A oiding A alanches: E ec i e Dispa ch Planning
o Compe ing S o age Uni s in Day-Ahead
Elec ici y Ma ke Simula ions
Ch is oph Schimeczek1,*, Felix Ni sch1,2, Johannes Kochems1, and K is ina Nienhaus1
1Ge man Ae ospace Cen e (DLR), Ins i u e o Ne wo ked Ene gy Sys ems, Cu ies . 4, 70563 S u ga ,
Ge many
2BOKU Uni e si y, Ins i u e o Sus ainable Economic De elopmen , Feis man els aße 4, 1180 Vienna, Aus ia
*Co esponding Au ho : Ch is oph.Schime[email p o ec ed]
No embe 2025
P ep in licensed unde CC BY 4.0
10.5281/zenodo.17087876
Highligh s
•No el dispa ch planning s a egies o compe ing s o age uni s
•Enable di e en op imisa ion a ge s and a ying awa eness o compe i o s
•No compe i ion awa eness: s o ages a e o e used (a alanche e ec ), p o i s educed
•Conside ing compe i o s coun e s “a alanche e ec s” and inc eases p o i s
•Model, algo i hms, and pa ame isa ions openly a ailable in ull
Abs ac
In elec ici y ma ke s, s o age ope a ion and bidding s a egies a e based on expec ed p ice sp eads. A
he same ime, hese sp eads a e a ec ed by he ope a ion o he s o ages. I many s o age uni s eac
o an expec ed p ice sp ead in a simila way, hei join ope a ion can signi ican ly educe he sp ead
ealised on he ma ke . Such epe cussions a e known as “a alanche e ec s”. This pape examines
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dispa ch planning s a egies in agen -based elec ici y ma ke simula ions ha coun e hose a alanche
e ec s. These s a egies u ilise a dynamic p og amming algo i hm o de e mine asks and bids. The
algo i hm can pu sue di e en op imisa ion a ge s combined wi h a ying awa eness le els o p ice
impac s. We apply hese s a egy a ian s o a pa ame isa ion o he Ge man elec ici y ma ke and
compa e esul ing p ices, dispa ch, and mone a y pe o mance o hei his o ical alues. Ou indings
illus a e ha , wi hou p ice impac awa eness, s o age uni s a e 220% o e used in simula ions leading o
high mone a y losses. Sys em-cos minimisa ion yields he highes co ela ion (86%) wi h he his o ical
dispa ch, bu elec ici y p ices a e ep oduced mos accu a ely (87% co ela ion) using p o i maximisa-
ion. Disagg ega ing s o age uni s esul s in a be e i o his o ical da a han an agg ega ed single-uni
ep esen a ion. Discha ged ene gies and ope a ional p o i s a y s ongly ac oss he di e en modelling
expe imen s. Ou esea ch highligh s he impo ance o de ailed s o age modelling o accu a ely assess
s o age ma ke alues. One iden i ied s a egy is based on implici collusion and equi es only minimal
da a also a ailable in he eal wo ld. I s o age ope a o s beha e acco dingly, ma ke moni o ing and
an i us egula ions may be equi ed.
Keywo ds
agen -based modelling, ene gy s o age, lexibili y op ion, dispa ch planning, a alanche e ec , compe i ion
1 In oduc ion
As in e mi en enewable ene gy gene a ion echnologies, such as wind and sola powe , eplace ossil-
uel powe plan s a ound he wo ld (IEA 2024), balancing elec ici y supply and demand becomes mo e
challenging (Mlilo, B own, and Ah ock 2021). Ene gy s o age sys ems, such as ba e y s o age o pumped
hyd o s o age, can con ibu e o his balance a a ying empo al scales. Applica ions ange om sho -
e m o seasonal s o age and om small-scale o la ge scale sys ems (Lund e al. 2015). Especially
ba e y s o age sys ems also gain an inc easingly impo an ole in wholesale elec ici y ma ke s (Di ya
and Øs e gaa d 2009). Fo ins ance, in Ge many, he ins alled capaci y o la ge-scale ba e y s o age ose
al eady o mo e han 2 GW (Ago a Ene giewende 2025). In addi ion, he e a e a ound 220 GW o ne wo k
connec ion eques s o la ge-scale s o age sys ems (p magazine Deu schland 2025), o which 24 GW
a e assumed o be iable (IEA 2025). An ongoing decline o s o age cos s is os e ing his de elopmen .
Ba e y pack p ices in China ha e declined om a ound 260 $/kWh o below 100 $/kWh be ween 2017
and 2024 (Wal e , Bond, and Bu le -Sloss 2024).
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In u u e sys ems, la ge ene gy s o age capaci ies may ha e a signi ican impac on elec ici y p ice
dynamics (Elal y e al. 2024). I such impac s a e no p ope ly accoun ed o du ing dispa ch planning, he
esul ing dispa ch is subop imal. Fo example, i one s o age ope a o expec s e y low elec ici y p ices
a ime A and e y high p ices a ime B, his could esul in cha ging and discha ging ac ions planned o
ime A and B, espec i ely. I many ope a o s ha e a simila p ice expec a ion, hei combined dispa ch
could aise p ices a ime A and lowe p ices a ime B leading o signi ican ly educed – o e en in e ed
– p ice sp eads. Such ou comes a e known as “a alanche e ec s” and ha e been obse ed in models
ega ding, e.g., household demand-side lexibili y (Go wal e al. 2011), he hea ing sec o (Spe be
e al. 2025), and he anspo sec o (K¨uhnbach, S u e, and Klingle 2021; Ensslen e al. 2018). This
highligh s he need o no el me hods o assess he p o i abili y and sys em e ec s o s o age sys ems.
These me hods need o conside ha he economic pe spec i e o indi idual s o age uni s is in luenced
by he ma ke en i onmen comp ising nume ous compe i o s. I is he e o e o g ea impo ance o
accoun o he in luence o compe i o s and o model he beha iou o a s o age uni accu a ely (Ni sch,
Schimeczek, and Be sch 2025).
1.1 Rela ed Wo k
Op imisa ion models a e commonly used o model elec ici y sys ems, ocusing on minimizing sys em
cos s unde assump ions o pe ec compe i ion and cen al planning (Haugen e al. 2024; Ge baule and
Lo enz 2017). Howe e , hey do no accoun o s a egic beha iou o indi idual in es o s and ope a o s
seeking o maximise hei p o i . Game- heo e ic app oaches can add ess his sho coming and also assess
ma ke powe (Williams and G een 2022). Ye , mos models also assume pe ec in o ma ion.
Agen -based models (ABMs) o e a way o inco po a e impe ec in o ma ion and s a egic beha iou ,
simula ing eal-wo ld ac o s’ decision-making p ocesses in elec ici y ma ke s (Klein, F ey, and Reeg
2019). These models ha e been used o explo e elec ici y ma ke s (Chang e al. 2021) and allow mod-
elle s o analyse economic pe spec i es o s o age ope a o s in cu en and u u e scena ios, conside ing
epe cussions om he o e all sys em (Bis line e al. 2020).
