pd(A) Pd(B) i(A) i(B) $/MWh $/MWh MW MW RR Penalty E I A B

Isolated markets

L A B T MW L T price T penalty L T price

Interconnected markets

P’d(B) P’d(A) A B

Isolated markets

L A B L violation T price T penalty

Transmission violation

L A B L’ T price

The “trick” seems to work

… change the limit and re-run …

B A G2 G1 G3 C D 181 MW/1000$2000 1350 MW 1350 MW 1250 MW/ (0,1500) $50 $50 50 MW/ (0,50) $80 50 MW/ (0,50) $190

$1764 $2336 $2907

373 MW/1000$2000

^1069 MW/1000$2000 ^746 MW/700$2000

373 MW/1000$2000

Transmission violations

… change the limit and re-run does not work… Alternatives do …

a) Solve the primal. Solution:

kt it

F Pg * / *

b)

) ( / )) ( (

* max max * max kt kt kt kt kt

F abs F Then Tol F F abs F If   

c) Solve Dual

 

kt it kt kt kt j jt kj i it ki kt it it it t it it it t it it it it it t j jt i it t t i it it Pg

F Pg Solution t k f f F Pd Dfax Pg Dfax F t i up dn RRUp IL Pg Pg RRDn IL t i g g Pg Pg Pg t Pd Pg to Subject IL Pg c Minimize * / * : , , , , , , : 60 /

max max 1 max min

                          

    

     

      

 

t k f f t i up dn t i g g t ed unrestrict t i IL c f f Dfax up dn up dn g g to Subject Pd Dfax F f Pd Dfax F f RRUp IL up RRDn IL dn Pg g Pg g Pd Maximize

, , , , 60 / : ) ( ) (

                                                                       

      

                      

Primal Dual

Problem formulation

Transmission congestion pricing cost causation – cost recovery

 

         

,... ..., / ,... ,..., / ,... ,..., : , , , ,..., 1 ; ) * ( ) ( ) * ( min ) (

                 

   

p p Solution t k i Dfax p t k i Uplift L i g g GenCost p Uplift to subject F F Uplift L LowerBound        



   

,...), ,..., ( : , , ) ( max ,... ,...,

          



MPP g g Solution t i ramp g g ramp t i M g m st g GenCost p p p MPP

 

  

             

F F g GenCost p MPP L UpperBound ) * ( * ) ( ) 1 (



i g g and MPP then MPP If

   

,...) ,..., ( ,...) ,..., (



m

• r

T uplift

… change the

limit and re-run does NOT work… Initially violated line BC NOT binding

node 1st run 2nd run alternative A 50.0 50.0 50.0 B 1764.3 199.3 80.0 C 2907.1 190.0 190.0 D 2335.7 194.7 135.0 line 1st run 2nd run alternative AB 2000.0 163.3 44.0 BC 2000.0 0.0 179.0

Alternative does .. Initially violated lines AB & BC both binding

$50 $50 $80 $190 $1764 $2336 $2907

Transmission violations

violated $50 $199 $194 $190 binding NOT binding ! $50 $80 $135 $190 binding 1st run 2nd run alternative

B A G2 G1 101 MW/ (0,150) $50

$50

10 MW/ (0,10) $75

$2050 ^101 MW/100$2000

T limit relaxation

111 MW B A G2 G1 (101+) MW/ (0,150) $50

$50

(10-) MW/ (0,10) $75

$75 (101+)* MW/(101 +) $2000

111 MW

B A G2 G1 91 MW/ (0,150) $50

$50

10 MW/ (10,50) $75

$50 91 MW/100$2000

T congestion over-compensation

101 MW B A G2 G1 91+ MW/ (0,150) $50

$50

10- MW/ (10-,50) $75

$75 (91+)* MW/(91 +) $2000

101 MW

B A G2 G1 91 MW/ (0,150) $50

$50

10 MW/ (10,50) $75

$50 91 MW/100$2000

T congestion over-compensation

101 MW B A G2 G1 100 MW/ (0,150) $50

$50

1 MW/ (0,50) $75

$75 100 MW/100 $2000

101 MW

Are we using the right tool?

Economic sensitivities

$

CM

bottleneck!

it seems that ..not always

Dfaxes Congestion Management ($)

Where is the “root” of such confusion?

