HORIZON-CL5-2022-D3-01-11
Demons a ion o inno a i e o ms o s o age and hei success ul ope a ion and in eg a ion in o
inno a i e ene gy sys em and g id a chi ec u es
D6.3 Technical-Economic Sizing, Ope a ion
and Con ol Tools o I iga ion Sys em
Mode nisa ion in o Ene gy S o age Sys ems
Documen p ope ies
FUNDING PROGRAM HORIZON EUROPE
GRANT AGREEMENT NUMBER 101096197
PROJECT AGISTIN
DELIVERABLE ID D6.3
TITLE Technical-economic sizing, ope a ion and con ol ools o i iga ion sys em mod-
e nisa ion in o ene gy s o age sys ems
DISTRIBUTION LEVEL
DUE DATE 30-06-2025
DATE SUBMITTED 30-06-2025
VERSION V1.0
WORK PACKAGE WP6
LEAD PARTICIPANT UPC
TOTAL NUMBER OF PAGES 151
PU
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
All in ellec ual p ope y igh s a e owned by he AGISTIN conso ium membe s and a e p o ec ed by he
applicable laws. Excep whe e o he wise speci ied, all documen con en s a e: “© AGISTIN p ojec - All
igh s ese ed”. Rep oduc ion is no au ho ized wi hou p io w i en ag eemen . The comme cial use o
any in o ma ion con ained in his documen may equi e a license om he owne o ha in o ma ion.
All AGISTIN conso ium membe s a e also commi ed o publish accu a e and up- o-da e in o ma ion and
ake he g ea es ca e o do so. Howe e , he AGISTIN conso ium membe s canno accep liabili y o
any inaccu acies o omissions, no do hey accep liabili y o any di ec , indi ec , special, consequen ial,
o o he losses o damages o any kind a ising ou o he use o his in o ma ion.
Views and opinion s a ed in his epo e lec s he opinion o he au ho s and no he opinion o he
Eu opean Commission. The Eu opean Union is no liable o any use ha may be made o he in o ma ion
con ained in his documen .
Ve sion his o y
VERSION DATE COMMENT
V0.1 06-06-2025 FIRST DRAFT
V1.0 30-06-2025 FINAL VERSION FOR SUBMISSION
The Ad anced G id In e aces o inno a i e STo age IN eg a ion (AGISTIN) p ojec has ecei ed unding om he Eu opean’s
Union Ho izon Eu ope esea ch and inno a ion p og amme unde g an ag eemen N°101096197
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Con en s
1 In oduc ion 12
1.1 TheAGISTINP ojec .......................................... 12
1.2 Wo k package 6 and Objec i e o he Deli e able . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 S uc u eo heDeli e able ..................................... 13
2 I iga ion communi ies 14
2.1 Cu en si ua ion............................................ 14
2.2 Po en ial a ailable ene gy es ima ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Communi a de Regan s Seg ià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 O he communi ies........................................... 18
2.5 CEDER-CIEMAT ............................................ 22
3 Op imisa ion and edesign o ac i e ole o i iga ion sys ems as ene gy s o age in he elec ical
g id 23
3.1 In oduc ion............................................... 23
3.1.1 S a eo hea ......................................... 24
3.1.2 Objec i e............................................ 25
3.2 App oach ................................................ 26
3.2.1 O he app oaches / es ed app oaches . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Op imisa ion ool............................................ 27
3.3.1 De icemodels......................................... 27
3.3.2 Objec i e unc ion....................................... 39
3.3.3 Sol ing hep oblem ..................................... 39
3.3.4 Scalabili y ........................................... 40
3.4 S udycases............................................... 44
3.4.1 Academiccase......................................... 45
3.4.2 Comuni a de Regan s Les Planes i Aixalelles . . . . . . . . . . . . . . . . . . . . . . 47
3.4.3 Comuni a de Regan s Seg ià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.4 CEDER-CIEMAT........................................ 71
3.5 Conclusions............................................... 75
3.5.1 Fu u ewo k .......................................... 76
4 Ene gy s o age sizing o p e en wa e hamme on PV pumping sys ems 77
4.1 In oduc ion............................................... 78
4.1.1 Wa e hamme in PV pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1.2 Con ibu ions.......................................... 80
4.2 P oblemdesc ip ion.......................................... 80
4.3 Me hodology(O -g id)........................................ 82
4.4 S udycase ............................................... 85
4.4.1 Clouds ............................................. 86
4.4.2 Resul s ............................................. 87
4.4.3 Feasibili y and impac assessmen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
4.4.4 Sensi i i yanalysis ...................................... 90
4.5 Me hodology(G idconnec ed).................................... 93
4.5.1 PV disconnec s, pump does no s op . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.5.2 PV disconnec s, pump can s op . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5.3 PVdoesno disconnec ...................................100
4.6 AqueousECRba e y.........................................103
4.6.1 Resul s .............................................103
4.6.2 Resul s(G idconnec ed)...................................103
4.7 Conclusion ...............................................104
4.7.1 Fu u ewo k ..........................................105
5 Po en ial g id se ices 106
5.1 Legisla i econ ex ...........................................106
5.2 Applica ions in powe sys em ope a ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1 Long e ms o age.......................................107
5.2.2 Sho e ms o age ......................................108
5.2.3 Compa ison and equi emen s o long and sho e m s o age . . . . . . . . . . . . 109
5.2.4 Se ices wi h e enue in Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 Real- ime ope a ion & con ol o inno a i e i iga ion canal-based ene gy s o age sys ems 113
6.1 In oduc ion...............................................113
6.2 P oblemde ini ion...........................................116
6.3 Me hodology..............................................117
6.3.1 De elopmen o OFO-based con olle o pump-based i iga ion plan s . . . . . . 119
6.4 Pe o manceassessmen .......................................121
6.4.1 S udycase...........................................121
6.4.2 P elimina y esul s ......................................122
6.5 Conclusions...............................................123
6.5.1 Fu u ewo k ..........................................124
7 Fundamen al AGI opologies and con ol s a egies 125
7.1 In oduc ion...............................................125
7.2 Compa ing AC and DC mic og id app oaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.3 Con ol a chi ec u es o he con e e connec ed o he p ima y g id . . . . . . . . . . . . . 128
7.3.1 Dual-Po con ol .......................................129
7.4 Discussion on possible AGI con igu a ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.5 Models o s udy he connec ion o he p ima y g id . . . . . . . . . . . . . . . . . . . . . . . . 131
7.5.1 S eady-s a eModel......................................132
7.5.2 Linea Model..........................................133
7.6 Ini ialResul s..............................................135
7.6.1 Powe lowsolu ion .....................................136
7.6.2 Small-Signalanalysis ....................................137
7.6.3 PVs epchange........................................137
7.6.4 G idangles epchange....................................139
7.7 Fu u ewo k...............................................140
Bibliog aphy 141
4
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Lis o Figu es
2.1 E olu ion o he i iga ed and d y c ops ex ension in Spain be ween 2004 and 2023 . . . 15
2.2 Decla ed ag icul u al land in Ca alonia, classi ied in o i iga ed and d y (yea 2023) . . . . 15
2.3 Loca ion o he ese oi s o he analysed i iga ion communi ies nex o he main pa ici-
pa ing i e s and ibu a ies. Colou s co espond o di e en i iga ion communi ies. . . . . 16
2.4 Facili ies a he CR Seg ià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 I iga ion communi ies in he egion conside ed o u he analysis . . . . . . . . . . . . . . 19
2.6 Facili ies a he CR de Les Planes i Aixalelles . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 CEDER-CIEMAT case schema ic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Loca ion o he s a e o he a e e ences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 De ini ion o he a iables o a sou ce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Rese oi de ini ion .......................................... 29
3.4 De ini ion o he low di ec ion in a pipe de ice . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Cha ac e is iccu eo apipe..................................... 30
3.6 De ini ion o he low and elec ic powe di ec ion in a pump de ice . . . . . . . . . . . . . . 31
3.7 Ope a ing egion o a a iable speed pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.8 Ope a ing egion o linea app oxima ion model . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.9 De ini ion o he low and elec ic powe di ec ion in a new pump de ice . . . . . . . . . . . 34
3.10 De ini ion o he low and elec ic powe di ec ion in a u bine de ice . . . . . . . . . . . . . 35
3.11 Compa ison o di e en me hods using equali y, inequali y, and linea ized cons ain s. . . 42
3.12S udycasediag am........................................... 45
3.13 Maximum capaci y, al eady ins alled and newly sized (dim.) magni udes o he PV, ba e y
and u bineelemen s.......................................... 46
3.14 Volume a he ese oi s (R0, R1) and low o bo h pumps (P1, P2), i iga ion a ese oi 1
(I )and u bine(T1)........................................... 47
3.15 Powe balance o he sys em (de ined posi i e i consumed by he elemen ) and elec ici y
cos . ................................................... 47
3.16 Ba e y s a e o cha ge and powe (de ined posi i e i abso bed). . . . . . . . . . . . . . . . 48
3.17 CR Les Planes i Aixalelles s udy case base sys em. . . . . . . . . . . . . . . . . . . . . . . . 48
3.18 A e age daily i iga ion demand on CR Les Planes i Aixalelles (S: Summe , W: Win e ).
Real da a om 1 yea and 90% con idence in e al. . . . . . . . . . . . . . . . . . . . . . . . 48
3.19Va ia ionson hes udycase ..................................... 50
3.20Resul so hebasecase........................................ 51
3.21Resul so PaTcase(Case1)...................................... 51
3.22 Resul s o g id connec ed case (Case 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.23 Resul s o g id connec ed + PaT case (Case 3). . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.24 CR Seg ià-Sud Base case sys em. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.25 CR Seg ià-Sud wa e consump ion o i iga ion. . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.26 CR Seg ià-Sud sys em di ision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.27 CR Seg ià-Sud lowe and uppe di isions and assump ions. . . . . . . . . . . . . . . . . . . 55
3.28 G id equi alen GHG emission ac o , cos o elec ici y and sell p ice o he de ined ypical
days.................................................... 56
5
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3.29 CR Seg ià-Sud uppe esul s - Base case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.30 CR Seg ià-Sud uppe esul s - PaT case (Case 1). . . . . . . . . . . . . . . . . . . . . . . . . 61
3.31 CR Seg ià-Sud uppe esul s - g id connec ed case (Case 2). . . . . . . . . . . . . . . . . . . 62
3.32 CR Seg ià-Sud uppe esul s - PaT + g id connec ed case (Case 3). . . . . . . . . . . . . . . 63
3.33 CR Seg ià-Sud uppe esul s - emissions case (Case 3-em). . . . . . . . . . . . . . . . . . . 64
3.34 CR Seg ià-Sud lowe esul s - Base case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.35 CR Seg ià-Sud lowe esul s - g id connec ed case (Case 2). . . . . . . . . . . . . . . . . . . 68
3.36 CR Seg ià-Sud lowe esul s - PaT + g id connec ed case (Case 3). . . . . . . . . . . . . . . 69
3.37 CR Seg ià-Sud lowe esul s - emissions case (Case 3-em). . . . . . . . . . . . . . . . . . . 70
3.38 Spide plo s esul ing om he sensi i i y analysis. . . . . . . . . . . . . . . . . . . . . . . . . 71
3.39 CEDER case ep esen a ion wi h Pyomo blocks. . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.40 CEDER esul s - Case 1 in summe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.41 CEDER esul s - Case 1 in win e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.42 CEDER esul s - Case 2 in summe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.43 CEDER esul s - Case 2 in win e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.44 CEDER esul s - Case 3 in summe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.45 CEDER esul s - Case 3 in win e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.46 CEDER cos s esul s compa ison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1 Elec ical scheme o a PV pumping sys em. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Ske ch ep esen a ion o an i adiance d op e en . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 I adiance d op e en wi h ESS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Da a key poin s ha de ine a cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Loca ion o he i adiance senso and s udy case on he CR Seg ià-Sud acili ies. . . . . . . 85
4.6 Powe gene a ion and consump ion o a PV pump sys em in he Seg ià-Sud acili ies, co -
esponding o25 hJuly2022..................................... 86
4.7 Rank unc ion plo o clouds’ du a ion and shaded adian exposu e. . . . . . . . . . . . . . 87
4.8 Numbe o pump s opping e en s shading a ce ain ene gy, om da a and es ima o . . . 87
4.9 Cos s pe yea o di e en echnologies and base case. . . . . . . . . . . . . . . . . . . . . . 88
4.10 Cos s pe yea o di e en echnologies and base case and sensi i i y o in e es a e 𝑖
and cos o ene gy 𝑐𝑔𝑟𝑖𝑑 ........................................ 90
4.11 Sensi i i y o he cos s pe yea o di e en echnologies and base case o i adiance
h eshold 𝐺𝑡ℎ .............................................. 91
4.12 Cos unc ion and minimum alue o di e en i adiance h esholds be ween 100 and 600
W/m2. .................................................. 92
4.13 Ske ch ep esen a ion o he g id connec ed PV pumping sys em. . . . . . . . . . . . . . . . 93
4.14S a egy1................................................. 94
4.15 Cos s pe yea o di e en echnologies and g id connec ed case 1. . . . . . . . . . . . . . 96
4.16 Cos s pe yea o di e en echnologies and g id connec ed case 1 and sensi i i y o in-
e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝.......................... 96
4.17S a egy2................................................. 97
4.18 Cos s pe yea o di e en echnologies and g id connec ed case 2. . . . . . . . . . . . . . 99
4.19 Cos s pe yea o di e en echnologies and g id connec ed case 2 and sensi i i y o in-
e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝.......................... 99
4.20 Conside ed beha iou wi h g id and PV connec ed. . . . . . . . . . . . . . . . . . . . . . . . 100
4.21 Cos s pe yea o di e en echnologies and g id connec ed wi h PV. . . . . . . . . . . . . . 102
4.22 Cos s pe yea o di e en echnologies and g id connec ed case 1 and sensi i i y o in-
e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝..........................102
4.23 Op imal sizing 𝐸(1) o he Geyse Aqueous ECR ene gy s o age sys em o a ange o
capi al cos and sensi i i y o cos o ene gy 𝑐𝑔𝑟𝑖𝑑.........................104
5.1 ACER’s p oposal on Requi emen s o gene a ion in mixed- echnology si es . . . . . . . . 107
6
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
5.2 Di ision o equency egula ion, equency cu e example ( op) and powe ype espon-
sibili ies(bo om)............................................108
6.1 Online Feedback op imisa ion s uc u e based on g adien low. . . . . . . . . . . . . . . . . 117
6.2 Rela ionship be ween o line and online op imisa ion ools. . . . . . . . . . . . . . . . . . . . 120
6.3 Model o he simples es case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4 Tes ing o he plan wi h a good es ima ion o wa e consump ion o i iga ion. . . . . . . . 122
6.5 Tes ing o he plan wi h a w ong es ima ion o wa e consump ion o i iga ion. . . . . . . 123
7.1 Maximum Powe Poin T acking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2 AC sDCin e connec ions.......................................128
7.3 Example o a DC ol age con ol a chi ec u e. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4 Example o an AC g id- o ming con ol a chi ec u e wi h d oop con ol. . . . . . . . . . . . 129
7.5 Dual-Po con ol a chi ec u e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.6 Schemes o he analysed AGI con igu a ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.7 VSCelec icschememodel. .....................................131
7.8 Con olled cu en sou ce model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.9 Ini ialcases udyscheme........................................136
7.10 Linea and non-linea models compa ison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.11 Main con e e ac i e and eac i e powe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.12 Main con e e dc ol age and angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.13 Main con e e ac i e and eac i e powe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.14 Main con e e ol age and cu en magni udes. . . . . . . . . . . . . . . . . . . . . . . . . . 140
Lis o Tables
2.1 Po en ial a ailable ene gy s o age capaci y . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 CR Seg ià-Sud legacy equipmen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 CR Seg ià-Sud po en ial ene gy s o age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 CR Les Planes i Aixalelles legacy equipmen . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 CR Les Planes i Aixalelles po en ial ene gy s o age . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 CR Ga igues Sud legacy equipmen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 CR Ga igues Sud po en ial ene gy s o age . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.8 CR Zona O ien al de la Te a Al a legacy equipmen . . . . . . . . . . . . . . . . . . . . . . . 21
2.9 CR Zona O ien al de la Te a Al a po en ial ene gy s o age (*: equipmen planned o unde
cons uc ion) .............................................. 21
2.10 CEDER po en ial ene gy s o age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Resul s o ime and inal cos alue and compa ison be ween algo i hms and me hods. . . 43
3.2 Cha ac e is ics o he case’s elemen s (in p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Va iableslinkedbya cs........................................ 45
3.4 Cos sin€/p.u............................................... 46
3.5 Cha ac e is ics o he case’s elemen s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Casessumma y ............................................ 53
3.7 Cha ac e is ics o he CR Seg ia-Sud case’s de ices . . . . . . . . . . . . . . . . . . . . . . . 54
3.8 Resul s(Uppe )............................................. 57
7
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3.9 Resul s(Lowe )............................................. 65
3.10 Sensi i i y analysis o al cos a e age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.11 Objec i es alues and execu ion ime pe case and season. . . . . . . . . . . . . . . . . . . . 75
4.1 I iga ion communi ies wi h PV pumping sys ems in Ca alunya. . . . . . . . . . . . . . . . . 78
4.2 Cha ac e is ics o he PV pumping sys em . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Capi al and ope a ion cos s o he analysed ene gy s o age sys ems . . . . . . . . . . . . . 86
4.4 S a is ical desc ip ion o he p ope ies o he obse ed clouds. . . . . . . . . . . . . . . . . 86
4.5 S a is ical desc ip ion o he clouds da ase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6 Sizing esul s.............................................. 88
4.7 P ope ies o he ESS echnologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.8 PS3 sensi i i y analysis esul s o cos o ene gy and eal in e es a e . . . . . . . . . . . . 91
4.9 PS3 sensi i i y analysis esul s o i adiance h eshold . . . . . . . . . . . . . . . . . . . . . 91
4.10 G id connec ed base case cha ac e is ics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.11 G id connec ed sizing esul s (S a egy 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.12 PS3 sensi i i y analysis esul s o cos o ene gy, eal in e es a e and excess powe e m 96
4.13 G id connec ed sizing esul s (S a egy 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.14 G id connec ed sizing esul s (wi hou PV disconnec ion) . . . . . . . . . . . . . . . . . . . . 102
4.15 Maximum capi al cos o 𝐸(1) ≤0,1 kWh o di e en cos o ene gy alues . . . . . . . . . 103
4.16 Maximum capi al cos o di e en excess powe e m (g id connec ed cases) . . . . . . . . 104
5.1 Compa ison and equi emen s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1 Pa ame e s o he simple es case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.1 Maincon e e pa ame e s.......................................136
7.2 Powe lowsolu ion...........................................136
7.3 Sys em’seigen alues..........................................138
8
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Ac onyms
AC al e na ing cu en
ACATCOR Associació Ca alana de Comuni a s de Regan s
ACER Agency o Coope a ion o Ene gy Regula o s
aFRR au oma ic equency es o a ion ese e
AGI ad anced g id in e ace
AGISTIN Ad anced G id In e aces o inno a i e STo age IN eg a ion
CEDER Cen o de Desa ollo de Ene gías Reno ables
CIEMAT Cen o de In es igaciones Ene gé icas Medioambien ales y Tecnológicas
CR Comuni a de Regan s
DC di ec cu en
ECR elec ochemical ecupe a o
EMS ene gy managemen sys em
ENTSO-E Eu opean Ne wo k o T ansmission Sys em Ope a o s o Elec ici y
ESS ene gy s o age sys em
FCR equency con ainmen ese e
FENACORE Fede ación Nacional de Comunidades de Regan es
Flow edox low ba e y
Fw lywheel
GHG g eenhouse gas
IPOPT in e io poin op imise
LCOS le elised cos o s o age
Lead lead acid ba e y
LIB li hium-ion ba e y
mFRR manual equency es o a ion ese e
MINLP mixed in ege non-linea p og amming
MPPT maximum powe poin acking
NLP non-linea p og amming
9
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
as collec ed a ailable da a om public ende s [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Then,
o each ese oi p esen in he sys ems we es ima ed he po en ial ene gy de ined as:
𝐸=𝜌𝑔Δ𝐻𝑊, (2.1)
whe e 𝜌is he densi y o he wa e assumed 1 000 kg/m3,𝑔 he g a i y accele a ion cons an nea he
su ace o he Ea h, assumed 9,81 m/s2,Δ𝐻(m) he a e age di e ence o heigh s be ween a ese oi
and i s di ec sou ce and 𝑊(m3) he olume ic capaci y o he ese oi . The esul s a e summa ised in
Table 2.1. We published he whole da ase , which is publicly a ailable in [25].
