Discussion paper
FOR 27 2014
ISSN: 1500-4066 June 2014
INSTITUTT FOR FORETAKSØKONOMI DEPARTMENT OF BUSINESS AND MANAGEMENT SCIENCE
Nodal Pricing in a Coupled Electricity Market
BY
Endre Bjørndal, Mette Bjørndal,
AND Hong Cai
Nodal Pricing in a Coupled Electricity Market
Endre Bjørndal, Mette Bjørndal, Hong Cai Department of Business and Management Science
Norwegian School of Economics Bergen, Norway
Endre.Bjorndal@nhh.no, Mette.Bjorndal@nhh.no, Hong.Cai@nhh.no
Abstract—This paper investigates a pricing model for an electricity market with a hybrid congestion management method, i.e. part of the system applies a nodal pricing scheme and the rest applies a zonal pricing scheme. The model clears the zonal and nodal pricing areas simultaneously. The nodal pricing area is affected by the changes in the zonal pricing area since it is directly connected to the zonal pricing area by commercial trading. The model is tested on a 13-node power system. Within the area that is applying nodal pricing, prices and surpluses given by the hybrid pricing model match well with those given by the full nodal pricing model. Part of the network is better utilized compared to the solutions given by the full zonal pricing model.
However, the prices given by the hybrid system may send wrong economic signals which triggers unnecessary generation from existing capacities, exacerbates grid congestion, and induces higher re-dispatching costs.
Index Terms—Congestion Management; Nodal Pricing; Zonal Pricing; Electricity Market.
NOMENCLATURE
A. Sets and Indices
N Set of nodes
Nodal
N Set of nodes in the nodal pricing area
L Set of lines LDC Set of DC lines
Z Set of independent price areas
NZ Subset of nodes included in the price areazÎ Z
B. Parameters Set and Indices
Hij Admittance of the line between the nodes i and j
CA Pij Thermal capacity limit of the line from i to j
CA Pxz Upper limit on the flows from zone x to zone z
s(q)
pi Supply bid curve at node i
d(q)
pi Demand bid curve at node i C. Variables
s
qi Generation quantity (MWh/h) at node i
d
qi Load quantity (MWh/h) at node i
fij Load flow from node i to node j
qi Phase angle at node i
I. INTRODUCTION
In the European spot markets, zonal pricing is the most commonly used method to relieve grid congestion. Zonal pricing applies merit order to dispatch power from one location to another. It is a commercial pricing scheme which only to a limited extent takes physical laws and technical facts into account. A possible consequence of this is that there could be insufficient capacities in the network to transmit the contracted power, which requires the system operator to adjust the generation and consumption in order to change the physical flows in the network and to mitigate congestion [3].
Furthermore, zonal pricing gives a uniform price within each pricing area and thus does not provide sufficient price signals to market participants regarding scarce transmission capacity.
In contrast, nodal pricing, which is first discussed by [5], gives the optimal value for each location and produces feasible flows within the network, and is considered to give clearer market signals [2].
Some European countries are considering adopting nodal pricing systems. For instance, Poland has prepared to implement nodal pricing since 2010 and the whole implementation is expected to be finished in 2015 [6].
However, as the Polish power grid is connected to other continental countries, it is inevitable to be affected by (and affect) flows from other areas. It is thus a research question whether nodal pricing in such a case can still work as efficiently as it is supposed to do.
In this paper, we first propose a hybrid pricing model, which could be applied to a joint power market, in which the market is divided into different sub-systems, where some apply nodal pricing and others apply zonal pricing. It is important to note that a nodal pricing sub-system is not isolated from the other parts of the system and still has commercial trading with the connected zonal pricing sub- systems. In such a case, generation or consumption changes in the zonal pricing areas could still have an effect on the nodal pricing area because of the impact of loop flows. A 13-node power system serves to illustrate the hybrid pricing model. We compare the hybrid pricing scheme to the zonal and nodal pricing schemes to investigate how much a single pricing area can gain by applying nodal pricing in the context where its neighborhood areas apply zonal pricing.
