The Benefit of Coordinating Congestion Management in Germany

Transcription

1 1298 Discussio Papers Deutsches Istitut für Wirtschaftsforschug 2013 The Beefit of Coordiatig Cogestio Maagemet i Germay Friedrich Kuz ad Aexader Zerrah

2 Opiios expressed i this paper are those of the author(s) ad do ot ecessariy refect views of the istitute. IMPRESSUM DIW Beri, 2013 DIW Beri Germa Istitute for Ecoomic Research Mohrestr Beri Te. +49 (30) Fax +49 (30) ISSN prit editio ISSN eectroic editio Papers ca be dowoaded free of charge from the DIW Beri website: Discussio Papers of DIW Beri are idexed i RePEc ad SSRN:

3 The Beefit of Coordiatig Cogestio Maagemet i Germay Friedrich Kuz Aexader Zerrah May 13, 2013 The maagemet of cogestio withi the Germa eectricity trasmissio etwork has become more importat durig the ast years. This emergig reevace is caused by the icrease of reewabe geeratio ad the partia phaseout of ucear power pats. Both deveopmets yied a chage i the trasmissio fow patter ad thus the eed for cogestio maagemet. Currety, four Germa trasmissio system operators (TSOs) are i charge of maagig cogestio usig curative methods, particuary re-dispatch of power pats. However, the existece of four TSOs withi Germay iduces the questio whether coordiatio betwee them i maagig atioa cogestio woud be beeficia. To address this issue, we appy a geeraized Nash equiibrium mode to aayze differet degrees of coordiatio, coverig the Germa eectricity market with a detaied represetatio of the geeratio ad etwork structure. Our resuts idicate that the costs of cogestio maagemet decrease i a risig degree of coordiatio as TSOs take ito accout cogestio i other operators zoes. Tota costs are highest i case each TSO is soey resposibe for its ow zoe, ad owest if oe itegrated etity is i charge of mitigatig cogestio. We cocude that, i a setup with mutipe TSOs, iducig coordiatio, for istace through a commo market, has the potetia of owerig the overa costs of cogestio maagemet. JEL Codes: C61, L94, Q40 Keywords: Cogestio Maagemet, Coordiatio, Eectricity Ecoomics, Geeraized Nash Equiibrium, Germay The authors woud ike to thak Daie Huppma, Thure Traber, ad Christia vo Hirschhause for vauabe commets. Friedrich Kuz ackowedges the fiacia support by the Mercator Foudatio. Germa Istitute for Ecoomic Research (DIW Beri), Mohrestr. 58, D Beri, fkuz@diw.de Germa Istitute for Ecoomic Research (DIW Beri), Mohrestr. 58, D Beri, azerrah@diw.de 1

4 1 Itroductio Icorporatig icreasigy higher shares of reewabes i the Germa eectricity geeratio portfoio demads adjustmets i the etire eectricity system. For istace, markets ad their uderyig procedures are required to be redesiged to aow for the itegratio of itermittet geeratio. Furthermore, trasmissio of eectricity to oad ceters becomes more importat. Firsty, the geographica ocatio of reewabe resources i particuar wid ad soar ad thus their spatia geeratio patter depeds o atura coditios. Secody, reewabe capacities are istaed i a more decetraized fashio tha covetioa therma geeratio uits. Both aspects resut i ew requiremets o the trasmissio etwork to trasport eectrica eergy from geeratio to oad ceters. I the og term, the fexibiity of reshapig the trasmissio ifrastructure aows to meet the upcomig requiremets, fiay yiedig a effective itegratio of reewabe geeratio. I the short term, however, the trasmissio etwork is predetermied to the existig ifrastructure. Hece, the capacity of the existig trasmissio etwork may ot be aways sufficiet to trasport the requested amout of eectrica eergy. Cogestio ca occur, defied as a situatio i which the requested trasmissio capacity exceeds the avaiabe capacity of the existig etwork. I order to dea with this issue of imited trasmissio capacity, cogestio maagemet methods are deveoped to ease ie overfows either usig techica or ecoomic procedures. Kumar et a. (2005) provide a iterature survey o cogestio maagemet methods i dereguated eectricity systems: techica measures aim to icrease the capacity by adjustig oad fows i the trasmissio etwork through specific devices (for exampe FACTS, phase-shiftig trasformers, switchig of trasmissio ies), thereby avoidig chages i demad ad geeratio. O the other had, there are ecoomic methods, reyig o adjustig oda feed-is (oda geeratio ad/or demad) to reduce ie overoadigs. Those atter methods ca be divided accordig to their timig withi the market cearig process ito prevetive ad curative methods. Prevetive measures are appied before or durig the cearig of the daiy eectricity markets whereas curative methods are appied after fia market cearig. Expicit ad impicit auctios are exempary prevetive cogestio maagemet methods ad are appied, for istace, i cetra wester Europe for aocatig cross-border trasmissio capacity 1, or i the US regioa market of Pesyvaia-New Jersey-Maryad (PJM) 2 usig a oda pricig approach. Curative cogestio maagemet icudes the redispatch of power pats based o the fia market commitmets, ad couter-tradig. These methods are appied i most atioa eectricity markets i Europe to maage itera cogestio issues. Regardig the ecoomic evauatio of these maagemet methods, de Vries ad Hakvoort (2002) provide a study i which they show that prevetive as we as curative cogestio maagemet measures are equay efficiet i the short term perspective. Dig ad Fuer (2005) aayze the ecoomic effects of differet pricig ad cogestio maagemet regimes 1 See 2 See 2