The calcula ion does no conside he e iciency o he pumping sys ems and u bines o pump as u bine
(PaT)s equi ed o ex ac he ene gy. I does no examine ei he he ope a ion o ese oi s in se ies,
which will ha e an in luence on he amoun o ene gy ha can be ex ac ed on i iga ion communi ies
ha ha e se e al ese oi s in se ies. Since no all o he equi ed da a could be ga he ed, some alues
we e es ima ed as well as ese oi s we e excluded om he analysis.
Assuming a cos o 340 ±60 $/kWh [26] and a a io o 1 $ = 0,86 €(as pe June 2025), he capi al
in es men equi ed o an s a iona y ene gy s o age sys em (ESS) o such cha ac e is ics would ange in
643 ±114 M€.
0 30 60
km
Figu e 2.3 –Loca ion o he ese oi s o he analysed i iga ion communi ies nex o he main pa icipa ing i e s
and ibu a ies. Colou s co espond o di e en i iga ion communi ies.
2.3 Communi a de Regan s Seg ià-Sud
The Comuni a de Regan s Seg ià-Sud is loca ed in he p o ince o Lleida, a geog aphic coo dina es
N 41∘21’ 44” E 0∘27’ 14”, and has in luence o e he municipali ies o Alma e , Lla decans, Maials,
Se òs and To ebesses.
I s acili ies consis o 4 pumping s a ions wi h 18,4 MW o ins alled powe , 5 ese oi s wi h a o al
capaci y o 980 000 m3and 3 sola pho o ol aic (PV) plan s o alling 1,3 MWp (Figu e 2.4). Pumping
s a ions PS0 and PS1 deli e wa e om he i e Eb e o ese oi R1, om whe e i is dis ibu ed o
ese oi s R2, R3 and R4 ia pumping s a ion PS2. Pumping s a ion PS3 akes wa e om ese oi
R4 o ese oi R5. Two o he PV plan s a e loca ed a pumping s a ion PS2 and he emaining one is
p ojec ed o be ins alled a PS3 [21, 22, 27, 28, 29, 30].
Table 2.2 summa ises he equipmen p esen a he acili ies o he Comuni a de Regan s Seg ià-Sud
and Table 2.3 shows i s po en ial ene gy s o age as compu ed wi h (2.1).
16
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 2.1 –Po en ial a ailable ene gy s o age capaci y (*: olume was es ima ed om ese oi su ace). Da a om
[25].
I iga ion communi y Rese oi s E [MWh]
Aigües del Mon san * 6 5,04
Albí 3 6.44
Alge i Balague 6 111,73
Ascó 2a zona * 2 4,76
Auba ells 2 6,03
Bassano a 3 0,87
Benissane 2 10,45
Ga igues Sud 15 158,30
Gines a 2 11,46
Les Planes i Aixalelles 1 3,58
Mon edons-Valls 1 18,64
Mo a d’Eb e * 2 10,12
Mo a la No a * 1 3,83
Palma d’Eb e 3 47,84
Pe elló 2 10,15
Pinell de B ai 1 16,48
P og és * 1 1,60
Rasque a 2 34,13
Riu Rine 2 7,10
Sega a Ga igues 38 1 186,21
Seg ià Sud 5 255,01
To e de l’Espanyol * 4 5,28
To es de Seg e 1 101,02
Vilosell 1 12,26
Vingalís 2 18,10
Xe a Sènia 3 23,57
Zona O ien al Te a Al a 8 183,54
TOTAL 2 223,52
Table 2.2 –CR Seg ià-Sud legacy equipmen . (*: equipmen planned o unde cons uc ion)
Pumping s a ion N. Pumps Powe [kW] Flow [m3/h] Sola PV [kWp]
PS0 3 3 x 950 11 520 -
PS1 3 3 x 3 200 11 520 -
PS2 9 3 x 250
3 x 315
3 x 1 250
3 154
2 010
6 570
-
523,00
527,50
PS3 3 3 x 160 2 778 274,68*
Table 2.3 –CR Seg ià-Sud po en ial ene gy s o age
Rese oi Volume [m3] A e age al i ude [m] Ene gy [MWh]
Eb e Ri e (Riba oja) - 70 -
Rese oi R1 142 869 331 101,73
Rese oi R2 297 042 359 22,62
Rese oi R3 85 268 419 20,38
Rese oi R4 269 485 426 69,27
Rese oi R5 185 814 447 10,97
17
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Figu e 2.4 –Facili ies a he CR Seg ià-Sud. O opho o om Ins i u Ca og à ic i Geològic de Ca alunya [31], Wo ld
map om OpenS ee Map [32].
2.4 O he communi ies
Besides he CR Seg ià-Sud being al eady in he p ojec , we made a call o da a o he i iga ion com-
muni ies in ol ed wi h ACATCOR, he main Ca alan associa ion o i iga ion communi ies. Se e al ha e
answe ed and a e depic ed in Figu e 2.5. Eb e and Seg e, he wo main i e s o he egion which eed
he communi ies ese oi s, a e highligh ed as well.
Comuni a de Regan s de Les Planes i Aixalelles
The Comuni a de Regan s de Les Planes i Aixalelles is loca ed in he p o ince o Ta agona, a geo-
g aphic coo dina es N 41∘12’ 39” E 0∘34’ 32”, and has in luence o e he municipali ies o Ascó, Flix and
Vineb e.
Thei acili ies consis o a pumping s a ion, a ese oi and a sola PV plan (Figu e 2.6). The pumping
s a ion consis s o 2 pumps o 110 kW powe ed by a h ee-phase mo o wi h squi el cage o o . The
ese oi can hold a olume o 13 000 m3and is loca ed a an al i ude o 138 m o e sea le el, 101 m
abo e he pumping s a ion. The sola PV plan , in se ice since ma ch o 2023, is buil o 468 PV panels
o a o al o 215,28 kWp. An an i- eezing sys em allows he acili ies o wo k on colde condi ions,
ex ending he i iga ion season on win e ime [19, 33, 34].
Table 2.4 summa ises he equipmen p esen a he acili ies o he Comuni a de Regan s de Les Planes
i Aixalelles and Table 2.5 shows i s po en ial ene gy s o age as compu ed wi h (2.1).
18
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Eb e
Seg e
ARAGÓN
LLEIDA
TARRAGONA
Seg ià Sud
Ga igues Sud
Les Planes
i Aixalelles
Zona O ien al
Te a Al a
Figu e 2.5 –I iga ion communi ies in he egion conside ed o u he analysis. Wo ld map om OpenS ee Map
[32]. Da a om [8].
Table 2.4 –CR Les Planes i Aixalelles legacy equipmen
Pumping s a ion N. Pumps Powe [kW] Flow [m3/h] Sola PV [kWp]
PS1 1+1 (1+1) x 110 200 215,28
Table 2.5 –CR Les Planes i Aixalelles po en ial ene gy s o age
Rese oi Volume [m3] A e age al i ude [m] Ene gy [MWh]
Eb e Ri e (Ascó) - 37 -
Rese oi R1 13 000 138 3,58
19
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Figu e 2.6 –Facili ies a he CR de Les Planes i Aixalelles. O opho o om Ins i u Ca og à ic i Geològic de
Ca alunya [31], Wo ld map om OpenS ee Map [32].
Comuni a de Regan s del Ga igues Sud
The Comuni a de Regan s del Ga igues Sud is loca ed in he p o ince o Lleida, a geog aphic coo di-
na es N 41∘22’ 16” E 0∘39’ 42”, and has in luence o e he coun y o Les Ga igues.
Thei acili ies consis o 8 pumping s a ions, 15 ese oi s and 2 sola PV plan s [18, 35, 36].
Table 2.6 summa ises he equipmen p esen a he acili ies o he Comuni a de Regan s del Ga igues
Sud and Table 2.7 shows i s po en ial ene gy s o age as compu ed wi h (2.1).
Table 2.6 –CR Ga igues Sud legacy equipmen
Pumping s a ion N. Pumps Powe [kW] Flow [m3/h] Sola PV [kWp]
PS1 3+1 (3+1) x 450 1 537 601,88
PS2 3+1 (3+1) x 315 1 353 462,24
PS3 1+1 (1+1) x 400 800 -
PS4 1+1 (1+1) x 75 118 -
PS5 3+1 (3+1) x 355 1 080 -
PS6 2+1 (2+1) x 110 608 -
PS1-IV 3+1 7 500 6 109 -
PS2-IV 3+1 8 400 6 109 -
Comuni a de Regan s de la Zona O ien al de la Te a Al a
The Comuni a de Regan s de la Zona O ien al de la Te a Al a is loca ed in he p o ince o Ta agona, a
geog aphic coo dina es N 41∘7’ 5” E 0∘22’ 23”, and has in luence o e he coun y o Te a Al a.
Thei acili ies consis o 4 pumping s a ions and 7 ese oi s [24].
Table 2.8 summa ises he equipmen p esen a he acili ies o he Comuni a de Regan s de la Zona
O ien al de la Te a Al a and Table 2.9 shows i s po en ial ene gy s o age as compu ed wi h (2.1).
20
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 2.7 –CR Ga igues Sud po en ial ene gy s o age
Rese oi Volume [m3] A e age al i ude [m] Ene gy [MWh]
Eb e Ri e (Flix) - 40,4 -
Rese oi R0 3 600 203 1,60
Rese oi R1 14 688 198 0,25
Rese oi R2 74 870 323 25,50
Rese oi R3 280 418 0,07
Rese oi R4 40 470 0,02
Rese oi R5 54 000 518 28,77
Rese oi R6 54 000 580 9,05
B eak 4 668 217 2,26
B eak BT-0 1 000 328 0,78
Rese oi E1 92 000 619 16,49
Rese oi E2 35 500 545 18,60
Rese oi E3 82 900 662 18,52
Rese oi E4 91 000 685 5,88
Rese oi E5 65 800 637 12,08
Rese oi E6 56 600 781 18,43
Table 2.8 –CR Zona O ien al de la Te a Al a legacy equipmen (*: equipmen planned o unde cons uc ion)
Pumping s a ion N. Pumps Powe [kW] Flow [m3/h] Sola PV [kWp]
PS0 3+1 (3+1) x 680 9 000 -
PS1 3+1 (3+1) x 8 351 9 000 -
PS2 12 (1+1) x 600 608 -
(2+1) x 794 1 109 -
(2+1) x 914 2 268 -
(3+1) x 914 4 266 -
PS3 2+1 (2+1) x 150 252 -
PS4* 2+1 (2+1) x 178 1 620 -
Table 2.9 –CR Zona O ien al de la Te a Al a po en ial ene gy s o age (*: equipmen planned o unde cons uc ion)
Rese oi Volume [m3] A e age al i ude [m] Ene gy [MWh]
Riba oja ese oi - 69 -
Tank 3 600 88 0,19
Rese oi R1 50 000 359 36,86
Rese oi R2.1 150 000 445 35,15
Rese oi R2.2 270 000 457 72,47
Rese oi R2.3 33 000 465 9,53
Rese oi R2.4 41 000 521 18,10
Rese oi R3 30 800 551 2,56
Rese oi R4* 70 000 503 8,68
21
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
2.5 CEDER-CIEMAT
Cen o de Desa ollo de Ene gías Reno ables (CEDER)-Cen o de In es igaciones Ene gé icas Medioam-
bien alesyTecnológicas(CIEMAT)isloca edin he p o inceo So ia a geog aphic coo dina es N41º36’22”
E 2º27’37” is a cen e dedica ed o he in es iga ion in enewable ene gies and s o age sys ems.
Since he cen e is no dedica ed o he supplying o wa e o ields and he acili ies a e ully dedica ed o
esea ch inali ies, he 3 ese oi s a e ela i ely smalle han in i iga ion communi ies. Table 2.10 shows
he cha ac e is ics o hese ese oi s.
Table 2.10 –CEDER po en ial ene gy s o age
Rese oi Volume [m3] A e age al i ude [m] Ene gy [MWh]
Rese oi R0 2 000 1 019 -
Rese oi R1 1 500 1 086 0,27
Rese oi R2 500 1 096 0,09
The pumping s a ion is composed o 4 pumps o 7,5 kW each connec ed o ese oi 1 and 2. The pumps
a e connec ed o a common bus wi h he g id and a 16 kW PV plan . Fu he mo e, a u bine o 40 kW
is ins alled in he same pumping s a ion. No e ha he pumping s a ion can pump o he ese oi 1 o 2
bu only can u bine om he ese oi 1, and ese oi 1 and 2 a e connec ed h ough a pipe wi h a al e.
A 90 kW low ba e y wi h 400 kWh capaci y is also p esen in he sys em. The sys em is ep esen ed
in Figu e 2.7.
Figu e 2.7 –CEDER-CIEMAT case schema ic. Figu e p o ided by CEDER-CIEMAT.
