INFLUENCE OF ANN-BASED MARKET PRICE FORECASTING
UNCERTAINTY ON OPTIMAL BIDDING
Jos´e L. Ma ´ınez Ramos
[email p o ec ed] An onio G´omez Exp´osi o
[email p o ec ed] Jes´us Riquelme San os
[email p o ec ed]
Alicia T oncoso Lo a
[email p o ec ed] Agus ´ın R. Ma ulanda Gue a
[email p o ec ed]
Depa men o Elec ical Enginee ing
Uni e si y o Se illa
Se illa, Spain
Abs ac - In oday’s de egula ed ma ke s, o ecas -
ing ene gy p ices is becoming mo e and mo e impo an .
In he sho e m, expec ed p ice p o iles help ma ke pa -
icipan s o de e mine hei bidding s a egies. Conse-
quen ly, accu acy in o ecas ing hou ly p ices is c ucial
o gene a ion companies (GENCOs) o educe he isk o
o e /unde es ima ing he e enue ob ained by selling ene gy.
In his pape , he in luenceo he accu acy o ANN-based
hou ly ene gy p ice o ecas ing on he bidding s a egy o
GENCOs is assessed. Fi s , a cus omized, ecu en Mul i-
laye Pe cep on is de eloped and applied o he 24-hou
ene gy p ice o ecas ing p oblem, and he expec ed e o s
a e quan i ied. Then, p ice p o iles a e used o compu e he
op imal bidding o ealis ic GENCOs, and he in luence o
o ecas ing e o s on bo h he bidding s a egies and he ex-
pec ed e enues is s udied.
Keywo ds - A i icial neu al ne wo ks, ene gy p ice
o ecas ing, compe i i e ma ke s, op imal bidding
1 INTRODUCTION
THE new compe i i e Spanish Elec ici y Ma ke has
been in ope a ion since 1998, and i is mainly based
on wo sepa a ed day-ahead ma ke s [7]:
•The ene gy ma ke , managed by he Ma ke Ope -
a o (MO), whe e p oduce s and consume s submi
p oduc ion and consump ion bids (blocks o hou ly
ene gyand he co espondingp ice in Eu os/MWh).
The MO p oduces a ma ke -clea ing p ice and se s
o accep ed p oduc ion and consump ion bids o
e e y hou . Cons ain managemen is subsequen ly
pe o medby he Sys em Ope a o (SO), aking also
in o accoun he scheduled bila e al con ac s and
adjus ing he esul o he ene gy ma ke o a oid
ansmission conges ion. Fu he mo e, addi ional
ma ke s o mino adjus men s a e also pe o med
on an hou ly basis.
•The ma ke o egula ion ese es. Once he en-
e gy ma ke and he subsequen cons ain manage-
men p ocedu e a e inished, he SO es ablishes he
equi emen s o ope a ing ese es (an hou ly band
in MW up and down) ha a e needed o equency
con ol o each o he 24hou s o he ollowingday.
The ese e ma ke alloca es he bands among he
gene a o s ha a e capable o p o iding seconda y
equencycon ol by using gene a o s’ up and down
bids which include he o e ed band (MW) and he
p ice (Eu os/MW). A ma ke o addi ional ene gy
ese es (powe ha can be p o idedwi hin 15 min-
u es o a pe iod o wo hou s) is also pe o med.
In his con ex , o ecas ing ene gy p ices is ex emely
impo an . In he sho e m, expec ed p ice p o iles, bo h
in e ms o ene gy and ese e p ices, help ma ke pa ici-
pan s o de e mine hei bidding s a egies. Consequen ly,
accu acy in o ecas ing hou ly ene gy & ese e p ices
is c ucial o gene a ion companies (GENCOs) o educe
he isk o o e /unde es ima ing he e enue ob ained by
selling ene gy.
The mo i a ion o his pape is wo old: Fi s , wo
cus omized Mul i-laye Pe cep ons a e de elopedand ap-
plied o he 24-hou ene gy and ese e p ice o ecas ing
p oblems, espec i ely, and he expec ed e o s a e quan-
i ied. Secondly, p ice p o iles a e used o compu e he
op imal bidding o se e al ealis ic GENCOs, and he in-
luence o o ecas ing e o s on bo h he bidding s a egies
and he expec ed e enues is p esen ed. The objec i e is
o compu e he commi men schedule and he hou ly gen-
e a ion p o ile o he GENCO in o de o maximize he
expec ed bene i om selling bo h ene gy and ese e o
he co esponding ma ke s [2].