5 o the Itaia eectricity system. Their research shows that geeratio costs are idetica amog the ivestigated regimes, but the distributio of beefits ad costs amog market participats differs. Comparabe aayses are performed i Kuz (2012) for the Germa ad i Neuhoff et a. (2011) for the Europea eectricity system. The atter two studies, i cotrast to the previous aayses, idetify cost beefits from adjustig cogestio maagemet regimes: as the redispatch of power pats is restricted to atioa uits, higher cogestio maagemet costs are observed tha i a perfecty coordiated oda pricig regime. The issue of coordiatio i cogestio maagemet amog differet trasmissio system operators (TSOs) is further ivestigated i Oggioi et a. (2012). The authors deveop a geeraized Nash equiibrium mode which is abe to refect differet degrees of coordiatio amog regioa TSOs. It is appied i Oggioi ad Smeers (2012) ad Oggioi ad Smeers (2013) to styized eectricity systems. It is show that the degree of coordiatio i cogestio maagemet affects redispatch costs. I this paper, we buid o the equiibrium mode deveoped i Oggioi et a. (2012). I order to ivestigate differet degrees of coordiatio amog Germa TSOs i coductig atioa cogestio maagemet, we suggest a ew method of sovig the arisig cass of probems based o mutipicativey decomposig the mutipiers of shared costraits. Towards gaiig umerica isights, we empoy a detaied represetatio of the Germa eectricity system coverig the high-votage trasmissio etwork, which is divided ito four baacig zoes each of which beig maaged idepedety by oe of the four TSOs. Our resuts revea that the eve of coordiatio amog the four Germa TSOs i mitigatig atioa cogestio i the trasmissio etwork impacts cogestio maagemet costs. Whie the cosidered cases are by costructio idetica i the spot market dispatch of power pats ad hece the cogestio patter, they diverge i the utiizatio of avaiabe redispatchig resources. I a setup with perfect coordiatio impemeted through oe sige TSO resposibe for a zoes a east-cost redispatch ca be achieved. I the restricted cases with imperfect coordiatio betwee mutipe TSOs, the redispatchig voumes ad costs rise. This is particuary due to more expesive measures beig required to ease overoadigs i the trasmissio etwork. The remaider of this paper is structured as foows: Sectio 2 itroduces the ecoomic redispatch mode which captures the issue of coordiatig cogestio maagemet amog mutipe TSOs. The deveoped mode is appied to a dataset coverig the Germa eectricity system which is described i Sectio 3. We preset our resuts i Sectio 4, ad discuss them i Sectio 5. Fiay, Sectio 6 cocudes. 2 The Mode Our mode cosists of two stages: first, i the pre-stage, the eectricity spot market is ceared by equaizig suppy ad demad i a cost-miimizig fashio without takig etwork imitatios ito accout. Thereafter, i the mai stage, pats ad oad are redispatched to correct for etwork ifeasibiities that potetiay may have emerged. Our focus ies o this mai cogestio maagemet phase for which we aayze three cases: 3

6 firsty, a urestricted bechmark case with oe sige TSO beig resposibe for redispatch across a zoes. Secody, a restricted coordiated case with severa TSOs, each of which beig boud to resources withi its ow zoe but i charge for etwork feasibiity across a zoes, ad thirdy a restricted ucoordiated case where, agai, TSOs are boud to ow resources but are resposibe for mitigatig overfows oy withi their ow zoes. I a three cases, the two stages are ot coected by ay kid of feedback mechaism, the pre-stage is soey supposed to create a market-cearig dispatch that serves as data for the mode s mai stage. 2.1 Pre-Stage: Market Cearig The power system cosists of a set of odes N = { 1,..., N } at each of which there is ieastic demad q ad determiistic ijectio of reewabes that is wid, soar ad biomass geeratio g res. I this respect, the reewabe techoogies are assembed i R = {W id, Soar, Bio} res. Residua demad is served by dispatchabe pats p P = {p 1,..., p P } each of which beig ocated at a certai ode. Each covetioa pat exhibits costat margia geeratio costs c p ad a maximum capacity of gp max. For coveiece, we abstract from further techica features such as miimum geeratio requiremets, rampig costraits ad so forth. Note that reewabes geeratio is either dispatchabe or subject to ay ucertaity, but eters the mode as determiistic data. Exports to or imports from eighborig coutries are take ito accout impicity by adjustig our demad data (see Sectio 3). Mimickig the Germa market desig, which features o expicit or impicit auctios of atioa trasmissio capacities, we mode a uiform price across a odes. Moreover, we assume perfect competitio ad the absece of ay strategic behavior at the pre-stage: the market is ceared o a power exchage ru by a sige cost miimizig etity, dispatchig geeratio G p for each pat, thereby equaizig suppy ad residua demad without takig the power etwork ito accout: mi G p c p G p (1) p G p gp max p (2) G p = ( q ) g res (3) p res where G p 0. As the objective fuctio (1) ad the costraits (2), (3) are affie, the formuatio costitutes a LP such that a soutio is ecessariy gobay optima. We deote the resutig dispatch of this pre-stage market cearig as vector g = [g p1...g pp ] g p. 3 3 Note that variabes are deoted by capita etters, parameters by owercase etters. Here, the pre-stage optimizatio resut becomes data for the mode s mai stage. 4

7 2.2 Urestricted Case: a Sige TSO I the mai stage of the mode, the power etwork comes ito pay. I case the prestage market cearig outcome yieds cogestio o oe or severa ies, the TSO is i charge of reievig it. 4 Note that the firms owig the geeratig uits do ot have ay discretio here: accordig to Germa aw they are obigated to execute the orders of the TSO whose grid they are coected to i case of etwork istabiity. 5 As a bechmark, et a sige TSO be resposibe for cogestio maagemet withi the whoe system by optimay redispatchig pats p P, arragig oad sheddig or curtaiig reewabes geeratio at odes N. Remember that each pat is associated to a specific ode. I this respect, et the subset of a pats coected to ode be redered by P() P. Deote the redispatched quatity at each pat G p R, the amout of oad sheddig at a ode by LS R +, ad the quatity of reewabes curtaimet for each ode by Cur res R +, res R. Note that redispatched quatities at each pat ca be positive or egative. I our mode, we regard oad ad reewabes curtaimet as kids of emergecy measures which a TSO ca draw upo i case the actua resources do ot suffice. This iterpretatio is backed up by Germa aw, which prescribes such actios as ast resort to maitai system stabiity. 6 Margia geeratio costs at pat p amout to c p, as above, whereas oe MW of oad sheddig costs c LS, for wid, soar, ad biomass curtaimet c res res R. 7 The TSO s objective (4) cosists i miimizig redispatchig costs subject to severa geeratio costraits: (5) prescribes that the overa chages i geeratio ad oad et out each other, whereas (6), (7) estabish that geeratio at each pat p may be o arger tha its capacity imit gp max, ad oegative. Reca that g p represets the dispatched quatity from the market cearig stage. Restrictios (8), (9) esure that oad sheddig ad reewabes curtaimet at ode is at most as arge as demad q, or the produced quatities g res respectivey. Network feasibiity the cetra issue of this probem is expressed i coditio (10): for each ie, the tota fow, positive as we as egative, may be o arger tha the ie capacity p max. Loop fows are captured with hep of the PTDF 8 matrix, of which the (, )-eemet reders the fractio of the tota fow 4 Reca that overfows may soey origiate from the pre-stage market dispatch that equaizes residua oad ad dispatchabe suppy. They do ot emerge from ay kid of ucertaity cocerig reewabes or oad forecasts as demad ad wid, soar, ad biomass productio eter the mode as determiistic data. 5 The ega basis is aid dow i 13.1, 13.1a of the Germa Eergy Idustry Act (Eergiewirtschaftsgesetz). Moreover, a reguatio by the Germa Federa Network Agecy BNetzA substatiates further operatioa guideies, see BNetzA (2012b) 6 The icusio of such measures is i ie with Germa aw, which aows the o-ijectio of reewabe geeratio uder certai circumstaces (see the Germa Eergy Idustry Act (Eergiewirtschaftsgesetz), 13.2, 13.2a, ad the Germa Reewabe Eergy Act Ereuerbare-Eergie-Gesetz, 11, 12), ad aso demad-side participatio (see the Germa Eergy Idustry Act 13.2). 7 The Germa Rebewabe Eergy Act 12, stipuates that i case of reewabes curtaimet operators of the site get compesated for betwee 95% ad 100% of their foregoe profits. We quatify our cost parameter accordig to this reguatio. The costs for the curtaimet of demad are supposed to refect the vaue of ost oad ad are set to 5000 EUR/MWh. 8 Power trasfer distributio factor 5