22
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3 Op imisa ion and edesign o ac-
i e oleo i iga ionsys emsasen-
e gy s o age in he elec ical g id
Cu en ly, i iga ion sys ems a e iewed by he bulk powe g id as ene gy demand poin s. Hence, he only
o m o in e ac ion ha occu s be ween hese sys ems is limi ed o he unidi ec ional powe low om
he g id o he pumping s a ions o he i iga ion sys em. The demand p o ile o he pumping s a ions is
co ela ed wi h he imes when ene gy has a lowe p ice (o -peak pe iods). Howe e , he wa e s o ed
in ese oi s a di e en heigh s can be ega ded as a o m o ene gy s o age. In o de o elease he ull
po en ial o i iga ion sys ems as g id-se ice p o ide s, a edesign o he sys em componen s is equi ed
o inc ease i ope a ional capaci y.
The e o e, wi hin he amewo k o his p ojec , we analyse he po en ial capaci y o ese oi -based i i-
ga ion sys ems o adop an ac i e ole in he elec ical g id p o iding se ices such as ene gy s o age.
This chap e is s uc u ed as ollows:
i Sec ion 3.1 in oduces he opic and e iews he s a e o he a solu ions.
ii Sec ion 3.2 in oduces ou app oach.
iii Sec ion 3.3 desc ibes he me hodology and op imisa ion ool we de eloped o add ess he opic.
i Sec ion 3.4 analyses se e al s udy cases applying he de eloped me hodology.
Sec ion 3.5 concludes he s udy and p o ides addi ional u u e esea ch se led on he ob ained
esul s.
3.1 In oduc ion
I iga ion communi ies’ wa e dis ibu ion sys ems may ake many o ms depending on whe he hey a e
p essu ised o open canals and whe he hey use wa e s o age in he o m o ese oi s o deli e s aigh
om he main wa e sou ce. On his wo k, we ocus on pump- ed ese oi -based i iga ion sys ems. In
such sys ems, a pumping s a ion ans e s wa e om he main sou ce o an in e media e ese oi o a
highe ese oi . F om he e, a se ies o canals o pipes deli e wa e o he use s, usually by g a i y.
The ene gy equi emen s o he pumping s a ions o hese sys ems a e signi ican , anging om hun-
d eds o MWh o GWh. These equi emen s can accoun o mo e han 70 % o hei ope a ing cos s. In
he Languedoc-Roussillon Regional Hyd aulic Ne wo k (F ance) 95 % o he annual 80 GWh s em om
pumping s a ions [37]. Howe e , ene gy demand is cha ac e ised by a seasonal na u e, wi h he sys em
emaining close o inac i e du ing win e mon hs, when i iga ion demand d ops.
23
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
In se e alcases, i iga ioncommuni iesdecide oins all sola pho o ol aic (PV)pumping sys ems. On-si e
PVgene a ion educesene gyconsump ion om he elec icalg ido eplacesdieselpumping sys ems.
Despi e hei po en ial, he ole o i iga ion sys ems as ac i e playe s in he elec ici y g id has ha dly
been in es iga ed o conside ed. As ene gy s o age and demand esponse become inc easingly ele an
o g id s abili y [38], he unique cha ac e is ics o i iga ion sys ems pose hem as aluable p o ide s o
g id se ices.
To p o ide g id se ices, i is essen ial o main ain enough wa e in ese oi s, enabling he lexibili y
o shi ene gy consump ion o e en supply powe back o he g id. Achie ing his will equi e p ecise
long- e m planning and, i necessa y, he eplacemen o speci ic asse s o pumping s a ions.
3.1.1 S a e o he a
P e ious wo ks ha e add essed he ma e o imp o ing ene gy e iciency and educing ene gy demand o
i iga ion sys ems. As no iced by [37], his can be achie ed by op imising hei design and ope a ion and
applying co ec ing measu es, as well as using he exis ing in as uc u e o ene gy p oduc ion ei he
om sola o hyd aulic sou ces. Many di e en p oposals can be ound in he li e a u e o exploi he
po en ial ha hyd opowe i iga ion sys ems can p o ide. We classi ied hese e e ences acco ding o
whe he hey add ess ese oi -based ene gy s o age, ake ad an age o he wa e low unning h ough
open canals, o ex ac powe om excess p essu e on i iga ion hyd an s (Figu e 3.1). No ice ha se e al
o hem a e loca ed in Eu ope, which may sugges a localised aise o he in e es on he opic bu could
also eme ge om geog aphic esea ch bias on unding, publica ion and ecommenda ion [39] as well as
ou own bias.
Legend
Rese oi s
Canals
Hyd an s
Figu e 3.1 –Loca ion o he s a e o he a e e ences.
Rese oi -based ene gy s o age
On he Vida bha egion (India), [40] es ima ed he capaci y o 19 p ojec s in ol ing mic o-hyd o powe
gene a ion on i iga ion dams, wi h esul s anging om 150 kW o 2 200 kW. On F oyennes (Belgium),
[41] selec ed and es ed a 30 kW pump unning in e e se, o pump as u bine (PaT), wi h a a iable
equency d i e o a mic o pumped-s o age hyd opowe (PSH) acili y. The acili y consis ed o wo
650 m3s o m-wa e basins, a o al o 110,2 kWp o PV peak powe , ou 2,4 kWp wind u bines and
a cen alised con olle which in eg a ed e e y hing wi h a mic o ene gy g id. On Pe h (Aus alia), [42]
de eloped and es ed a wo laye ene gy managemen sys em (EMS) o a mhouses o manage a PV-
PSH acili y and he scheduling o he i iga ion sys em. The me hodology comp ised he u ilisa ion o
neu al ne wo k models o he p edic ion o wea he and demand, in combina ion wi h a gene ic algo i hm
o cos minimisa ion. The EMS was e i ied on a sys em consis ing on a 3,0 kW pump and a 0,768 kW
24
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
u bine. Same au ho s modelled on [43] a PSH sys em which was alida ed on an expe imen al se up.
On he Moun Lo y Ranges (Aus alia), [44] de eloped a combined 3,0 kW PaT wi h PV o household
demand s o ing wa e in i iga ion ese oi s. They compa ed he pe o mance o he analysed sys em o
a comme cial ba e y ene gy s o age sys em and es ima ed he o me le elised cos o s o age (LCOS) o
be 30 % lowe han he la e . On Ca alonia (Spain), we p elimina ily analysed a simple i iga ion sys em
consis ing o a single 13 000 m3 ese oi wi h a g id connec ed 110 kW pump and a 215,3 kWp PV
pumping sys em and no iced i was easible o un he sys em o ene gy s o age in win e [45].
Flow on canals
On Chia-Nan (Taiwan), [46] elabo a ed a p elimina y loca ion analysis o u bine placemen on i iga ion
canals and ins alled a 1,5 kW wa e wheel in a canal on Yunlin (Taiwan) [47]. On he Piedmon (I aly),
[48] analysed he combined use o i iga ion and hyd oelec ic p oduc ion and es ima ed be ween 3,5
MW and 9,0 MW o ex a combined hyd aulic powe could be ob ained h ough he in oduc ion o small
hyd opowe plan s in i iga ion sys ems. As epo ed by [49], on he Canal de P o ence (F ance) an
ag eemen be ween he public company esponsible o he wa e managemen and he main i iga o s
union made i possible o in es in a hyd opowe plan which uses he low o he canal o gene a e
5 GWh annually. On Calab ia (I aly), [50] de eloped a me hodology and e alua ed he placemen o
mic o hyd opowe plan s on i iga ion sys ems’ pipelines, calcula ing om 100 kW o 300 kW o easible
ins alled powe on he analysed case s udy and no icing in es men e u ns hea ily depend on na ional
subsidies o enewable ene gy. On Valencia (Spain), [51] analysed he deploymen o A chimedes sc ew
u bines o ex ac om 1 o 5 annual GWh om he canal.
Excess p essu e on hyd an s
On Andalusia (Spain), [52] alida ed, on a model, a me hodology o PaT selec ion o ex ac he po en ial
o excess p essu e poin s and in [53] es ima ed a po en ial o 21,05 GWh pe yea on Se illa and Có doba
(Spain) using he same powe ex ac ion me hod. On Vello e (India), [54] de eloped a pico hyd opowe
gene a ion sys em wi h a 0,74 kW induc ion mo o o ex ac powe di ec ly om an i iga ion hyd an o
gene a e 150 W. On Có doba (Spain), [55] analysed he en i onmen al and economic impac o a 0,66
kWp PV wi h a 4 kW PaT sys em o eco e ene gy om excess p essu e and compa ed i o ha o a 6
kVA diesel gene a o . The s udy concluded ha he impac s a e conside ably lowe o he no el sys em,
e en o ha o a lone PV plan , bu he co esponding ba e y highly con ibu es on he mine als and me -
als aspec o he en i onmen al impac . On Alican e (Spain), [56] p oposed an op imisa ion me hodology
and de eloped so wa e o size and choose he bes loca ion o mic o hyd opowe sys ems o i iga ion
sys ems, conside ing di e en con igu a ions wi h loa ing PV, g ound PV, PaT, ba e y ene gy s o age
and g id connec ion.
3.1.2 Objec i e
To ou bes knowledge, he e is no open sou ce so wa e ha can accu a ely analyse and op imise i iga-
ion sys ems o ac i e pa icipa ion on he g id, conside ing no only he ene gy low bu also he bounds
and easible ope a ing poin s o he hyd aulics equipmen . The main no el con ibu ion o his wo k is
he de elopmen o a mul i-physics open sou ce op imisa ion ool based in Py hon and u ilising he Py-
omo lib a ies [57, 58]. The ool acili a es he e icien and clea o mula ion o op imisa ion p oblems, by
linking p e-de ined models. The ool hen in okes a nume ical sol e algo i hm o compu e a solu ion o
he p oblem. The in icacies o he sol e a e no add essed in his documen 1. We p esen ed an ini ial
1Reade s in e es ed in he subjec a e e e ed o [59].
25
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
• Hyd aulic powe (3.14):
𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡)
• Elec ical powe (3.15):
𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡)
• Flow limi s (3.13):
𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖≤𝑄𝑖(𝑡)≤𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖
Pump (linea app oxima ion)
Quad a ic exp essions can inc ease he compu a ional cos o he p oblem, as seen in he 𝐻-𝑄cha ac-
e is ic cu e in he pump model. The e o e, elaxing his exp ession is an in e es ing app oach.
P e iously, he elaxa ion o he same exp ession was achie ed by subs i u ing he equali y cons ain
wi h an inequali y cons ain in he 𝐻-𝑄exp ession, allowing he elimina ion o he a iable ep esen ing
he pump speed, as sugges ed in [65]. Thanks o his imp o emen , i is now possible o cons uc a
pump model whe e he quad a ic exp ession is eplaced wi h a linea app oxima ion while main aining
he inequali y cons ain .
Fo a be e app oxima ion o he o iginal cu e, he me hod di ides he space be ween 𝑄𝑖and 𝑄𝑖in o
𝑁𝐿,𝑖 in e als, ixing hese poin s on he o iginal cu e. Then, a cons ain is o mula ed o each line
using an inequali y, ensu ing ha he ope a ing a ea lies below he app oxima ion and, he e o e, below
he o iginal cu e—wi hou equi ing any bina y a iables.
Figu e 3.8 illus a es an example o his app oxima ion using h ee equidis an in e als, along wi h he
ope a ing a ea o he op imisa ion p oblem.
𝑄
𝑄𝑖𝑄1,𝑖 𝑄2,𝑖
Δ𝑄=𝑄𝑖−𝑄𝑖
Δ𝑄/𝑁𝐿,𝑖
𝑄𝑖
𝐻
Figu e 3.8 –Ope a ing egion o linea app oxima ion model
The cons ain s a e buil by using he ollowing exp essions:
𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖
𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...,𝑁𝐿(3.16)
𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖
𝑁𝐿,𝑖 𝑙=1,...,𝑁𝐿(3.17)
𝐻𝑙,𝑖 =( 𝑛𝑖
𝑛𝑁,𝑖)2𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖(𝑡))2𝑙=1,...,𝑁𝐿(3.18)
Cons ain (3.16) ep esen s he line ha app oxima es he cu e, while (3.17) is used o calcula e he
key poin s ha minimize he e o . Finally, (3.18) p ojec s he key low poin s on o he o iginal nominal
cu e o he pump.
32
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Wi h he modi ica ion he a iables and pa ame e s a e:
Linea Pump summa y
Va iables:
• Flow (inle ):
Qin,i∈[−𝑄𝑖,0]. Connec ion: (3.3)
• Flow (ou le ):
Qou ,i∈[0,𝑄𝑖]. Connec ion: (3.3)
• Head:
Hi∈[0,𝐴𝑖]. Connec ion: (3.2)
• Hyd aulic powe :
ph,i∈[0,𝑝ℎ,𝑖]
• Elec ic powe :
pe,i∈[0,𝑝𝑒,𝑖]. Connec ion: (3.3)
• Pump ON:
𝛽ON,i∈{0,1}
Cons ain s:
• P essu e (3.16):
𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖
𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...,𝑁𝐿
• Flow key poin s (3.17):
𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖
𝑁𝐿,𝑖 𝑙=1,...,𝑁𝐿
• Flow poin s p ojec ion (3.18):
𝐻𝑙,𝑖 =( 𝑛𝑖
𝑛𝑁,𝑖)2𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖(𝑡))2𝑙=1,...,𝑁𝐿
• Flow cohe ence (3.12):
𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡)
• Hyd aulic powe (3.14):
𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡)
• Elec ical powe (3.15):
𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡)
• Flow limi s (3.13):
𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖≤𝑄𝑖(𝑡)≤𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖
Pump (sizing)
Sizes and se s up a new pump. Since new u bo-machine y a e designed ad hoc, we conside hei a ed
elec ical powe as he decision a iable 𝑝𝑑𝑖𝑚,𝑖(W). The a iables ha de ine he 𝑖- h new pump a e inle
an ou le lows Qin,i∈[−𝑄𝑖,0]and Qou ,i∈[0,𝑄𝑖](m3/s), de ined posi i e i exi ing he pump, dynamic
head Hi≥0(m), hyd aulic powe ph,i∈[0,𝑝ℎ,𝑖](W) and elec ic powe pe,i∈[0,𝑝𝑒,𝑖](W). Flows and
elec ic powe connec wi h (3.3) while head connec s wi h (3.2). We assume no u he in o ma ion on
33
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
he pump is a ailable, hen i is cha ac e ised jus by i s o ecas ed a e age e iciency 𝜂𝑖and o mula ed
wi h (3.12), (3.14), (3.15) and (3.19). 𝑝𝑑𝑖𝑚,𝑖 ≥𝑝𝑒,𝑖(𝑡) (3.19)
Qou
Qin
pe
Figu e 3.9 –De ini ion o he low and elec ic powe di ec ion in a new pump de ice
Pump (sizing) summa y
Va iables:
• Sized powe :
𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑑𝑖𝑚,𝑖]
• Flow (inle ):
Qin,i∈[−𝑄𝑖,0]. Connec ion: (3.3)
• Flow (ou le ):
Qou ,i∈[0,𝑄𝑖]. Connec ion: (3.3)
• Head:
Hi≥0. Connec ion: (3.2)
• Hyd aulic powe :
ph,i∈[0,𝑝ℎ,𝑖]
• Elec ic powe :
pe,i∈[0,𝑝𝑒,𝑖]. Connec ion: (3.3)
Cons ain s:
• Sizing (3.19):
𝑝𝑑𝑖𝑚,𝑖 ≥𝑝𝑒,𝑖(𝑡)
• Flow cohe ence (3.12):
𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡)
• Hyd aulic powe (3.14):
𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡)
• Elec ical powe (3.15):
𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡)
Tu bine (sizing)
Con e s hyd aulic powe in o o a ional mechanical powe and hen o elec ic powe h ough he use
o mechanically coupled gene a o s. Since no u bines a e cu en ly p esen in he sys em, we modelled
hem ollowing a sizing app oach as well. The a iables ha de ine he 𝑖- h new u bine a e inle an
ou le lows Qin,i∈[−𝑄𝑖,0]and Qou ,i∈[0,𝑄𝑖](m3/s), de ined posi i e i exi ing he u bine, dynamic
head Hi≥0(m), hyd aulic powe ph,i∈[−𝑝ℎ,𝑖,0](W) and elec ic powe pe,i∈[−𝑝𝑒,𝑖,0](W), de ined
posi i e i consumed. Flows and elec ic powe connec wi h (3.3) while head connec s wi h (3.2). We
assume no u he in o ma ion on he u bine is a ailable, hen i is cha ac e ised jus by i s o ecas ed
34
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
a e age e iciency 𝜂𝑖and o mula ed wi h (3.12), (3.14), (3.20) and (3.21). The u bine is conside ed o be
ope a ed wi h adjus able speed, which allows o a g ea e ange o ope a ion and is specially con enien
o ex ac powe om i iga ion ese oi s [66].
