Optimal Industrial Clusters: Flex4Fact Summer Research Report

P ojec Repo
Op imal Indus ial Clus e s
Flex4Fac Summe Resea ch Repo
Au ho (s)
Madeline Ki ch, Mikael S øen, Miguel Muñoz, Thiago Sil a,
Ma c Juanpe a, Pau Fisco-Comp e
Repo Numbe
2024:00958 — Un es ic ed
Clien (s)
In e nal
Technology o a be e socie y
SINTEF Indus y
Add ess:
P.O. Box 4760 To ga den, NO-7465
T ondheim
Telephone: +47 40005100
[email p o ec ed]
En e p ise Numbe :
919 303 808
KEYWORDS:
Flexible indus y, Op imal
Scheduling, Indus ial Clus e ,
Renewables
P ojec Repo
Op imal Indus ial Clus e s
Flex4Fac Summe Resea ch Repo
VERSION
1.3
DATE
3 d Sep embe 2024
AUTHOR(S)
Madeline Ki ch, Mikael S øen, Miguel Muñoz, Thiago Sil a, Ma c Juanpe a,
Pau Fisco-Comp e
CLIENT(S)
In e nal
CLIENT’S REFERENCE
PROJECT NUMBER
102027880
NUMBER OF PAGES AND ATTACHMENTS
26
ABSTRACT
We s udy he in eg a ion o digi iza ion, sma scheduling, local enewable
ene gy p oduc ion, and a iable ene gy p ices in diffe en indus ial com-
panies o make an op imiza ion en i y o indus ial clus e ene gy use. We
discuss wo ene gy op imiza ion app oaches: a cen alized choice o all en-
e gy consump ion and local-le el ading o ene gy su plus and de elop a
g aph-based package o implemen hese mechanisms gi en mixed-in ege
p og amming models o each o he fi ms. Tes ing ou modeling package
wi h da a om he EU p ojec Flex4Fac , we show ha clus e ing dec eases
agg ega e cos s due o he lack o sell-back penal ies, and he ela i e be-
nefi among fi ms depends on in e nal p ices.
PREPARED BY
Miguel Muñoz O iz
SIGNATURE
CHECKED BY
La s Hellemo
SIGNATURE
APPROVED BY
F ode Rømo
SIGNATURE
REPORT NUMBER
2024:00958
ISBN
978-82-14-07014-9
CLASSIFICATION
Un es ic ed
CLASSIFICATION THIS PAGE
Un es ic ed
1 o 26
Miguel Muñoz O iz (Sep 3, 2024 14:52 GMT+2)
La s Hellemo (Sep 3, 2024 14:55 GMT+2)
Documen His o y
VERSION DATE VERSION DESCRIPTION
1.0 16.08.2023 Final e sion a e Summe Resea che ’s s ay a SINTEF
1.1 12.04.2024 Re ised e sion sen o QA
1.2 05.07.2024 Final e sion wi h QA
1.3 03.09.2024 Final e sion wi h small co ec ions be o e signa u e
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Con en s
1 In oduc ion 4
2 Concep ual F amewo k 6
2.1 Theo e ical esul s ......................................... 7
2.2 Ma ke Models .......................................... 8
2.3 Mechanism 1: Au oma ic T ading ................................. 9
2.4 Mechanism 2: Cen alized choice ................................. 10
3 P oblem Fo mula ion o Indus ial Clus e s 11
3.1 Fac o y Scheduling ........................................ 11
3.1.1 P oblem Fo mula ion ................................... 11
3.1.2 Objec i e Func ion .................................... 12
3.1.3 Cons ain s ........................................ 12
3.1.4 Implemen a ion ...................................... 14
3.1.5 Pe o mance imp o emen s ............................... 14
3.2 Agg ega o Implemen a ion .................................... 14
3.3 P ac ical Challenges ........................................ 17
4 Case s udies 18
4.1 Main assump ions and da a .................................... 18
4.2 P oduc ion Scheduling in he Fac o ies .............................. 18
4.3 Ene gy Agg ega o o Indus ial Clus e ............................. 18
4.3.1 Effec o = 0.5 ...................................... 20
4.3.2 Effec o = 0.2 ...................................... 21
5 Conclusions and nex s eps 24
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Chap e 1
In oduc ion
The elec ici y sys em depends on a delica e balance be ween supply and demand. As s o ing ene gy is cos ly,
when expec ed demand exceeds supply, he g id will o en ap in o high-p ice supplie s o shu down end-use s
en i ely. T adi ional gene a ion sou ces such as na u al gas and coal a e dependable and ( ela i ely) adap able
o demand p ofiles, educing he po en ial scale o his p oblem. Howe e , as he gene a ion sha e o a iable
enewable ene gies such as sola and wind g ows, so will he need o s onge ma ke mechanisms o mi iga e
po en ial imbalances.
Flex4Fac (G an ag eemen ID: 101058657, DOI: 10.3030/101058657), a p ojec unded by he Eu opean
Union and coo dina ed by SINTEF Manu ac u ing AS, seeks o add ess how a specific bu impo an g oup o
elec ici y consume s—indus ial manu ac u e s—can hough ully engage in he ansi ioning ene gy ma ke .
Indus ial use s consume la ge amoun s o o al elec ici y bu ha e pa icula challenges in adap a ion o
ene gy p ices and a ailabili y. Since indus ial p ocesses a e so complex, e en o mula ing a se o op ions can
be difficul , o en equi ing he digi aliza ion o ac o y p ocesses. The ask o he Flex4Fac is bo h o wo k on
he de elopmen o new ma ke models and me hods o engagemen be ween manu ac u e s and he g id and
de elop a compu a ional in as uc u e ha will acili a e hei inclusion; o c ea e an “end- o-end ecosys em...
o enable flexible manu ac u ing... in ene gy in ensi e indus ial sec o s” [5].