2 ANN-BASED MARKET PRICE FORECASTING
As s a ed be o e, his pape is no aimed a de eloping
he bes ma ke p ice o ecas ing echnique, bu o assess
how ele an he o ecas ing e o s a e, so a as he bene-
i s o a GENCO a e conce ned.
The ANN app oach has been chosen because o i s
success ul pe o mance in he load o ecas ing p oblem
[3, 4]. La ge e o s a e expec ed in his case, howe e ,
as he in luence o he load le el on ma ke clea ing p ices
is only mode a e, and o he unp edic able ac o s play an
impo an ole in non-pe ec oligopolis ic ma ke s.
Usually, i is manda o y o GENCOs o p o ide he
seconda y egula ion se ice, o which he e is an ad-
di ional income. The e o e, in o de o p epa e he day-
14 h PSCC, Se illa, 24-28 June 2002
Session 07, Pape 1, Page 1
ahead bid, an es ima ion o p ices o his complemen a y
se ice mus be a ailable, in addi ion o ene gy p ices.
The s udy epo ed in his pape is based on he hou ly
Spanish ene gy and seconda y egula ion p ices eco ded
om Janua y 2001 o Augus 2001. As weekends and hol-
idays cons i u e sepa a e cases, only da a co esponding o
wo king days ha e been e ained and analyzed.
Figu es 1 and 2 show he hou ly a e ages and s an-
da d de ia ions (s.d.) o bo h p ices o he wo king days
o Ma ch 2001, in cen s o Eu o pe kWh and cen s o
Eu o pe kW espec i ely. A e age spo p ices la ge han
2 cen /kWh ake place du ing he mo ning and e ening
peak hou s (10am-2pm and 8-10pm espec i ely). Excep
o a ew alley hou s, he s.d. o his p ice exceeds 20%
o he mean alue, eaching e en 40% a 8pm and 9pm.
No e ha he s.d. o egula ion ma ke p ice is, in ela i e
e ms, much highe han ha o he ene gy ma ke p ice,
which means ha his ac o is less p edic able.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1
5
9
13
17
21
Hou s
cen /kWh
Mean
Mean + S.D.
Mean - S.D.
Figu e 1: Hou ly a e age o spo ma ke p ices o Ma ch 2001.
0
1
2
3
4
5
6
1
5
9
13
17
21
Hou s
cen /kW
Mean
Mean + S. D.
Mean - S. D.
Figu e2: Hou ly a e age o seconda y egula ion p ices o Ma ch 2001.
Figu e 3 ep esen s he ene gy p ices o wo selec ed
days o Ma ch 2001. The signi ican di e ences in he
p ices o he peak hou s can no be explained by a change
in he demand p o ile, p obably e ealing ma ke powe
mechanisms.
0
1
2
3
4
5
6
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Hou s
cen /kWh
Thu sday-1s
F iday-30 h
Figu e 3: E olu ion o ene gy p ices o wo days o Ma ch 2001.
2.1 S uc u e o he ANN
A b ie desc ip ion o he ANN adop ed in his wo k
is p o ided in his sec ion ( he eade in e es ed in ANN
backg ound is e e ed o [5] and [6]).
An ANN is composed o a ce ain numbe o pe cep-
ons o ganized by laye s. Each pe cep on has se e al in-
pu s and a single ou pu , whose alue is a non-linea unc-
ion o he inpu s. Each pe cep on’s inpu is a ec ed by
a weigh ing ac o , which mus be de e mined du ing he
aining phase. Usually, an ANN is composed o h ee lay-
e s (inpu , hidden and ou pu ), whe e he ou pu s o a laye
eed he inpu s o he nex laye .
The wo main s eps in ol edin he use o an ANN a e:
•De e mining i s opology, which basically consis s
o de ining he numbe o pe cep ons in he in e -
media e hidden laye .
•Ob aining he inpu weigh ing ac o s o a gi en
non-linea unc ion ( aining p ocess).
