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

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

Dual space shows “the other side of the coin”! $ MW

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

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

Interconnected markets T price A T MW L B T penalty L T price L

Isolated markets B A P’d(A) P’d(B)

Transmission violation B A T price L T penalty L violation

The “trick” seems to work … change the limit and B re-run … A T price L L’

Transmission violation s 1250 MW/ (0,1500) $50 $50 G1 A ^1069 MW/1000$2000 G2 50 MW/ (0,50) $80 B 181 MW/1000$2000 $1764 373 MW/1000$2000 $2336 ^746 MW/700$2000 D 373 MW/1000$2000 G3 1350 MW 1350 MW C 50 MW/ (0,50) $190 $2907

… change the limit and re-run does not work… Alternatives do … a) Solve the primal. Solution: Pg * / F * it kt   max * max If ( F abs ( F )) / F Tol Then b) kt kt kt  max * F abs ( F ) kt kt c) Solve Dual

          Minimize c Pg IL / 60 it it t   Pg t i Subject to : Primal      Pg Pd t it jt t i j        min max Pg Pg Pg g , g i , t it it it it it          IL RRDn Pg Pg IL RRUp dn , up i , t  t it it it 1 t it it it              max max F Dfax Pg Dfax Pd F f , f k , t kt ki it kj jt kt kt kt i j Solution : Pg * / F * Maximize it kt            , g i , g , dn , up , f , f            min max g Pg g Pg         it it it it  Pd   t jt            dn IL RRDn up IL RRUp   j i it t it it t it          t                max max f ( F Dfax Pd ) f ( F Dfax Pd )     kt kt kj jt kt kt kj jt     k j j Dual Subject to :                g g dn up dn up   t it it it it it 1 it 1              Dfax f f c IL / 60 i , t ki kt kt it t k   unrestrict ed t t        g 0 g 0 i , t it it      dn 0 up 0 i , t it it        f 0 f 0 k , t kt kt

Problem formulation            max LowerBound ( L ) min Uplift ( F F * ) i kt kt kt    p , , , i t k Transmission congestion pricing subject to cost causation – cost recovery            Uplift ( p GenCost ) ( g g * ) i ; 1 ,..., L i it it it it t   Uplift 0 i i    0 k , t kt        p Dfax i , k , t it t kt ki k                 L 1 L 1 L 1 L 1 L 1 L 1 Solution : p ,..., p ,... / ,..., ,... / ..., ,... i 1 it 1 t k 1 kt T uplift            L 1 L 1 L 1 MPP p p p GenCost g ,..., ,... max ( ) i i 1 it it it it g t    st m g M i , t it it it      ramp g g ramp i , t  it it it 1 it    L L L 1 1 1 Solution : ( g ,..., g ,...), MPP i 1 it i                    L 1 L 1 L 1 max UpperBound ( L 1 )  MPP ( p GenCost ) g *  ( F F * ) i it it it kt kt kt   i t t k          L 1 L 1 L 1 L 1 If MPP 0 then MPP 0 and ( g ,..., g ,...) ( 0 ,..., 0 ,...) i or m 0 i i i 1 it it

… change the limit and re-run does NOT work… Alternative does .. Initially violated Initially violated lines line BC NOT AB & BC both binding 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

Transmission violation s $50 $50 $80 $50 $1764 violated $2336 2 nd run $199 binding $190 $194 1 st run NOT binding ! $2907 $190 $50 alternative $80 binding $135 $190

T limit relaxation G2 101 MW/ (0,150) $50 10 MW/ (0,10) $75 ^101 MW/100$2000 G1 111 MW A B $50 $2050 G2 (101+  ) MW/ (0,150) $50 (10-  ) MW/ (0,10) $75 (101+  )* MW/(101 +  ) $2000 G1 111 MW A B $50 $75

T congestion over-compensation G2 91 MW/ (0,150) $50 10 MW/ (10,50) $75 91 MW/100$2000 G1 101 MW A B $50 $50 G2 91+  MW/ (0,150) $50 10-  MW/ (10-  ,50) $75 (91+  )* MW/(91 +  ) $2000 G1 101 MW A B $50 $75

T congestion over-compensation G2 91 MW/ (0,150) $50 10 MW/ (10,50) $75 91 MW/100$2000 G1 101 MW A B $50 $50 G2 100 MW/ (0,150) $50 1 MW/ (0,50) $75 100 MW/100 $2000 G1 101 MW A B $50 $75

Economic sensitivities Are we using the right tool? Dfaxes bottleneck! CM $ Congestion Management ($) it seems that ..not always

Where is the “root” of such confusion? …. I have always had the feeling that … … zzzzzzz …. .. deep down … nobody really rise help (Dfax-) understands me .. . lower help (Dfax+) .. or that people find me boring … bla … bla bla ….

Physical sensitivities: relative to the slack, do not change with dispatch,.. changing the reference does not help, … nor changing the name line AE (Dfaxes, PTDF,..): 1 0.8 Sundance Gen 0.6 E D Brighton 0.4 Gen 0.2 0 A A B C D E -0.2 B C -0.4 Gen Gen Gen Alta Park city -0.6 Solitude -0.8 -1 E A distributed B

S undance Gen 69.6 MW/ (50,400) $95 69.6 MW/ (50,400) $95 E D Brighton $10 $10 $95 $95 224.1 224.1 270 MW 270 MW Gen 3 3 6 6 . . 474.1 MW/ (350,500) $10 474.1 MW/ (350,500) $10 6 6 1 1 250* 250* 190 190 A $15 $15 80 80 350* 350* $317.5 $317.5 B $258.2 $258.2 270 MW 270 MW C 150 MW/ (20,150) $11 150 MW/ (20,150) $11 116.3 MW/ (10,150) $15 116.3 MW/ (10,150) $15 Gen Gen 270 MW 270 MW Gen Alta P ark city S olitude

line AE Dfax Demand Generation slack A B C D E MW MW E 0.89 0.74 0.68 0.52 0.00 A 0.00 266.32 A 0.00 -0.15 -0.21 -0.37 -0.89 B 270.00 0.00 distributed 0.24 0.09 0.03 -0.13 -0.65 C 270.00 0.00 D 270.00 69.58 B 0.15 0.00 -0.06 -0.22 -0.74 E 0.00 474.11 sum sum slack DfaxDem 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.  Dfxa * Pd ki i i

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         f c Pg c EcSens k j kj j kj j j