Ou wo k ela es o he ma ke design and compu a ional modeling o a subse o his la ge ma ke : in-
dus ial clus e s. Indus ial clus e s a e communi ies o manu ac u e s concen a ed in a small geog aphic
a ea. Many indus ial fi ms ha e s a ed p oducing ene gy locally, a phenomenon known as p osuming [9].
P osuming can ake he o m o on-si e Pho o ol aic (PV) sola panels, nea by wind u bines, o eplacing na -
u al gas wi h hyd ogen [4]. Ye , he elec ici y ma ke is p esen ly ill-sui ed o deal wi h hei supply. As such,
p osume s ace s eep sell-back a es should hey ha e su plus ene gy, p esen ing a na u al ma ke place o en-
e gy exchange among fi ms wi hin a clus e . Fi ms wi h ex a ene gy can sell hei s locally o an in e media e
a e o o he s consuming ene gy, gene a ing a Pa e o imp o emen . Cap a a e al. [2], a p e ious Flex4Fac
s udy, documen ed his Pa e o imp o emen in a case s udy o ubbe p oduc ion, showing po en ially signi-
fican ene gy cos and emissions sa ings om making a cen alized clus e decision.
Inspi ed by Cap a a e al. [2], we s udy and model in de ail he p oblem o local-le el ene gy sha ing and op-
imiza ion indus ial clus e s, iewing hem as a mic ocosm o he challenges a la ge “end- o-end ecosys em”
migh ace— om incen i e compa ibili y cons ain s o he linkage o digi al wins. We o malize he se -up in
he language o mechanism design, showing ha a pe ec (di ec ) mechanism is una ainable, and, gi en his,
offe wo po en ial app oaches: pa icipa ion-based cen alized choice and au oma ic ading ha a e simple
and anspa en . Second, we p esen a mixed-in ege p oblem o mula ion and abs ac g aph-based compu-
a ional package o bo h ac o y-scheduling and ene gy agg ega ion sui ed o he essen ial needs o clus e s.
We es his model on Flex4Fac da a and show ha cos s dec ease, and he ela i e benefi o diffe en fi ms
is sensi i e o ou choice o he in e nal discoun a e o sell-back penal y.
The emainde o his epo is s uc u ed as ollows. Chap e 2p o ides a ho ough desc ip ion o he
concep ual amewo k, business models, and heo e ical esul s. Chap e 3p esen s mixed-in ege o mula-
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ions o ac o y p oduc ion scheduling and a ma ke (agg ega o ) pla o m. Chap e 4p esen s case s udies
and hei sensi i i y o he choice o in e nal discoun a es. Chap e 5concludes.
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Chap e 2
Concep ual F amewo k
This chap e discusses he mechanism design se -up o indus ial clus e ene gy sha ing.
The high-le el s uc u e is as ollows: We define fi ms as he sum o ene gy managemen and ac o y
scheduling sys ems. The ene gy managemen (EM) sys em adminis a es he ene gy balance a he ac o y,
aking in o accoun ene gy flows om hei own enewable sou ces, be ween o he fi ms in he clus e , and
wi h he g id. The ac o y scheduling (FS) sys em op imizes he ac o y’s p oduc ion p ofiles based on demand
and sys em cons ain s. We model he ac o ies indi idually (business as usual o BAU) and in a cen alized
clus e . The key diffe ence is ha in he clus e case, he e is an in e media y en i y, he agg ega o , be ween
he fi ms and he g id. The agg ega o uses p ice in o ma ion and he ela i e cos o fi m’s p oduc ion op ions
o pick he lowes -cos choice o he clus e . A diag am o he wo op ions (indi idual ac o ies and clus e s)
a e shown in fig. 2.1.
To make his p oblem ac able, a se o simpli ying assump ions in line wi h [2] a e needed. Fi s , en-
e gy cos s a e assumed known and linea . This means ha fi ms a e able o pick when hey wan o p oduce
gi en he p ices o he sys em and ha consuming wice as much cos s wice as much. Second, i is assumed
ha diffe en fi ms ha e he abili y o coo dina e ene gy use p ofiles. A leading example would be collec i e
weekly scheduling: Each fi m would like o make a fixed amoun o he good o e he pe iod bu may p esen
al e na i e op ions o when ha p oduc ion would occu . Thi d, a ze o ansac ion cos o ene gy loss a e as-
sumed when anspo ing elec ici y ac oss fi ms, which is a easonable assump ion conside ing he low cos
and limi ed loss o sho dis ances.
Fi m’s P oblem. In he simples model, fi ms make a fixed amoun o goods o a gi en s a egic pe iod
bu can decide when and how hey would like o p oduce o e he sho e in e media e ime s eps. Each fi m
also has a local ( enewable) ene gy sou ce which hey may use a some cos . Las ly, he fi m can decide i
hey would like o op in o a la ge Agg ega o sys em. Below he language used in assignmen o alloca ion
p oblems [1] is p esen ed.
Fo mally, le Ibe he se o fi ms (agen s) and J=ℝ𝑇 he se o possible ene gy demand ec o s o he
Agg ega o a each o he 𝑇ope a ional pe iods (objec s). The no a ion 
𝑗(𝑖)={𝑗𝑖,1,…,𝑗𝑖,𝑇}means ha fi m
𝑖is consuming 𝑗𝑖,𝑡ene gy uni s om he g id a imes 1≤𝑡≤𝑇. Fu he mo e, each fi m has a se o ene gy
ec o s 𝑆(𝑖) o which hey a e able o mee he p oduc demand. Thus i 𝑗∉𝑆(𝑖), demand will no be me .