Resea ch on bidding s a egies o ene gy s o age sys ems, such as hyd oelec ic plan s, is well-
es ablished (Fle en and K is o e sen 2007; Azad e al. 2020). (Fa ahani, Samimi, and Sha e i 2023)
de elop a p o i -maximising s a egy o ba e y s o age sys ems, bu neglec compe i ion and ma ke
p ice impac s. This limi a ion is also ound in (Liu e al. 2025), who p opose a p o i -maximising dynamic
p og amming scheduling s a egy o pumped hyd o s o age. The in es iga ion o compe i ion be ween
di e en lexibili y op ions (FOs), e.g., ene gy s o age and demand-side lexibili y, is co e ed o a lesse
3
ex en . (M¨obius e al. 2023) deploy a wo-s age s ochas ic op imisa ion model and ind subs i u ional
compe i ion be ween he FOs, bu do no p o ide di e se ope a ional s a egies. (K. Pandˇzi´c, H. Pandˇzi´c,
and Kuzle 2019) apply a mul i-s age op imisa ion app oach o h ee compe ing s o age uni s and ind
ha s o age p o i s a e signi ican ly highe when he uni s coo dina e hei dispa ch. Wi hou dispa ch
coo dina ion, howe e , s o age p o i s and dispa ch pa e ns we e uns able.
As compu a ional powe inc eases, deep- ein o cemen lea ning (DRL) models a e eme ging o sim-
ula ing elec ici y ma ke s (Ha de , Qussous, and Weidlich 2023). Ye , hey o en ail o conside p ice
impac s o p o ide in e p e able esul s (Ha de , Weidlich, and S aud 2023). (Okwuibe e al. 2020) use
DRL o ind in elligen bidding s a egies o p osume s o be submi ed o local elec ici y ma ke s. How-
e e , he beha iou o p osume s on local ene gy communi y ma ke s di e s om ha o la ge scale uni s
on day-ahead ma ke s. Thus, he ans e o esul s o hose ma ke s equi es mo e wo k. In he s udy
by (Badoual and Mou a 2021), a p ice-making s o age is conside ed. They ind ha a new s a egy based
on an ac o -c i ic app oach ou pe o ms a baseline s a egy. Howe e , he in eg a ion o compe i ion
among mul iple FOs wi h ma ke powe emains unexplo ed. A obus s a egy, e en when compe ing
FOs a e aken in o accoun , is p esen ed in (Dong e al. 2021). Howe e , he case s udy is pe o med
on his o ical ma ke da a only. Fu he wo k is needed o assess he pe o mance o hese models unde
high enewable ene gy sha es.
1.2 No el y
While he e is a subs an ial amoun o li e a u e on bidding s a egies o s o age uni s, ou wo k o e s
se e al key me hodological ad an ages, while ollowing a ho ough open science app oach. Fi s , we
de elop a lexible scheduling algo i hm using dynamic p og amming which allows o s udy p ice- aking
as well as p ice-making s a egies. Addi ionally, we include a sophis ica ed app oach o accoun o
p ice e ec s o mul iple s o age uni s. This enables us o s udy he implica ions o compe ing s o age
uni s and o explici ly con ol a alanche e ec s. While we p o ide no di ec quan i a i e measu e o
a alanche e ec s, we p o ide benchma ks o he dispa ch planning algo i hm a ian s based on his o ical
da a ob ained om (Bundesne zagen u 2025), enabling us o quan i y ou modelling wi h espec o he
ep oduc ion o eal-wo ld ma ke dynamics. In con as o DRL s a egies, we e ain ull anspa ency
o e he scheduling algo i hms applied. Compa ed o game- heo e ic app oaches, ou me hodology o e s
supe io pe o mance. Second, ou wo k p o ides a powe ul enhancemen o he open-sou ce and s a e-
o - he-a ABM AMIRIS1(Schimeczek, Nienhaus, e al. 2023). Speci ically, all s a egies desc ibed in
his pape a e openly a ailable wi h AMIRIS. The e o e, AMIRIS is now no only highly capable o
1Agen -based Ma ke model o he In es iga ion o Renewable and In eg a ed ene gy Sys ems
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his o ical benchma king simula ions (Mau e , Ni sch, e al. 2024), bu can also add ess u u e scena ios
wi h high sha es o enewable ene gies and compe ing FOs. Thi d, all p esen ed benchma king analyses
a e based on open da a (Schimeczek, Ni sch, and Kochems 2025). This enables use s o ep oduce ou
esul s and o conduc hei own analyses in a con enien manne . In summa y, we p o ide lexible
and powe ul algo i hms o simula e compe ing ene gy s o age uni s, and he eby con ibu e o a be e
unde s anding o cu en and u u e elec ici y ma ke s.
The emainde o his pape is s uc u ed as ollows. Sec ion 2 ou lines he undamen als o he ABM
AMIRIS. We p esen he indi idual s o age s a egies by desc ibing hei cha ac e is ics and po en ial
applica ions. In Sec ion 3, a case s udy is conduc ed o e alua e he pe o mance o he p esen ed s o age
s a egies, bo h on an indi idual s o age sys em le el bu also on he o e all ene gy sys em le el. We
discuss ou p esen ed modelling app oach in Sec ion 4. Fu he mo e, we con as ou esul s wi h exis ing
li e a u e. Finally, in Sec ion 5, we summa ize ou indings and o e sugges ions on u he esea ch
a enues.
2 Me hods
To simula e he compe i ion o ene gy s o age uni s, we enhance he open Agen -based Ma ke model
o he In es iga ion o Renewable and In eg a ed ene gy Sys ems AMIRIS wi h powe ul algo i hms
o dispa ch planning and p ice o ecas ing. All o his is desc ibed in he ollowing subsec ions.
2.1 Elec ici y Ma ke Modelling
AMIRIS is a comp ehensi e and powe ul open-sou ce ool (Schimeczek, Nienhaus, e al. 2023) o model
elec ici y ma ke s. I has been designed o assis esea che s in analysing complex challenges ela ed o
u u e ene gy ma ke scena ios, ma ke designs, and ene gy policy ins umen s. AMIRIS can simula e
s a egic bidding beha iou o a ious ma ke ac o s, conside ing no jus ma ginal p ices bu also he
e ec s o suppo ins umen s, unce ain ies, and ma ke powe (F ey e al. 2020). Ou pu s comp ise, e.g.,
elec ici y p ices, dispa ched ene gy as well as inancial lows be ween he ep esen ed agen s. AMIRIS is
e ol ing cons an ly - esul s in his wo k we e ob ained wi h e sion 3.7.2 con ained in he accompanying
da a elease (Schimeczek, Ni sch, and Kochems 2025).
The s uc u e o AMIRIS, depic ed in Figu e 1, is based on se en main agen ca ego ies: ma ke s,
ade s, powe plan ope a o s, demand agen s, policy p o ide s, o ecas e s, and lexibili y p o ide s.
The day-ahead ma ke pe o ms he ma ke clea ing based on he bids p o ided by ade s. Powe plan
ope a o s gene a e elec ici y acco ding o he ma ke success o hei co esponding ade . Demand
5
Figu e 1: Schema ic ep esen a ion o agen ypes and hei in e ac ions in AMIRIS e sion 3.7.2
agen s buy ene gy om he day-ahead ma ke , while policy p o ide s in luence he egula o y landscape
and, in u n, a ec he dispa ch decisions o o he agen s (Reeg 2019). Fo ecas s o elec ici y p ices
and o he me i o de a e p o ided by dedica ed o ecas e s. Flexibili y p o ide s (ene gy s o age, load
shi ing uni s, hea -pumps, elec ic ehicles, and elec olyse s) u ilise hese o ecas s o op imise hei
bidding s a egy, he eby c ea ing a dynamic simula ion en i onmen (Ni sch, Schimeczek, and Be sch
2025).
AMIRIS is based on he FAME amewo k (Schimeczek, Deissen o h-Uh ig, e al. 2023; Ni sch,
Schimeczek, F ey, e al. 2023). The model has been applied o assess di e en FO echnologies and con-
cep s, such as Ca no ba e ies (Ni sch, We zel, e al. 2024), ba e y s o age sys ems (Ni sch, Deissen o h-
Uh ig, e al. 2021), hea -pumps (Spe be e al. 2025), demand esponse (Kochems 2024), and ma ke
coupling (Ni sch and El Ghazi 2023). In his wo k, we enhance he o ecas ing me hod and he dispa ch
planning o ene gy s o age uni s o simula e and assess hei compe i ion. O he FOs a e dis ega ded.