8 from ode to a hub ode through ie. Ijectio at a ode is give by the sum of the geeratio of a pats at, the redispatched quatity, reewabes geeratio g res ad oad sheddig quatity mius demaded quatity ad reewabes curtaimet quatity. The TSO s costraied optimizatio probems thus reads as foows: mi [c p G p ] + G,LS,Cur res G p + p [ p LS res Cur res ] [ c LS LS + res c res Cur res ] (4) = 0 (ρ) (5) g p + G p g max p 0 p (λ 1 p) (6) g res ptdf, (g p + G p ) + p P() res g p G p 0 p (λ 2 p) (7) q + LS 0 (λ LS ) (8) + Cur res 0, res (λ res ) (9) g res q + LS res Cur res pmax 0 (µ +, where the mutipiers i paretheses ρ R, λ 1 p, λ 2 p R + p, λ LS R +, λ res R + res, µ +, µ R + represet the shadow price of the respective costrait. The correspodig KKT coditios costitute a mixed iear compemetarity probem: 0 = c p + ρ + λ 1 p λ 2 p + s.t. p P() 0 c LS + ρ + λ LS 0 c res ρ + λ res 0 = p G p + [ + [ ptdf, ( µ + ptdf, ( µ + ptdf, ( µ + LS res µ µ µ Cur res ) (10) ) ] G p free p (11) ) LS 0 (12) ) Cur res 0, res (13) ] ρ free (14) 0 g p G p + g max p λ 1 p 0 p (15) 0 g p + G p λ 2 p 0 p (16) 0 q LS λ LS 0 (17) 0 g res Cur res λ res 0, res (18) 6

9 0 p max + 0 p max ptdf, ptdf, p P() (g p + G p ) + res p P() (g p + G p ) + res g res g res q + LS res q + LS res Cur res Cur res µ µ + 0, (19) 0, (20) Note that we have a iear objective fuctio (4), ad for (5) - (10) the iear costrait quaificatio hods. A soutio for (11) - (20) is thus ecessariy gobay optima. 2.3 Restricted Cases: Mutipe TSOs To expose the effect of coordiatio, i this subsectio we divide the set of odes ito zoes for each of which there exists oe TSO soey abe to maipuate quatities i its ow zoe. Each TSO is resposibe to esure its zoa system baace whie he is restricted to the redispatchig resources ocated i its zoe. To this ed, cosider T zoes withi each of which a sige tso T = {tso 1,..., tso T } is resposibe for redispatchig pats, or oad sheddig ad reewabes curtaimet respectivey. Note that each pat p is associated to a specific ode, ad each ode to a specific TSO. Thus, deote the subset of a odes withi the zoe of a TSO by N (tso) N, ad reca the subset of a pats coected to a ode beig deoted by P() P. Therefore, the set of a pats ocated withi the zoe of a certai TSO ca be expressed as P (N (tso)). However, the TSOs ifuece each other via the shared costraied of etwork feasibiity o which the actios of a TSOs have a effect for a ies. Keep i mid that a TSO redispatchig i its zoe causes a effect ot oy withi that zoe, but due to oop fows aters fows o a ies i a zoes. To represet this setup as a geeraized Nash game, et G tso,p, LS tso,, Curtso, res deote the redispatched quatities of tso at pat p, the oad sheddig, ad the reewabes curtaimet of tso at ode. Reca that the game is restricted isofar as maipuatios at pats or odes i a specific zoe ca oy be udertake by the respective TSO. The optimizatio probem agai cosists i miimizig redispatchig costs uder idividua ad shared costraits ad for each payer reads: [ ] mi G,LS,Cur res p P(N (tso)) p P(N (tso)) G tso,p + [c p G tso,p ] + N (tso) [ N (tso) LS tso, res c LS LS tso, + res Cur res tso, ] c res Cur res tso, (21) = 0 tso (ρ tso ) (22) 7

10 g p + G tso,p g max p 0 p P(N (tso)) (λ 1 p) (23) g p G tso,p 0 p P(N (tso)) (λ 2 p) (24) q + LS,tso 0 N (tso) (λ LS ) (25) + Curtso, res 0 N (tso), res (λ res ) (26) g res ptdf, (g p + G tso,p ) + p P() res g res q + LS tso, res Curtso, res, tso pmax 0 (µ +, tso, ) (27) Costraits (22) - (26) take effect for each TSO separatey. Aso ote that the shared costrait here the etwork restrictio (27) is specific for each TSO as the dua variabes µ + tso, ad µ tso, aow for a idividua vauatio of the respective costraits. Mathematicay, however, this yieds a uderdetermied system i the way it is typica for geeraized Nash games: idetica costraits are vaued differety by each payer, therefore the probem cosists of more free variabes tha distict equatios. To cope with that issue i a ecoomicay ad mathematicay soud maer, we modify the probem by assumig ex ate a exogeousy differet accoutig of each payer towards the shared costraits itroduced through a coefficiet γ,tso 0. At the same time, we reduce the umber of free variabes by repacig the payer-ie-specific vauatios µ tso,, µ+ tso, by oy ie-specific mutipier variabes µ +, = µ +, tso 1, =... = µ +, tso T,. I other words, we decompose the idividua mutipiers ito a payer-specific exogeous parametric part γ,tso ad a edogeous mutipier µ +, µ that is the same across a payers, i.e. µ +,tso = γ,tso µ +. As a resut, we have as may equatios as variabes ad the system ca be soved. The reative vauatio of the same shared costrait is pied dow exogeousy by γ,tso, motivated by theoretic cosideratios. The absoute eve, however, is determied withi the soutio of the mode i the mutipiers µ +,. Cosequety, we repace (27) by (28): γ,tso ptdf, (g p + G tso,p ) + p P() res g res q +LS tso, ) Curtso,] res pmax res 0, tso (µ +, ) (28) Observe that the shared etwork restrictio (28) is mutipied with γ,tso. The correspodig KKT coditios for (21) - (26) ad (28) ca be formuated as mixed iear 8