When fi ms chose among 𝑀p ofiles as in [2], ‖𝑆(𝑖)‖=𝑀.
Each fi m has p e e ences 𝜋𝑖o e he possible consump ion bundles, defined o e he se 𝑆(𝑖)⊂J
𝜋𝑖∶J|𝑆(𝑖)→ℝ
These p e e ences 𝜋𝑖(𝑗𝑖)accoun o he cos s independen o non-local ene gy use o supply. They ell us
how diffe en ene gy consump ion p ofiles cos o implemen , excluding hose cos s associa ed wi h acqui ing
o selling ene gy h ough he Agg ega o . Examples o componen s o hese p e e ences include wages o
wo ke s, s a -up and s opping cos s, and ma e ial cos s.
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Figu e 2.1: Clus e and benchma k defini ion
Benchma k. The s a us-quo en i onmen is modeled as one whe e fi ms ace p ice 𝑝𝑡 o an ene gy uni
a ime 𝑡and sell back ene gy o he g id a a lowe p ice han he g id p ices 𝑟∈(0,1)whe e 𝑟is he sell-back
penal y. Fi ms pick a p ofile 𝑗𝑖and ace o al cos 𝐶𝐵𝐴𝑈
𝐶𝐵𝐴𝑈(𝑖)=𝜋𝑖(𝑗𝑖)+ 𝑇
∑
𝑡=1[𝕀𝑖,𝑡𝑗𝑖,𝑡𝑝𝑡+(1−𝕀𝑖,𝑡)𝑟𝑝𝑡𝑗𝑖,𝑡]
whe e 𝕀𝑖,𝑡an indica o o posi i e ene gy demand (i.e. 𝑗𝑖,𝑡>0).
Agg ega o . The Agg ega o is a cen al en i y ha can help acili a e he decision o ene gy use and sha ed
cos s. The objec i e is o minimize he sum o indi idual objec i es while s ill mee ing indi idual incen i e-
compa ibili y cons ain s. Fo mally, i can pick op ions on alloca ions and subsidies which map he se o fi ms
o hei ecei ed allo men s. We define 𝜇∶I→Jbe he alloca ion unc ion so ha 𝜇(𝑖)=𝑗𝑖, and 𝑡∶I→ℝ|I|
be he subsidy unc ion compensa ing he lose s ( hose made wo se-off by hei Agg ega o assignmen s).
Objec i e. The Agg ega o ’s objec i e is
𝑇𝐶𝐴𝑔𝑔=∑
I𝜋𝑖(𝜇(𝑖))+ 𝑇
∑
𝑡=1[𝕀𝑡𝑝𝑡∑
I𝜇(𝑖)𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑
I𝜇(𝑖)𝑡]
whe e 𝕀𝑡is he indica o o posi i e ne demand a ime 𝑡. The alloca ions 𝜇(I)mus sa is y he condi ion o
he fi ms on being pa o he clus e (𝑡(𝑖)≤𝐶𝐵𝐴𝑈(𝑖)) and easibili y o mee ing needed p oduc ion quo a
(𝑗𝑖∈J|𝑆(𝑖)).
2.1 Theo e ical esul s
We p esen he e wo heo e ical esul s: (1) clus e ing ene gy choice and use will always weakly dec ease o al
cos s, and (2) e en in a simple case, a di ec mechanism canno exis .
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A clus e ed sys em, no ma e he mechanism, is gua an eed o a leas weakly dec ease o al cos s i
epo ing is u h ul. The dec ease in cos is due o he ac ha in e nal ading will always sa e money due
o he diffe ence be ween he pu chase and sell-back cos s.
Lemma 1. Unde a clus e ed sys em, each p ofile se esul s in weakly lowe cos s wi h inequali y when any
wo fi ms would indi idually buy and sell a he same ime. Fo mally o p ofile choices 𝜇∗(I)={𝑗1,…,𝑗𝑁},
∃𝑡∈𝑇and (𝑖1,𝑖2)∈I2s. . 𝕀𝑖1,𝑡≠𝕀𝑖2,𝑡.
The p ofile fixed cos s a e independen o ene gy agg ega ion, hence we will ocus on he powe cos s. I
all fi ms buy o sell a ime 𝑡, hen we can ac o ou he indica o s o yield iden ical cos s.
∑
I𝜋𝑖(𝑗𝑖)+ 𝑇
∑
𝑡=1[𝕀𝑡𝑝𝑡∑
I𝑗𝑖,𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑
I𝑗𝑖,𝑡]=∑
I𝜋𝑖(𝑗𝑖)+ 𝑇
∑
𝑡=1[𝕀𝑡𝑝𝑡∑
I𝑗𝑖,𝑡+(1−𝕀𝑡)𝑟𝑝𝑡∑
I𝑗𝑖,𝑡]
I no , hey diffe by ∑
𝕀𝑖,𝑡≠𝕀𝑡(𝕀𝑡−𝕀𝑛,𝑡)𝑗𝑖,𝑡𝑟𝑝𝑡−(𝕀𝑡−𝕀𝑖,𝑡)𝑗𝑖,𝑡𝑝𝑡
=−(1−𝑟)𝑝𝑡∑
𝕀𝑖,𝑡≠𝕀𝑡(𝕀𝑡−𝕀𝑖,𝑡)𝑗𝑖,𝑡
=−Sign(𝑗𝑖,𝑡)(𝕀𝑡−𝕀𝑖,𝑡)(1−𝑟)𝑝𝑡∑
𝕀𝑖,𝑡≠𝕀𝐴𝑔𝑔|𝑗𝑖,𝑡|
=−(1−𝑟)𝑝𝑡∑
𝕀𝑖,𝑡≠𝕀𝑡|𝑗𝑛,𝑡|<0
Since 𝑟∈(0,1), he Agg ega o cos less he benchma k cos is nega i e; agg ega ion weakly sa es cos s o
all op ions and a all ime s eps.