Each s o age agen con ols a single ene gy s o age uni . Thus, he e ms s o age agen , s o age ope a o ,
and s o age uni can be ega ded synonymous in his wo k.
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2.2 Dispa ch Planning S a egies
Dispa ch planning s a egies o s o age agen s in AMIRIS a e de e mined by sol ing op imisa ion p ob-
lems. We conside wo s a egy a ian s: one ha maximises he s o age agen ’s p o i s and one ha
minimises o al sys em cos . These s a egies acili a e analyses be ween maximum ma ke powe and
ull compe i ion. The a ian s can easily be swapped o new simula ions and e en combined when using
mul iple s o age agen s. A cos -minimising s a egy is o en implici ly applied in ene gy sys em op imisa-
ion models which minimise he cos o he dispa ch o all powe plan s (Ege e 2016) and also o powe
plan in es men s (Hi h, Ruhnau, and Sga la o 2021).
Figu e 2: Illus a ion o he dynamic p og amming algo i hm and i s bidding s a egy o a s o age wi h
h ee s a e o cha ge (SOC) le els and h ee ime s eps (plus one o he ini ial s a e) wi h di e en
elec ici y p ices (g een), no conside ing losses due o cha ging o discha ging e iciencies; s a ing a a
s o age le el o 1 MWh, he bes pa h as well as ela ed bid and ask p ices a e shown in blue.
To ind he op imal dispa ch, AMIRIS s o age agen s use dynamic p og amming (Bellman 1957).
In his common solu ion app oach, he s o age uni ’s possible s a e o cha ge (SOC) is disc e ised in
ene gy le els, and he ime is disc e ised in ime s eps. This is illus a ed in Figu e 2, whe e disc e ised
ene gy le els a e ep esen ed by s acked black lines which a e epea ed o each conside ed ime s ep.
Res ic ions on he minimum and maximum SOC di ec ly ansla e in o a ailable ene gy le els. The
numbe o ime s eps is limi ed by he leng h o he o esigh ho izon. S a ing a he las conside ed
ime s ep and p og essing backwa ds, he alue o each SOC le el is de e mined by he alue o he bes
possible ansi ion o a ollow-up le el. This ansi ion yields he bes esul o he sum o i) he alue
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o a po en ial ollow-up le el and ii) he alue o he ansi ion o ha le el. T ansi ions a e e alua ed
based on o ecas s o he elec ici y p ice and he amoun o elec ici y p o ided o o aken om he g id
co esponding o he ansi ion, see Sec ion 2.3. Po en ial ollow-up s a es a e es ic ed by he maximum
cha ge and discha ge powe s o he s o age uni . Once he alues and op imal ansi ions o all SOC
le els and ime s eps ha e been assessed, he op imal pa h o SOC le els ollowing he cu en ene gy
le el is de e mined in a o wa d pass. Since all po en ial ollow-up le els mus be checked o each SOC
le el, he compu a ional cos scales quad a ically wi h he SOC disc e isa ion. To educe compu a ional
o e head, we employ memoiza ion echniques.
In Figu e 2, he alue o all s o age le els is assumed o be ze o in he las ime s ep. This simpli ica ion
neglec s he alue o s o age a he end o he o ecas ing pe iod, also known as wa e alue (see e.g. (Sco
and Read 1996)). To conside he alue o s o age a he end o he o ecas ing pe iod, long- e m
simula ions can be used o de i e he wa e alues. I such a e no a ailable, a olling ho izon app oach
wi h equen ee alua ions can be applied ins ead. Such app oaches ha e been p o en o yield good
esul s o ene gy sys em modelling (Ma quan , E ins, and Ca melie 2015). We also expe ienced he
olling ho izon app oach o yield good esul s i he ene gy o powe (E2P) a io o he s o age uni is
small compa ed o he o esigh ho izon.
The bes pa h o SOC le els de e mines he amoun o ene gy o sell o o o buy om he elec ici y
ma ke o e e y ime s ep. To de e mine associa ed o e p ices, we apply di e en a ionales depending
on he op imisa ion a ge . In case o sys em cos minimisa ion we wan o ensu e ha he de e mined
dispa ch pa h is ollowed and use minimal o maximal allowed o e p ices. When p o i maximisa ion is
employed we es ima e he oppo uni y cos o changing he SOC le el based on he p e iously de e mined
SOC e alua ions. Fo asks, he o e p ice P mus compensa e o he p ojec ed loss o alue when mo ing
om ime o + 1, which equals he di e ence be ween he es ima ed s o age alue V +1 o he ini ial
SOC le el iand he inal SOC le el , di ided by he associa ed change in ene gy ∆Ei, :
Pi→
=Vi
+1 −V
+1
∆Ei, (1)
Fo bids, he o e p ice mus no exceed he p ojec ed money ha can be made om he addi ional
ene gy, esul ing in an exchange o ini ial and he inal SOC le els iand in Equa ion 1.
Figu e 2 demons a es all aspec s o he algo i hm wi h delibe a ely simple numbe s. The s o age
de ice’s SOC is disc e ized in o h ee le els wi h 0, 1, and 2 MWh. Since he E2P a io is wo, he
SOC can only change by 1 MWh pe ime s ep. Th ee ime s eps a e conside ed, an addi ional ou h
ime s ep indica es he ini ial s a e o he s o age de ice. As he e is no wa e alue conside ed he e,
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he s o age alues ( ed numbe s) a e assumed o be ze o o all SOCs in he las ime s ep. P ojec ed
elec ici y p ices change om 7 o e 4 o 10 €/MWh. The bes ollow-up SOC le els a e indica ed by
do ed a ows. An exempla y pa h s a ing wi h a hal - illed s o age is highligh ed in blue. Bid and ask
p ice calcula ions associa ed wi h he ansi ions a e also shown in blue.
The ou lined algo i hm is well known bu s ands and alls wi h he elec ici y p ice o ecas . Fo
small amoun s o ins alled s o age, o ecas s do no necessa ily need o conside he eedback o s o age
dispa ch on he elec ici y p ices. This is assumed in Figu e 2. The dispa ch o la ge o many s o age
de ices, hough, could ha e signi ican p ice impac s ha po en ially lead o a alanche e ec s. Thus, we
also need o o ecas p ice changes due o s o age dispa ch.
2.3 Fo ecas ing
Elec ici y p ice o ecas s used by AMIRIS agen s a e calcula ed based on h ee ypes o in o ma ion o
any espec i e ime s ep: i) Wha he elec ici y p ice would be wi hou dispa ch om s o age agen s, ii)
how he p ice would change wi h addi ional supply o demand, and iii) how s ongly he dispa ch o a
s o age agen aligns wi h he dispa ch o all compe i o s. In o de o answe hese ques ions, he o ecas e
agen collec s p elimina y bids and asks om he supply and demand agen s o all u u e ma ke clea ing
e en s wi hin he o esigh ho izon. Wi hou bids and asks o s o age agen s, he o ecas e agen clea s
he ma ke using he same algo i hm as he day-ahead ma ke agen o answe ques ion i). The esul ing
me i o de is hen inspec ed o assess how addi ional demand o supply om s o ages would change he
clea ing p ice. This “sensi i i y o ecas ” answe s ques ion ii). To answe ques ions iii), we ack he
dispa ch o all s o age agen s. Fo each ime s ep, we calcula e he o al dispa ch om s o age agen s
as well as he sha e o each s o age agen in his dispa ch o al. The in e se o his sha e ep esen s an
agen -speci ic mul iplie o calcula e he dispa ch o all s o age agen s - including compe i o s - using he
agen ’s own dispa ch. This mul iplie is apidly changing o e ime and depends on he cha ac e is ics
o he di e en s o age agen s. To achie e a mo e s able alue, we a e age o e mul iple ime s eps.