𝑝𝑒,𝑖(𝑡)=𝑝ℎ,𝑖(𝑡)𝜂𝑖(3.20)
𝑝𝑑𝑖𝑚,𝑖 ≥−𝑝𝑒,𝑖(𝑡) (3.21)
Cons ain (3.14)in ol es ap oduc o wo a iables. To educe hecomplexi yo hep oblem we p opose
he ollowing app oxima ion: 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖𝑛,𝑖(𝑡)
𝐻𝑖,(3.22)
whe e
𝐻(m) is he es ima ion o he dynamic head and can be de e mined, o ins ance, as
𝐻𝑖=Δ𝑧𝑖−( 𝑝ℎ,𝑖
𝜌𝑔Δ𝑧𝑖)2,(3.23)
wi h Δ𝑧𝑖(m) he di e ence o heigh s be ween he ese oi s he u bine ope a es wi h.
Qin
Qou
pe
Figu e 3.10 –De ini ion o he low and elec ic powe di ec ion in a u bine de ice
Tu bine summa y
Va iables:
• Sized powe :
𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑑𝑖𝑚,𝑖]
• Flow (inle ):
Qin,i∈[−𝑄𝑖,0]. Connec ion: (3.3)
• Flow (ou le ):
Qou ,i∈[0,𝑄𝑖]. Connec ion: (3.3)
• Head:
Hi≥0. Connec ion: (3.2)
• Hyd aulic powe :
ph,i∈[−𝑝ℎ,𝑖,0]
• Elec ic powe :
pe,i∈[−𝑝𝑒,𝑖,0]. Connec ion: (3.3)
Cons ain s:
• Sizing (3.21):
𝑝𝑑𝑖𝑚,𝑖 ≥−𝑝𝑒,𝑖(𝑡)
• Flow cohe ence (3.12):
𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡)
• Hyd aulic powe (3.14):
𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖𝑛,𝑖(𝑡)𝐻𝑖(𝑡)
• Elec ical powe (3.20):
𝑝𝑒,𝑖(𝑡)=𝑝ℎ,𝑖(𝑡)𝜂𝑖
35
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Pump as u bine (PaT)
Pumps as u bines is a con o e sial opic on hyd aulics and hyd opowe . Ex ac ing powe wi h he
applica ion o a pump ins ead o a u bine is an easily implemen able and economical solu ion o small
hyd opowe pu poses [67]. De ining hei cha ac e is ics is s ill a complex and complica ed p oblem and
equi es da a ha is usually no a ailable. Howe e , o he au ho s’ wo k analysing and e iewing pumps
wo king as u bines p o ed use ul o us when de ining hei beha iou in he op imisa ion model. In
[68] he au ho s e iewed PaT pe o mance p edic ion and s abili y li e a u e and [41] implemen ed a 30
kW PaT wi h a a iable equency d i e on hei s o m-wa e basin based mic o ene gy g id. F om his
wo ks we ex ac ed ha single s age cen i ugal PaTs a e he mos ecommended, pump geome y is a
undamen alpa ame e o p edic he pe o manceo i wo kingas a u bine, he pe o manceo PaTs may
ange om 50 o 80 %, and ha ope a ing he PaT wi h a a iable equency d i e inc eases i s ope a ing
ange and may ise i s e iciency o closely ma ch ha o wo king in pump mode. The op imisa ion ool
does no conside an explici de ice o a PaT, bu i s implemen a ion can be achie ed by de ining a pump
and a u bine p ope ly connec ed in pa allel, as exempli ied in [45].
Ene gy balance node
All equipmen ha consumes o deli e s elec ical powe , 𝑝𝑒(W), a e connec ed o ene gy balance nodes
which agg ega e and dis ibu e he powe among he connec ed de ices. Fo a se o elec ical de ices
𝒳connec ed o he same ene gy balance node, he balance imposed is
∑
𝑥∈𝒳𝑝𝑒,𝑥(𝑡)=0. (3.24)
Ene gy balance node summa y
Va iables:
• None
Cons ain s:
• Powe balance (3.24):
∑𝑥∈𝒳𝑝𝑒,𝑥(𝑡)=0
Elec ical g id
Deli e s o accep s elec ical powe om connec ed de ices. We modelled he g id as an ideal ol -
age sou ce limi ed by he maximum powe o he connec ion, which may be ei he a physical o a legal
cons ain . The a iables ha de ine he 𝑖- h g id a e he o al powe pi∈[−𝑝𝑖,𝑝𝑖](W) and he powe s
lowing om and o he g id p om,i∈[0,𝑝𝑖]p o,i∈[0,𝑝𝑖](W), de ined posi i e i consumed. To al elec ic
powe connec s wi h (3.3). A g id de ice is go e ned by i s own powe balance (3.25) and, addi ionally,
a bounda y may be se on a speci ic imes amp 𝑡𝑐 o ep esen a con ac ual es ic ion (3.26).
𝑝𝑖(𝑡)=𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡) (3.25)
𝑝𝑖(𝑡𝑐)≤𝑝𝑖,𝑡𝑐(3.26)
Elec ical g id summa y
Va iables:
36
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
• Powe ( o al):
pi∈[−𝑝𝑖,𝑝𝑖]. Connec ion: (3.3)
• Powe ( om):
p om,i∈[0,𝑝𝑖]
• Powe ( o):
p o,i∈[0,𝑝𝑖]
Cons ain s:
• Powe balance (3.25):
𝑝𝑖(𝑡)=𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡)
Sola PV
Con e s i adiance in o elec ical powe . The amoun o powe i can gene a e depends on he size o
he plan 𝑝𝑖𝑛𝑠𝑡,𝑖(W), he e iciency o he con e e 𝜂𝑖and he wea he condi ions, i.e. he i adiance le el
𝐺𝑖(𝑡)(W/m2). We conside he size o he plan may be inc eased. The a iables ha de ine he 𝑖- h
PV plan a e he gene a ed powe pi∈[−𝑝𝑖,0](W), de ined posi i e i consumed, and he new sized
powe 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖−𝑝𝑖𝑛𝑠𝑡,𝑖](W). Gene a ed elec ic powe connec s wi h (3.3). The gene a ed powe
is de ined wi h (3.27) whe e he me eo ological o ecas 𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 alues a e exp essed in pe uni as
(3.28). 𝑝𝑖(𝑡)≥−(𝑝𝑖𝑛𝑠𝑡,𝑖+𝑝𝑑𝑖𝑚,𝑖)𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡(𝑡)𝜂𝑖(3.27)
𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡(𝑡)=𝐺𝑖(𝑡)
1000 (3.28)
Sola PV summa y
Va iables:
• Powe :
pi∈[−𝑝𝑖,0]. Connec ion: (3.3)
• New sized powe :
𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖−𝑝𝑖𝑛𝑠𝑡,𝑖]
Cons ain s:
• Powe balance (3.27):
𝑝𝑖(𝑡)≥𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡)
Ba e y (sizing)
S o es ene gy om an elec ical sou ce. Ou op imisa ion p oblem conside s he sizing o new ba e -
ies. The a iables ha de ine he 𝑖- h ba e y a e he o al powe ans e pi∈ [−𝑝𝑖,𝑝𝑖](W), de ined
posi i e i consumed, he cha ge and discha ge powe pch,i∈[0,𝑝𝑖]pdc,i∈[0,𝑝𝑖](W), he s o ed en-
e gy Ei∈ [0,𝐸𝑖𝑆𝑂𝐶𝑖](Wh) and he sized powe 𝑝𝑑𝑖𝑚,𝑖 ∈ [0,𝑝𝑖](W) and capaci y 𝐸𝑑𝑖𝑚,𝑖 ∈ [0,𝐸𝑖]
(Wh). Elec ic powe connec s wi h (3.3). The sized powe limi s he cha ge, discha ge and o al powe
(3.29), (3.30), (3.31) and he sized capaci y limi s he ene gy s o ed h ough he s a e o cha ge bounds
𝑆𝑂𝐶𝑖∈[𝑆𝑂𝐶𝑖,𝑆𝑂𝐶𝑖](3.32), (3.33). Ene gy s o ed a ia ion cons ain is disc e ised using he back-
wa d Eule me hod conside ing he cha ge and discha ge e iciencies 𝜂𝑐ℎ,𝑖𝜂𝑑𝑐,𝑖(3.34).
37
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
𝑝𝑖(𝑡)=𝑝𝑐ℎ,𝑖(𝑡)−𝑝𝑑𝑐,𝑖(𝑡) (3.29)
𝑝𝑐ℎ,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 (3.30)
𝑝𝑑𝑐,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 (3.31)
𝐸𝑖(𝑡)≤𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖(3.32)
𝐸𝑖(𝑡)≥𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖(3.33)
{𝐸𝑖(𝑡)=𝐸𝑖(𝑡−Δ𝑡)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖) 𝑖𝑓𝑡>𝑡0
𝐸𝑖(𝑡)=𝐸𝑖(𝑡=𝑡𝑓)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖)o he wise (3.34)
Ba e y summa y
Va iables:
• Powe :
pi∈[−𝑝𝑖,𝑝𝑖]. Connec ion: (3.3)
• Cha ging powe :
pch,i∈[0,𝑝𝑖]
• Discha ging powe :
pdc,i∈[0,𝑝𝑖]
• Ene gy s o ed:
Ei∈[0,𝐸𝑖𝑆𝑂𝐶𝑖]
• New sized powe :
𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖]
• New sized capaci y:
𝐸𝑑𝑖𝑚,𝑖∈[0,𝐸𝑖]
Cons ain s:
• Powe balance (3.29):
𝑝𝑖(𝑡)≥𝑝𝑐ℎ,𝑖(𝑡)−𝑝𝑑𝑐,𝑖(𝑡)
• Cha ging powe limi (3.30):
𝑝𝑐ℎ,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖
• Discha ging powe limi (3.31):
𝑝𝑑𝑐,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖
• Maximum cha ge (3.32):
𝐸𝑖(𝑡)≤𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖
• Minimum cha ge (3.33):
𝐸𝑖(𝑡)≥𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖
• S o ed ene gy (3.34):
{𝐸𝑖(𝑡)=𝐸𝑖(𝑡−Δ𝑡)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖) 𝑖𝑓𝑡>𝑡0
𝐸𝑖(𝑡)=𝐸𝑖(𝑡=𝑡𝑓)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖)o he wise
38
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3.3.2 Objec i e unc ion
We a e in e es ed in wo main objec i es o his op imisa ion p oblem: an op imal a e age daily planing
s a egy o minimize he ope a ional cos while p o iding s o age se ices o he g id and sa is ying he
i iga ion demand; and an op imal sizing o new elemen s (e.g ba e ies, pumps, u bines) o edesign o
he al eady ins alled elemen s (e.g PV plan s), o minimize he sum o he ope a ing cos s 𝐶𝑜𝑝 (€) and
capi al cos s 𝐶𝑐𝑎𝑝(€) (3.35). Ope a ing cos s may conside he ene gy exchanges wi h he g id and o he
main enance cos s while capi al cos s accoun o he addi ional ins alled capaci y o he new elemen s.
𝑓(⋅)=𝐶𝑜𝑝+𝐶𝑐𝑎𝑝 (3.35)
The objec i e unc ion is u he de ailed in he pa icula s udy cases along Sec ion 3.4.
We also de ined an objec i e unc ion om he pe spec i e o he adminis a ion o a g id ope a o wi h
he pu pose o educing he o e all g eenhouse gas (GHG) emissions o he g id. Ins ead o de ining
ope a ion cos s in mone a y alue we applied he emission ac o o he g id o he ene gy exchanges
wi h he g id. This objec i e unc ion assumes an a e age beha iou o he g id and does no dis inguish
he echnologies pa icipa ing in he daily ma ke . Fu he de ails a e gi en in he pa icula s udy case in
Sec ion 3.4.3.
3.3.3 Sol ing he p oblem
To sol e he op imisa ion p oblem a sui able op imisa ion algo i hm is equi ed. We ha e achie ed suc-
cess ul esul s wi h he ollowing ee open sou ce so wa e:
• Couenne: b anch and bound algo i hm h ps://gi hub.com/coin-o /Couenne.
• Bonmin: Bonmin (Basic Open-sou ce Nonlinea Mixed IN ege p og amming) is an open-sou ce
sol e o MINLP p oblems h ps://gi hub.com/coin-o /Bonmin. I inco po a es di e en
algo i hms o sol e he models: B anch and bound (B-BB) is he simples and de aul algo i hm,
based on sol ing a con inuous non-linea p og am a each node o he sea ch ee and b anching
on a iables [69]. Ou e app oxima ion decomposi ion (B-OA), in oduced i s in [70] and [71], is
implemen ed using Ipop o sol e he non-linea p og amming (NLP) p oblems and Cbc o sol e
he mixed-in ege linea p og amming (MILP) p oblems. The Quesada and G ossman b anch and
cu (B-QG) algo i hm, p esen ed in [72], consis s o an algo i hm o sol e con ex MINLP p oblems
based on LP and NLP sub-p oblems, by a oiding he sequen ial solu ion o NLP sub-p oblems and
MILP mas e p oblems, ha is equi ed in he s anda d implemen a ion o he gene alized Bende s
decomposi ion (GBD) and B-OA algo i hms, achie ing up o an 84 % educ ion o he numbe o
nodes ha need o be examined. The hyb id ou e app oxima ion based in b anch-and-cu (B-Hyb)
sol es mo e NLPs o educe he size o he ee, by educing he algo i hm o he classical NLP
B-BB and he B-OA algo i hm [70]. The ou e -app oxima ion based b anch-and-cu wi h speci ic
con igu a ion (B-ECP) algo i hm is based on he B-QG algo i hm bu implemen ing a linea iza ion-
based algo i hm [73]. Finally, he i e a ed easibili y pump algo i hm (B-iPF) combines be ween
sol ing NLP and MILP p oblems [70].
• In e io Poin Op imize (IPOPT): in e io poin algo i hm o ind local solu ions o non-linea op i-
misa ion p oblems h ps://gi hub.com/coin-o /Ipop . I is a non-linea p og amming (NLP)
sol e so i is only sui able when no bina y a iables a e p esen among he p oblem.
39
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3.3.4 Scalabili y
This sec ion de ails he pe o mance and scalabili y issues hee me hodology is and has been subjec o,
as well as some app oaches we a emp ed o educe hei e ec :
• Bina y and non-linea p oblem: he in oduc ion o non-linea i ies and bina y a iables om hy-
d aulics’ beha iou makes he analysis a MINLP p oblem. Non-linea i ies a ise om he quad a ic
cha ac e is ic cu eso pipes andpumps (3.8)(3.11) andhyd aulicpowe compu a ion (3.14), which
is implici ly cubic. We equi ed bina y a iables o model whe he a pump is ac i e (3.13). The lin-
ea ised pump app oach (3.16) and he app oxima ion o he u bines’ dynamic head (3.22) add ess
non-linea i ies ega ding pumps and u bines. Howe e , u he wo k is equi ed o educe he e-
maining de ini ions.
• Dynamics: We app oached ime dependency and dynamics o he ese oi and ba e y de ices
(3.6) (3.34) ollowing an Eule disc e isa ion me hodology, such ha he o mula ion p ese es sim-
plici y.
• Time pe iod: E en ela i ely small i iga ion sys ems equi e conside able compu a ional powe and
obus algo i hms o be op imised o ime pe iods conside ing 24 o 48 hou s. Such a me hodology
does no ha e (ye ) he capabili y o sol e big sys ems o 8 760 hou s o conside a ull yea .
We ha e add essed his issue in he s udy cases by analysing wo e e ence days, hen ex ac ing
conclusions o he ull yea .
• La ge sys ems: sys ems wi h a la ge numbe o non-linea de ices such as pumps, pipes o u -
bines, a e demanding o e en in ac able o he sol e ’s algo i hm. Al hough his issue has been
dampened by linea ising some hyd aulic cons ain s, i is s ill a e y p esen issue.
• Ini ialisa ion: he abili y o ind global op imum o e en ind a solu ion is highly dependen on he
ini ialisa ion alues o he a iables. This is specially ele an on la ge sys ems. Fixing he alues
o a iables wi h p io knowledge does also help o each global minimum solu ions.
Relaxa ion esul s
In his sec ion we show he esul s om es ing h ee modelling s a egies o he pump de ice: consid-
e ing an equali y quad a ic cha ac e is ic cu e cons ain , inequali y cha ac e is ic cu e cons ain (3.11)
and linea izing he cha ac e is ic cu e exp ession (3.16). Fu he mo e, we explo e se e al Bonmin sol e
algo i hms o he di e en op imisa ion p oblems: Quesada and G ossman (B-QG), B anch and Bound
(B-BB), Ex ended Cu ing Plane (B-ECP) and Ou e App oxima ion (B-OA); which we e he algo i hms
ha pe o med he bes in he analysed p oblems.