11 compemetarity probem: tso the foowig set of coditios has to hod: [ 0 = c p + ρ tso + λ 1 p λ 2 ( p + ptdf, γ,tso µ + µ ) ] G tso,p free s.t. p P() tso, p P(N (tso)) (29) 0 c LS + ρ tso + λ LS 0 c res ρ tso + λ res + ptdf, γ,tso ( µ + ptdf, γ,tso ( µ + µ µ ) LStso, 0 tso, N (tso) (30) ) Cur res tso, 0 0 = p P(N (tso)) G tso,p + N (tso) [ LS tso, res Cur res tso, tso, N (tso) (31) ] ρ free tso (32) 0 g p G tso,p + g max p λ 1 p 0 tso, p P(N (tso)) (33) 0 g p + G tso,p λ 2 p 0 tso, p P(N (tso)) (34) 0 q LS tso, λ LS 0 tso, N (tso) (35) 0 g res Curtso, res λ res 0 tso, N (tso) (36) 0 γ,tso 0 γ,tso p max p max + ptdf, ptdf, p P() (g p + G tso,p ) + res p P() (g p + G tso,p ) + res g res g res q + LS tso, res q + LS tso, res Curtso, res µ 0, tso (37) Curtso, res µ + 0, tso (38) As expaied above 9, i this geeraized Nash game, we itroduce differet degrees of coordiatio betwee the payers exogeousy with hep of the parameters γ,tso that 9 Note that as og as γ,tso > 0 for some tupe, tso (37), (38) do ot ose or gai ay iformatio by beig mutipied with γ,tso as the eft-had iequaity ca aways be divided by that gamma. The differet ex ate vauatios, however, take effect i (30) - (32) where they represet tso s sesibiity towards the costrait s mutipier. 9

12 refect the vauatio of the shared etwork restrictio of ie by the respective TSO. I order to gai a coveiet ad cocise represetatio, we coect these parameters i a (L T SO)-matrix Γ = [γ,tso ]. As a exampe, cosider [ ] 1 1 Γ = (39) 0 1 I this case, tso 1 ad tso 2 evauate cogestio o ie 1 equay (first row), but tso 1 does ot take ito accout cogestio o ie 2 at a (secod row). 10 Reca that for each TSO the respective etry of Γ is mutipied with the shared etwork feasibiity costrait of ie. I case of a zero-etry, the TSO thus does ot see the ie i its optimizatio probem see (37), (38). For our aaysis, we put forward two cofiguratios of Γ. I versio restricted coordiated a TSOs are equay resposibe for each ie, which i tur impies that there exists coordiatio, for istace through a commo market with the same shadow prices across a payers. This is impemeted for Γ beig a matrix of oes. I the case restricted ucoordiated each TSO takes ito accout oy ies withi its ow zoe ad those ruig betwee its zoe ad a eighborig oe. The accordig coums of Γ thus cosist of zeros ad oes at the respective etries. Reca that i ay case each payer s access is restricted to resources ocated i its ow zoe. Comparig our approach to the iterature, Oggioi et a. (2012) aayze a simiar Geeraized Nash framework, but impemet a soutio techique foowig Nabetai et a. (2011), requirig certai techica assumptios to be fufied. Cotrary to their approach of a additive decompositio of the idividua mutipiers for the commo costraits, our mutipicative method provides a ituitive techique of impemetig exogeous variatios i the cosideratio of sige ies by idividua payers. Moreover, our approach is capabe to easiy switch off the resposibiity of payers for specific costraits, i.e. ies, simpy by the respective etry γ,tso = 0. 3 Data The appicatio of the described mode covers the eectricity system of Germay for the year 2011 with a detaied represetatio of the high-votage trasmissio etwork. I the foowig subsectios, we preset our data sources as we as assumptios o trasmissio, geeratio, ad oad. 3.1 Trasmissio We focus our aaysis o the maagemet of the Germa high-votage trasmissio etwork icudig votage eves of 220 ad 380 kv. For coveiece, we assume that there 10 The etries of Γ are geeray ot restricted to γ,tso {0, 1}, as we cofigure it i our appicatio, but provide a high eve of fexibiity: for istace, the first row i the exampe coud aso be [2 1]. I that case, tso 1 woud vaue cogestio o ie 1 twice as much as tso 2. 10