Based on he a e aged “compe i ion mul iplie ”, each indi idual s o age agen can es ima e he u u e
o al dispa ch o all s o age agen s using i s own dispa ch plans. By combining his app oach wi h
he sensi i i y o ecas each s o age agen can es ima e he o al impac o all s o age agen s on u u e
elec ici y p ices.
Figu e 3 illus a es his mechanism using a schema ic ep esen a ion o he me i o de . Wi hou
s o age ac i i y, he gi en demand and supply cu es de e mine he p ice p. The o ecas includes no
only his p ice, bu also how sensi i e i is o changes in demand o supply. Thus, each agen can conside
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Figu e 5 shows he de elopmen o compe i ion mul iplie es ima es o 18 compe ing s o age uni s
du ing a simula ed yea . Fo mos o he s o age uni s, he mul iplie es ima es s abilise a e one week.
The s o age uni s whose mul iplie s ake he longes o s abilise a e hose wi h he highes E2P a io.
The selec ed decay ime o 168 hou s enables mid- e m adap ions o he compe i ion mul iplie s due o
changed ma ke si ua ions while p o iding sho - e m s abili y. To assess whe he he ini ial es ima es
o he compe i ion mul iplie s a e easonable, we compa e hem o he a e aged compe i ion mul iplie s
a he end o he simula ion. We ind ha he ini ial mul iplie es ima es a e o by less han a ac o o 4.
This co ec ion ac o o he ini ial es ima es has a Pea son co ela ion o -0.9 wi h he RTE. The e o e,
compe i ion mul iplie s o s o ages wi h high RTE a e ini ially o e es ima ed, and hose o s o ages
wi h low RTE begin unde es ima ed. This can be explained by a numbe o dispa ch oppo uni ies ha
can only be exploi ed wi h high RTE, bu inc eased compe i ion in si ua ions wi h high p ice sp eads.
3.2.2 Back es ing Pe o mance
Table 2 shows he pe o mance me ics associa ed wi h 18 compe ing s o age agen s in he back es ing
scena io. Compa ed o he single-agen ep esen a ion, he mul i-agen ep esen a ion imp o es pe o -
mance wi h espec o he p ice and dispa ch co ela ions. MAE and RMSE imp o e o he p ice- ake
and sys em-cos minimisa ion a ian s, bu sligh ly wo sen o he p o i -maximisa ion a ian . To al
discha ged ene gy is educed in all cases, as he de eloped algo i hm only p o ides a good, no a pe ec ,
es ima e o he compe i o s’ beha iou . This educ ion b ings he p o i and he sum o dispa ched ene gy
o he sys em-cos minimisa ion a ian close o he his o ical esul s.
Me ic P o i Maximisa ion
P ice Take
Sys em Cos Minimisa ion
Compe i ion Es ima e
P o i Maximisa ion
Compe i ion Es ima e
P ice co ela ion 0.66 0.85 0.87
MAE in EUR/MWh 8.46 5.37 5.24
RMSE in EUR/MWh 11.93 8.12 7.83
Dispa ch co ela ion 0.87 0.86 0.79
Rela i e discha ged ene gy 222% 107% 72%
Rela i e p o i s -161% 109% 129%
Table 2: Pe o mance me ics o h ee a ian s o he s o age dispa ch s a egy wi h 18 compe ing s o age
agen s in he back es ing scena io yea ; discha ged ene gy o als a e ela i e o his o ical dispa ch. P o i s
a e ela i e o a ic i ious p o i ha would ha e been ecei ed om he his o ical dispa ch and his o ical
day-ahead ma ke p ices. Compa ed o single-agen ep esen a ion, o al discha ged ene gy is educed
while dispa ch co ela ion and MAE imp o e o all s a egy a ian s.
Figu e 6 shows he cumula i e hou ly dispa ch om all s o age uni s and associa ed elec ici y p ices
o he h ee dispa ch s a egy a ian s agains his o ical da a o he same week as in Figu e 4. Se -
e al di e ences can be spo ed when compa ing hese wo igu es. These di e ences a e caused by he
16
Figu e 6: Elec ici y p ices esul ing om simula ion o s o age dispa ch wi h 18 compe ing s o age
agen s in week 43 o he back es ing scena io using di e en s a egy a ian s compa ed o he his o ical
elec ici y p ices ( op); associa ed hou ly s o age dispa ch om simula ions and his o ical da a (below)
disagg ega ion o s o age capaci y in o dis inc uni s wi h speci ic RTE and E2P a ios, as well as he
added unce ain y om compe i ion. Resul s o he p ice- ake a ian exhibi sligh ly educed cha ging
and discha ging peaks. Howe e , he high-e iciency s o age uni s a e o e used and addi ional cha ging
and discha ging ac i i ies lead o addi ional peak- alley in e sion e en s o he elec ici y p ice on he
i h day. The sys em-cos minimising and p o i -maximising a ian s show less p onounced cha ging and
discha ging peaks, and a e mo e closely ela ed o he his o ical dispa ch.
Figu e 7 shows he same week as Figu e 6 bu depic s he indi idual dispa ch o h ee s o age uni s
wi h he p o i -maximising s a egy a ian . The s o age uni s di e s ongly wi h espec o hei
echnical pa ame e s, causing di e en dispa ch pa e ns. I can be seen ha he mos ac i e uni is ha
wi h he highes RTE (pu ple). This uni cha ges and discha ges o se e al hou s each day, while he
uni wi h he lowes RTE (g een) can ba ely exploi any o he small unde - he-day p ice sp eads. The
high-e iciency uni pe o ms bo h cha ging and discha ging ac i i ies be ween Oc obe 25 h and 27 h,
whe eas he uni wi h la ges E2P (o ange) u ilises i s s o age capaci y o cha ging only. In his way,
i can exploi he ela i ely low p ices a ha ime compa ed o hose du ing he i s h ee days o he
ollowing week (no shown).
17
Figu e 7: Elec ici y p ices esul ing om he simula ion o s o age dispa ch wi h 18 compe ing s o age
agen s in week 43 o he back es ing scena io using he p o i -maximising dispa ch a ian ( op); s a e o
cha ge o h ee s o ages uni s wi h di e en ene gy- o-powe a ios and ound- ip e iciencies (bo om)
3.3 Inc eased Compe i ion
The impac o compe i ion inc eases wi h highe s o age capaci ies. To demons a e he applicabili y
o he p esen ed me hod o highly compe i i e scena ios, we de ia e om he back es ing scena io and
inc ease he amoun o ins alled s o age by 20 GW. Mo i a ed by ecen de elopmen s in Ge many, we
concen a e on sho - e m s o age ha esembles, e.g., ba e ies. We conside 5 GW addi ional capaci y,
each o E2P a ios o 1, 2, 3, and 4. All addi ional uni s a e assigned a simila RTE. Table 3 shows he
pa ame e s o he addi ional s o age uni s.
S o age Uni Iden i ie Con e e Powe S o age Capaci y RTE
Ba e y 1 5 GW 5 GWh 0.865
Ba e y 2 5 GW 10 GWh 0.865
Ba e y 3 5 GW 15 GWh 0.865
Ba e y 4 5 GW 20 GWh 0.865
Table 3: Powe , capaci y and ound- ip e iciency o s o age uni s added o he back es ing scena io;
uni iden i ie s a e equal o hei ene gy- o-powe a io. The same ound- ip e iciency is assumed o
all addi ional s o age uni s.