Sec ion 3.3.1 comp esses all o he de ini ions and elaxa ions, howe e below ollows a quick summa y
o in oduce he esul s:
The head exp ession o a a iable speed pump is gi en by a quad a ic cons ain , bo h in e ms o low
and o a ional speed. Fo he 𝑖- h pump, a ime 𝑡:
𝐻𝑖(𝑡)=(𝑛𝑖(𝑡))2𝐴𝑖−𝐵𝑖(𝑄𝑜𝑢𝑡,𝑖(𝑡))2.
In [61] is p oposed o ans o m he p e ious exp ession in o an inequali y. This modi ica ion se s he
wo king a ea o he pump and allows o he emo al o he o a ional speed a iable 𝑛𝑖(𝑡):
𝐻𝑖(𝑡)≤𝑛2
𝑖𝐴𝑖−𝐵𝑖(𝑄𝑜𝑢𝑡,𝑖(𝑡))2.
40
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
The p e ious elaxa ion suppo s a linea app oxima ion. This can be achie ed by gene a ing a piecewise
unc ion o 𝑁𝐿linea unc ions ha app oxima e he cu e inside he wo king limi o he pump [𝑄𝑖,𝑄𝑖].
This app oach does no only educe he complexi y o he dynamic head exp ession bu o he hyd aulic
powe as well.
To educe he impac o he app oxima ion in he solu ion and ensu e ha he model e u ns inside he
ac ual dynamic head cu e we ook a conse a i e app oach by se ing he linea app oxima ion below i .
A linea cons ain is buil pe each segmen ha app oxima es he cu e, each consis ing in an inequali y
o a oid using bina y a iables as in a egula piecewise unc ion:
𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖
𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...𝑁𝐿.
The e o e, by inco po a ing he app oxima ion we eplace a quad a ic cons ain o 𝑁𝐿linea cons ain s
and 2 ex a a iables pe s ep ime o op imisa ion.
𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖
𝑁𝐿,𝑖 𝑙=1,...𝑁𝐿
𝐻𝑙,𝑖 =𝑛2
𝑖𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖)2𝑙=1,...𝑁𝐿
The e o e, by applying his we do no use a quad a ic exp ession bu we add 𝑁𝐿cons ain s and 2 ex a
a iables pe ime s ep o he p oblem.
We es ed 5 di e en sys ems wi h 6 di e en algo i hms: Case C0 is explained in de ail in Sec ion 3.4.1
and he emaining 4 in Sec ion 3.4.2. Case C0 conside s 5 ime s eps and consis s on a wo ese oi
sys em wi h wo pumps, one u bine, a PV sys em connec ed o he g id and he sizing o a possible
ba e y. The o iginal execu ion ime was 16.75 seconds. Cases C1, C2, C3 and C4 consis in wo 24
hou ypical a e aged days ( o a o al o 48 ime s eps), one o summe and one o win e , o e a
sys em wi h wo ese oi s, a g id connec ed pump and a PV pump which is no connec ed o he g id.
Case C2 conside s a pump as a u bine, in case C3 he PV plan is connec ed o he g id as well and
case C4 op imises he ope a ion o he sys em wi h bo h he PV plan connec ed o he g id and a pump
unning as a u bine. The sou ce o he da a used o analyse his sys em is a eal case scena io nea he
Eb e i e in he egion o Ca alunya (Spain). The o iginal execu ion imes we e 9 minu es, 12 minu es,
65 minu es and 7 minu es espec i ely.
We measu ed he pe o mance o he compu a ions in e ms o execu ion ime 𝑇𝑒(s) and inal cos alue
𝐺(€). The elaxa ion echniques mus deli e lowe execu ion imes and no dis ance he solu ion om
he eal global op imum, which could de i e om he elaxa ions de ining a di e en p oblem. The s udy
cases we e sol ed using an In el i5-8265U CPU @ 1.60 GHz lap op wi h 8 GB o RAM. We an each case
o a o al o 10 expe iences. Howe e , in la ge execu ion ime cases only 2 expe iences we e sol ed,
which is he case o B-BB cases C2 and C3 wi h equali y cons ain , B-BB case C2 wi h 3 in e al linea
cons ain and B-BB case C1 wi h 4 in e al linea cons ain .
The box plo s displayed in Figu es 3.11a, 3.11b and 3.11c compa e he execu ion imes o each anal-
ysed echnique and algo i hm. B-OA is no p esen ed since i esul ed simila o B-QG. A s a symbol (⋆)
ma ks hose cases ha did no con e ge o a solu ion o a gi en me hod and algo i hm. Figu e 3.11a
compa es he equali y (Eq) me hod wi h inequali y (Ine), Figu e 3.11b compa es he equali y wi h lin-
ea ized app oxima ion wi h 3 in e als (Lin3) and las ly Figu e 3.11c compa es equali y and linea ized
wi h 4 in e als (Lin4).
Table 3.1 summa ises he esul s o B-BB, B-QG, B-OA and B-ECP o each me hod and case. Base
alues a e highligh ed wi h unde line, while he o he alues exp ess in pe cen age he ela i e di e ence
o he base alue.
41
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
01234
Time (u. .)
−1
0
1
SoC, Powe (p.u.)
SoC
Powe
Figu e 3.16 –Ba e y s a e o cha ge and powe (de ined posi i e i abso bed).
Rese oi 1
Pumps
Rese oi 0
I iga ion
Pipe
PV Ba e y
G id
Hyd o
Powe
Figu e 3.17 –CR Les Planes i Aixalelles s udy case base sys em.
0
6
12
18
23
0
100
200
Demand (m3/h)
Time (h)
S
W
Figu e 3.18 –A e age daily i iga ion demand on CR Les Planes i Aixalelles (S: Summe , W: Win e ). Real da a
om 1 yea and 90% con idence in e al.
48
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
PV plan is se o sizing. The uppe ese oi has a capaci y o 13 000 m3and is limi ed o a minimum
olume o 9 000 m3, which co esponds o 3 days o au onomy du ing he i iga ion season. This lowe
limi is a bi a y and se by he plan ope a o . To main ain ope abili y, i s ini ial and inal olumes, 𝑊𝑅1(𝑡0)
and 𝑊𝑅1(𝑡𝑓) espec i ely, a e se o be wi hin a ±5 % ange (3.38). A su icien ly la ge ese oi models
he i e . Table 3.5 summa ises he base case cha ac e is ics.
1,05𝑊𝑅1(𝑡0)≥𝑊𝑅1(𝑡𝑓)≥0,95𝑊𝑅1(𝑡0)(3.38)
Table 3.5 –Cha ac e is ics o he case’s elemen s
De ice Cha ac e is ics
Rese oi 1 Volume ∈[9 000, 13 000] m3
Heigh w. . . Rese oi 0 ∈[105, 111] m
Pipe Quad a ic losses coe . = 60 s2/m5
Pumps𝑎Powe = 110 kW, 𝜂= 0,8, 𝜂𝑝𝑎𝑡= 0,5
Flow ∈[0,6, 1,9] p.u.
Nominal low = 0,056 m3/s
A = 120 m, B = 3 865 s2/m5
PV Peak powe = 215,3 kWp
Con e e e iciency = 0,98
Ba e y Max. size ene gy/powe 200 kWh/200 kW
Allowed s a e o cha ge ∈[0,2, 1,0] p.u.
Cha ge/discha ge e iciency = 0,8
𝑎𝜂e iciency and 𝜂𝑝𝑎𝑡e iciency as a u bine
The objec i e unc ion designed o his s udy conside s he cos o buying 𝑐𝑏𝑢𝑦,𝑔and p ice o selling 𝑐𝑠𝑒𝑙𝑙,𝑔
elec ici y o he g id, as well as he capi al expendi u es o sizing a new ba e y 𝑐𝑝,𝑏𝑎𝑡,𝑐𝑒,𝑏𝑎𝑡.
𝑓(x)= 𝑇
∑
𝑡=0[𝑝𝑓,𝑔(𝑡)𝑐𝑏𝑢𝑦,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)𝑐𝑠𝑒𝑙𝑙,𝑔(𝑡)]Δ𝑡+
+𝑝𝑑𝑖𝑚,𝑏𝑎𝑡𝑐𝑝,𝑏𝑎𝑡+𝑒𝑑𝑖𝑚,𝑏𝑎𝑡𝑐𝑒,𝑏𝑎𝑡,(3.39)
whe e xis he decision ec o composed o 𝑝𝑓,𝑔 (kW), he powe consumed om he g id and 𝑝𝑡,𝑔(kW)
he powe injec ed o he g id. Δ𝑡is he ime s ep, which is equal o 1h in he s udy case. Based on
i iga ion demand (Figu e 3.18), he case s udy conside s, in pa allel, wo s anda d days which co espond
o summe and win e and also de e mine he i adiance on he PV plan . 𝑝𝑑𝑖𝑚,𝑏𝑎𝑡(W) and 𝑒𝑑𝑖𝑚,𝑏𝑎𝑡(Wh)
a e he powe and ene gy sized o he ba e y. The elec ici y p ices a e based on he ma ke om he
Ibe ian Peninsula, and he cos s o sizing he ba e y ene gy 𝑐𝑒,𝑏𝑎𝑡 =0,2054 €/(Wh day) and powe
𝑐𝑝,𝑏𝑎𝑡 =0,0410 €/(W day) a e based on [74] o a Li-ion ba e y, no malised o 1 day and conside ing
20 yea s o he p ojec li e ime.
We conside ed he ollowing modi ica ions o e he base case, which a e de ailed in Figu e 3.19.
1. Pump as u bine: The pump connec ed o he g id can now be ope a ed e e sibly, i.e. pump as
u bine (PaT), ac ing as a low e iciency F ancis u bine. The o he pump is kep connec ed o he
PV and ba e y sys em. The PaT is modelled as a pump and a u bine ope a ing in pa allel, wi h
he addi ion o (3.40) p e en ing hem om ope a ing simul aneously.
𝑄𝑜𝑢𝑡,𝑇𝑢𝑟𝑏𝑖𝑛𝑒(𝑡)𝑄𝑜𝑢𝑡,𝑃𝑢𝑚𝑝(𝑡)=0 ∀𝑡 (3.40)
49
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
2. G id connec ed: Bo h pumps a e connec ed o a common bus wi h he g id, PV panels and ba e y
sys em.
3. PaT + G id connec ed: Fusing bo h p e ious cases, elec ical elemen s a e connec ed o a common
bus wi h he g id and one pump is allowed o un in e e sible mode.
Case 1 Case 2 Case 3
PAT PAT
Figu e 3.19 –Va ia ions on he s udy case. De ices which p esen changes a e highligh ed.
O e all, in his s udy case, we analyse whe he he e e sible use o pumps allows s o ed ene gy o be
ha nessed. In addi ion, we also conside he sizing o ba e ies o de e mine he e ec o he p ice o
ene gy on he decision o ins all such equipmen .
Resul s
The esul s ob ained om he base case (Figu e 3.17) ep esen an op imal pe o mance acco ding o
wha is cu en ly known. This means using he PV pumping sys em a i s ull po en ial and backing
i up wi h he g id-connec ed pump du ing low-cos pe iods. No ba e y is ound equi ed o sized o
any o he cases s udied due o i s high capi al cos s. The sys em wo ks a ull capaci y in summe and
is unde u ilised in win e , as can be obse ed on Figu es 3.20a and 3.20b. Figu e 3.20a displays he
powe s consumed (>0) by he PV plan 𝑃𝑃𝑉, PV pump 𝑃𝑝,𝑃𝑉, g id connec ed pump 𝑃𝑝,𝑔, he a ailable
PV powe
𝑃𝑃𝑉 and he powe exchanged wi h he g id 𝑃𝑔, as well as he cos and sell p ice o elec ical
ene gy. Figu e 3.20b does he same o he lows deli e ed o ese oi 1 om bo h pumps 𝑄𝑝,𝑃𝑉 and
𝑄𝑝,𝑔and he i iga ion demand 𝑄𝑖𝑟𝑟, along wi h he olume p esen a he ese oi and i s bounds. This
nomencla u e is kep h ough he o he cases.
1. Pump as u bine: Allowing he g id connec ed pump o ope a e as a u bine a o s he usage o
he pumping acili y as a PV s o age sys em, in which he PV pump ans e s wa e o he highes
ese oi du ing peak i adiance hou s, hen he PaT con e s i s po en ial ene gy in o elec ici y o
eed he g id du ing high sell p ice pe iods. This beha iou is illus a ed in Figu es 3.21a-3.21b
in compa ison o he unde u ilisa ion om he base case (Figu es 3.20a-3.20b). Summe season
p esen s no di e gence om he base case and is he e o e omi ed om his discussion.
2. G id connec ed: Connec ing he whole acili y o he g id allows o ene gy exchanges, which ex-
ac he ull po en ial o he PV sys em. Pumps ope a ion is escheduled, as Figu es 3.22a-3.22b
po ays, and he a ailable PV powe ully exploi ed.
3. PaT + G id connec ed: In such ci cums ances he op imisa ion mus decide whe he o injec he
ene gy o he g id s aigh om he PV plan o s o e i in he o m o po en ial ene gy in he ese oi
and injec i du ing highe sell p ice pe iods. Wi h he da a ed and pa ame e s se o he s udy case,
he esul ing ope a ion (Figu es 3.23a-3.23b) indica es ha unning he PaT du ing he highes sell
p ice hou s a win e is he op imal scheduling.
Table 3.6 summa ises he ope a ion and sizing cos s pe day, a e simula ing each case o summe
and win e condi ions. I also displays he compu a ion ime in seconds on a 11 h Gen In el Co e i7 @
3.40 GHz lap op wi h 16,0 GB o RAM. F om Table 3.6, i can be seen ha he Base case is he mos
50
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Time (h)
0
6
12
18
23
P ice (€/MWh)P ice (€/MWh)
P (kW)P (kW)
300
200
100
300
200
200
100
0
-100
-200
200
100
0
-100
-200
100
Summe
Win e
(a) Resul ing consumed powe .
Qp,PV Qp,g Qi
10000
8000
0.1
0.0
13000
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)Volume (m3)
Summe
0.1
0.0
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)
Win e
10000
8000
13000
Volume (m3)
(b) Flows and Rese oi 1 olume.
Figu e 3.20 –Resul s o he base case.
Time (h)
0
6
12
18
23
P ice (€/MWh)P ice (€/MWh)
P (kW)P (kW)
300
200
100
300
200
200
100
0
-100
-200
200
100
0
-100
-200
100
Summe
Win e
(a) Resul ing consumed powe .
Qp,PV Qp,g Qi
10000
8000
0.1
0.0
13000
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)Volume (m3)
Summe
0.1
0.0
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)
Win e
10000
8000
13000
Volume (m3)
(b) Flows and Rese oi 1 olume.
Figu e 3.21 –Resul s o PaT case (Case 1).
51
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Time (h)
0
6
12
18
23
P ice (€/MWh)P ice (€/MWh)
P (kW)P (kW)
300
200
100
300
200
200
100
0
-100
-200
200
100
0
-100
-200
100
Summe
Win e
(a) Resul ing consumed powe .
Qp,PV Qp,g Qi
10000
8000
0.1
0.0
13000
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)Volume (m3)
Summe
0.1
0.0
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)
Win e
10000
8000
13000
Volume (m3)
(b) Flows and Rese oi 1 olume.
Figu e 3.22 –Resul s o g id connec ed case (Case 2).
Time (h)
0
6
12
18
23
P ice (€/MWh)P ice (€/MWh)
P (kW)P (kW)
300
200
100
300
200
200
100
0
-100
-200
200
100
0
-100
-200
100
Summe
Win e
(a) Resul ing consumed powe .
Qp,PV Qp,g Qi
10000
8000
0.1
0.0
13000
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)Volume (m3)
Summe
0.1
0.0
-0.1
0
6
12
18
23
Time (h)
Q (m3/s)
Win e
10000
8000
13000
Volume (m3)
(b) Flows and Rese oi 1 olume.
Figu e 3.23 –Resul s o g id connec ed + PaT case (Case 3).
52
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
expensi e solu ion, whe eas emodelling o he Case 3 opology (g id connec ed PV + PaT) esul s he
mos p o i able op ion.
Table 3.6 –Cases summa y
Case Base Case 1 Case 2 Case 3
Cos [€/day] 12,50 7,03 -12,05 -15,30
Exec. ime [s] 4 10 5 12
3.4.3 Comuni a de Regan s Seg ià-Sud
This s udy case, p esen ed in [76], is based on he acili y o he Comuni a de Regan s (CR) Seg ià-Sud
(Sec ion 2.4). The o iginal i iga ion sys em akes wa e om he i e Eb e and aises i o a sys em o
5 ese oi s h ough 4 pumping s a ions composed o se e al kW o MW pumps. The e ical dis ance
be ween he i e and he highes ese oi is abou 380 m. The elec ical powe ha supplies he pumps
comes om he powe g id and om h ee PV plan s wi h 523,00 kWp, 527,50 kWp and 274,68 kWp
ins alled peak powe . The PV plan s a e owned by he i iga ion communi y and a e no g id connec ed.