The second esul is ha he e is unlikely o be a di ec mechanism o achie ing he op imal ou come, o
ai ly edis ibu ing he su plus.
Theo em 2. (Di ec Mechanism Impossibili y). Assume an al e na i e p ofile dec eases he cos o one fi m and
inc eases he cos o ano he , and bo h fi ms ha e p obabilis ic knowledge o he o he ’s p e e ences, which
a e con inuous on a bounded and o e lapping egion. Then no u h ul, efficien , budge balanced mechanism
exis s which will always dec ease fi m cos s.
Ou nega i e esul is an exac applica ion o he Meye son-Sa e wai e Theo em whe e one fi m is he
“buye ” and he o he is a “selle .” Gi en he impossibili y esul o a e y simple se ing, we he e o e canno
ule ou he ac ha fi m ace incen i es o lea e ou op ions o a ificially al e hei p e e ences should choice
be cen alized. Conside he case when ac o y scheduling happens weekly, and all fi ms made wo se off by
he new sys em will ecei e subsidies. A fi m al eady knowing hei likely alloca ion may hen epo highe
non-ene gy cos s in o de o ge addi ional money om he agg ega o . In addi ion, i hey know ha ano he
op ion is p e e able o hem, hey may lea e ou ha ene gy p ofile om hei op ion se en i ely. The e o e,
e en hough he Agg ega o can always lowe cos s, he scale o benefi and he ai ness o he cos -sha ing
is c i ically dependen on he sys em implemen a ion, he ela i e p e e ences o he fi ms, and he deg ee o
in o ma ion-sha ing.
2.2 Ma ke Models
The bes sys em design is likely o be a unc ion o he equency o agg ega ion, and ela i e size o he fi ms.
Below we discuss wo ypes o ma ke sys ems and heu is ics as o when bo h o hem may be beneficial.
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Figu e 3.1: Clus e and benchma k defini ion
cons ain s, and objec i es. The edges a e link cons ain s, exp essions ela ing a iables in diffe en models
(nodes). Las ly, g oups o nodes can o m subg aphs.
When modelling he fi ms wi h Plasmo, hey a e ep esen ed by a subg aph wi h h ee nodes: a ac o y
scheduling (FS) node, an ene gy managemen (EM) node, and a messenge node. We c ea e ac o y scheduling
and ene gy managemen JuMP models in sepa a e packages. Al e na i ely, he use can speci y hei own JuMP
model. These a e hen a ached o hei espec i e nodes and—along wi h he specified ac o y name—define
a ac o y s uc u e. The messenge node akes in cons ain s om he FS and EM models o define he easible
se o each fi m. This node, e-labeled wi h he name o he fi m, is he poin o con ac wi h he Agg ega o .
The Agg ega o need no ha e knowledge o he specific inpu s o needs gi en ise o he gi en domain and
p e e ences. A diag am o he in o ma ional flow in he Plasmo model is ep esen ed in fig. 3.1.
The node connec ing all fi ms ep esen s he clus e o agg ega o , and i is defined as "main". Below he
diffe en equa ions o his node will be p esen ed o i s implemen a ion in Plasmo. As he node "main" is an
op imiza ion model as well as he o he nodes, se e al a iables and cons ain s a e defined.
Table 3.3: Pa ame e s o he agg ega o o "main" node
Pa ame e Desc ip ion
𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟
𝑡Floa , powe p ice a ime 𝑡
𝑀In ege , big numbe
𝑟Floa in (0,1), discoun a e. A ime 𝑡 he g id sell-back p ice is hus 𝑟𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟
𝑡.
The powe balances a main a e defined in eq. (3.18), eq. (3.19) and eq. (3.20).
𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔
𝑡≤𝑀⋅𝐼𝑡∀𝑡∈𝑇(3.18)
𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔
𝑡≤𝑀⋅(1−𝐼𝑡) ∀𝑡∈𝑇(3.19)
𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔
𝑡−𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔
𝑡=𝑃𝑎𝑔𝑔
𝑡∀𝑡∈𝑇(3.20)
The o al powe o he agg ega o , 𝑃𝑎𝑔𝑔
𝑡, is based on he powe balances o he o he ene gy managemen
and ac o y nodes, and hus a linking cons ain ep esen ed in eq. (3.21). The a iable 𝑃𝑏𝑎𝑙
𝑛,𝑡 is he powe balance
o each o he ene gy managemen and ac o y nodes:
𝑃𝑏𝑎𝑙
𝑛,𝑡 =𝑃𝐸𝑀𝑆
𝑛,𝑡 −𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦
𝑛,𝑡 ∀𝑡∈𝑇,𝑛∈𝑁(3.21)
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Table 3.4: Decision a iables ela ed o he agg ega o o "main" node
Decision Va iables Desc ip ion
𝑃𝑏𝑎𝑙
𝑛,𝑡 Powe balance o each fi m 𝑛a ime 𝑡
𝑃𝐸𝑀𝑆
𝑛,𝑡 Powe om he ene gy managemen sys em o each fi m 𝑛a ime 𝑡
𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦
𝑛,𝑡 Powe demand o he ac o y o each fi m 𝑛a ime 𝑡
𝐶𝑚𝑜𝑑𝑒𝑙
𝑚,𝑛 To al non-powe cos o each model 𝑚used o each fi m 𝑛
𝑃𝑎𝑔𝑔
𝑡Floa , he agg ega o ’s powe a ime 𝑡
𝐶𝑎𝑔𝑔 Floa , he agg ega o ’s cos
𝐶𝑡𝑜𝑡𝑎𝑙,𝑎𝑔𝑔 Floa , he agg ega o ’s o al cos
𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔 Floa , he agg ega o ’s powe cos
𝐼𝑡Bina y, i defines powe sold and bough o he cons ain s a ime 𝑡
𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔
𝑡Floa , bough powe by he agg ega o a ime 𝑡
𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔
𝑡Floa , sold powe by he agg ega o a ime 𝑡
𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦
𝑛,𝑡 and 𝑃𝐸𝑀𝑆
𝑛,𝑡 a e he powe demand a he ac o y and om he ene gy managemen sys em ( o example
powe om PV o a ba e y) espec i ely o fi m 𝑛and ime 𝑡. These a iables a e c ea ed in p ac ice in he
espec i e scheduling and ene gy managemen sys em op imiza ion models, and hey a e linked oge he a
he ene gy managemen sys em node o ha ac o y 𝑛, using wha Plasmo defines a linking cons ain , which
is a cons ain ha in ol es a iables om diffe en op imiza ion models.
𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦
𝑛,𝑡 uses in his case he o mula ion in eq. (3.22) o he case o a scheduling model explained in
sec ion sec ion 3.1. Howe e , he powe demand o mula ion will depend on he specific scheduling model
used o ha specific ac o y.
𝑃𝑓𝑎𝑐𝑡𝑜𝑟𝑦
𝑛𝑠𝑐ℎ,𝑡 =𝑃𝑝𝑟𝑜𝑑
𝑡+𝑃𝑠𝑡𝑎𝑟𝑡
𝑡+𝑃𝑐ℎ𝑎𝑛𝑔𝑒
𝑡,∀𝑡∈𝑇(3.22)
Whe e 𝑛𝑠𝑐ℎ ep esen s a ac o y ha models hei scheduling using he desc ip ion in sec ion sec ion 3.1,𝑃𝑝𝑟𝑜𝑑
𝑡
is he powe consumed by he manu ac u ing o he p oduc s, 𝑃𝑠𝑡𝑎𝑟𝑡
𝑡is he powe consump ion caused by s a -
ing p oducing a p oduc , and 𝑃𝑐ℎ𝑎𝑛𝑔𝑒
𝑡is he powe consump ion o igina ed when changing om one p oduc
o he o he in he line, as desc ibed in eqs. (3.23) o (3.25) espec i ely.
𝑃𝑝𝑟𝑜𝑑
𝑡=∑
𝑙∈𝐿∑
𝑝∈𝑃[𝑝𝑟𝑙,𝑝,𝑡⋅𝐶𝐸
𝑝]𝑡=∆𝑇𝑆𝑇
𝑝,...,𝑇 (3.23)
𝑃𝑠𝑡𝑎𝑟𝑡
𝑡+𝑡′−1=∑
𝑙∈𝐿∑
𝑝∈𝑃[𝑠𝑡𝑙,𝑝,𝑡⋅𝐶𝐸𝑆𝑇
𝑝,𝑡′−𝑡]𝑡=1,...,𝑇−∆𝑇𝑆𝑇
𝑝,𝑡′=𝑡,...,𝑡+∆𝑇𝑆𝑇
𝑝|𝑡′≤𝑇(3.24)
𝑃𝑐ℎ𝑎𝑛𝑔𝑒
𝑡+𝑡′−1 =∑
𝑙∈𝐿∑
𝑝∈𝑃[∑
𝑝′∈𝑃|𝑝′≠𝑝𝑐ℎ𝑙,𝑝,𝑝′,𝑡⋅𝐶𝐸𝐶𝐻
𝑝,𝑝′,𝑡′−𝑡]𝑡=∆𝑇𝑆𝑇
𝑝,...,𝑇−∆𝑇𝐶𝐻
𝑝,𝑝′,𝑡′=𝑡,...,𝑡+𝑡+∆𝑇𝐶𝐻
𝑝,𝑝′|𝑡′≤𝑇
(3.25)
On he o he hand, 𝑃𝐸𝑀𝑆
𝑛,𝑡 is he powe coming om he EMS. In he case s udies i ep esen s a e y simple
model wi h a fixed no malized PV p ofile mul iplied by a fixed, ins alled PV capaci y, as shown in eq. (3.26).
𝑃𝐸𝑀𝑆
𝑛,𝑡 =𝑝𝑃𝑉
𝑡⋅𝑐𝑎𝑝𝑝𝑣
𝑛∀𝑛∈𝑁,𝑡∈𝑇(3.26)
Whe e 𝑝𝑃𝑉
𝑡is a no malized p ofile o PV p oduc ion o ime 𝑡, which is scaled up wi h he fixed ins alled PV
capaci y 𝑐𝑎𝑝𝑝𝑣
𝑛a fi m 𝑛. Howe e , his 𝑃𝐸𝑀𝑆
𝑛,𝑡 can belong o a mo e complex ene gy managemen models,
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including ba e ies, in es men s e c. Fu u e analyses will use he model Ene gyModelsX [6] o his pu pose.
Nex , he powe balance a he agg ega o is ep esen ed in eq. (3.27), and i is again a liking cons ain . As
men ioned abo e each ene gy managemen sys em a a fi m 𝑛has a a iable 𝑃𝑏𝑎𝑙
𝑛,𝑡, con aining he balance
be ween he ene gy flows om he ene gy managemen sys em models (e.g. PV p oduced) and he powe
demand a he ac o y, defined in he specific scheduling models. The sum o all he 𝑃𝑏𝑎𝑙
𝑛,𝑡 om all fi ms is
linked o he powe balance o he agg ega o , defined as a a iable in he agg ega o op imiza ion model in
"main". 𝑃𝑎𝑔𝑔
𝑡=∑
𝑛∈𝑁𝑃𝑏𝑎𝑙
𝑛,𝑡 (3.27)
The powe cos s o he agg ega o a e calcula ed as ollows, in eq. (3.28).
𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔=∑
𝑡∈𝑇𝑃𝑏𝑜𝑢𝑔ℎ𝑡,𝑎𝑔𝑔
𝑡⋅𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟
𝑡−𝑃𝑠𝑜𝑙𝑑,𝑎𝑔𝑔
𝑡⋅𝑃𝑟𝑖𝑐𝑒𝑝𝑜𝑤𝑒𝑟
𝑡⋅𝑟(3.28)
The o he non-powe cos s o he agg ega o depend on he cos s om he ene gy managemen and fi m
nodes, as desc ibed in eq. (3.29), and depending on he model use. Fo he analyses p esen ed in his epo ,
none o hese ex a cos s we e conside ed, bu hey can ep esen in es men s, ma e ial cos s, main enance
cos s, labou cos s e c. This is again a linking cons ain ha connec s he diffe en op imiza ion models used
h ough cos a iables in his case. 𝐶𝑎𝑔𝑔=∑
𝑛∈𝑁,𝑚∈𝑀𝑜𝑑𝑒𝑙𝑠𝐶𝑚𝑜𝑑𝑒𝑙
𝑚,𝑛 (3.29)
Finally, he o al cos s o he agg ega o , which equa es he objec i e unc ion o he agg ega o consis s on
he sum o he non-powe and powe cos s, as desc ibed in eq. (3.30).
𝐶𝑡𝑜𝑡𝑎𝑙,𝑎𝑔𝑔=𝐶𝑎𝑔𝑔+𝐶𝑝𝑜𝑤𝑒𝑟,𝑎𝑔𝑔 (3.30)
3.3 P ac ical Challenges
The main challenges om he modelling implemen a ion came om a aching models o JuMP nodes and
synch onizing link cons ain s in TimeS uc in he case o i e a ing h ough he ime pe iods. Plasmo does no
allow o e e encing a node by a s ing (ie “Fi m 1”), meaning ha o find he node, we ha e o sea ch o e
he labels a ached o all nodes in he g aph. While edious om a coding se -up an age poin , he e is no
pe o mance loss since he messenge nodes mus only be ound once. In addi ion, Plasmo doesn’ allow o
he same model o a ach o mo e han one node. Thus, in cons uc ing g aphs, he ins ance models mus
be e-defined be o e assigning hem o he FS/EM nodes. Following wo k in he p ojec has made i easie
o na iga e h ough he diffe en nodes and models by among o he s, using s anda d naming o nodes and
models.
Fo TimeS uc , i seems impo an o be ca e ul in e e encing ime s eps as he sol ing is done o in ege
ime 1≤𝑡≤𝑇. Using collec (T)o se ing an i e a o was a use ul wo ka ound. A las no e is ha
many o hese e o s would occu silen ly. P in ing ou link cons ain s, and es ing simple cases is he e o e
e y impo an . Based on hese challenges, TimeS uc has been upda ed o make i easy o i e a e h ough
ope a ional pe iods in u u e implemen a ions.
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Chap e 4
Case s udies
This chap e p esen s a es analysis pe o med o a gene ic indus ial clus e , wi h he main pu pose o es ing
he amewo k and i s po en ial. The main ocus will be on he scheduling and he indus ial clus e p esen ed
in he p e ious chap e . Fo each o hese models, he se up, main assump ions and esul s will be p esen ed.
4.1 Main assump ions and da a
The e a e wo main pa ame e s ha a e ob ained om eal da a. The fi s one is elec ici y p ices, ob ained
o 120 hou s (in he pe iod 3 d-11 h o Ma ch 2023 and hou ly esolu ion) o Spanish1spo p ices. Fo he PV
p ofiles o he diffe en coun ies, a p ofile PVGIS2is used. This p ofile is om a gene ic PV sys em in no he n
Spain, no malized wi h i s maximum capaci y. The p ofile will be hen scaled up o each fi m ha has i s own
PV sys em based on he ins alled capaci y. The p ofiles a e shown in fig. 4.1. The es o he alues a e defined
as dummy alues.
4.2 P oduc ion Scheduling in he Fac o ies
The scheduling es is applied on a single ac o y, compa ed o a baseline ac o y wi hou an op imized sched-
ule. The case ega ds a ac o y wi h 3 p oduc s and wo lines. The p oduc s p1 and p2 can be p oduced on he
same line (l1) while p3 is he only p oduc p oduced a i s own line (l2). p1 and p3 equi e one wo ke while p2
equi es h ee. The ene gy consump ion p ofiles a e a he simila o he h ee p oduc s.
The e a e a ailable wo ke s h oughou he en i e empo al ho izon, bu he numbe s a e educed o he
nigh shi all week (5 wo ke s on day ime and 3 in he nigh ime), so his will effec he p oduc ion a nigh ime
since i we p oduce p2 we a e unable o p oduce any hing on he o he line. Elec ici y p ices a y wi h ime,
ollowing he p ofile men ioned in sec ion 4.1.
The diffe ence be ween baseline and sma scheduling is wo cons ain s. Fo he baseline case each
p oduc can only ha e one s a up o he whole pe iod and he model is unable o change be ween p oduc s.
One limi a ion o his app oach is ha he p oblem migh be in easible, e.g. i hey educe he numbe o
wo ke s a nigh , hen hey migh no be able o p oduce he equi ed p oduc amoun s.