We e alua e bo h he sys em-cos minimising and p o i -maximising dispa ch s a egy a ian s o
he case o 18 compe ing s o age agen s. Due o he changed scena io se up, we do no compa e wi h
his o ical da a. Ins ead, we compa e wi h he o iginal back es ing scena io o assess he impac o he
18
addi ional s o age uni s. Table 4 highligh s he absolu e p o i s and discha ged ene gies in bo h scena ios
and o bo h dispa ch s a egy a ian s. In case o sys em-cos minimisa ion, he addi ional uni s a e
s ongly pu o use and he discha ged ene gy o al ises om 7.3 TWh in he back es ing scena io o
10.7 TWh in he inc eased capaci y scena io. This, howe e , educes he o al p o i om 105 M€ o
75 M€, due o p ice sp ead dampening (see below). Wi h he p o i maximisa ion s a egy a ian , he
discha ged ene gy o al mode a ely inc eases om abou 5 TWh o 6.6 TWh in he inc eased capaci y
scena io due o he highe - han-a e age e iciency o he addi ional uni s. The o al p o i inc eases as
well, bu only om 124 M€ o 137 M€.
Me ic Scena io Sys em Cos Minimisa ion P o i Maximisa ion
Discha ged Ene gy To al Back es ing 7.32 4.95
in TWh Inc eased Capaci y 10.71 6.61
To al P o i s Back es ing 105.3 124.2
in M€Inc eased Capaci y 75.4 137.8
Table 4: Discha ged ene gy and p o i o als o 18 compe ing s o age uni s in he back es ing scena io
and he scena io wi h inc eased s o age capaci y using ei he cos -minimising o p o i -maximising s a e-
gies; wi h sys em cos minimisa ion, s o age capaci ies a e s ongly used, hus educing p o i s. P o i
maximisa ion shows a mode a e inc ease o s o age usage, and a small inc ease o s o age p o i s.
As Figu e 8 shows, he p o i -maximising dispa ch s a egy a ian (g een colou s) c ea es e y simila
p ices in he back es ing scena io and he addi ional capaci y scena io. This s a egy a ian es ic s he
use o addi ional s o age powe and capaci y o main ain highe p ice sp eads. Howe e , he sys em-cos
minimising dispa ch a ian (pink colou s) uses he addi ional capaci ies especially a he beginning o
he shown week o u he educe he di e ences be ween p ice minima and maxima when compa ed o
he back es ing scena io. Fo e e ence, we also p o ide p ices om a scena io wi hou any s o age uni s
(g ey colou ) o demons a e he he s o age uni s’ p ice impac .
Figu e 9 compa es he ins alled con e e powe and s o age capaci y o he o iginal back es ing
scena io wi h ha o he addi ional ba e y s o age uni s. Al hough he newly ins alled ba e y s o age
uni s accoun o mo e han iple he con e e powe , he o al ins alled s o age capaci y is only inc eased
by abou 20%. Since he sys em-cos minimising dispa ch s a egy a ian p oduced a dispa ch closes o
he eal-wo ld (see abo e), we assess his s a egy he e. Due o he highe RTE o he addi ional ba e y
uni s compa ed o he exis ing pumped-hyd o s o age uni s, he ba e y uni s gene a e abou 52% o he
p o i s and p o ide 59% o he dispa ched ene gy.
19
Figu e 8: Elec ici y p ices in he las week o a scena io wi hou any s o age uni s (g ey), o he back-
es ing scena io (ligh colou s), and o he scena io wi h inc eased s o age capaci y (da k colou s) o
cos -minimising (pink) and p o i -maximising (g een) s a egy a ian s
4 Discussion
We es ed a ian s o s o age dispa ch s a egies wi h di e en op imisa ion a ge s and a ying awa eness
o p ice impac s om s o age dispa ch. Fo bo h, a single la ge s o age uni and disagg ega ed s o age
uni s, we obse ed signi ican o e use o he s o age uni s i hese a e no awa e o hei p ice impac s.
The e o e, p ice- ake dispa ch s a egies should be combined wi h p edic ions ha al eady include an
expec ed impac o s o age uni s on he p ice. This can make pe o ma i e p edic ions necessa y (Ha d
and Mendle -D¨unne 2025) ha conside he impac o elec ici y p ice p edic ions on he simula ion
ou come (Ni sch, Schimeczek, and Be sch 2025).
Wi h a single s o age uni ha is pe ec ly awa e o i s own p ice impac s, p ice-make beha iou is
ound. When combined wi h he op imisa ion a ge o sys em cos minimisa ion, esul s a e equi alen o
hose o a global cos minimisa ion model (To alba-Diaz e al. 2020). Employing he op imisa ion a ge
o p o i maximisa ion, hough, can illus a e he impac o ma ke powe on p o i s and s a egically
educed dispa ch. This also leads o highe sys em cos (To alba-Diaz e al. 2020).
To simula e compe i ion, he de eloped algo i hm es ima es mul iplie s esembling he e ec i e com-
bined s o age powe . This allows o app oxima e he impac on elec ici y p ices om all compe i o s
and o a oid a alanche e ec s. The mul iplie s a e indi idually adap ed o each s o age uni o conside
he impac o di e en E2P and RTE cha ac e is ics. This app oach aligns he dispa ch o he s o age
uni s, by le ing hem assume ha he dispa ch o compe ing s o age uni s will co ela e wi h hei own
dispa ch. In case o he p o i -maximising s a egy, his p esumed dispa ch alignmen s ongly es ic s
20
Figu e 9: Scena io wi h ex ended s o age; sha e o ins alled con e e powe and s o age capaci y wi h
sum o o iginal pumped-hyd o s o ages in blue ( op); sha e o p o i s and dispa ched ene gy be ween
newly ins alled uni s in pink, b own, g een, and gold as well as he co esponding o al o all o iginal
uni s in blue using he sys em-cos minimising dispa ch a ian (bo om)
s o age usage in o de o inc ease p o i s. This co esponds o collusion which is also ound in o he
s udies assessing he e ec s o coo dina ed s o age beha iou (K. Pandˇzi´c, H. Pandˇzi´c, and Kuzle 2019).
Howe e , when applied wi h a cos -minimising s a egy, he dispa ch alignmen o indi idual s o age
uni s also p e en s hei o e use, bu o a lesse ex en and simila o a global cos -minimisa ion. Thus,
he alignmen aspec o he algo i hm in his case simula es he ou come o (almos ) pe ec compe i-
ion. When compa ed wi h he his o ical dispa ch o s o age uni s, we ind highe coincidence le els
o he simula ed dispa ch when applying a cos -minimising s a egy. This could mean ha eal-wo ld
s o age uni s do no u ilise signi ican ma ke powe and ha he Ge man elec ici y ma ke was close
o pe ec compe i ion wi h insigni ican collusion o s o age uni s in he assessed yea . This implica ion,
howe e , is o be aken wi h a g ain o sal , since o he aspec s can impac s o age ope a ion as well,
mos p ominen ly he pa icipa ion in in a-day and ese e ma ke s.
Despi e i s simila i y o ene gy sys em op imisa ion models, ou p esen ed app oach allows o combine
21
di e en op imisa ion a ionales o mul iple agen s. Thus, pa ial ma ke powe could be simula ed. Ad-
di ionally, he in e play be ween compe ing s o age sys ems and o he ma ke designs, such as enewable
ene gy emune a ion policies (Kochems e al. 2024), can be s udied using his app oach. Fu he mo e, i
can easily be enhanced o conside he indi idual p edic ion unce ain ies o di e en s o age ope a o s.