Figu e 3.24 shows a scheme o he CR Seg ià-Sud acili ies and Table 3.7 summa ises he cha ac e is ics
o i s de ices.
I 5
Pipe45
Pipe14
Pipe01
Pipe12
Pipe13
R4
R2
R3
R5
G id
I 4
I 3
I 2
R1
R0
PS1
PS2 PS3
I 1
(a) global
P1g
PS1
PV24
P23s
P23gP22g
P24s
P24g
PV23
PS2
P3g
P3s
PV3
PS3
(b) pumping s a ions
Figu e 3.24 –CR Seg ià-Sud Base case sys em.
The pumping s a ions cu en ly ope a e be ween midnigh and 8 a.m., when bo h he elec ical powe and
ene gy e m p ices a e he lowes . Du ing he day, he ene gy p oduced by he PV plan s is used o d i e
he PV pumps i enough sola powe is a ailable. I iga ion equi emen s a e a hei highes in summe ,
bu in win e , he need o i iga ion conside ably educes. Figu e 3.25 displays he a e age daily i iga ion
demand o each ese oi s a i ied in win e and summe seasons, wi h a 95 % con idence in e al2.
Ou scope is limi ed by he scalabili y issues he op imisa ion me hodology p esen s (Sec ion 3.3.4). To
educe he complexi y o he p oblem we spli he sys em in wo sec ions uppe and lowe , as depic ed
in Figu es 3.26-3.27. The subdi isions assume he ollowing p emises:
•Lowe sec ion: Rese oi R0 ( i e Eb e) has in ini e capaci y, modelled as a la ge enough alue,
such ha i can p o ide and abso b as much wa e as equi ed wi hou i ha ing an e ec on i s
manome ic heigh . I iga ion om ese oi s R2 and R3 a e di ec ly agg ega ed o R1 and hei
pe inen hyd aulic elemen s a e no conside ed. I iga ion om ese oi R5 is di ec ly agg ega ed
o R4 and i s pe inen hyd aulic elemen s a e no conside ed.
2We could no e ec i ely ob ain eliable da a om Rese oi 4, hus we assumed he demand o be simila o Rese oi 5
since hey a e loca ed nex o each o he and sha e simila al i udes and c op a eas [22]
53
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 3.7 –Cha ac e is ics o he CR Seg ia-Sud case’s de ices
De ice Cha ac e is ics
Rese oi s R0: 𝑊∈[120, 240] 103m3,𝑧∈[129, 131] m
R1: 𝑊∈[96, 143] 103m3,𝑧∈[336, 339] m
R2: 𝑊∈[250, 297] 103m3,𝑧∈[355, 365] m
R3: 𝑊∈[70, 86] 103m3,𝑧∈[418, 421] m
R4: 𝑊∈[184, 270] 103m3,𝑧∈[427, 431] m
R5: 𝑊∈[128, 186] 103m3,𝑧∈[448, 451] m
Pipes Pipe01: 𝐾= 27,90 s2/m5
Pipe12: 𝐾= N/D
Pipe13: 𝐾= 6,12 s2/m5
Pipe14: 𝐾= 27,81 s2/m5
Pipe45: 𝐾= 6,10 s2/m5
Pumps𝑎P1 (x3): 𝑃= 3 200 kW, 𝜂= 0,922, 𝜂𝑝𝑎𝑡= 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 1,06 m3/s,
A = 300 m, B = 62,208 s2/m5
P22 (x1): 𝑃= 315 kW, N/D
P23 (x2): 𝑃= 250 kW, 𝜂= 0,82, 𝜂𝑝𝑎𝑡= 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 0,285 m3/s,
A = 105,81 m, B = 324 s2/m5
P24 (x2): 𝑃= 1 250 kW, 𝜂= 0,92, 𝜂𝑝𝑎𝑡 = 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 0,913
m3/s, A = 148 m, B = 103,7 s2/m5
P3 (x2): 𝑃= 160 kW, 𝜂= 0,86, 𝜂𝑝𝑎𝑡 = 0,7, 𝑄∈[0,6, 1,2] p.u., 𝑄𝑛= 0,469 m3/s,
A = 37,8 m, B = 38,9 s2/m5
PV PV23: 𝑃𝑖𝑛𝑠𝑡= 523,0 kWp, 𝜂= 0,98
PV24: 𝑃𝑖𝑛𝑠𝑡= 527,5 kWp, 𝜂= 0,98
PV3: 𝑃𝑖𝑛𝑠𝑡= 274,7 kWp, 𝜂= 0,98
𝑎𝜂e iciency and 𝜂𝑝𝑎𝑡e iciency as a u bine
0
6
12
18
23
0
300
600
Demand (m3/h)
Time (h)
(a) Rese oi 1
0
6
12
18
23
0
300
600
Demand (m3/h)
Time (h)
(b) Rese oi 2
0
6
12
18
23
0
300
600
Demand (m3/h)
Time (h)
(c) Rese oi 3
0
6
12
18
23
0
300
600
Demand (m3/h)
Time (h)
(d) Rese oi 5 (same o Rese oi 4)
Figu e 3.25 –CR Seg ià-Sud wa e consump ion o i iga ion.
54
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
•Uppe sec ion: Rese oi R0 will p o ide he equi ed amoun o wa e o ese oi R1, hence he
la e has in ini e capaci y, modelled as a la ge enough alue. Rese oi s R2 and R3 and hei
pe inen hyd aulic elemen s a e no conside ed.
These assump ions en ail he ollowing cons ain s on he p esen analysis:
• I is no possible o include ese oi s R2 and R3 and hei pe inen hyd aulic elemen s.
• Re e se low canno be conside ed o Pipe01 on he lowe sec ion and o Pipe14 on he uppe
sec ion.
• The o al ope a ing cos ob ained by he op imisa ion does no co espond o he o al ope a ing
cos o he acili y.
• The o al ope a ing cos o he acili y is no ob ainable due o he emo al o ese oi s R2 and R3.
• An es ima e o al cos o ope a ing he R0-R1-R4-R5 ci cui can be ob ained by adding he Base
case ope a ing cos s o he le -ou pumping s a ion on ei he sec ion (cos s om pumping s a ion
PS1 on he uppe sec ion and cos s om pumping s a ion PS3 on he lowe sec ion).
I 5
Pipe45
Pipe14
Pipe01
Pipe12
Pipe13
R4
R2
R3
R5
G id
I 4
I 3
I 2
R1
R0
PS1
PS2 PS3
I 1
LOWER UPPER
Figu e 3.26 –CR Seg ià-Sud sys em di ision.
Pipe14
Pipe01 R4
G id
I 4+5
I 1+2+3
R1
R0
PS1 PS2
(a) lowe
I 5
Pipe45
Pipe14 R4 R5
G id
I 4
R1
PS2 PS3
(b) uppe
Figu e 3.27 –CR Seg ià-Sud lowe and uppe di isions and assump ions.
Fo each di ision we conside ed analogous modi ica ions o e he Base case as o he CR Les Planes i
Aixalelles analysis (see Sec ion 3.4.2):
1. Pump as u bine: The g id connec ed pump can be ope a ed e e sibly (PaT), wi h a lowe e iciency
conside ed 𝜂𝑝𝑎𝑡 = 0,7 based on [41]. The o he pump is kep connec ed o he PV sys em. The
pumps selec ed o such unc ion a e Pump24g in lowe sec ion and Pump3g in uppe sec ion. The
PaT is modelled as s a ed in Sec ion 3.3.1, wi h a pump and a u bine ope a ing in pa allel and he
addi ion o (3.40) p e en ing hem om ope a ing simul aneously.
2. G id connec ed: All PV sys ems and pumps a e connec ed o a common bus o he g id. The sys em
is allowed o impo and expo elec ici y om he g id applying he co esponding cos s and p ices.
55
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
3. PaT + G id connec ed: Combining bo h p e ious cases, all o he elec ical elemen s a e connec ed
o a common bus wi h he g id and he o iginally g id connec ed pump is allowed o un in e e sible
mode (Pump24g in lowe sec ion and Pump3g in uppe sec ion).
No ice ha , due o imposing he condi ion o cycle by limi ing he minimum olume alue o he ese oi s
a he end o he ime pe iod (see Sec ion 3.3.1), he o al olume o wa e ha he sys em ob ains om
he i e is s ic ly he i iga ion demand on all o he cases.
The objec i e o his s udy case is o analyse he beha iou o a mul i- ese oi sys em and he e ec s o
unning a PaT a se e al loca ions. We de ined wo ep esen a i e days o he elec ical g id cos s and
GHG emission ac o , depic ed in Figu e 3.28, which consis o he a e age daily e olu ion o he mon hs
o Janua y (win e ) and Augus (summe ) o 2024 [77]. We also analyse he sensi i i y o he solu ion o
he luc ua ion o pa ame e s o ele ance which p esen a signi ican unce ain y o a e likely o e ol e in
he u u e: i iga ion demand, p ice o expo ing elec ici y o he g id and he e iciency o unning PaTs.
GHG,g cbuy,g csell,g
0
6
12
18
23
0,12 300
200
100
Time (h)
P ice (€/MWh)
Emission ac o
( CO2-eq/MWh)
0,08
0,04
(a) win e
GHG,g cbuy,g csell,g
0
6
12
18
23
0,12 300
200
100
Time (h)
P ice (€/MWh)
Emission ac o
( CO2-eq/MWh)
0,08
0,04
(b) summe
Figu e 3.28 –G id equi alen GHG emission ac o , cos o elec ici y and sell p ice o he de ined ypical days.
Da a om [77].
We de ined he objec i e unc ion o he analysis o he CR Seg ià-Sud sys em om he poin o iew
o he communi y, which objec i e is o educe he ope a ing cos s. The unc ion conside s he cos o
buying 𝑐𝑏𝑢𝑦,𝑔 (€/MWh) and p ice o selling 𝑐𝑠𝑒𝑙𝑙,𝑔 (€/MWh) elec ici y o he g id and he ene gy impo s
𝑝𝑓,𝑔(MW) and expo s 𝑝𝑡,𝑔(MW):
𝑓(x)= 𝑇
∑
𝑡=0[𝑝𝑓,𝑔(𝑡)𝑐𝑏𝑢𝑦,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)𝑐𝑠𝑒𝑙𝑙,𝑔(𝑡)]Δ𝑡 (3.41)
We also de ined an objec i e unc ion om he pe spec i e o he adminis a ion o a g id ope a o wi h
he pu pose o educing he o e all GHG emissions o he g id, which we applied o Case 3 and named
i Case 3-em:
𝑓(x)= 𝑇
∑
𝑡=0[𝑝𝑓,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)]𝑓𝐺𝐻𝐺,𝑔(𝑡)Δ𝑡 (3.42)
wi h 𝑓𝐺𝐻𝐺,𝑔 ( CO2-eq/MWh) he GHG emission ac o o he g id. This objec i e unc ion assumes an
a e agebeha iou o he g idand does no dis inguish he echnologiespa icipa ing in he dailyma ke .
Resul s (Uppe )
This sec ion p esen s he esul s ob ained om he uppe sec ion o he i iga ion sys em analysis, which
a e summa ised on Table 3.8 and Figu es 3.29-3.33. The compu a ion ime o each case, unning he
COIN-OR Bonmin algo i hms [75] on a 11 h Gen In el Co e i7 @3.40 GHz lap op wi h 16,0 GB o RAM,
56
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 3.8 –Resul s (Uppe )
Case Base Case 1 Case 2 Case 3 Case 3-em
Compu a ion ime [s] 5,80 23,44 34,92 14,81 39,20
Ene gy impo ed a e age [kWh/d] 1 233,51 1 074,86 227,30 234,78 783,74
” win e [kWh/d] 0,00 0,00 1,20 0,00 17,01
” summe [kWh/d] 2 467,02 2 179,72 453,39 469,56 1 550,46
Ene gy expo ed a e age [kWh/d] - 202,17 1 067,50 1 051,99 1 376,02
” win e [kWh/d] - 385,55 2 071,96 2 027,12 2 089,75
” summe [kWh/d] - 18,78 63,04 76,86 662,29
Maximum impo ed powe win e [kW] 0,00 0,00 1,20 0,00 17,01
” summe [kW] 485,11 501,71 375,46 391,64 311,12
Maximum expo ed powe win e [kW] - 112,00 480,50 480,50 480,50
” summe [kW] - 18,78 57,84 57,84 219,69
GHG emissions a e age [kgCO2-eq/d] 119,17 94,60 -52,92 -51,96 - 68,43
” win e [kgCO2-eq/d] 0,00 -34,68 -144,56 -143,20 -146,15
” summe [kgCO2-eq/d] 238,35 223,89 38,71 39,28 9,29
Ene gy expense a e age [€/d] 166,85 144,89 31,19 32,17 118,87
” win e [€/d] 0,00 0,00 0,15 0,00 3,11
” summe [€/d] 333,70 289,77 62,23 64,33 243,62
Ene gy income a e age [€/d] - 26,24 87,30 88,41 119,61
” win e [€/d] - 50,03 167,19 167,87 163,56
” summe [€/d] - 2,45 7,40 8,95 75,65
To al cos a e age [€/d] 166,85 118,65 -56,10 -56,24 -0,74
” win e [€/d] 0,00 -50,03 -167,04 -167,87 -160,45
” summe [€/d] 333,70 287,32 54,83 55,34 158,67
57
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Win e
Pumping s a ion 3
Summe Pumping s a ion 2
P (kW)
0,12
500
0
-500
0,08
0,04
Pumping s a ion 2 Pumping s a ion 3
PPV PPV Pp24s Pp24g PgPPV PPV Pp3s Pp3g Pg
GHG ( CO2-eq/MWh)
P (kW)
300
0
-300
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
Time (h)
0
6
12
18
23
P (kW)
300
0
-300
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
Time (h)
0
6
12
18
23
P (kW)
500
0
-500
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
(a) Resul ing consumed powe
1
0
270
230
184
-1
Rese oi 5
Summe Rese oi 4
Rese oi 5
Win e Rese oi 4
Q (m3/s)WR4 (103m3/s)
1
0
186
160
128
-1
Q (m3/s)WR5 (103m3/s)
1
0
270
230
184
-1
Q (m3/s)WR4 (103m3/s)
1
0
186
160
128
-1
Q (m3/s)WR5 (103m3/s)
Time (h)
0
6
12
18
23
Time (h)
0
6
12
18
23
(b) Flows and olume o ese oi s R4 and R5
Figu e 3.33 –CR Seg ià-Sud uppe esul s - emissions case (Case 3-em).
64
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 3.9 –Resul s (Lowe )
Case Base Case 2 Case 3 Case 3-em
Compu a ion ime [s] 12,36 399,11 1 273,53 15,44
Ene gy impo ed a e age [kWh/d] 13 571,40 13 061,10 13 567,10 15 251,30
” win e [kWh/d] 5 371,68 5 107,54 5 695,48 4 680,16
” summe [kWh/d] 21 771,20 21 014,60 21 438,70 25 822,40
Ene gy expo ed a e age [kWh/d] - 551,58 620,40 930,01
” win e [kWh/d] - 1 000,09 971,06 390,21
” summe [kWh/d] - 103,07 269,75 1 469,81
Maximum impo ed powe win e [kW] 1 245,88 1 112,90 2 484,61 1 054,80
” summe [kW] 2 315,78 2 272,36 3 853,23 3 448,49
Maximum expo ed powe win e [kW] - 265,56 381,98 168,52
” summe [kW] - 61,60 166,68 875,00
GHG emissions a e age [kgCO2-eq/d] 1 153,78 1 053,35 1 049,50 652,74
” win e [kgCO2-eq/d] 464,23 361,76 414,46 275,01
” summe [kgCO2-eq/d] 1 843,32 1 744,94 1 684,55 1 030,47
Ene gy expense a e age [€/d] 1 754,31 1 706,36 1 698,71 2 432,11
” win e [€/d] 515,31 505,64 538,14 770,86
” summe [€/d] 2 993,32 2 907,08 2 859,28 4 093,36
Ene gy income a e age [€/d] - 46,68 66,50 110,64
” win e [€/d] - 81,57 105,69 34,75
” summe [€/d] - 11,79 27,31 186,53
To al cos a e age [€/d] 1 754,31 1 659,68 1 632,21 2 321,47
” win e [€/d] 515,31 424,06 432,44 736,10
” summe [€/d] 2 993,32 2 895,30 2 831,97 3 906,83
65
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
En i onmen al analysis
F om a GHG emissions poin o iew, conside ing he ypical day g id’s equi alen CO2 ac o e olu ion
in summe and win e (Figu e 3.28) and null o he i iga ion sys em, esul s in posi i e emissions o all
cases. Case 3-em, as expec ed, de i es he bes o such a pu pose and u ilises i s ene gy s o age ca-
pabili ies o maximise he ene gy deli e ed o he g id du ing high emission ac o hou s (mos ly e ening
in summe ). Fai compensa ions should howe e apply o he i iga ion communi y since his ope a ion
s a egy is no as economically bene icial as Case 3 solu ion wi h an a e age di e ence o 689,26 €/d o
an a e age educ ion o 396,76 kgCO2-eq/d in emissions.