p b c c S c p
i.
th d o c d
to m s f th 2 s th E fl li c v s li tr
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f c o th T h th n o a n
The conge paper, i.e., nod based on centr control method congestion. Th Section II. S compares attain preliminary con The power .e., the nodal p he system is t different netw objective func customers’ wil difference is de
, , ,
maxd s
q q f
i N
:(
s d
i i
j i
q
q
ij ij( i
f H
ji ij
CAP f
( ,i j i N j
CAPzx
In the noda o approximate much faster so solution, and th fairly well with he nodal prici 2 is the energy supplyqsi and d
he power whi Equation (3) is flowfij on a t ine and the d connected poin voltage direct set does not fol ines can be ransmission li
C A Pi j (4). Flow feasible and th could go from of the loop flow
Within each he physical fl Therefore, pow high price nod
here are no o node. These fl only take the account. We r networks in th
estion manage dal pricing, zon ralized optimi d chosen by th
he description Section III gi ned results for nclusions are g II r market consi
pricing and zo to maximize t work constrain ction, express llingness to p efined as socia
0 ( )
d qi d
i N
p q dq
, ) :( , )
ij
i j L j j i L
f
), ( , )
j i j l
, ,
j CAPij i j
) ( , )
x x
z z
ij
j L i j L
N j N
N i N
f f
al pricing area, e the power fl olution than t he results give h the full AC s
ng areas are c y balance equ demandqid at n ch is transpor s the loop flow transmission l
difference of nts. Equation
current (HVD llow the loop f treated as ines are restric ws within the hus are called a high price n w constraints.
h zonal pricin ows, i.e. loop wer will alway de until prices opportunities t flows are not economic b refer to such he zonal prici
ement method nal pricing, an ization subject he system ope n of the mod ives a nume r different pric given in Sectio . MODEL
ists of two typ onal pricing are the social welf nts ((2)-(5)). E
sing the diffe pay and the p al welfare.
0 ( )
s qi s
p q dqi
ji,
L
f i N
\LDC,i j, N
Nodal
jN
ji xz
f CAP
, the DC appro low. The DC a
the full altern en by the DC a
solution [4]. T constrained by
uation, ensurin node i is equal rted from (fij) w law, which d ine by the ad load angles (3) also introd DC) transmiss
flow law beca controllable.
cted by the the nodal pricing d physical flo node to a low ng area, there a p rule and ther ys go from a s for all node to buy power
necessarily fe ut not physic
flows as com ing areas are
ds discussed i nd hybrid pricin
t to the powe erator to reliev dels is provid erical exampl
cing schemes.
on IV.
pes of pricing eas. The objec fare (1), consi Equation (1) erence betwee production cos
Nodal
N
oximation [7] i approximation nating current approximation The network fl y (2) to (4). Eq
ng the differe l to the differe ) and to (fji) n determines the
dmittancesHi j
(qi- qj ) of i duces a set fo ion lines, LDC ause flows on H
Power flow ermal capacity g area are phy ows. Physical price node, b are no restricti rmal capacity
low price nod s are the sam
from a lower easible becaus
cal restriction mmercial flow constrained b
in this ng, are er flow ve grid ded in le and . Some
g areas, ctive of idering is the en the st. The
(1) (2) (3) (4)
(5) is used n gives t (AC) n match
lows in quation ence of ence of node i.
power of the ts two or high . This HVDC ws on y limits ysically flows because
ions on limits.
de to a me, i.e., r price se they ns into ws. The by the
ener
C A P
conn diffe A law vari pric takin betw com conn phys com betw by a zona pric
T cost are t unif How diffe ther
A. D [ of th inve of th choo 1 ex mark
T with (SE) 13 deco Ther AC exce 10-1 corr cabl assu iden T and data start exam pric assu mod appl
rgy balance e
Pxz are used t nected pricing erences among As the zonal p (3), the mode ablesqi. Henc ing areas and ng into accoun ween the diff mmercial flows
nected to a zo sical power ex mmercial excha ween the zonal aggregate capa al pricing ma
ing).