…. I have always had the feeling that … .. deep down … nobody really understands me .. . .. or that people find me boring … bla … bla bla …. … zzzzzzz …. rise help (Dfax-) lower help (Dfax+)

Physical sensitivities: relative to the slack, do not change with dispatch,.. changing the reference does not help, … nor changing the name (Dfaxes, PTDF,..):

line AE

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 A B C D E E A distributed B

A B C D E

S undance S

• litude

Brighton Alta P ark city

A B C D E

Gen Gen Gen Gen Gen

224.1 224.1 1 6 6 . 3 1 6 6 . 3 350* 350* 80 80 250* 250* 270 MW 270 MW 270 MW 270 MW 150 MW/ (20,150) $11 150 MW/ (20,150) $11 270 MW 270 MW 190 190 116.3 MW/ (10,150) $15 116.3 MW/ (10,150) $15 $15 $15 69.6 MW/ (50,400) $95 69.6 MW/ (50,400) $95 $95 $95 474.1 MW/ (350,500) $10 474.1 MW/ (350,500) $10 $10 $10 $317.5 $317.5 $258.2 $258.2

slack A B C D E E 0.89 0.74 0.68 0.52 0.00 A 0.00 -0.15 -0.21 -0.37 -0.89 distributed 0.24 0.09 0.03 -0.13 -0.65 B 0.15 0.00 -0.06 -0.22 -0.74 line AE Dfax

Demand MW Generation MW A 0.00 266.32 B 270.00 0.00 C 270.00 0.00 D 270.00 69.58 E 0.00 474.11

slack

sum DfaxDem sum DfaxGen total E 522.65 272.65

• 250.00

A

• 196.67
• 446.67
• 250.00

distributed 0.00

• 250.00
• 250.00

B

• 74.40
• 324.40
• 250.00

Distributed slack: “impact” of demand on flow is zero. if demand is assumed to grow/decrease “conformingly” (proportionally to the pattern/distribution for which the Dfaxes are calculated) such evaluation is not required for any demand level. This may be the reason for such a choice of reference.

i i ki

Pd Dfxa *



Economic sensitivities

Binding transmission constraint LaGrange multiplier:

incremental savings/costs (re-dispatch) caused by an increment/decrement in constraint limit

De-composition of LaGrange multiplier provides ECONOMIC SENSITIVITIES

 

    

j kj j j kj j k

EcSens c Pg c f 

Economic sensitivities

ECONOMIC SENSITIVITIES: generators whose output is adjusted to produce an incremental change on the constraint flow, defining its economic value (conflicting/similar constraints,..)

 

    

j kj j j kj j k

EcSens c Pg c f 

Demand

MW price payment Generation MW price payment LoadB 270.0 317.5 85721.8 Alta 150.0 15.0 2250.0 LoadC 270.0 258.2 69702.6 Parkcity 116.3 15.0 1744.7 LoadD 270.0 95.0 25650.0 Solitude 0.0 258.2 0.0 Sundance 69.6 95.0 6609.8 Brighton 474.1 10.0 4741.1 Total 181074.4 15345.6 VTI= 165728.8

line

Flow price bus from price bus to VTI Lagrange Lagrange*Flow AB 350.0 15.0 317.5 105870.8

• 456.9
• 159899.7

AD 166.3 15.0 95.0 13305.3 0.0 0.0 AE 250.0 10.0 15.0 1250.0

• 23.3
• 5829.1

BC 80.0 317.5 258.2

• 4746.4

0.0 0.0 CD 190.0 95.0 258.2 31000.0 0.0 0.0 DE 224.1 10.0 95.0 19049.2 0.0 0.0 Total (VTI) 165728.8

• 165728.8

g AB AE c AB AE Parkcity 3.26 -1.00 15.00 48.85 -15.00 Sundance

• 5.57 -0.22

95.00 -528.80 -20.47 Brighton 2.31 1.22 10.00 23.10 12.15 TOTAL 5.57 1.22 LaGrange -456.86 -23.32 SEc

Conclusion: Dual pricing seems to be the way to go MW

$

A B

G1 G2 G3

250 MW/ (250 250 MW/ (250-

• 1500, $30)

1500, $30) 800 MW/ (0 800 MW/ (0-

• 1300, $20)

1300, $20) 50 MW/ (50 50 MW/ (50-

• 100, $40)

100, $40) 1100 MW 1100 MW 800 MW/ (1000) 800 MW/ (1000)

$ (A) $ (B) $ (T) virtual congestion $ (A) $ (B) $ (T) virtual congestion 20 30 10 20 40 20 T uplift no T uplift … sub-optimal dispatch/reality … …. T congestion over-compensation (Pgmin) ….

example

… from Ring’s ..

800 50 250 20 30 40 primal dual

dual dual

dual dual Side payments Min side payments

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