The daily wa e consump ion is main ained o all he cases, as s a ed abo e, since a cycle condi ion is
imposed in he ese oi de ice. In essence, he modelling o he sys em implici ly conside s he ex a
daily impac on he wa e sou ce and cancels i .
Sensi i i y analysis
This sec ion co e s a sensi i i y analysis on he mos ele an pa ame e s o he uppe sec ion o he
Seg ià-Sud i iga ion sys em. The esul s o he sensi i i y analysis a e displayed in Table 3.10 and he
spide plo s in Figu e 3.38. Spide plo s plo a cu e o each a iable on a single 𝑥−𝑦plo showing he
change in goal alue o e a ela i e change o he a iable alues om he base case. Thei pu pose is o
display in o ma ion abou a ce ain numbe o a iables including hei limi s, impac on he ou come and
he amoun o change equi ed o each a b eak e en poin [78].
We applied he ollowing a ia ions o e he base case:
• I iga ion demand 𝑄𝑖𝑟𝑟±20 %. As e iewed in Sec ion 2.1, he e is an in e es om he adminis a-
ion o inc ease he sha e o i iga ed land as well as a educ ion o he wa e demand om hese
c ops. We concei e wo scena ios: an inc ease o he gene al i iga ion demand due o a subs i u-
ion o d y land o i iga ed o a dec ease o he gene al i iga ion demand d i en by wa e e iciency
equi emen s.
• Selling p ice o elec ici y 𝑐𝑠𝑒𝑙𝑙 ±20 % om 8:00 h o 16:00 h. The mass implemen a ion o sola
PV may d i e ma ke p ices down du ing high in ensi y sola hou s, as i has been no iced om sel -
consump ion su plus p ices eaching nega i e alues in Spain [77]. We also analyse he opposi e
scena io whe e he ma ke p ices inc ease ins ead, which would dec ease he incen i es o d i e
he acili ies as an ene gy s o age sys em.
• E iciency o PaT 𝜂𝑝𝑎𝑡 ∈(0,5, 0,8). As s a ed in Sec ion 3.3.1, i is no a i ial ask o de ine he
cha ac e is ics and beha iou o a PaT, he e o e we based he ange o alues o i s pe o mance
in p e ious wo k and li e a u e [41, 68].
Table 3.10 –Sensi i i y analysis o al cos a e age (€/d). (𝑡) ma ks he cases whe e he sys em makes use o he
pump as a u bine.
Case Base Case 1 Case 2 Case 3
base 166,85 (𝑡)118,65 -56,10 (𝑡) -56,24
-20% 𝑄𝑖𝑟𝑟 95,90 (𝑡) 45,12 -126,13 (𝑡)-126,52
+20% 𝑄𝑖𝑟𝑟 267,63 (𝑡)214,98 24,35 24,35
-20% 𝑐𝑠𝑒𝑙𝑙 166,85 (𝑡)119,00 -40,10 (𝑡) -41,50
+20% 𝑐𝑠𝑒𝑙𝑙 166,85 (𝑡)118,28 -71,77 -71,77
𝜂𝑝𝑎𝑡= 0,5 166,85 (𝑡)137,22 -56,10 -56,10
𝜂𝑝𝑎𝑡= 0,6 166,85 (𝑡)125,62 -56,10 (𝑡) -56,34
𝜂𝑝𝑎𝑡= 0,8 166,85 (𝑡)112,00 -56,10 (𝑡) -56,63
66
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Win e
Pumping s a ion 2
Summe Pumping s a ion 1
Pumping s a ion 1 Pumping s a ion 2
Time (h)
0
6
12
18
23
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
Pp1g1 Pp1g2 Pg
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
PPV PPV Pp24s Pp24g Pg
Time (h)
0
6
12
18
23
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
(a) Resul ing consumed powe
Rese oi 4
Summe Rese oi 1
Rese oi 4
Win e Rese oi 1
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,4+5 Qp24s Qp24g
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
(b) Flows and olume o ese oi s R1 and R4
Figu e 3.34 –CR Seg ià-Sud lowe esul s - Base case.
67
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Win e
Pumping s a ion 2
Summe Pumping s a ion 1
Pumping s a ion 1 Pumping s a ion 2
Time (h)
0
6
12
18
23
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
Pp1g1 Pp1g2 Pg
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
PPV PPV Pp24s Pp24g Pg
Time (h)
0
6
12
18
23
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
(a) Resul ing consumed powe
Rese oi 4
Summe Rese oi 1
Rese oi 4
Win e Rese oi 1
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,4+5 Qp24s Qp24g
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
(b) Flows and olume o ese oi s R1 and R4
Figu e 3.35 –CR Seg ià-Sud lowe esul s - g id connec ed case (Case 2).
68
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Win e
Pumping s a ion 2
Summe Pumping s a ion 1
Pumping s a ion 1 Pumping s a ion 2
Time (h)
0
6
12
18
23
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
Pp1g1 Pp1g2 Pg
3000
0
-3000
300
200
100
P (kW)
P ice (€/MWh)
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
PPV PPV Pp24s Pp24g Pg
Time (h)
0
6
12
18
23
600
0
-600
300
200
100
P (kW)
P ice (€/MWh)
(a) Resul ing consumed powe
Rese oi 4
Summe Rese oi 1
Rese oi 4
Win e Rese oi 1
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2
0
2
-2
143
120
96
Q (m3/s)
WR1 (103m3/s)
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,4+5 Qp24s Qp24g
0
2
-2
270
230
184
Q (m3/s)
WR1 (103m3/s)
(b) Flows and olume o ese oi s R1 and R4
Figu e 3.36 –CR Seg ià-Sud lowe esul s - PaT + g id connec ed case (Case 3).
69
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Win e
Pumping s a ion 2
Summe Pumping s a ion 1
Pumping s a ion 1 Pumping s a ion 2
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
Time (h)
0
6
12
18
23
3000
0
-3000
P (kW)
Pp1g1 Pp1g2 PgPPV PPV Pp24s Pp24g Pg
3000
0
-3000
P (kW)
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
P (kW)
1000
0
-1000
0,12
0,08
0,04
GHG ( CO2-eq/MWh)
Time (h)
0
6
12
18
23
P (kW)
1000
0
-1000
(a) Resul ing consumed powe
Rese oi 4
Summe Rese oi 1
Rese oi 4
Win e Rese oi 1
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2
0
1
-1
143
120
96
Q (m3/s)
WR1 (103m3/s)
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
Time (h)
0
6
12
18
23
Qi ,4+5 Qp24s Qp24g
0
1
-1
270
230
184
Q (m3/s)
WR1 (103m3/s)
(b) Flows and olume o ese oi s R1 and R4
Figu e 3.37 –CR Seg ià-Sud lowe esul s - emissions case (Case 3-em).
70
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
C (€/d)C (€/d)
Change om base (p.u.)
0
0,8 1,0 1,2
200
-200
0,8 1,0 1,2
0
200
-200
Base G id connec ed
Pump as u bine PaT + g id
ηpa
Qi csell
base
Figu e 3.38 –Spide plo s esul ing om he sensi i i y analysis.
3.4.4 CEDER-CIEMAT
The s udy case o Cen o de Desa ollo de Ene gías Reno ables (CEDER)-Cen o de In es igaciones En-
e gé icas Medioambien ales y Tecnológicas (CIEMAT) is modelled as ollows in Figu e 3.39. The cen e
con ains 3 small ese oi s o 2 000 m3, 1 500 m3and 500 m3, a small 16 kW PV plan and a 40 kW u -
bine. The e is a bank o pumps wi h a nominal powe o 7,5 kW each, which can only ope a e a nominal
powe o be disconnec ed. The e o e, he Disc e ePumps model used allows he ac i a ion o an in ege
numbe o pumps, anging om 0 o he o al numbe o ins alled pumps—in his case, 4 pumps. Ini ially,
he pumps and u bines a e connec ed o a common bus along wi h he PV plan and he g id, supplying
he elec ical loads o he cen e i sel .
In o de o model he sys em in a Pyomo en i onmen , i is necessa y o in oduce se e al blocks. Fo
example, he elec ical loads block is used o model he cen e ’s demand, and he hyd aulic swi ch block
is used o supply ei he he uppe (R2) o middle (R1) ese oi . No e ha a sou ce block is used be ween
ese oi 1 and ese oi 2 o model a pipe wi h a con ollable al e wi hou losses.
The Disc e e Pump used in his case is modelled by adding o he Pump de ice he nex cons ain :
𝑃𝑒,𝑖(𝑡)=𝑃𝑛,𝑖𝑁𝑜𝑛,𝑖(𝑡) (3.44)
Whe e 𝑃𝑛,𝑖 he nominal powe o he pump and is in oduced as a pa ame e in o he model. On he
o he hand, 𝑁𝑜𝑛,𝑖(𝑡)is a in ege a iable ha de ines he numbe o wo king pumps, he a iable ha e a
minimum o 0 and a maximum o 𝑁𝑝𝑢𝑚𝑝𝑠 ha is he o al numbe o ins alled pumps.
Va ious cases a e ca ied ou o e alua e he ool and he CEDER sys em. Each case conside s di e en
ini ial condi ions and assump ions:
• Case 1: No ba e y no PV sizing is conside ed.
• Case 2: Possibili y o sizing a new ba e y and ex a PV powe .
• Case 3: Ba e y is al eady p esen and ex a PV powe can be sized.
The model is cons uc ed using da a p o ided by CEDER, such as elec ical demand and sola i adia ion
measu emen s. Addi ionally, ano he sou ce is used o ob ain olun a y p ice o he small consume
(PVPC) da a.
71
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Pumps
x4
Tu bine
R0
R2
R1
Pipe 10
Sou ce21
Pipe 02
Swi ch
PV
Load
Ba e y
G id
CEDER Sys em
Figu e 3.39 –CEDER case ep esen a ion wi h Pyomo blocks.
Fo each case, wo simula ions a e pe o med: one conside ing ypical summe da a and ano he con-
side ing ypical win e da a. This app oach allows he s udy o he ool’s po en ial in each season wi h
di e en i adiance le els, elec ical demand, and elec ici y p ices.
The ini ial condi ions o a mo e accu a e app oach assume ha ese oi s 1 and 2 a e comple ely emp y,
while ese oi 0 is a maximum capaci y. I a ba e y is conside ed, i is also assumed o be comple ely
discha ged. This app oach ensu es ha no s o age sou ce has ini ial ene gy, whe he elec ical o g a i-
a ional.
Resul s
In each case, a plo is p esen ed showing he balance o powe consumed and gene a ed, whe e powe
injec ed in o he ene gy balance node is nega i e, while he emaining powe is posi i e. The e o e, PV
powe will be shown as nega i e since i is gene a ed and injec ed in o he EB node. Addi ionally, a line
plo ep esen s he PVPC and he selling p ice pe hou .
Case 1 : In summe , he sys em akes ad an age o high sola i adia ion du ing he day and u bines a
nigh o supply he elec ical demand. On he o he hand, in win e , he model akes ad an age o
low ene gy p ices a nigh o ac i a e he pumps and s o e wa e , which will be used du ing high
p ice peaks o mee he demand.
−40
−20
0
20
40
P (kW)
T ime (h)
P V
L oad
P umps
G id
Tu bine
cbu y ,g
cs el l ,g
100
200
300
P ice (€ /MWh)
0 6 12 18 23
(a) Resul ing consumed powe .
0612 18 23
0.00
0.01
Flow (m³/s)
T ime (h)
Pipe01 Pipe02 Pipe10
0
50
Volume (%)
0612 18 23 T ime (h)
R1 R0 R2
(b) Rese oi s le el.
Figu e 3.40 –CEDER esul s - Case 1 in summe .
72
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
−40
−20
0
20
40
P (kW)
T ime (h)
P V
L oad
P umps
G id
Tu bine
cbu y ,g
cs el l ,g
100
200
300
P ice (€ /MWh)
0 6 12 18 23
(a) Resul ing consumed powe .
0612 18 23
0612 18 23
0.00
0.02
Flow (m³/s)
T ime (h)
Pipe01 Pipe02 Pipe10
0
50
Volume (%)
T ime (h)
R1 R0 R2
(b) Rese oi s le el.
Figu e 3.41 –CEDER esul s - Case 1 in win e .
Case 2 : The p oblem de e mines he maximum PV powe capaci y, up o 66 kW. In summe , he sys em
u ilizes high sola i adia ion o s o e wa e in he uppe ese oi s and sells he excess ene gy. A
nigh , he s o ed wa e is u bined o supply he load demand. In win e , he sys em akes ad an age
o he high ins alled PV powe o sell elec ici y o he g id du ing pe iods o high p ices and o s o e
wa e in he uppe ese oi s. Then, du ing he nigh and peak p ice pe iods, he s o ed wa e is
used o u bining o gene a e ene gy and supply he elec ical loads. No ba e y is sized in his
op imisa ion case.
0612 18 23
−40
−20
0
20
40
P (kW)
T ime (h)
P V
L oad
P umps
G id
Tu bine
cbu y ,g
cs el l ,g
100
200
300
P ice (€ /MWh)
(a) Resul ing consumed powe .
0612 18 23
0.
0612 18 23
00
0.05
Flow (m³/s)
T ime (h)
Pipe01 Pipe02 Pipe10
0
100
Volume (%)
T ime (h)
R1 R0 R2
(b) Rese oi s le el.
Figu e 3.42 –CEDER esul s - Case 2 in summe .
Case 3 : In his case, he model conside s an al eady ins alled ba e y. Since he ba e y’s e iciency is
highe han ha o he wa e s o age sys em, he op imisa ion p io i izes cha ging and discha ging
he ba e y o e using he wa e sys em. The e o e, in summe , he su plus PV powe is used o
cha ge he ba e y, supply he loads a nigh , and sell elec ici y when p ices a e high. On he o he
hand, in win e , he sys em akes ad an age o low elec ici y p ices a nigh o cha ge he ba e ies
and discha ge hem du ing high-p ice pe iods. Again, no addi ional ba e y capaci y is sized.
Table 3.11 summa izes he ope a ion and sizing cos s pe day a e simula ing each case unde summe
and win e condi ions. I also displays he compu a ion ime in minu es on an 8 h Gen In el Co e i5 @
1,80 GHz lap op wi h 8,0 GB o RAM. F om Table 3.11, i can be seen ha Case 1 is he mos expensi e
73
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
uning, he sys em could s and passing clouds o a ew seconds. In u bines, app op ia e ga e and blade
egula ion manoeu es would achie e he same esul s [104].
Hyd aulic in as uc u e
Selec ing pipes’ geome y and cha ac e is ics o inc ease he elas ici y o he sys em help educe he e -
ec i e p essu e wa e eloci y. Fu he mo e, he addi ion o ai chambe s, su ge anks and p ope al ing
educe he maximum p essu e o such wa es [92, Ch.10]. Some au ho s p opose as well a aching a
supplemen a y sec ion o polyme ic ma e ials [94, 105, 106, 107].
4.1.2 Con ibu ions
The main con ibu ion o his wo k, as pa o he Ad anced G id In e aces o inno a i e STo age IN e-
g a ion (AGISTIN) p ojec , is he de elopmen o a sizing me hodology o ESS o mi iga e he nega i e
wa e hamme e ec s de i ed om clouds shading o e la ge PV pumping sys ems, which we ound no
p e ious wo k abou . The me hodology de ines a cos unc ion ha conside s capi al and ope a ion cos s,
including an s a is ical model o he clouds o conside hei e ec . The cos unc ion can be sol ed analy -
ically, equi ing no i e a i e me hods. We apply he me hodology o a eal s udy case using on-si e da a
and analyse he easibili y and sensi i i y o se e al ESS echnologies, conside ing hei en i onmen al
impac as well.
The objec i e o his chap e is o de elop a me hodology o size an ESS o la ge PV pumping sys ems,
while analysing se e al echnologies o de e mine hei easibili y in such applica ion. The aim o such
ESS is o imp o e he esponse o hese PV pumping sys ems when clouds shade he PV plan .
4.2 P oblem desc ip ion
Clouds shading o e PV pumping sys ems de i e in nega i e e ec s o he sys em such as wa e hamme .
This wo k p oposes he inclusion o an ESS o p e en wa e hamme by supplying he equi ed ene gy o
p oduce and su icien ly p olong a amp o powe when he pump s ops. Howe e , ene gy could also be
supplied o main ain he pump unning when he PV panels a e shaded by a passing cloud, p e en ing
he need o s op i . The e o e, he ESS is sized o accomplish wo goals: (1) keep he pump unning
when a cloud shades he PV plan and (2) s op he pump smoo hly, when equi ed, ollowing a amp o
powe .