The dual va ts/benefits of in
the nodal pric form as there a wever, prices erent, as the mal capacity l
Data [1] uses a stro he Nordic pow estigate the po
he transmissio ose this power xhibits the top rket.
There are in to hin Norway (N
). Node 11 rep represent D omposed into
re are in total interconne ept for Lines 13, and responding to les. All the lin umed to ntical admittan
This power its corresp a are used
ting point mining the
ing method ume in the del that zon lies nodal
equations (2) to restrict inte
g areas x an g zones.
pricing model el does not giv ce, flows on t d the nodal pri nt the physica ferent pricing
s. Therefore n onal pricing ar xchange within
ange within th l and nodal pr acity limits (5) arket (i.e., the ariables of (2 ncreasing inje ces. Prices with
are no restrict within the n model takes limits into acco
III. NUME
ongly simplifie wer market w ssibility of im on grid by var
r system as an pology and the otal 13 nodes i NO) and Nod presents Finlan Denmark (DK o 4 zones acc 21 lines in th ections, s 1-13,
9-11, HVDC nes are have nces.
system ponding as a
for hybrid d. We
hybrid ne NO
pricing
and aggregat er-zonal tradi nd z (5). Th
does not inclu ve solutions fo
the lines conn icing areas ca al law (3). Tha areas have nodes in a no rea are constra n the nodal pri he zonal prici ricing markets ), which is the whole netwo 2), which ar ections in the n hin each zona tions on the in nodal pricing
both the ph ount.
ERICAL EXAMP
ed and rather a with different mproving the ca
rying the zone n example for
e zone definiti in this system.
des 6 to 10 ar nd (FI) and N K). This po cording to th he model and
Fig. 1: T
e capacity lim ing between his creates p ude the loop f or the phase an
necting the zo annot be mode at is, traded flo to be treated odal pricing a ained by both icing area and ing area. Trad s is also restric e same as in a
ork applies zo re the marg nodes by one u al pricing area ntra-zonal tradi
areas could hysical laws
PLE
aggregated mo load scenarios apacity utilizat e definitions.
our analysis. F ion of this po . Nodes 1 to 5 re within Swe Node 12 and N ower market heir jurisdictio
most of them
AC line DC line
opology
mits two rice flow ngle onal eled ows d as
area the d the ding cted full onal inal unit, are ing.
be and
odel s to tion
We Fig.
wer are eden Node is ons.
are
e e
and that the rest use area prices.
B. Aggregate capacity limits
Aggregate capacity limits are used to restrict commercial trading between different pricing areas. In practice, setting adequate aggregate capacity limits is a challenging task because low limits would fail to fully use the network capacity while high ones could cause lots of congestion within a pricing area. In our analysis, we use the flows given by the full nodal pricing solution, i.e., where the whole network applies nodal pricing, as a basis to set the aggregate capacity limits.
The limits are equal to the absolute value of accumulated flows between two pricing areas given by the nodal pricing solution.1 The main reason for setting aggregate capacity limits in such a way is that the nodal pricing solution could be regarded as the optimal benchmark as it takes both the physical and economic constraints into account. These limits could be considered to optimize the utilization of the network given perfect information. Furthermore, this setting makes all the three pricing mechanisms (i.e., nodal pricing, zonal pricing, and hybrid pricing) comparable, because the traded volumes between two pricing areas are the same. When there is a price difference between two nodes connecting two different pricing areas, trading will continue until the price difference is eliminated or the aggregate capacity limit is reached. Note however that the actual flows resulting from the zonal and hybrid market clearings may still be infeasible.
We also assume that the aggregate capacity limits between two price areas are the same in both directions. For instance, the aggregate capacity limits from Norway to Sweden are equal to those from Sweden to Norway.