13 are o grid osses. The topoogy of the etwork, comprisig 342 substatios ad 866 trasmissio circuits, is based o ENTSO-E (2012b) ad covers the baacig area of the four Germa TSOs 50Hertz, Amprio, TeeT TSO, ad TrasetBW. The techica characteristics of the trasmissio circuits are based o Kießig et a. (2001) ad icude votage specific vaues for resistace, reactace, ad therma trasmissio capacities. The respective vaues for resistace ad reactace, accouted with the egth of idividua trasmissio circuits, provide the basis for the derivatio of the power trasfer distributio factors (PTDF). The PTDF matrix etais the iformatio to which extet trasmissio ies are utiized by a oda ijectio at a particuar substatio ad is costat i time as we abstract from ay chages i the etwork topoogy. Additioay, we derate the therma trasmissio capacity by 20% to accout especiay for security requiremets. 11 I order to reduce computatioa compexity, we cocetrate our aaysis soey o the maagemet of the Germa trasmissio system ad abstract from direct iteractios with eighborig coutries. To this ed, we treat the import ad export with these coutries as exogeous parameters. Moreover, this approach disetages the effect of coordiatio betwee payers withi a system from potetia re-optimizatios i a NTCbased iteractio betwee systems. The atter aspect is a mai driver of resuts i Oggioi et a. (2012). To iustrate that poit, cosider two coutries betwee which cross-border fows are subject to a et trafer capacity (NTC). If this NTC does ot etirey accout for the avaiabe physica capacity, the itercoector might ot be fuy empoyed i the market dispatch. I such case, redispatchig may occur, which is, however, the ot drive by actua ie cogestio, but by re-optimizatio cosideratios. I costructig our grid topoogy ad PTDF matrix, we take cross-border ies ad ies withi eighborig coutries impicity ito accout. To this ed, we cacuate a PTDF matrix for the whoe cetra Europea etwork, ad the cut off a odes ot ocated withi Germay. We are eft with virtua ies betwee those Germa odes from which itercoectors ru to adjacet coutries. These virtua ies, iheritig the characteristics from the uderyig actua ies i foreig coutries, are represeted by appropriate etries i our PTDF matrix. 3.2 Geeratio O the geeratio side, we expicity differetiate betwee covetioa therma geeratio, which ca be dispatched at specified margia geeratio costs, ad o-dispatchabe reewabe geeratio, whose houry eve is give to the mode as data ad has to be fed ito the grid. Therma geeratio is cosidered o bock eve, ad capacities as we as ocatios are based o BNetzA (2012c). It is assumed that geeratio faciities are coected to the earest substatio. I the course of the 2011 Fukushima icidets, the Germa govermet iitiated to immediatey shut dow severa od ucear power pats. 11 The resutig trasmissio reiabiity margi of 0.8 provides a covetioa approximatio of the N 1 criterio, see for exampe Leuthod et a. (2012). 11

14 We thus aso adjust our uderyig geeratio portfoio accordigy startig from mid- March Geeratio faciities are characterized by their iput fue (ucear, igite, hard coa, gas, oi, hydro) ad techoogy (steam process, gas turbie, combied cyce gas turbie). This iformatio is used to cacuate margia geeratio costs based o fue ad emissio costs, weighted by the power pat specific efficiecy of the geeratio process. Tabe 1 summarizes the assumptios o fue prices, refectig the average price i 2011 (Statistik der Kohewirtschaft, 2013) except for uraium ad igite which are based o ow assumptios. To accout for carbo emissio costs, a average certificate price of EUR per t CO2 is assumed, based o the EUA settemet price at the Europea Eergy Exchage (EEX). The efficiecy of the geeratio process depeds o the process itsef as we as the commissioig year of idividua power pats (Schröter, 2004). Additioay, we impose a error term i the rage of % o the derived efficiecy to further differetiate pats i terms of margia geeratio costs. Tabe 1: Average fue prices i Source: Statistik der Kohewirtschaft (2013) ad ow assumptios. Price [EUR/MWh th ] Uraium 3 Ligite 4 Coa Gas Oi Beside therma geeratio, reewabe eergies are take ito accout comprisig geeratio from wid, soar, ad biomass. As reewabes are cosidered to be o-dispatchabe, we directy use the houry tota wid ad soar geeratio of 2011 from EEX (2012). Cocerig biomass faciities, we assume costat geeratio at avaiabe capacity. Tota geeratio vaues of 2011 are depicted i Tabe 2. I order to derive a regioa reewabe geeratio patter, the ocatios of reewabe istaatios provided from 50Hertz et a. (2012a) are used as proxy. For simpicity ad tractabiity reasos, we assume a perfect positive correatio of reewabe geeratio across the mode regios. 3.3 Load The oad eterig our mode is assumed to be price ieastic ad thus fixed to the oad vaues for each hour of Beside domestic oad, exports to eighborig coutries ad pumpig are icuded, whereas etwork osses are egected. The houry oad patter is based o the data pubished by ENTSO-E (2012a) ad the Germa TSOs. Additioay, we upscae the demad patter to be cosistet with yeary oad vaues reported i Eurostat (2013a). Simiar to reewabe geeratio, atioa oad vaues eed to be distributed to 12

15 substatios i the trasmissio etwork. Foowig Leuthod et a. (2012), we break dow tota houry oad accordig to regioa GDP ad popuatio (Eurostat, 2013b). Our data for oad i Germay represet origia vaues for each hour of 2011 ad are compemeted by houry export quatities (ENTSO-E, 2012a). Tabe 2 depicts the fia demad o a yeary basis. Tabe 2: Load ad reewabe geeratio i (2012) Sources: Eurostat (2013a) ad EEX Yeary oad or geeratio [TWh] Load ic. exports ad pumpig Tota reewabe geeratio 94.7 of which Biomass 31.9 of which Soar 18.5 of which Wid Resuts We ru the urestricted mode ad both variats of the restricted mode restricted coordiated ad restricted ucoordiated o our dataset for a 8760 hours of the year I the foowig, we preset our resuts o etwork overfows, as we as cogestio maagemet costs ad voumes. 4.1 Network Cogestio from Spot Market Dispatch As a first step, we aayze which ies are subject to overoad. Note that the geographica cogestio patter does ot deped o the redispatch mode, but is soey determied by the pre-stage market cearig outcome. Figure 1 visuaizes our fidigs. Gray ies idicate that there is cogestio o the ie ess tha 500 hours, ad back ies visuaize overfows i more tha 500 hours of the year Overa, out of 560 ies, 31 are subject to cogestio i at east oe hour, ad 10 i at east oe hudred hours. Amog a 8760 hours, there are o overfows i 5236 hours, whereas i 3524 hours there is cogestio o at east oe ie, ad i 217 hours o at east five ies. The spatia patter is geeray i ie with actua cogestio reported by the Germa Federa Network Agecy (BNetzA) moitorig report (BNetzA ad BKartA, 2012): we reproduce frequet overfows o a ie from Thurigia to Bavaria, i cetra Bavaria as we as i the orthwester regio of Germay. Atogether, our mode iduces cogestio o umerous ies ad substatios that are aso metioed i BNetzA ad BKartA (2012) however, it as we geerates overfows i regios where it caot be detected i the actua Germa 2011 data. I this respect, especiay the wester/south-wester area has to be metioed. 13