4.3 Ene gy Agg ega o o Indus ial Clus e
The Agg ega ion sys em is es ed on a simula ed clus e . This clus e is composed o h ee fi ms (in he Wiz-
a ding Wo ld): Honeydukes, Olli ande s, and Hogshead. These h ee fi ms ha e a scheduling model o he one
1Downloaded om h ps://www. ee.es/
2h ps:// e.j c.ec.eu opa.eu/p g_ ools/en/
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Figu e 4.1: No malized PV p ofile and elec ici y p ices used o he case s udies.
Table 4.1: Inpu da a used in he analyses
Honeydukes Oli ande s Hogshead
P oduc s p1, p2, p3 p1, p2 p1
Demand pe p oduc (uni s) 1000, 3000, 4000 2000, 2000 2000
Wo ke s needed pe p oduc 1, 4, 1 1, 5 1
P oduc ion pe hou and p oduc (uni s) 50, 50, 50 50, 50 50
Ene gy use (kWh) pe hou and pe p oduc 10, 10, 10 10, 10 10
S a -up ene gy p ofile (all p oduc s, kWh/h) [20, 30] [20, 20] [40, 20]
Lines and p oduc s hey can p oduce l1 (p3), l2 (p1, p2) l1 (p1, p2) l1 (p1)
Ene gy p ofile in each line o change a p oduc (kWh/h) [20, 20] [20, 20] —
Ins alled PV capaci y (kW) 0 20 10
p esen ed abo e, in sec ion 3.1 and sec ion 4.2. Honeydukes makes h ee p oduc s on wo lines. Line 1 can
only make he hi d p oduc , and line 2 can pick be ween p oduc s 2 and 3. Olli ande s makes wo p oduc s
on 1 line. Hogshead makes one p oduc on one line. They all ace a se demand pe p oduc which hey can
mee using he a ailable lines and wo ke s.
They ha e a fixed amoun o ime and ene gy use o begin p oduc ion. Once in s eady-s a e, hey p oduce
a fixed amoun o he p oduc wi h a fixed ene gy consump ion. When swi ching, hey a e ha e se ime and
ene gy cos s o ansi ioning be ween s eady s a es. These swi ching alues can depend on he se o p oduc s
ha a e being mo ed be ween. In addi ion, each p oduc equi es some numbe o wo ke s o p oduce. This
is he same o s a ing, swi ching and s eady-s a e o a gi en p oduc . The inpu da a used o he analyses is
p esen ed in sec ion 4.3
On he ene gy managemen side, Honeydukes has no local supply and mus always pu chase elec ici y
om he g id o he Agg ega o . Olli ande s and Hogshead can use hei own PV cells. Da a o he p ofile o
PV p oduc ion is scaled om he nominalized p ofile desc ibed in sec ion 4.1 abo e depending on he ins alled
capaci y o hese wo fi ms ha has PV.
The op imiza ion will be o e one s a egic pe iod (120 hou s) using elec ici y spo p ices om Spain de-
sc ibed in sec ion 4.1. P ices peak du ing imes o highe demand (o en midday) and gene ally a e dec easing
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Figu e 4.2: Ene gy p ofiles o he case BAU and 𝑟=0.5. They ep esen he ene gy balance o each fi m, also
showing a p ofile wi h only he ac o y demand wi hou PV as a dashed line, and he o al ene gy balance o
all fi ms in a black, do ed line.
la e in he week.
The analysed cases a e buil based on he compa ison be ween he Benchma k (indi idual op imiza ion)
and Cen alized Choice algo i hms. Apa om hese wo main scena ios, he analysis is complemen ed by
sensi i i ies o he sell-back discoun a e 𝑟. In o de o calcula e he cos o each indi idual fi ms ene gy use
we use 𝑟=0.7 o calcula e he in e nal p ices desc ibed in 2.
4.3.1 Effec o = 0.5
Recall ha when 𝑟=0.5(a alue aligning wi h [2]), fi ms selling ene gy o he g id by he fi ms will ecei e
50% o he p ice. We discuss his in Sec ion 2.4. So he i he p ice is 2Eu os, hey would ge 1Eu o. In he
Benchma k case o 𝑟=0.5, fi ms do no ha e enough demand o equi e con inuous p oduc ion. As such,
hey a e able o sa e money by pos poning p oduc ion o he end o he week and selling back excess on he
ea lie days. fig. 4.2 shows bo h he ne ene gy use om he fi ms and he ene gy use ela ing o he fi m’s
ac o y. The g ey line shows he o al powe demand o he g id om he Agg ega o assuming a Monday -
F iday wo k-week (hou s 0 o 120). As seen in fig. 4.1, elec ici y p ices dec ease o he las days o he week,
and his will p omo e he main pa o he p oduc ion o happen du ing hese days. In addi ion, he e is a
conside able amoun o PV p oduc ion excep o he second hal o he hi d day. This allows p oduc ion and
ene gy exchange du ing he day o mos days. We can see hese effec s o he PV-p oduc ion and elec ici y
p ice p ofiles in he esul s below.
Unde Cen alized Choice, shown in fig. 4.3, since hey can make gains om in e -fi m selling we see ha in
he middle o he week, some ac o ies begin p oduc ion, boos ed by he abili y o Olli ande s and Hogshead
o supply discoun ed ene gy. Supplie s (Olli ande s and Hogshead) can sell su plus ene gy om PVs a a highe
p ice. Ene gy use s (Honeydukes and Olli ande s) can buy ene gy a a cheape a e han la e in he week. Like
in benchma k case, all fi ms ake ad ance o he cheap end o week p ices o which he e is a la ge agg ega e
spike in ene gy demand om he g id.
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Figu e 4.3: Ene gy p ofiles o he Clus e case and 𝑟=0.5. They ep esen he ene gy balance o each fi m,
also showing a p ofile wi h only he ac o y demand wi hou PV as a dashed line, and he o al ene gy balance
o all fi ms in a black, do ed line.