C. Some results from a high load scenario
Since congestion is likely to happen when demand is high, we choose a high demand hour for the following analyses. The total consumption volume given by the full nodal pricing solution is approximately 86% of the consumption prognosis at “10 years” winter temperature [1]. Data on the model and supply and demand information2 are presented in the appendix.
1) Prices
Fig. 2 gives the prices at each node in different congestion management schemes. Prices within the zonal pricing market (Nodes 6 to 13) given by the hybrid pricing solution are identical to those given by the zonal pricing solution. This shows that if the aggregate capacity limits remain the same and the same proportion of the aggregate capacity limits is used, the prices within the zonal pricing market will not be affected by the congestion management scheme in the nodal pricing market.
1 For instance, the transfer capacity from Norway to Sweden is calculated as
* *
,
, ,
NO NO
SE SE
NO SE ij ji
i j L i j L
i N j N
j N i N
CAP f f
, where fij* and fji*are solutions given by nodalpricing model.
2Formats of Supply and demand curves are displayed in Fig. A1. The corresponding data for parameters can be founded in Table AI and Table AII.
The comparison between the prices in the nodal part of the hybrid system (i.e., Nodes 1 to 5) and the nodal prices for the whole system generates some interesting observations. In general, the two series of prices, presented in Fig. 2, match fairly well, with a notable exception for Node 5. At Node 5 the price given by the hybrid system is 132.5 NOK, while the full nodal price is only 91.6 NOK.
Fig. 2: Prices in different congestion management schemes
The reason for the high price at Node 5 in the hybrid system is that the three nodes that are directly connected with Sweden (i.e., Nodes 2, 4 and 5) face high demands from Sweden. In the hybrid system, the prices at these three points are set to be identical because flows going from these nodes to Sweden are modeled as direct flows without considering physical restrictions (i.e., the loop flow law).
As long as the thermal capacity of the lines connecting these three nodes to the zonal pricing area has not been fully used, i.e., there is no congestion in these lines, the prices at the three nodes should be equal. Otherwise, Sweden could always choose to buy power from the node with the lowest price, since the zonal pricing model does not take the laws of physics entirely into account. Therefore, Node 5 in the hybrid system gets a price as high as those at Nodes 2 and 4.
2) Fully loaded and overloaded lines
Physical flows3 given by the zonal pricing scheme might not be feasible because it does not take scarce transmission capacity and the laws of physics into account. In the hybrid pricing model, the physical constraints are modeled for only parts of the system, so that there can still be infeasible flows in the zonal pricing area. Furthermore, areas applying nodal pricing are connected to other AC network areas applying zonal pricing, and could be affected by the loop flows in such areas. Investigating the capacity utilization of a transmission line, which is defined as the ratio of the physical flow to thermal capacity, helps to explain the reason why the price at Node 5 in the hybrid system is higher than the one in the nodal pricing system.
3 To calculate the physical power flows of the zonal and hybrid pricing solution, we fix the values of nodal load d
qi, generation s
qi and flows over the DC lines fij(w h e re (i, j)LDC)using the solutions given by the models. We use these values as inputs for a detailed network model to re-compute the final line flows. This network model takes loop flow into consideration ((2) to (3)), minimizes the losses caused by dispatching, but does not consider thermal capacity constraints (4). Thus we obtain the power flows that will result from injections and withdrawals in the nodes given by the zonal and hybrid pricing solutions.