In compa ison o ABMs ha employ machine-lea ning o model s o age compe i ion, such as (Ni sch,
Schimeczek, and Be sch 2025) and (Ha de , Weidlich, and S aud 2023), ou app oach p o ides supe io
compu a ional pe o mance as he e is no aining equi ed. Ins ead, ou algo i hm’s so pa ame e s,
ini ial weigh and decay ime cons an (see Sec ion 2.3), p o ed o yield s able esul s o e a wide ange
o he pa ame e space (see Appendix B). This indica es ha he de aul pa ame e s can p obably be
used wi hou adap a ion o a wide ange o scena ios. Addi ionally, he employed dynamic p og amming
algo i hm yielded good esul s du ing execu ion, e en wi h a qui e coa se ene gy esolu ion o one en h
o he con e e powe pe s o age uni . The a e age un ime o scena ios wi h 18 compe ing s o age
uni s o a ull yea wi h hou ly esolu ion was abou 30 seconds pe simula ion on a pe sonal compu e
(In el Co e i7-1370, 32 GB o Memo y). A pe o mance es wi h 1 o 128 s o age agen s is shown in
Appendix C. I demons a es ha ou app oach scales linea ly wi h he numbe o s o age agen s included
in simula ions and hus enables la ge-scale pa ame e s udies, e en on limi ed ha dwa e. While p o iding
o he bene i s, equi alen case s udies o ABMs u ilising machine lea ning o model s o age compe i ion,
demons a e aining imes in he ange o hou s (Mau e , Ha de , e al. 2025) on he same machine.
An addi ional bene i o he p esen ed implemen a ion is ha i allows o quan i y he lowe and uppe
limi s o s o age p o i abili y by swi ching be ween he wo implemen ed op imisa ion a ionales o cos -
minimisa ion and p o i -maximisa ion. The cos -minimisa ion a ionale p o ides a “pe ec compe i ion”
es ima e and ac s as a lowe bounda y o sys em cos s and s o age p o i s. The p o i -maximisa ion
a ionale, on he o he hand, demons a es collusion among s o age uni s and hus ep esen s an equi alen
uppe bounda y o hose quan i ies. Howe e , i implies ha ma ke ac o s employ simila algo i hms o
p ice o ecas ing, compe i ion es ima ion, and dispa ch planning. In case his o ical dispa ch in o ma ion
is published a ew hou s a e eal ime, such collusion beha iou could heo e ically be ealised by ac ual
ma ke ac o s. Fo he Ge man ma ke , co esponding da a is a ailable (Bundesne zagen u 2025). Thus,
in o de o p e en he abuse o collec i e ma ke powe , an i us egula ions migh be necessa y. A
leas , he dispa ch beha iou o s o ages and o he lexibili y op ions should be moni o ed.
To showcase he capabili y o ou algo i hm o deal wi h highe le els o compe i ion, we inc eased he
o al s o age powe in a s ylized scena io. Depending on he dispa ch s a egy a ian s, we obse ed only a
mode a e inc ease o o al p o i s o s o age uni s a bes , o e en a signi ican educ ion. In gene al, such
s udies could con as echnology-speci ic economic assessmen s ha ely on his o ical p ice p ojec ions,
22
e.g. (Mussawa and Mayyas 2025). Howe e , ou s ylized e alua ion did no conside an inc ease o
enewables in he scena io. These would likely inc ease he p ice sp eads and hus p esen addi ional
dispa ch oppo uni ies o s o age uni s. We expec s o age p o i s in such a scena io o be highly
dependen on he compe i ion wi h o he lexibili y sou ces, such as lexible loads, inc eased in e na ional
ading, lexibili y om sec o coupling echnologies, e.g. elec olyse s, hea pumps o elec ic ehicles.
In Ge many, compa ed o he de ailed expansion pa hway goals o a iable enewable gene a o s de ined
in he Ge man enewables ac (Fede al Go e men o Ge many 2023), he e is no o e all goal conce ning
he capaci y pa hway o lexibili y sou ces. The e a e some s a egic policy goals, such as ins alling a
leas 500,000 hea pumps pe yea and eaching 15 million elec ic ehicles by 2030 (Fede al Minis y o
Economic A ai s and Clima e Ac ion (BMWK) Ge many 2023). Howe e , hese goals a e no binding
and, o he case o hea pumps, ha e been ailed in he pas yea s. In con as , he e is a la ge unce ain y
abou how he capaci y mix will e ol e and in luence emune a ion pe spec i es o s o ages. This migh
change wi h he obliga ion o in oducing indica i e lexibili y goals o EU membe s a es acco ding o
A icle 19 o (Pa liamen and Council 2019). Fu he mo e, we did no conside o he e enue s eams
o s o age uni s om, e.g., in aday ma ke s o peak sha ing, as illus a ed in (Kuma esh e al. 2025).
These ac i i ies would likely in luence he simula ed dispa ch and, ul ima ely, he modelled elec ici y
p ices, depending on how s o age uni s op imise ac oss mul iple ma ke s simul aneously. Also, we did no
accoun o e enue s eams om policy ins umen s ha a e subjec o deba e, bu no ye in oduced.
Rele an policy ins umen s could be lexibili y ma ke s o capaci y emune a ion mechanisms, which by
EU law mus be open o s o ages o lexible loads acco ding o A icle 22 o (Pa liamen and Council
2019). The la e can e en be combined wi h dedica ed e enue s eams om suppo mechanisms o
non- ossil lexibili y acco ding o A icle 19g and 19h o (Pa liamen and Council 2019). Those addi ional
e enue s eams could impac bidding beha iou in day-ahead ma ke s and consequen ially a ec dispa ch
pa e ns and s o age p o i s.
Compa ing wi h o he app oaches as p esen ed in (Sioshansi e al. 2022), ou me hod inco po a es
s a egic beha iou o s o age uni s, bu is no based on an equilib ium app oach. While g an ing
high compu a ional e iciency and he possibili y o include unce ain y in o decisions, ou me hod lacks
ma hema ical p oo . A compa ison o he esul s o single and mul iple s o age uni s indica es ha ou
app oach o compe i ion modelling is a leas plausible. S ill, a di ec compa ison wi h game- heo e ic
models would be necessa y o s eng hen us in he p esen ed app oach.
23
5 Conclusions and Ou look
We de eloped an algo i hm o dispa ch scheduling o compe ing s o age uni s based on dynamic p o-
g amming and sma elec ici y p ice o ecas ing. The algo i hm and i s a ian s we e in eg a ed in he
agen -based elec ici y ma ke model AMIRIS. We used a back es ing scena io o Ge many o compa e
p o i -maximising and sys em cos -minimising dispa ch s a egy a ian s. Fu he mo e, we applied ag-
g ega ed and disagg ega ed ep esen a ions o he s o age uni s o assess he dispa ch s a egies wi h
espec o a alanche e ec s, ma ke powe and compe i ion. A scena io se up wi h addi ional ba e y
s o age uni s demons a es he applicabili y o ou app oach also o highly compe i i e si ua ions.
Resul s o he p ice- ake s a egy a ian highligh he isk o a alanche e ec s when p ice impac s
due o s o age dispa ch a e no conside ed. Such a alanche e ec s can be a oided wi h ou p esen ed
algo i hm ha allows o equip agen s wi h he necessa y awa eness o s o age uni s’ p ice impac s.