16 Figure 1: Spatia cogestio patter Note, however, that amog those ies severa are icuded withi the Germa Law o Network Expasio 12 as prioritized measures to be pursued withi a medium-ru time frame. Aso the Germa Network Deveopmet Pa of , which is compied by the TSOs, assumes i its aayses those ies to be buit i the earer future. Thus, athough there are some discrepacies betwee the cogestio patter our mode detects ad the actuay observed patter i the wester/south-wester regio, those ies our mode geerates overfows o had bee idetified as proe to cogestio by the actuay resposibe parties. Our fidigs (as we as the origia 2011 data) represet a spatia dispersio withi the Germa eectricity system: the oad ceters i the south ad southwest are remote from regios with excess geeratio, i.e. the easter igite ad orther wid geeratio areas. This imbaace eads to a high eve of fows o the reevat ies ad, together with a high votage grid ot costructed to serve this eeds, thus to cogestio o the respective ies. 12 Eergieeitugsausbaugesetz (ELAG), passed i Netzetwickugspa 2012, see 50Hertz et a. (2012b, pp ) 14

17 4.2 Redispatchig Costs ad Voumes We ow tur to the resuts of the mode s mai stage ad aayze the outcomes with respect to redispatchig costs ad voumes. To this ed, we sum the absoute vaues of a, positive ad egative, redispatch voumes as we as oad ad reewabes curtaimet istaces, ad deote this quatity as tota voume. The redispatchig costs ca be stated as tota ad specific costs. Tota costs describe the expeditures that accrue to a TSO for icreasig geeratio pus compesatio paymets for oad ad reewabes shed, reduced by the received paymets from geerators that decrease their geeratio eve. I this respect, specific costs are cacuated by dividig tota costs by the tota voume ad ca be iterpreted as et paymets per redispatched uit. Tabe 3 summarizes our fidigs. Our cetra resut is ituitive: tota redispatchig costs decrease with a higher degree of coordiatio. For the urestricted mode, redispatchig costs amout to 8.7 miio EUR, whereas for the restricted coordiated case, i which a TSOs are equay resposibe for each ies but ca oy access ow resources, they add up to 56.4 miio EUR. This differece of roughy 47.7 miio EUR ca be attributed to coordiatio, for exampe by a commo poo or market for redispatchig resources. For the restricted ucoordiated mode, where each TSO has access soey to ow resources ad moreover oy takes care of cogestio withi its ow zoe, tota redispatchig costs amout to miio EUR. This differece of roughy 81.8 miio EUR ca thus be traced back to coordiatio, for istace through a commo market for trasmissio capacity. Tabe 3: Resuts for redispatchig costs ad voumes Tota Tota Specific Mode Voume Costs Costs a [TWh] [mi. EUR] [EUR/MWh] Urestricted Restricted Coordiated Restricted Ucoordiated For the restricted mode variats, costs ad voumes are summed over payers. Resuts are rouded to oe decima. a Specific costs are cacuated by dividig tota costs by the tota voume. Cocerig the redispatch voume, o such cear picture emerges: tota yeary quatity is owest for the urestricted mode with about 4.1 TWh, compared to 5.2 TWh i the restricted coordiated mode. Formay, this icrease refects the zoa eergy baace see equatio (22): if each of the four payers, istead of oe TSO across a zoes, has to respect this costrait separatey, each redispatch measure must be baaced withi a zoe. Thus, it is ot possibe that curative actios directy set each other off across zoes i terms of the eergy baace. To iustrate this zoa baace effect, cosider a ie ocated i oe zoe ad cogested i directio west to east. A sige TSO woud, for exampe, ower geeratio at oe pat at the wester ed of ad icrease geeratio of a 15

18 pat ocated east to it by the same amout. If, however, there are mutipe TSOs ad the easter pat ies i aother zoe, both measures woud ot set off each other ay more to keep up the respective zoa baace, ad further quatities withi both zoes woud have to be activated. I the restricted ucoordiated mode, the tota redispatch voume amouts to 4.9 TWh, which is betwee the other cases: o the oe had, due to the ack of coordiatio, measures i oe zoe coud ead to ew cogestio i other zoes, drivig the voume up compared to the urestricted case. O the other had, as foreig TSOs are ot resposibe for cogestio withi a payer s ow zoe, the zoa baace effect is ot active, which reduces the redispatchig voume compared to the restricted coordiated case. 14 Moreover, there is a tedecy to utiize more expesive redispatch resources. Costs per uit of redispatch rise from 2.1 EUR/MWh i the urestricted sige TSO bechmark, over 10.8 EUR/MWh for the restricted coordiated mode, to 28.1 EUR/MWh i the restricted ucoordiated mode. These high costs are maiy drive by a greater extet of oad sheddig. Figures 2 ad 3 visuaize how costs ad voumes are distributed across redispatchig measures, i.e. covetioa pat redispatchig, reewabes curtaimet ad oad sheddig. 100 Share of redispatch voume i % Urestricted Geeratio redispatch Load sheddig Restricted coordiated Restricted ucoordiated Reewabes curtaimet Figure 2: Redispatch voumes, broke dow ito techoogy shares 14 Puttig it abstract, assume the exempary setup as i the text. Uder the restricted coordiated regime, miimay four geeratio uits are ecessary to reief cogestio whie respectig zoa baaces, whereas i the urestricted case ad restricted ucoordiated mode, miimay two pats are ecessary. I the atter case, moreover, pats i foreig zoes wi ever be utiized. 16

19 100 Share of redispatch costs i % Urestricted Geeratio redispatch Load sheddig Restricted coordiated Restricted ucoordiated Reewabes curtaimet Figure 3: Redispatchig costs, broke dow ito techoogy shares As Figure 2 reveas, across the three modes, the mai fractio of the redispatch voume stems from chagig pats geeratio. Reewabes curtaimet ad oad sheddig pay oy a mior roe. The redispatchig costs, which rise i absoute terms as coordiatio decreases, are maiy drive by the use of expesive oad sheddig, as visuaized by Figure 3. Whie i the urestricted sige TSO case, tota costs ad costs per uit are ow, the high specific costs for the restricted modes ca be attributed to the icreasig share of oad sheddig measures. Note i this cotext, however, that the highest eve of oad sheddig, occurrig i the restricted ucoordiated mode, does oy comprise about 16.5 GWh, which represets about 0.003% of tota yeary demad. Summig up, the eve of coordiatio amog the four Germa TSOs i maagig atioa cogestio i the trasmissio etwork strogy impacts cogestio maagemet costs. 5 Discussio Whie the cosidered cases are by costructio idetica cocerig the iitia spot market dispatch of power pats ad hece the cogestio patter, they diverge i the utiizatio of avaiabe redispatchig resources. I a setup with perfect coordiatio i.e. oe sige TSO for a zoes the east-cost redispatch ca be achieved. I the restricted cases with imperfect coordiatio betwee separate TSOs, redispatchig voumes ad associated 17