80 100 120 140 160 180 200
1 2 3 4 5 6 7 8 9 10 11 12 13
NOK/MWh
Node Zonal pricing Hybrid pricing Nodal pricing
d p m th d L g h c im li c h
s te g g o g c lo h o z h E w b b b a c is c L e g b p
In the full demand from prices because much lower, b he overloaded different cong Line 5-6 ma generated at th has significant cost is not the mportantly, th imits the pow congestion, pr higher margina
Conseque system gives w
erm and long generated by generation is u other areas du generation w connecting No oaded in the f however, it b overloaded, de zonal price sol high price trig Extra generatio will only inten be solved by because the sys As discusse by the changes also be infeasib compared to th s alleviated congestion hap Line 4-5 is fea explained by generation at N both Line 5-6 a
Table sum pricing areas f
Nodal pri
Fig. 3
nodal system, Sweden. Nod e of this. In co
ecause Line 5 d and fully lo gestion manag kes it impos his node to ot tly less value only reason f he low price wer to be supp roduction at N al cost, implyin
ently, the high wrong econom
g term proble the existing unnecessary, b
ue to the ca will exacerbat
de 5 and other full nodal pric becomes over espite it being lutions. Finally ggers more inv on capacity in nsify grid cong
re-dispatching stem uses mor ed before, the s in the zonal ble flows in th he zonal pricin in the hyb ppens in Lines asible in the z the previous Node 5. Increa and Line 4-5 to mmarizes the t
for all three p
icing Zon
3: Congestion for
, Nodes 2, 4 a es 2 and 4 ar omparison, the 5-6 is fully-loa oaded lines re gement schem ssible to tran ther areas, so
. In other wo for the low pri is due to th plied to other Node 5 will ng a higher no
h price at No mic signals, wh ems. First, m generation c because it cann apacity constr
te congestion r nodes. Note t ce solution. In rloaded. Line
within limits y, the situation vestments in n this area is gestion. The ex g, which lead re costly powe nodal pricing pricing area.
he nodal pricin ng scheme, co brid pricing
s 5-6 and 4-5, zonal pricing s s discussion ased generatio o be overloade traded volume pricing schem
nal pricing
different pricing F O
and 5 also fac re indeed give e price at Nod aded. Fig. 3 di egarding these mes. Congest
nsmit more the extra gene ords, low gene ice at Node 5 e congestion r areas. Witho be higher an odal price.
ode 5 in the hich may caus more power w
capacity. This not be transmi raint. Second, n in those that Line 5-6 i n the hybrid s 4-5 also be in the full nod n may worsen generation ca unnecessary, xtra congestion ds to increase er in re-dispatc area can be af Therefore, the ng area. As in
ngestion in Li scheme. Ho even if the fl scheme. This
regarding the on at Node 5 ed.
es between di mes. Traded vo
Hybrid pricin
schemes ully loaded lines Overloaded lines
ce high en high de 5 is isplays e three
ion in power eration eration . More which out the nd at a
hybrid e short will be s extra itted to , more
lines is fully system, ecomes dal and n if the apacity.
and it n must ed cost ching.
ffected ere can Fig. 3, ine 2-3 wever, low on can be e high
causes ifferent olumes
betw area zona utili
W Nod flow allev the clea Furt othe zona
1 to 1 to 6 to 12 t
a. NO b. Am the zon
N relie that Line com exam in th 107%
140%
from coul
Tab
L L L L
I the facto noda takin the Line facto The betw desi
3)
reve not hybr cost refle
ng
ween the noda as are the sam
al pricing and ize the existing We notice tha de 7 in zone ws going from
viate the cong full zonal pri ar price signals thermore, pric er pricing area al and hybrid s
Table I: Trad
o 5 (NO)a 6 to o 5 (NO) 12 o 10 (SE) 11 to 13(DK) 6 to
O is the area applying no mong Node 10, 12 and 1 nal or the hybrid pricing
Nodal pricing eve grid conge
it could also i es 4-5, 5-6 a mpared to thos mple also sho he area apply
%), and on the
%), but also in m 108% to 1
ld increase cos
ble II: Utilization Zo Line 2-4 114 Line 4-5 98%
Line 5-6 130 Line 8-10 108
In conclusion, corresponding ors. First, the f al pricing an ng into accoun
lines connecti e 5-6) is the ors together l se results hi ween the nod ign of the hybr ) Surplus
Table III su enue in differe directly comp rid solutions ts are not ad ect that the zo
al pricing area me for all thre d hybrid prici g network.