Acco ding o au ho s’ p e ious expe ience, i is de-
cided o eed he ANN wi h a shi ing window o p ices
comp ising 24 hou s. This means ha he inpu laye is
composed o 24 pe cep ons. As a as he numbe o ou -
pu pe cep ons is conce ned, wo possibili ies ha e been
e alua ed [6]:
a) A single ou pu whose alue is dic a ed by he p e-
ious 24 hou s. Unde his scheme, e y popula
in load o ecas ing, he window is shi ed one hou
each ime.
b) Twen y ou ou pu s co esponding o he p ices o
a whole day, whose alues a e de e mined by hose
o he p e ious day. This implies ha he window is
shi ed 24 hou s each ime.
Tes esul s ha e shown be e accu acy o scheme b),
which is he only one conside ed in he sequel [6].
In o de o ully de ine he ANN, i is necessa y o
de e mine he numbe o pe cep ons in he in e media e
laye and he numbe o days equi ed o he aining p o-
cess. Figu e 4 shows, o 12, 24 and 36 neu ons in he hid-
den laye , he a e age o ecas ing e o in he ene gy p ice
14 h PSCC, Se illa, 24-28 June 2002
Session 07, Pape 1, Page 2
co esponding o he wo king days o Feb ua y 2001, a
ep esen a i e mon h, e sus he numbe o days used o
ain he ANN. As can be no ed, 20 days a e su icien o
ain he ANN, he numbe o neu onsno being so impo -
an . Simila conclusions a e eached o he ANN de o ed
o o ecas ing he spinning ese e p ice. Fo he esul s
p esen ed below, 24 and 12 neu ons in he hidden laye
ha e been used o o ecas he spo ma ke ene gy and e-
se e se ice p ices, espec i ely, and he ac ual p ices o
he 20 p e ious days a e used o ain he ANNs o p edic
he nex day.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
5
10
15
20
25
30
35
40
45
Days
E o (cen /kWh)
n12
n24
n36
Figu e 4: A e age o ecas ing e o in he ene gy p ice.
2.2 Resul s
Abou wo mon hs o he a ailable pe iod (Janua y -
Feb ua y 2001) a e used in se e al expe imen s o ind ou
and une he bes ANN opology, while he emaining ma-
e ial (Ma ch-Augus 2001) is de o ed o check he o e-
cas ing e o s and o pe o m he ma ke simula ions o he
second pa o he pape .
Figu e 5 p esen s he absolu e alue o he e o o he
o ecas ed spo ma ke p ices o he wo days o Ma ch
2001 leading o he la ges and smalles a e age e o s.
0
0.5
1
1.5
2
2.5
3
1
3
5
7
9
11
13
15
17
19
21
23
Hou s
E o (cen /kWh)
F iday 23
Monday 12
Figu e 5: Absolu e alue o he e o o he o ecas ed ene gy p ices.
Figu e 6 shows he hou ly a e age o he o ecas ed
ene gyp ices co esponding o Ma ch 2001, as well as he
esul ing p edic ione o s (ob ainedby di e encewi h he
ac ual p ices o igu e 1). No e ha he o ecas ing e o s
a e la ge du ing peak hou s. Figu e 7 p o ides he same
in o ma ion o he p ice o he ese e se ice.
0
0.5
1
1.5
2
2.5
3
3.5
1
4
7
10
13
16
19
22
Hou s
cen /kWh
E o s
Fo ecas ed
Figu e 6: Hou ly a e age o he o ecas ed ene gy p ices (Ma ch 2001).
0
0.5
1
1.5
2
2.5
3
3.5
4
1
4
7
10
13
16
19
22
Hou s
cen /kW
E o s
Fo ecas ed
Figu e 7: Hou ly a e age o he o ecas ed ese e p ices (Ma ch 2001).
Finally, ables 1 and 2 p esen he a e age and s.d. o
ac ual p ices, he a e age o o ecas ing e o s and he
maximum e o s o Sp ing and Summe seasons. Fo
he spo ma ke p ice, he a e age e o anges om 12%
(Summe ) o 15% (Sp ing) o he hou ly a e age p ice.