20 costs rise. Particuary, this is due to more expesive redispatch measures beig required to ease overoadigs i the trasmissio etwork. Hece, our resuts revea that cogestio maagemet costs icrease substatiay with a ower degree of coordiatio. Through the impemetatio of market mechaisms for redispatchig resources as we as trasmissio capacity, trasparet vauatios of commo costraits i terms of market prices are achievabe, which have the potetia to icrease the degree of coordiatio. I the foowig subsectios, we discuss severa further perspectives o our mode: we compare the setup ad resuts with the actua situatio i Germay, ad aayze coordiatio beefits with respect to security issues, ad etwork extesio. Fiay, we preset a sesitivity aaysis ad commet o imitatios as we as possibe extesios. 5.1 Degree of Coordiatio i Germay Reatig our mode setup ad resuts to the curret regime i Germay, we ivestigate which of our three mode cases of iter TSO coordiatio resembes the prevaiig situatio cosest. Basicay, the uderyig Germa egisatio 15 as we as its operatioaizatio guideies by the TSOs 16 attribute the resposibiity for reievig a overfow to that TSO i whose zoe the cogested ie is ocated, which correspods to our restricted ucoordiated case. I October 2012, the Germa Federa Network Agecy (BNetzA) substatiated i a reguatio that cross-zoa redispatch actios may they be ecessary to reief cogestio that otherwise coud ot be removed or ot sha be coordiated betwee the affected TSOs (BNetzA, 2012a). Beside this short advisory formuatio, however, o cocrete coordiatio measures, procedures or etities are proposed or iitiated. Cocerig biatera or mutiatera agreemets, we are aware of three such coaboratios: firsty, the Security Service Cetre (SSC) 17, a cooperatio iitiative betwee the Germa TSO Amprio ad the Dutch TSO TeeT, the atter beig aso oe of the four payers o the Germa market. SSC s goa cosists i preparig commo cogestio forecasts ad givig advice o coordiatig measures. Moreover, the private etities Coreso 18, with a focus o wester Europe, ad TSC (Trasmissio System Operator Security Iitiative) 19, with a focus o cetra Europe, whose sharehoders are TSOs from severa Europea coutries, provide coordiated etwork security aayses across ad withi coutries. However their emphasis does ot disticty ie o the operatioa perspective of redispatchig measures withi Germay. 20 Thus, the curret situatio i Germay basicay resembes our restricted ucoordiated case athough some coordiatio iitiatives are actuay impemeted however, ot o a broad ad comprehesivey orgaized scope. 21 Turig to the of the Eergy Idustry Act 16 Laid dow i the VDN Trasmissio Code 2007 (Verbad der Netzbetreiber, 2007, pp.2-3, 37). 17 See 18 See 19 See 20 For istace, i case a highy stressed etwork situatio is predicted, iter TSO redispatch measures for Germay are aso suggested as reief (Coreso, 2011, p.4) 21 As a future perspective, the ENTSO-E Network Code o Capacity Aocatio ad Cogestio Maagemet sha pave the way for more iteratioa, ad aso Germa itra-atioa coordiatio of 18

21 actuay prevaied 2011 figures o cogestio maagemet i Germay, BNetzA (2012a, p.10) reports a redispatchig voume of approximatey 3.5 TWh, ad tota costs of more tha 120 miio EUR, yiedig per uit costs of eary 35 EUR/MWh. Additioay, about 0.42 TWh of reewabes ijectio, mosty wid power was curtaied refectig roughy 0.9% of the tota wid geeratio causig additioa costs of 33 miio EUR (BNetzA ad BKartA, 2012, p.59). Cocerig the extera vaidity of our approach, thus, our mode outcomes resembe the actua umbers. There exist some differeces, however, keep i mid that we have to pi dow severa modeig simpificatios ad assumptios. We discuss those issues i greater detai beow. 5.2 Impact of Demad-Side Participatio I order to ivestigate how a voutary participatio of demad side measures ifueces redispatchig costs, we vary the eve of oad sheddig costs c LS. Reca that i our mai mode specificatio they amout to c LS = 5000 EUR/MWh ad thus refect the vaue of ost oad i case demad has to be curtaied. A decrease to 300 EUR/MWh eads to a differet iterpretatio: accordig to a recety specified reguatio by the Germa Federa Govermet, 22 oads may i pricipe aso participate as reguar redispatch measures. I this cotext, a compusory price rage betwee 100 EUR/MWh ad 400 EUR/MWh is specified. 23 Coservativey assumig a price coser to the the upper imit, c LS = 300 EUR/MWh ad re-ruig our mode quatifies the extet of costs that coud be saved by a comprehesive demad side participatio i cogestio maagemet. Tabe 4 presets our resuts: for the urestricted mode, they stay virtuay costat, whereas throughout the restricted mode cases, tota redispatchig costs decrease compared with the basic mode: i the restricted coordiated case, they amout to 52%, ad i the restricted ucoordiated case to 28% of the costs i the basic mode ayout. Specific costs, i.e. costs per uit, as we are owered to 56% (restricted coordiated case), ad 37% respectivey (restricted ucoordiated case). The icusio of demad side measures, thus, bears the potetia for substatia cost savigs. 5.3 Impicatios for Security Aspects The remova of etwork cogestio is utimatey ecessary to provide security of suppy. I this respect, ies that are oaded to the edge of their capacity costitute a risk: if uforesee evets occur, such as pat or ie outages, it is ex ate ucear how overa etwork fows wi be atered. However, the more ies are fuy oaded, the more ikey it is that oe of those caot accommodate a potetiay icreased fow o it, ad the redispatchig measures. See ENTSO-E (2012c, p.29) 22 Reguatio o Dispatchabe Loads ( Verordug zu abschatbare Laste vom 28. Dezember 2012) 23 See Reguatio o Dispatchabe Loads ( Verordug zu abschatbare Laste vom 28. Dezember 2012),