at in the full no SE is relative
Node 7 to No gestion in Lin icing or hybri s at Node 7 to ces in Norway as, so there w system to relie
ed volumes betwe
p o 10 (SE) 28
to 13(DK) 10 (FI) 21 o 10 (SE)
odal pricing while SE, D 13, Node 13 has the low g schemes. Therefore, th
g in a hybrid estion to a cer intensify the g and 8-10, the se given by th ws that conge ying nodal pri e cross border n the area app 10%). Increa st associated w
n rate of overloade onal pricing
4% 1
% 7
0% 1
8% 1
, the wrong pr g increased co
flows over the nd zonal prici nt the full pow ing Node 5 an
bottleneck of lead to the w ighlight the dal pricing an rid pricing sys
ummarizes th ent pricing sol parable becau in general are ddressed. How
onal pricing a
a (Nodes 1-5) ee mechanism ing schemes odal pricing m ely low, which odes 5 and 6. T ne 5-6 and Lin id pricing mo
reflect its cost y are much low will not be cou
eve congestion
een pricing areas ( Zonal pricing
No pri 804 2804 000 1000 19 219
31b
DK, FI are the pricing a west price. However, thi here will not be flow go
pricing conte rtain extent. H grid congestion e utilization r he zonal pricin
estion not only icing (Line 4 r links (Line 5 plying zonal pr ased congestio with re-dispatc
ed lines for differe Nodal pricing 100%
71%
100%
100%
rice signal giv ongestion is t e cross-border ing areas can wer flow laws nd the zonal p f the whole s wrong price si
importance nd zonal pric
tem.
he social sur lutions. The to use the flows
e infeasible an wever, the di
area is affecte
and other pric ms. However, fail to optim model, the pric h creates coun The counter flo ne 4-5. Howev odels do not g t competitiven wer than those unter flows in n.
(Unit: MWh) odal icing
Hybri pricin 4 2804 0 1000
219
areas applying zonal pric s fact is not known in ei oing from DK to SE.
ext could help However, we f n. For instance rates all incre ng scheme. T y becomes wo -5, from 98%
-6, from 130%
ricing (Line 8- on in these li
hing.
ent pricing schem Hybrid pricing 100%
107%
140%
110%
ven at Node 5 the result of t lines between nnot be mode
s. Second, one pricing area ( system. The ignal at Node of the interf ing areas in
rpluses and g otal surpluses in the zonal nd re-dispatch fferent surplu ed by the pric
cing the mally ce at nter ows ver, give ness.
e in the
id ng
cing.
ither
p to find e, in ease This orse
% to
% to -10, ines
mes g
and two n the eled e of (i.e., two e 5.
face the
grid are and hing uses cing
s h s r e im tr n p r fr
a.
ar sh
N s b g s d T r g s g
N S F D
m it p n b th n r n h
th
scheme in the hybrid system, surpluses are id
evenue decrea expensive pow mport power raded volume nodal price ar pricing schem educes the gr from 120 to 88
Tabl
Zonal pricing 1 Hybrid pricing 1 Nodal pricing 1 N Zonal pricing 4 Hybrid pricing 4 Nodal pricing 4
. Also referred to merch
rea is ii
i
MSp q
hared by the two system
Meanwhile Nodes 1 to 5) social welfare by 14 compare grid revenue co surplus. The de decrease in con This means th
eallocates the grid revenue surpluses of th given by the fu
Zonal pr Production Con NO 24225 SE 21583 FI 11958 DK 5212
This paper management m t in a 13-nod pricing model nodal pricing s border lines ha he hybrid pric nodes connecti esults highligh nodal pricing hybrid pricing The author heir comments
nodal pricing , i.e., Nodes 6 dentical to the ases. As the wer sources in from the no es, the average
rea increases e to 132.5 in rid revenue ob 8.
e III: Surpluses d Nodes 1 to Producers
501 1
588 1
638 1
Nodes 6 to 13 (Zo
4237 3
4237 3
4220 3
handizing surplus (MS) ( j i)ij
i j
p p f
. Reve
m operators.
e, the grid reve is greatly imp in the hybrid ed to the zona omes at the ex ecrease in con
nsumption in hat the nodal e producer su compared to he hybrid solu ull nodal system
Table IV: Produ
ricing N
nsumption Produc 20421 2402 24168 2144 12177 1195 6212 523
IV.
r presents a methods for a h e power syste
works well i solution as a b appen to be the cing model ma ing such lines ht the importa and zonal pr system.