As expec ed, he la ge he s.d. o p ices he highe he
a e age o ecas ing e o . No e ha egula ion p ice e o s
a e a he high, ob iously due o he in luence o ex e nal
ac o s such as uni ailu es on he ese e ma ke .
Daily P ices (cen /kWh)
A e age s. d. A e age Maximum
eal p ice absolu e e o s e o s
Ma ch-May 2.2588 0.7801 0.3464 2.671
June-Augus 3.5482 1.0597 0.428 2.0736
Table 1: Fo ecas ing e o s o he ene gy p ices.
F equency Regula ion Se ice (cen /kW)
A e age s. d. A e age Maximum
p ice absolu e e o s e o s
Ma ch-May 0.7965 0.9864 0.5309 5.12
June-Augus 0.5986 0.4471 0.4916 4.49
Table 2: Fo ecas ing e o s o he ese e p ices.
14 h PSCC, Se illa, 24-28 June 2002
Session 07, Pape 1, Page 3
3 OPTIMAL BIDDING OPTIMIZATION
PROBLEM
A e ob aining he o ecas ed ene gy and ese ep ice
p o iles, he GENCO mus de e mine he op imum com-
mi men and hou ly gene a ion schedule in o de o max-
imize he expec ed bene i om selling bo h ene gy and
spinning ese e. In his pape , pe ec compe i ion is as-
sumed, and, in consequence, no GENCO has he possibil-
i y o modi ying he ma ke clea ing p ices. A e com-
pu ing he op imal hou ly gene a ion scheduling based on
he o ecas ed p ices, he GENCO may choose o o e he
scheduled ene gy a ze o p ice o ensu e ha he o e will
be accep ed, o o o e he ene gy a ma ginal cos , as
Game Theo y ecommends. I he GENCO has ma ke
powe , he op imiza ion p oblem mus e lec i s capabil-
i y o modi y he ma ke -clea ing p ices by con olling he
o al amoun o ene gy and ese e o e ed [8].
The op imal gene a ion scheduling p oblem can be
posed as a mixed-in ege linea p og amming model as
p oposed in [2], allowing complex ope a ing cos s o be
modeled, e.g., non-con ex cos unc ions and exponen ial
s a -up and shu -down cos s, along wi h ope a ing con-
s ain s such as amp limi s.
3.1 Objec i e Func ion
The o al bene i o a GENCO o e a 24-hou schedul-
ing pe iod, gi en he ene gy and spinning ese e hou ly
p ices, λ and µ espec i ely, is de ined by
BT=
24
X
=1
λ ·P +µ ·(P −P )(1)
− {C(P )·U +UC(S )·Y +DC ·Z }
whe e P is he a e age gene a ed powe a hou ,C(P )
is he ope a ing cos , P is he a ailable maximum powe
a hou ,S is he numbe o hou s he he mal uni has
been shu -down a he end o hou ,UC(S )is he s a -
up a iable cos , DC is a shu -down ixed cos , U ,Y and
Z a e 0/1 a iables which a e equal o one i he he mal
uni is commi ed a hou , s a ed-up o shu -down a he
beginning o hou , espec i ely.
3.2 Cons ain s
The maximiza ion o he objec i e unc ion is subjec
o he ollowing cons ain s ( = 1,...,24):
•Uppe and lowe gene a ion limi s:
Pm·U ≤P ≤PM·U (2)
•Maximum up and down amps:
P = min {PM·(U −Z +1) + SD ·Z +1,
P −1+RU ·U −1+SU ·Y }(3)
P = max {Pm, P −1−RD ·U }(4)
whe eP is he minimumgene a edpowe a hou ,
PMand Pma e he maximum and minimum powe
o he he mal uni , RU and RD a e he maximum
up and down amps, SU and SD a e he maximum
s a -up and shu -down amps, espec i ely.
•Minimum up and down imes:
(X −1−UT )·(U −1−U )≥0(5)
(S −1−DT )·(U −U −1)≥0(6)
whe e X is he numbe o hou s he he mal uni
has been on a he end o hou , and UT and DT
a e he minimum up and down imes.
•Logic cons ain s:
Y −Z =U −U −1(7)
Y +Z ≤1(8)
X = [X −1·(1 −Y ) + 1] ·U (9)
S = [S −1·(1 −Z ) + 1] ·(1 −U )(10)
The abo e model is sol ed by using he CPLEX op i-
miza ion module unde GAMS [1].