22 Tabe 4: Redispatchig costs ad voumes i case of demad side participatio Tota Tota Specific Mode Voume Costs Costs a [TWh] [mi. EUR] [EUR/MWh] Urestricted Restricted Coordiated Restricted Ucoordiated For the restricted mode variats, costs ad voumes are summed over payers. Resuts are rouded to oe decima. a Specific costs are cacuated by dividig tota costs by the tota voume. system is more proe to breakdows. 24 To assess the impact of coordiatio o security of suppy, we compare the oadig situatio i our mode resuts after the redispatch has bee carried out. Figures 5-7 i the appedix visuaize the geographica patter. I the urestricted case, ess ies are at the edge of their capacity tha i the restricted cases: aayzig a 8760 hours, 19 ies are subject to beig fuy oaded for at east oe hour i the urestricted case, whereas this figure amouts to 25 i the restricted coordiated, ad 29 i the restricted ucoordiated case. Aso those ies which are at the edge of capacity are fuy oaded i ess hours i the urestricted case tha i the restricted cases. Moreover, the absoute umber of oad sheddig or reewabes curtaimet itervetios as we ca be iterpreted as a security idicator for etwork stabiity: accordig to 13.2 of the Germa Eergy Idustry Act, each such chage ca be cassified as kid of a ast resort measure i case redispatchig of covetioa power pats does ot suffice to remove overfows. Comparig our mode outcomes, i the urestricted case o curtaimets have to be carried out, i the restricted coordiated case 977 istaces do occur, ad i the restricted ucoordiated case this figure amouts to Therefore, the coordiatio of cogestio maagemet aso impies a gai i etwork security by reaizig the potetia of decreasig the umber of curtaimet istaces as we as ies at the edge of capacity. 5.4 Impicatios for Network Expasio Theory suggests that cogestio maagemet ca be see as a substitute for physica etwork expasio i the og-ru. To this ed, suppose the existig ies do ot suffice to serve the trasmissio eeds i each hour: o the oe had, ew ies ca be erected i order to mitigate overfows, which comes at a specific cost. Aterativey, cogestio ca be maaged by redispatchig pats, which as we comes at a specific cost. Sovig this tradeoff theoreticay yieds a cost-miima combiatio of both measures, cosider Figure 24 I this cotext, keep i mid that we approximate the N 1 criterio by a trasmissio reiabiity margi of 80%. 20

23 4 that schematicay depicts this issue. 25 Obviousy, the costs for capacity expasio are icreasig i the amout of ie capacity buit (soid ie), ad the costs for cogestio maagemet decrease i overa ie capacities. Here, we differetiate betwee high (upper dashed ie), ad ow cogestio maagemet costs (ower dashed ie), the atter as the resut of a higher degree of coordiatio or as we demad side participatio. Tota costs are cacuated as the sum of expasio ad cogestio costs ad exhibit a U-shape (upper dotted ad dashed ies). 26 Cost miima capacity i coordiated case Cost miima capacity i ucoordiated case Cost Expasio cost Cogestio cost coordiated Tota cost coordiated Capacity Cogestio cost ucoordiated Tota cost ucoordiated Figure 4: Tradeoff betwee capacity ivestmet costs ad cogestio maagemet costs This schematic argumetatio reveas that the miimum of tota costs is achieved at a smaer ie capacity i case of ow cogestio costs compared to the cost miima ie capacity for high cogestio costs. Decreased cogestio costs, for exampe iduced by a higher degree of coordiatio, thus ca have the effect that ess ie capacity has to be buit i order to achieve the cost-miima quatity. By pricig them i, the security 25 For the tradeoff cogestio maagemet versus capacity expasio, see for exampe Kirsche ad Strbac (2004, p.241), from which we as we took the graphica argumetatio. 26 It is straightforward that the sope of the cogestio maagemet cost curves as a fuctio of totay erected capacity is egative, for the capacity expasio costs curve positive. The exact curvature, however, is per se ucear. For brevity of the argumet, however, we here assume the shapes to be as depicted. 21

24 cosideratios discussed above aso fit ito this argumetatio: coordiatig redispatch yieds a higher eve of security. Without coordiatio, this same eve coud be achieved by empoyig more expesive measures, which woud shift the cogestio costs curve further up. Hodig the eve of security costat, thus, agai ess ie capacity is ecessary i case redispatchig measures are coordiated Limitatios Our mode ad its appicatio is subject to severa imitatios. Preseted resuts thus have to be iterpreted takig these ito accout. First, the modeig abstracts from itertempora decisios iheret to eectricity systems such as edogeous dispatch of pump-storage faciities. Secod, it is a pure dispatch mode ad heceforth does ot take ito accout imitatios of geeratio uits through uit commitmet restrictios, as for exampe miimum geeratio, oie ad offie time restrictios. Third, the determiatio of trasmissio fows is based o approximatig a AC oadfow approach, ad security aspects such as the N-1 criterio are ot cosidered i a expicit maer. Reca that we approximate these poits, the N-1 criterio as we as reactive power fows, by a reductio of the avaiabe trasmissio capacity to 80%. Regardig the appicatio of the mode, outcomes are sesitive to iput data. The data used here are based o pubicy avaiabe sources, which etais that assumptios are required to break dow atioa vaues o demad or reewabe geeratio ito regioa eves. Specificay, the topoogy of the etwork is of particuar importace as it determies iefows ad heceforth required cogestio maagemet actios. Furthermore, TSOs may aso be abe to accept temporary overoadig of trasmissio ies or to adjust the etwork topoogy by switchig actios which feeds back to cogestio maagemet costs. Kuz (2012) shows that this fexibiity reduces cogestio maagemet costs substatiay as fows i the trasmissio etwork ca be partiay cotroed. I the preseted appicatio we abstract from these operatioa measures ad assume a fixed etwork topoogy with defied trasmissio imits. Takig these aspects ito accout, it is per se ucear how resuts chage: as further rigidities as we as fexibiities coud be icuded, o cear-cut statemet ca be give i which directio resuts woud chage. 6 Cocusios The Germa eectricity system spaws a spatia oad ad geeratio patter iducig etwork cogestio i a icreasig umber of hours (BNetzA ad BKartA, 2012). Oe reaso cosists i the Eergiewede, the reorgaizatio of geeratio towards reewabe sources, together with a high votage grid ot yet recostructed to serve the emergig eeds. As a short term curative method, the redispatchig of power pats ca be a reief to ie overfows. I our paper, we expore whether the differet TSOs, which is a 27 Note, however, that firm iferece woud require a deeper discussio of that issue. Here, we stick to this brief sketch of the argumetatio ad eave a more detaied aswer ope for future research. 22