ACKNO
s thank Stein.
s and help on t
area. Within to 13, the con e zonal price s zonal pricing n this case, it odal price are e price to imp greatly from the hybrid pr btained by the
differences (Unit:
5 (Nodal pricing Consumers 19301 19064 18931
onal pricing area 38912
38912 38708
) (see [7]). The mathem enues from cross-borde
enue for the no proved from 1 pricing schem al pricing sche
xpense of a re nsumer surplus Norway, as d pricing part o urpluses, consu
the zonal p ution are becom
m.
uction and consum Nodal pricing
ction Consumption 26 20223 48 24064 58 12177 34 6203
CONCLUSIO
model with hypothetical jo em. Results sh in such a con benchmark. Ho e bottlenecks o ay give wrong and trigger m ance of the in ricing areas in
OWLEDGMENT
W. Wallace, E this paper.
the zonal part nsumer and pro solution, but th g area has the
is always wil ea. Given the port power fro
109.7 in the ricing scheme e zonal pricin
1000 NOK) g area, i.e., NO)
Grida Su 118 2092 282 2093 393 2096 as, i.e., SE,DK an
120 4326 88 4323 257 4318
matical formulation for M er commercial trading a
odal pricing ar 18 to 282. Th me increases s eme. The incre
duction in con s is associated displayed in Ta
of the hybrid umer surpluse pricing mode ming closer to
mption
Hybrid pric Production Consu 24098 20 21583 24 11958 12 5212 6 ON
hybrid cong oint market an how that the ntext, using th owever, when of the whole s price signals more congestio
nterface betwe n the design
Evangelos Pan t of the
oducer he grid e more
ling to e same
om the e zonal e. This ng area
um 0 4 3 nd FI)
8 6 5
MS of an are equally
rea (i.e., he total slightly ease in nsumer with a able 4.
model es and l. The o those
cing umption 0294 4168 2177 6212
gestion nd tests hybrid he full n cross-
system, for the on. The een the of the
nos for
[1]
[2]
[3]
[4]
[5]
[6]
[7]
L 1 1 1 2 2 2 4 4 5 5
Bjørndal, Mette congestion man policy 35, no. 3 ( Hogan, William transmission." Jo 242.
Kunz, Friedrich Generation in Technische Univ Overbye, Thoma AC and DC po Sciences, 2004.
Conference on, p Schweppe, Fred Bohn. "Spot pric Sikorski, Toma International Co Technologies. St Wu, Felix, Prav theorems on examples." Jour
Line Lower limit 1-2 2000.0 1-3 16500.0 1-13 1000.0 2-3 2800.0 2-4 800.0 2-10 2000.0 4-5 400.0 4-8 600.0 5-6 400.0 5-7 400.0
F Table A Node De 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 9 20 10 20 11 20 12 20 13 20
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APPE Table AI: Li r Upper
limit 2000.0 16500.0 1000.0 2800.0 800.0 2000.0 400.0 600.0 400.0 400.0
Fig. A1: Supply an AII: Parameters for
emand
a b 000 0.88 000 0.2 000 0.5 000 0.5 000 1.5 000 1.7 000 1.7 000 0.5 000 0.2 000 0.2 000 0.15 000 0.7 000 0.5
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act networks atory Economics 4 ongestion and Int
ctricity Markets."
2012 . , and Yan Sun. "
els for LMP calc the 37th Annual 2004.
Tabors, M. C. Car ." (1988).
cing project in tions. Efficiency e. 2011.
blo Spiller, and access: Proo y Economics 10, n ENDIX
ine capacity
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nd demand Curve r bidding curves a
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s from coordina wer market." En
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ofs and cou no. 1 (1996): 5-23
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