4 TEST RESULTS
The op imiza ion model desc ibed in he o me sec-
ion is used in conjunc ionwi h he ANN-based o ecas ed
p ices o assess he bene i s o wo di e en GENCOS,
whose main pa ame e s a e shown in able 3. Fuel cos s
ha e been scaled so ha he inc emen al cos o gene a-
o s equals he a e age ma ke p ice and hal he a e age
p ice, espec i ely. S a -up cos s a e unc ions o he ime
he gene a o ha e been shu -down, wi h ime-cons an s
o 2 and 12 hou s. Finally, s a -up and shu -down amp
a es ha e been equalled o he no mal up and down amp
limi s, and no minimum up o down ime cons ain s ha e
been imposed.
The esul s epo ed below e e o Ma ch 2001, con-
side ed a ep esen a i e mon h.
Economical da a
GENCO C(P )UC
(Eu os/h) (Eu os)
Gas- u bine 594.58 + 29 ·P 6541.7·(1 −e
−
S
2)
Coal- i ed 359.5 + 14.5·P 12588.6·(1 −e
−
S
12 )
Technical da a
GENCO PmPMRU RD
(MW) (MW/h)
Gas- u bine 100 350 350 350
Coal- i ed 100 350 50 50
Table 3: GENCOs main echnical and economical da a.
4.1 Case A: Con en ional coal- i ed gene a o
This uni akes se e al hou s o ully s a up and i s
ixed cos is high. Howe e , i s a iable cos is abou one
hal o he a e age ma ke clea ingp ice. In pas egula ed
ma ke s, his would ha e been a base uni usually wo king
a a ed powe .
14 h PSCC, Se illa, 24-28 June 2002
Session 07, Pape 1, Page 4
Figu e 8 compa es he o al daily bene i s ob ained
wi h o ecas ed p ices wi h hose ha would ha e been
ob ained i ac ual p ices had been known in ad ance. The
mon hly a e age di e ence is 7.7%, he la ges de ia ion
aking place on Ma ch 12 (please no e ha , as weekends
a e excluded om he analysis, his is day #8 in he ig-
u es). As shown in igu e 5, his is also he day leading
o he la ges ene gy p ice o ecas ing e o . No e ha he
bene i ob ained wi h pe ec in o ma ion is always la ge
han o equal o he p o i achie ed om o ecas ed p ices.
This is no he case, howe e , when p o i s a e analyzed a
he hou ly ame, because he objec i e unc ion conside s
he daily pe iod as a whole.
Figu e 9 ep esen s he hou ly p o i based on o e-
cas ed p ices ( igh ) and he scheduled ene gy (le ) on
Ma ch 1. Excep o he alley hou s, he uni maximizes
i s p o i a a ed powe . Ano he excep ion a ises a 7pm,
when he income om he egula ion se ice is so high
ha i is be e o he uni o educe he scheduled powe .
In o de o assess he in luence o he ese e income on
he op imal bidding s a egy, he expe imen is epea ed by
igno ing his e m in he objec i e unc ion. As shown in
igu e 10, he p o i dec eases du ing some alley hou s
and a 7pm, in spi e o he inc eased gene a ed ene gy.
Howe e , his kind o uni s a e no signi ican ly in luenced
by his income componen , as he p o i educ ion o he
scheduling shown in igu e 10 is only 2%.
-20000
0
20000
40000
60000
80000
100000
120000
140000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Day
P o i (Eu os)
P o i wi h o ecas ed p ices
P o i wi h ac ual p ices
Figu e 8: To al daily bene i o he coal- i ed gene a o .
0
100
200
300
400
1
3
5
7
9
11
13
15
17
19
21
23
Hou
Ene gy (MWh)
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
P o i (Eu os)
Ene gy
P o i
Figu e 9: Hou ly bene i s and scheduled ene gy o he coal- i ed uni .
0
100
200
300
400
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Hou
Ene gy (MWh)
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
P o i (Eu os)
Ene gy
P o i
Figu e 10: Hou ly bene i s and scheduled ene gy o he coal- i ed uni .
Rese e incomes no conside ed.