This has been p o en o wo k wi h single o mul iple compe ing s o age uni s. I was shown ha he
simula ion o compe ing s o age uni s can imp o e model quali y wi h espec o he ep oduc ion o
his o ical dispa ch beha iou . The p o i -maximising s a egy a ian p oduced he bes esul s when
modelling his o ical elec ici y p ice dynamics bu seems o o e es ima e p o i s and unde es ima e he
s o age usage. Me ics o he sys em-cos minimising a ian imp o ed he mos due o he disagg ega ed
ep esen a ion o s o age uni s. Wi h his a ian , s o age p o i and dispa ch we e closes o his o ical
ma ke esul s. This aligns wi h ma ke heo y expec a ions ha in highly compe i i e sys ems ewe
ma ke powe is p e alen (Plea sikas 2018).
In summa y, ou me hod allows o inco po a e s o age compe i ion in o agen -based simula ions using
a anspa en and unde s andable dispa ch planning app oach. I enables esea che s and decision-make s
o assess he ma ke dynamics o compe ing s o ages wi hin impe ec ma ke s, whe e policy impac s and
unce ain ies a e also conside ed. Since we base ou analyses on open sou ce modelling and open da a,
he algo i hm and i s esul s a e ully eplicable.
S ill, he e a e se e al oppo uni ies o u he esea ch and de elopmen . Fi s ly, ex ending he
analysis o include mul i-ma ke espec i ely mul i-use scena ios, such as in aday ma ke s, peak sha -
ing o ancilla y se ices, will p o ide a mo e ho ough unde s anding o how lexibili y op ions can be
op imised ac oss di e en ma ke con ex s. Secondly, u he echnical s o age de ails could be added
o he assessmen , including he deg ada ion o s o age sys ems o sel -discha ge a es, in o de o en-
hance he accu acy o he ope a ional simula ions. Thi dly, an impo an nex s ep would be o alida e
he obus ness o he p esen ed app oach wi h espec o o he ma ke si ua ions, e.g., by expanding
he analysis o u he his o ical yea s. Especially he yea s 2020 o 2024 could se e as an acid es
24
o he app oach due o he ha sh changes in ma ke condi ions in hose yea s, e.g., om changing de-
mand pa e ns and na u al gas p ices. Fu he mo e, compa isons wi h ein o cemen lea ning models
and game- heo e ic models could p o ide a mo e comp ehensi e e alua ion o he s a egic in e ac ions
among a ious ma ke pa icipan s. Quan i a i e compa isons wi h hese model ypes a e equi ed o u -
he subs an ia e he indica ed bene i s o he p esen ed app oach ega ding pe o mance, scalabili y, and
accu acy. Las , he de eloped dispa ch planning algo i hm could be ex ended o co e o he FOs, e.g.,
hea pumps, elec olysis uni s, o mobili y and load shi ing applica ions. Pu suing hese a enues would
c ea e a mo e in o med basis o designing policy and egula ing ma ke s, enabling obus simula ions o
highly enewable ene gy sys ems.
Glossa y
ABM agen -based model
DRL deep- ein o cemen lea ning
E2P ene gy o powe
FO lexibili y op ion
MAE mean absolu e e o
RMSE oo mean squa e e o
RTE ound- ip e iciency
SOC s a e o cha ge
Nomencla u e
Dispa ch Planning
ime s ep indices
Po e p ice o an elec ici y ask o bid
V alue o a disc e ized s o age le el
iini ial s o age le el a he beginning o a ansi ion
inal s o age le el a he beginning o a ansi ion
∆Eene gy del a o a ansi ion
p(expec ed) elec ici y p ice
p′expec ed elec ici y p ice including dispa ch om own s o age
p′′ expec ed elec ici y p ice including dispa ch om all s o ages
Fo ecas ing
, ′ ime s ep indices
ms o age dispa ch mul iplie es ima e
25
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A Back es ing Scena io
He e, we p o ide he mos impo an pa ame e s o he back es ing scena io and i s a ian s. The
scena io is based upon a scena io o he Ge man day-ahead elec ici y ma ke in he yea 2019 (Nienhaus
e al. 2025). All da a a e openly accessible (Schimeczek, Ni sch, and Kochems 2025).
Technical and economic pa ame e s o con en ional powe plan s a e shown in Table A.1. Ins alled
capaci ies a e spli in o blocks o speci ied size. Uni e iciencies a e in e pola ed be ween he speci ied
minimum and maximum. Ma k-downs o ma kups a e also in e pola ed pe uni be ween he speci ied
minimum and maximum. High (low) ma kups o ma k-downs a e assigned o uni s wi h low (high) e i-
ciency. Va iable ope a ion expendi u es (OPEX) a e assumed pe he mal MWh and o he wise cons an
pe echnology. Na u al gas powe plan s a e spli in o open and closed cycle gas u bines (OCGT,
CCGT). Cos and emission pa ame e s o associa ed uels a e shown in Table A.2. Technical and eco-
nomical pa ame e s o enewable powe plan s a e shown in Table A.3. Renewable capaci ies a e no spli
in o uni s, bu chunks wi h same emune a ion pa ame e s. Mos capaci ies a e bound o a emune a ion
scheme, o which eed-in a i s (FIT) and a iable ma ke p emia (MP) a e used.
Signi ican e o was pu in o he compila ion o an accu a e pa ame isa ion o he s o age uni s
since (Open Powe Sys em Da a 2020) do no co e pumping powe o ese oi capaci ies and ha e
only e y ough es ima es o ound- ip e iciency. Rega ding he s o age uni s in Ge many, we de i ed
33
Technology
Ins alled
Capaci y
in MW
Block
Size
in MW
E iciency
Minimum
in %
E iciency
Maximum
in %
Va iable
OPEX
in €/MWh
Ma kup
Minimum
in €/MWh
Ma kup
Maximum
in €/MWh
Nuclea 9,524 900 33.0 33.1 0.5 -150 -90
Ligni e 21,067 500 31.1 45.0 2.0 -60 0
Ha d coal 22,458 300 33.9 49.2 2.5 -15 5
Na u al gas CCGT 13,572 200 51.6 61.7 1.2 -10 10
Na u al gas OCGT 13,206 100 32.7 44.9 1.2 10 50
Oil 3,934 100 31.1 39.7 1.2 0 0
Table A.1: Technical and economical pa ame e s o con en ional powe plan s
Fuel A e age p ice in EUR/MWh CO2in kg pe he mal MWh
Nuclea 2.0 0
Ligni e 5.0 364
Ha d coal 10.98 341
Na u al gas 16.67 201
Oil 37.08 264
Table A.2: A e age p ices and CO2emissions o di e en uels
ins alled cha ging and discha ging powe s as well as s o age capaci ies om (Giesecke, Heime l, and
Mosonyi 2014). Fo ound- ip e iciencies we combined age da a o he s o age om (Open Powe
Sys em Da a 2020) wi h e iciency da a om (Giesecke and Mosonyi 2005) plus own es ima es, and
compa ed he esul s wi h (Ha de , Miskiw, e al. 2025). We also included i e s o age uni s in Aus ia
connec ed o he Ge man g id. Thei cha ging and discha ging powe s as well as s o age capaci ies we e
aken om (Weh le 2023). We es ima ed ound- ip e iciencies based on wa e lows du ing cha ging and
discha ging. Rega ding he single s o age uni in Luxembou g, we used da a om hei websi e. Table A.4
shows echnical pa ame e s o he agg ega ed and disagg ega ed s o age uni s. In bo h scena ios, ini ial
s a e o cha ge o all s o age uni s was abou 43 %. In o al, 28 indi idual s o age uni s wi h ins alled
con e e powe abo e 30 MW we e conside ed. These we e ei he agg ega ed in o a single uni , o 18
uni s. In he la e case, only uni s wi h e y simila ound- ip e iciency and ene gy- o-powe a io
we e agg ega ed. Fo he agg ega ion, we added up he cha ging powe s, discha ging powe s, and s o age
capaci ies o he indi idual uni s. Rega ding he ound- ip e iciencies, we applied an a e age weigh ed
by he con e e powe .