Las ly, we plo he diffe ence in benchma k e sus clus e cos s o he fi ms in fig. 4.3. These a e c ea ed
by e-defining in e nal p ices o he buying and selling o he ene gy as discussed in o Cen alized Choice. We
see he e ha all fi ms benefi , and ha Honeydukes benefi s he mos . As we will see, his is a na u al esul
o he ela i e p ices on in e nal and ex e nal exchange. Since he baseline diffe ence be ween 𝑟,𝑟is p e y
small, he ma k-up benefi o he in e nal selle s is minimal compa ed o ha o in e nal buye s. This a o s
he non-p oduce (Honeydukes).
4.3.2 Effec o = 0.2
As we aise he ex e nal selling discoun , his inc eases he incen i e o he ene gy o be used in e nally. In
he benchma k case his implies ha he fi m should p io i ize use o i s PV p oduc ion. The new benchma k
esul s a e plo ed in fig. 4.5 and Clus e esul s in fig. 4.6. As we imagine heo e ically, in bo h cases he e is
highe demand in he high-p ice s a o he week since he loss om ex e nal ading is mo e cos ly. Since
Honeydukes has no cheap PV ene gy o use, i s ill s a s a he end o he week. Olli ande s begins much
ea lie in he week and Hogshead, which has less demand o ulfill, con inues o pos pone p oduc ion. In he
Clus e case, his esul is amplified. Since Honeydukes has cheap ene gy i can now also ake om he o he
fi ms, i begins p oduc ion on Tuesday. Likewise, Olli ande s akes om Hogshead o s a on Monday.
As we use pos -p ocessing o e alua e cos sa ings, he e is now clea benefi o clus e ing gi en o he
ene gy p oduce s (Olli ande s and Hogshead), e e sing he ea lie end. The alues a e p esen ed in fig. 4.7.
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Figu e 4.4: Cos sa ings o each fi m when he clus e case is compa ed o he benchma k case, =0.5
Figu e 4.5: Ene gy p ofiles o he benchma k case and =0.2. They ep esen he ene gy balance o each fi m,
also showing a p ofile wi h only he ac o y demand wi hou PV as a dashed line, and he o al ene gy balance
o all fi ms in a black, do ed line.
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Figu e 4.6: Ene gy p ofiles o he Clus e case and =0.2. They ep esen he ene gy balance o each fi m, also
showing a p ofile wi h only he ac o y demand wi hou PV as a dashed line, and he o al ene gy balance o
all fi ms in a black, do ed line.
Figu e 4.7: Cos sa ings o each fi m when he clus e case is compa ed o he BAU case, =0.2
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Chap e 5
Conclusions and nex s eps
Ou p ojec wo ked o model ways o fi ms in a clus e o join ly op imize and, in so doing, sa e cos s and bes
use local ene gy a ailabili y. Going abou his equi ed ca e ul a en ion o how ac o ies made ene gy-use
decisions and how one can link hem in a simple compu a ional model. F om a ma ke -design side, clus e ing
sa es money e en i fi ms pick he same p oduc ion and enewable ene gy p ofiles as be o e because o he
benefi o local selling. Ye , how o pick he bes op ion and sha e he benefi s is an open ques ion. Cen alized
decision-making has high cos -sa ing alue, bu is imp ac ical i fi ms ha e diffe en objec i es and would like
o ha e con ol o hei p oduc ion. Au oma ic ading may offe a p omising al e na i e since i allows fi ms o
ope a e as hey a e now wi h he added bonus o exchanging ene gy wi h o he fi ms should hey ha e ex a.
The p esen ed modelling amewo k is sui able o a wide a ie y o uses. Fi ms could ade op ions whe e
hey gi e money o no p oduce in o de o go abou ac o y main enance. We can also easily adap he case
o include emissions o fi ms seeking o mee emissions quo as o accoun o a ca bon p ice. Ou nex s eps
on he Agg ega o model a e as ollows:
•Inco po a ing compu a ionally- ac able ways o sha e fi m in o ma ion wi h he agg ega o .
•Including emissions in o he Agg ega ion analysis.
•Conside ing enewable ene gy in es men s.
Fo he p oduc ion scheduling side, i is impo an o add mo e unc ionali ies o model diffe en indus ial
p ocesses, such as imp o ing wo k o ce cons ain s (no only numbe o wo ke s, bu also equi emen s in
specialized asks), mo e demand ulfilling op ions o implemen ma e ial flow, was e and ecycling e c.
On he heo y side, i is impo an o be e unde s and conc e e cases when indus ial ene gy sha ing
would happen. Using his, we can offe ailo ed ideas abou how one may p ope ly un a local indus ial clus e
ma ke . Fu u e analyses will be buil on mo e de ailed da a om he use cases in Flex4Fac , o ac ually measu e
he benefi s o a indus ial clus e in eal li e si ua ions.
Beyond he scope o his pape is including an Agg ega o in sho - e m Demand Response (DR) ma -
ke s. Cha ac e is ics depend on he ime scale o demand esponse, bu ou gene al ad ice is o make p icing
scheduling and op ions as anspa en as possible o all clus e pa icipan s. This will help lessen any efficiency
loss in ha ing a wo-le el (agg ega o , DR) app oach o ene gy cos s.
Mos o all, we hope ha ou wo k can be used as a basis o he some o mo e complex echnological
and economic ques ions he Flex4Fac p ojec will seek o add ess, and o he s looking a he cons uc ion o
new business models and digi al sys ems o help acili a e and mi iga e he economic impac o he ene gy
ansi ion.
PROJECT NUMBER
102027880
REPORT NUMBER
2024:00958
VERSION
1.3 24 o 26