4.2 Case B: Gas- u bine gene a o
This is a as -ac ing, high a e agecos uni whose op i-
mal bidding s a egy is qui e di e en om ha o Case A.
Figu e 11, he coun e pa o 8, shows ha he p o i
a ained wi h o ecas ed p ices is e y simila o ha ob-
ained i exac p ices we e a ailable he day be o e, excep
o days #8, 13, 14, and 15. As discussed in Case A, unex-
pec edly high ene gy p ice o ecas ing e o s a e espon-
sible o his de ia ion on Ma ch 12 (day #8). Howe e ,
he la ge p o i gap obse ed on days #13 o #15 is ully a -
ibu able o he ex emelyhigh unce ain y ha ook place
in he ese e p ice du ing hese days. This is con i med
by he ac ha he ne income is nea ly indis inguishable
om he one ob ained wi h exac p ices, when exac p ices
a e adop ed o he egula ion se ice only ( hi d se ies in
igu e 11).
-20000
0
20000
40000
60000
80000
100000
120000
140000
1
3
5
7
9
11
13
15
17
19
21
Day
P o i (Eu os)
P o i wi h o ecas ed p ices
P o i wi h ac ual p ices
P o i wi h o ecas ed ma ke and ac ual egula ion p ices
Figu e 11: To al daily bene i o he gas- u bine gene a o .
As in Case A, he scheduledene gyand p o i achie ed
wi h o ecas ed p ices on Ma ch 1 is shown in igu es 12
and 13, wi h and wi hou conside a ion o he income a is-
ing om he ese e se ice, espec i ely. Unlike in Case
A, he p o i di e ence be ween bo h si ua ions is e y im-
po an . When he objec i e unc ion akes in o accoun
he egula ion se ice income ( igu e 12), he uni is dis-
pa ched mos o he ime a minimum powe . Only a peak
hou s does he ene gy p ice jus i y maximum powe . No e
14 h PSCC, Se illa, 24-28 June 2002
Session 07, Pape 1, Page 5

ha he ne income is nega i e om 4 o 7 am, in spi e o
which he uni is no shu -down. The o al p o i in his
si ua ion is 40300 Eu os.
0
100
200
300
400
1
3
5
7
9
11
13
15
17
19
21
23
Hou
Ene gy (MWh)
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
P o i (Eu os)
Ene gy
P o i
Figu e 12: Hou ly bene i s and scheduled ene gy o he gas- u bine uni .
0
100
200
300
400
1
3
5
7
9
11
13
15
17
19
21
23
Hou
Ene gy (MWh)
-12000
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
12000
14000
P o i (Eu os)
Ene gy
P o i
Figu e 13: Hou ly bene i s and scheduled ene gy o he gas- u bine uni .
Rese e incomes no conside ed.
When he egula ion se ice income is igno ed in he
op imiza ion model, he uni s a s up only a 9am, and
he o al p o i educes o 10000 Eu os. This sugges s ha
abou 3/4 o he ne p o i o his uni is due o he ese e
income. The e o e, in cases like his, he unce ain y in he
ese e clea ingp ices may ha e a signi ican in luence on
he o e all p o i .
5 CONCLUSIONS
This pape add esses he in luence o he accu acy o
ANN-based hou ly ene gy p ice o ecas ing on he bid-
ding s a egy o GENCOs. Fi s , wo cus omized Mul i-
laye Pe cep ons ha e been applied o he 24-hou en-
e gy and ese e p ice o ecas ing p oblems, espec i ely,
using eal da a o he Spanish ene gy and ese e ma -
ke s. Fo he ene gyma ke p ice, he a e age e o anges
om 12% (Summe ) o 15% (Sp ing) o he hou ly a e -
age p ice, e o s being much highe in he ese e p ice
o ecas ing, as expec ed. Secondly, o ecas ed p ice p o-
iles ha e been used o compu e he op imal bidding o
wo ealis ic GENCOs, a coal- i ed gene a o and a gas-
u bine plan , and he in luence o o ecas ing e o s on
bo h he bidding s a egies and he expec ed e enues ha e
been p esen ed.
ACKNOWLEDGMENTS
The au ho s would like o acknowledge he inancial
suppo o he Spanish DGES unde g an s PB97-0719and
DPI2001-2612.
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