B So Pa ame e S udy
The so pa ame e s w0and τwe e in oduced in Sec ion 2.3. These pa ame e s de e mine he es ima ion
o he compe i ion mul iplie s. As men ioned in Sec ion 3.2.1, he choice o hese pa ame e can impac
he pe o mance o compe ing s o age uni s: I w0is oo small, he compe i ion mul iplie es ima es show
34
Technology Ins alled Capaci y in MW Va iable OPEX in €/MWh Remune a ion Schemes
Pho o ol aics 47,753 0 FIT, MP
Wind onsho e 53,553 0 FIT, MP
Wind o sho e 7,504 0 MP
Run o Ri e 5,268 0 FIT
Biogas 7,833 0 -
O he Renewables 454 1.2 -
Table A.3: Technical and economical pa ame e s o enewables powe plan s
Uni Cha ging Powe
in MW
Discha ging Powe
in MW
RTE
in %
Capaci y
in MWh
Agg ega ed 9,188 9,325 76.8 227,731
1 400 370 66.0 1,147
2 153 165 76.5 590
3 2,340 2,336 74.3 9,470
4 360 358 76.0 1,725
5 143 145 80.0 693
6 231 219 71.2 1,103
7 661 623 77.5 3,584
8 80 80 69.6 460
9 46 43 59.8 264
10 90 90 74.8 563
11 463 457 70.0 2,990
12 1,078 1,002 77.4 6,823
13 327 493 76.7 3,950
14 1,540 1,532 80.7 13,235
15 360 360 90.3 3,650
16 242 289 74.0 4,234
17 450 525 82.8 50,050
18 224 238 82.8 123,200
Table A.4: Technical pa ame e s o he agg ega ed and disagg ega ed (1-18) s o age uni s; Cha ging and
discha ging powe s e e o he maximal g id in e ac ion. S o age capaci ies e e o he in e nally s o ed
ene gy (a e applica ion o he cha ging e iciency, be o e applying discha ging e iciency).
s ong luc ua ions a he beginning o he simula ion. I w0is oo la ge, he measu ed mul iplie da a
is supp essed o a longe ime span. The decay ime τcan be compa ed o he a e aging window o a
mo ing a e age. I i is chosen oo small, luc ua ions inc ease, bu i i is chosen oo la ge, adap a ions
ake oo long. Howe e , he e is no s ic way o deduce he bes alue o hese pa ame e s. The e o e,
we conduc ed a pa ame e s udy o w0and τ o iden i y a pa ame e combina ion ha yields good esul s
o he s o age compe i ion. Fu he mo e, he pa ame e s udy can indica e how sensi i e he esul s a e
wi h espec o he choice o he wo pa ame e s.
O e all, esul s o p ice co ela ion (Table B.1), dispa ch co ela ion (Table B.2), and p o i abili y
(Table B.3) a e e y s able o e he assessed pa ame e anges. The di e ence be ween he bes and
wo s alue o p ice co ela ions di e s by 0.0014, which co esponds o a ela i e di e ence o 0.2%.
Simila ly, he bes and wo s alue o dispa ch co ela ions a e 0.0024 apa , co esponding o a ela i e
35
di e ence o 0.3%. P o i abili y alues a y by up o 0.0077. This co esponds o a maximum ela i e
change o 0.6%. Bes alues o p ice co ela ion and p o i abili y can be ound a high alues o w0
and τ, whe eas bes alues o dispa ch co ela ion a e loca ed a low alues o w0and τ. Howe e , he
sensi i i y o he esul s on he choice o w0and τis so weak, ha his choice has no ele an impac on
he esul s p esen ed in Sec ion 3.
τ/w01 3 6 12 24
48 0.8665 0.8662 0.8667 0.8665 0.8666
96 0.8668 0.8664 0.8666 0.8667 0.8668
168 0.8668 0.8669 0.8669 0.8669 0.8669
336 0.8668 0.8668 0.8672 0.8671 0.8674
730 0.8672 0.8672 0.8674 0.8676 0.8675
Table B.1: Co ela ion o elec ici y p ices wi h his o ical p ices in he back es ing scena io o 18 s o age
uni s and a ia ions o w0and τ; highe alues o τyield a sligh ly highe co ela ion. The lowes (highes )
co ela ion is ma ked in cyan (magen a) colou .
τ/w01 3 6 12 24
48 0.7891 0.7886 0.7888 0.7879 0.7887
96 0.7895 0.7886 0.7893 0.7885 0.7892
168 0.7895 0.7886 0.7884 0.7886 0.7884
336 0.7892 0.7886 0.7876 0.7880 0.7876
730 0.7896 0.7888 0.7885 0.7876 0.7872
Table B.2: Co ela ion o o al dispa ch om 18 s o age uni s wi h his o ical dispa ch in he back es ing
scena io o a ia ions o w0and τ; lowe alues o w0yield a sligh ly highe co ela ion. The lowes
(highes ) co ela ion is ma ked in cyan (magen a) colou .
τ/w01 3 6 12 24
48 128.5% 128.6% 128.6% 128.6% 128.7%
96 128.8% 128.8% 128.8% 128.8% 128.8%
168 128.8% 128.8% 128.8% 128.7% 128.7%
336 128.9% 129.0% 129.0% 129.0% 129.0%
730 129.2% 129.3% 129.3% 129.3% 129.3%
Table B.3: To al p o i o 18 s o age uni s ela i e o ic i ious p o i s ha would esul om he his o ical
dispa ch a his o ical day-ahead ma ke p ices he in he back es ing scena io o a ia ions o w0and
τ; la ge alues o w0and τyield sligh ly be e p o i s. The lowes (highes ) p o i is ma ked in cyan
(magen a) colou .
C Pe o mance Benchma k
The op imisa ion o s o age dispa ch using dynamic p og amming scales wi h O(n) ega ding he amoun
o o ecas in e als and wi h o O(n2) wi h he numbe o ene gy le els, see Sec ion 2.2. The o ecas ing
algo i hm is based on Equa ion 3, which scales wi h O(n) ega ding he numbe o in ol ed agen s.
36
Equa ion 5 looks like i has a linea scaling, oo, bu is in ac implemen ed as a ecu si e se ies o e
ime, p o iding O(1) pe o mance in each ime s ep. O e all, a linea un ime scaling is expec ed wi h he
numbe o in ol ed agen s. To demons a e his, a pe o mance benchma k is conduc ed on a pe sonal
compu e (In el Co e i7-1370, 32 GB o Memo y) using a single compu a ion p ocess and he back es ing
scena io in oduced be o e. De ia ing om ha scena io, he o al numbe o s o age agen s is a ied
be ween one and 128 agen s. Fo each numbe o s o age agen s, i e simula ions a e conduc ed o p o ide
a s able measu e o he a e age simula ion wall ime.
Figu e C.1 shows he a e age simula ion wall ime o he simula ions depending on he numbe o
s o age agen s. The o se o app oxima ely 10 s is caused by he o he agen s in he simula ion, which
a e no changed in his se up. A linea scaling can be obse ed o a la ge numbe o s o age agen s.
Figu e C.1: A e age wall ime o a simula ion depending on he numbe o s o age agen s; he wall ime
scales app oxima ely linea ly wi h he numbe o s o age agen s.
37