Figu e 4.3 po ays he ene gy supplied by he ESS, ep esen ed by he blue highligh ed a ea. When a
cloud e en ini ia es, he ESS commences o p o ide he lack o ene gy esul ing om he cloud shading
o a oid s opping he pump ( 1in Figu e 4.3). I he cloud con inues o long enough, he ESS supplies
he equi ed ene gy o smoo hly s op he pump ( 2 in Figu e 4.3). This implies he ESS capaci y is sized
o he sum o he ene gy equi ed o he amp and ha equi ed o a ce ain assumed cloud:
𝐸𝐸𝑆𝑆 =𝐸(1)+𝐸(2),(4.1)
wi h 𝐸(1) (kWh) he ene gy equi ed o sa e a ce ain cloud e en and 𝐸(2) (kWh) ha equi ed o shi
om unning powe 𝑃𝑝𝑢𝑚𝑝(kW) o a comple e s op 𝑃=0kW in he app op ia e ime Δ𝑡𝑟𝑎𝑚𝑝(s).
To es ablish he ene gy 𝐸(1)i is essen ial o e alua e he ac ual wea he ci cums ances and beha iou on
he eal si e. By ga he ing and analysing ele an on-si e da a we can de elop a p obabili y model which
will be applied o comp ehend he scale and beha iou o he clouds and, subsequen ly, o size he ESS
acco dingly o ha pa icula si ua ion.
80
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
𝐺,𝑃
𝐺
𝑃𝑡
𝐺𝑡ℎ
𝑃𝑝𝑢𝑚𝑝
Sa e he
cloud
Cloud is
oo long
S op pump
smoo hly
12
Δ𝑡𝑟𝑎𝑚𝑝
Figu e 4.3 –I adiance d op e en wi h ESS.
The da a equi ed may be ga he ed by an i adiance senso loca ed in he PV sys em o i s icini ies. This
senso measu es he ambience i adiance and may be al eady ins alled o ack and communica e he
a ailable powe o he powe con e e .
A h eshold alue 𝐺𝑡ℎ (W/m2) disce ns in eal ime whe he a cloud is shading he PV plan . A cloud is
conside ed when he h eshold alue is eached and i s ays un il ha alue is no o e come (Figu e 4.4),
hus de ining he du a ion o he cloud: Δ𝑡𝑐𝑙𝑜𝑢𝑑 =𝑡𝑛−𝑡0,(4.2)
whe e 𝑡0(s) is he obse a ion be o e in e sec ing he h eshold alue o he i s ime and 𝑡𝑛(s) he
obse a ion a e in e sec ing i o he second (and las ) ime. Consequen ly we use he measu es ha
esul in he wo s case-scena io, i.e. he longes du a ion.
The maximum i adiance d op Δ𝐺𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑(W/m2) is also conside ed in o de o size he maximum powe
ha he ESS is equi ed o supply: Δ𝐺𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑 =𝐺𝑡ℎ−𝐺𝑚𝑖𝑛.(4.3)
The adian exposu e shaded by a cloud (J/m2) is exp essed as he a ea comp essed be ween he h esh-
old alue o i adiance and he measu ed i adiance and co esponds o he blue highligh ed a ea in Figu e
4.4. Since he da a a e disc e e, he a ea be ween wo obse a ions 𝐴𝑖(J/m2) equals o ha o a ape-
zoid 𝐴𝑖=𝐺𝑖−𝐺𝑡ℎ+𝐺𝑖+1−𝐺𝑡ℎ
2Δ𝑡𝑖,(4.4)
whe e Δ𝑡𝑖(s) is he ime elapsed be ween obse a ions 𝐺𝑖and 𝐺𝑖+1(W/m2).
The e minal a eas, his is he ones be ween he h eshold alue and 𝐺0o 𝐺𝑛, a e assumed o in e sec
in he midpoin be ween bo h obse a ions. Acco dingly o 𝐴0, and analogously 𝐴𝑛−1:
𝐴0=(𝐺1−𝐺𝑡ℎ)Δ𝑡0
2,(4.5)
𝐴𝑛−1 =(𝐺𝑛−1−𝐺𝑡ℎ)Δ𝑡𝑛−1
2.(4.6)
The esul ing adian exposu e shaded by a cloud 𝐴𝑐𝑙𝑜𝑢𝑑(J/m2) is he summa ion o he a eas o he ape-
zoids: 𝐴𝑐𝑙𝑜𝑢𝑑 =𝑛−1
∑
𝑖=0𝐴𝑖.(4.7)
The ene gy shaded by a cloud 𝐸𝑐𝑙𝑜𝑢𝑑 (kWh) is calcula ed wi h (4.8) and he maximum powe d op
𝑃𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑(kW) wi h (4.9). These alues a e ela ed o he speci ic PV sys em and e e o hose equi ed
o achie e he same le el o ene gy and powe wi h an i adiance equal o 𝐺𝑡ℎ.
𝐸𝑐𝑙𝑜𝑢𝑑 =𝐴𝑐𝑙𝑜𝑢𝑑
1000 𝑃𝑃𝑉 𝜂𝑃𝑉
3600 ,(4.8)
81
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
𝐺𝐺0𝐴𝑖
𝐴0𝐴𝑛−1
𝐺𝑖
𝐺1
Δ𝑡𝑐𝑙𝑜𝑢𝑑
𝐺𝑚𝑖𝑛
𝐺𝑛
𝑡
𝑡𝑛
𝑡0
𝐺𝑡ℎ
Figu e 4.4 –Da a key poin s ha de ine a cloud.
𝑃𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑 =𝐺𝑚𝑖𝑛,𝑐𝑙𝑜𝑢𝑑
1000 𝑃𝑃𝑉 𝜂𝑃𝑉,(4.9)
whe e 𝜂𝑃𝑉 is he e iciency o he PV and in e e sys em and 𝑃𝑃𝑉 he peak powe o he PV sys em
(kWp).
Finally, i is c ucial o dis ega d all ins ances o suspec ed cloud shading ha a e ac ually a ibu able o
nigh ime. These alues a e emo ed abiding by he ollowing ule: i he da e o he a i al o he cloud
𝑡0is di e en han ha o i s wi hd awal 𝑡𝑛i is conside ed nigh ime and he obse a ion is emo ed.
4.3 Me hodology (O -g id)
This sec ion de ines he me hodology we de eloped o size an ESS o he PV pumping sys em o imp o e
i s pe o mance and p e en he undesi able e ec s om clouds. As de ined in Sec ion 4.2, he ESS
equi es o be sized on i s powe 𝑃𝐸𝑆𝑆 and capaci y 𝐸𝐸𝑆𝑆, which is spli in o 𝐸(1)and 𝐸(2)as de ined in
(4.1).
Powe 𝑃𝐸𝑆𝑆
Since he maximum powe o be p o ided will no su pass he pump’s wo king powe , he same is he
powe equi ed by he ene gy s o age sys em 𝑃𝐸𝑆𝑆:
𝑃𝐸𝑆𝑆 =𝑃𝑝𝑢𝑚𝑝.(4.10)
The wo king powe is de e mined by he ope a ing poin o he sys em and may no coincide wi h he
nominal powe o he pump.
Capaci y 𝐸(2)
We can ind he ene gy equi ed o he amp o be p o ided when s opping he pump 𝐸(2) wi h he
esul ing iangle om Figu e 4.3: 𝐸(2) =𝑃𝑝𝑢𝑚𝑝Δ𝑡𝑟𝑎𝑚𝑝
2.(4.11)
The app op ia e s opping ime Δ𝑡𝑟𝑎𝑚𝑝 (s) should be es ima ed, de ined analy ically, expe imen ally o
gi en by he ope a o s. Me hods o ob ain i s alue a e ou o he scope o his wo k.
82
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Numbe o clouds 𝑁
Da a analysed on Sec ion 4.4.1 sugges he numbe o clouds pe day 𝑁shading mo e han a ce ain
ene gy 𝐸 ollows a law o powe wi h nega i e exponen
𝑁(𝐸)=𝐾𝐸𝛼,(4.12)
wi h 𝐾>0and 𝛼<0. Applying p ope ies o loga i hms, i can also be exp essed as a linea model:
log(𝑁(𝐸))=log(𝐾)+𝛼log(𝐸). (4.13)
The e o e, we can i a linea eg ession model using he me hod o leas squa es o es ima e i s pa am-
e e s. Fo eadabili y pu poses, in his case, we apply a change o a iables such ha 𝑦 =𝑙𝑜𝑔(𝑁(𝐸)),
𝛽=𝑙𝑜𝑔(𝐾)and 𝑥=𝑙𝑜𝑔(𝐸):
𝛼=∑𝒩
𝑖=1(𝑥𝑖−𝑥)(𝑦𝑖−𝑦)
∑𝒩
𝑖=1(𝑥𝑖−𝑥)2(4.14)
𝛽=𝑦−𝛼𝑥 (4.15)
being 𝒩 he o al numbe o da a poin s ep esen ing he cu e.
To al cos 𝐶
The o al cos 𝐶(€) conside s he capi al and ope a ing cos s o he ESS i sel and he cos s associa ed
o non-p oduc i e ime, i.e. he pump s opping, du ing he li e ime o he ESS. We subdi ided he o al
cos 𝐶in o i e concep ual pa s, ela ed o capi al cos s (4.17)-(4.18) and ope a ion cos s (4.19)-(4.20)
o he ESS and ope a ion cos s o he acili y (4.22). These subdi isions allow o a be e subsequen
unde s anding and analysis o he esul s:
𝐶=𝐶𝑐𝑎𝑝,𝐸+𝐶𝑐𝑎𝑝,𝑃 +𝐶𝑜𝑝,𝐸+𝐶𝑜𝑝,𝑃 +𝐶𝑜𝑝,𝑠,(4.16)
whe e 𝐶𝑐𝑎𝑝,𝐸 (€) is he o al capaci y capi al cos s o he ESS, 𝐶𝑐𝑎𝑝,𝑃 (€) he o al powe capi al cos s o
he ESS, 𝐶𝑜𝑝,𝐸 (€) he o al a iable ope a ing cos s o he ESS, 𝐶𝑜𝑝,𝑃 (€) he o al ix ope a ing cos s o
he ESS and 𝐶𝑜𝑝,𝑠(€) he o al s op ope a ing cos s o he PV pumping acili y.
Capi al cos s
Capi al cos s include he expenses o pu chasing he ESS. Fo such an equipmen capi al cos s can be
subdi ided in ene gy capaci y capi al cos s 𝐶𝑐𝑎𝑝,𝐸(€) and powe capi al cos s 𝐶𝑐𝑎𝑝,𝑃 (€). These cos s a e
compu ed as he p oduc o he uni p ice and i s co esponding e m:
𝐶𝑐𝑎𝑝,𝐸 =𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸(1)+𝐸(2)), (4.17)
𝐶𝑐𝑎𝑝,𝑃 =𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.18)
wi h 𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 (€/kWh) he o al cos pe uni o ene gy o he ESS and 𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆 (€/kW) he o al cos
pe uni o powe o he ESS.
Ope a ion cos s
Ope a ion cos s include he main enance expenses 𝐶𝑜𝑝,𝐸 (€) and 𝐶𝑜𝑝,𝑃 (€) o he ESS and he s opping
cos s, de ined as he non-p oduc i e ime ha will ha e o be compensa ed wi h g id connec ed pumps
𝐶𝑜𝑝,𝑠(€). Va iable ope a ing cos s conside he ene gy employed du ing bo h case 1 , whe e he ESS can
p o ide enough ene gy o sa e he cloud, and 2 , whe e he pump is s opped (Figu e 4.3). O he wise,
ixed ope a ing cos s ela e o he ins alled powe capaci y:
𝐶𝑜𝑝,𝐸 =𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(1)(𝑁−
𝑁(𝐸(1)𝐷𝐸𝑆𝑆))+
+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸(1)+𝐸(2))
𝑁(𝐸(1)𝐷𝐸𝑆𝑆), (4.19)
83
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
whe e 𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆 (€/kWh) is he a iable ope a ing cos s o he ESS pe u ilised kWh, 𝑁is he a e age
numbe o s ops pe day wi hou ESS, 𝐿𝐸𝑆𝑆(days) is he a e age li e ime o he ESS and 𝐷𝐸𝑆𝑆 (p.u.) he
dep h o discha ge o he ESS. Conside
𝑁as he pa icula es ima o o 𝑁 om (4.12), which is discussed
u he in Sec ion 4.4.1; 𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.20)
whe e 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆 (€/kW) is he ix ope a ing cos s o he ESS:
𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆 =𝑇
∑
𝑡=1 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆,0
(1+𝑖)𝑡,(4.21)
wi h 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆,0(€/(kW⋅y)) he ix ope a ing cos s pe yea o he ESS a he yea o in es men , 𝑇is he
𝐿𝐸𝑆𝑆 exp essed in yea s and 𝑖 he eal in e es a e (p.u.);
𝐶𝑜𝑝,𝑠 =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆
𝑁(𝐸(1)𝐷𝐸𝑆𝑆), (4.22)
whe e 𝑐𝑠𝑡𝑜𝑝 (€) is he cos pe s op (4.23). In ou s udy case cos pe s op conside s ha he pumping
sys em will ha e o ope a e g id connec ed du ing nigh ime, howe e i should be adap ed o he speci ic
cha ac e is ics o each PV pumping acili y. Fo ins ance, on a emo e isola ed a ea wi h no g id connec ion
possibili y o he app oaches would be conside ed such as jus no pumping o u ilising a diesel-d i en
pump. The o me should con empla e losses due o lack o wa e o i iga ion and he la e he p ice o
uel. 𝑐𝑠𝑡𝑜𝑝 =3600(𝑡𝑠𝑡𝑜𝑝
2+𝑡𝑛𝑤+𝑡𝑠𝑡𝑎𝑟𝑡
2)𝑃𝑝𝑢𝑚𝑝𝑐𝑔𝑟𝑖𝑑 (4.23)
Subs i u e he e ms in o (4.16) and cos 𝐶can be exp essed as a unc ion o he capaci y 𝐸(1):
𝐶(𝐸(1))=𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸(1)+𝐸(2))+
+𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆 +
+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(1)(𝑁−
𝑁(𝐸(1)𝐷𝐸𝑆𝑆))+
+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸(1)+𝐸(2))
𝑁(𝐸(1)𝐷𝐸𝑆𝑆)+
+𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆 +
+𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆
𝑁(𝐸(1)𝐷𝐸𝑆𝑆),
(4.24)
Capaci y 𝐸(1)
Finally, by de i ing 𝐶𝑑𝐶
𝑑𝐸(1) =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆𝐷𝛼
𝐸𝑆𝑆𝐾𝛼𝐸𝛼−1
(1) +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁+
+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(2)𝐷𝛼
𝐸𝑆𝑆𝐾𝛼𝐸𝛼−1
(1) +
+𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆,
(4.25)
we analy ically ob ain he exp ession o he capaci y 𝐸(1)which minimises he cos (4.26):
𝑑𝐶
𝑑𝐸(1) =0 ⇒ 𝐸(1) =( −𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁−𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆
𝐿𝐸𝑆𝑆𝐷𝛼
𝐸𝑆𝑆𝐾𝛼(𝑐𝑠𝑡𝑜𝑝+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐸(2)))1/(𝛼−1).(4.26)
84
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
4.4 S udy case
In his sec ion, we apply he me hodology de eloped in he p e ious sec ion o a eal scena io loca ed
in he egion o Lleida (Ca alonia, Spain), no h-eas e n Ibe ian Peninsula, and u ilising he acili ies o
he i iga ion communi y Comuni a de Regan s Seg ià-Sud. The acili ies a e loca ed a geog aphical
coo dina es N 41∘21’ 40 E 0∘27’ 31. The whole sys em comp ises 5 ese oi s and 3 pumping s a ions.
Figu e 4.5 shows an o opho o o such sys em. The e a e cu en ly wo wo king PV pumping sys ems
and u he one unde cons uc ion, which co esponds o ha o he s udy case. Such sys em is desc ibed
in Table 4.2. Rese oi s on he s udy case’s PV pumping sys em a e 1 km apa and hei di e ence o
heigh s is 20 m. The i adiance senso ha p o ided he his o ic da a is loca ed on one o he PV plan s.
The PV plan u ilises a No h-Sou h ho izon al axis acking sys em which inc eases he numbe o hou s
he sys em can pump pe day, as demons a ed by [102].
Table 4.2 –Cha ac e is ics o he PV pumping sys em [28].
Concep Value
Peak powe 𝑃𝑃𝑉 275 kWp
In e e ’s e iciency 𝜂𝑃𝑉 0,98
I adiance h eshold 𝐺𝑡ℎ 400 W/m2
Pump nominal powe 𝑃𝑝𝑢𝑚𝑝,𝑁 160 kW
Pump wo king powe 𝑃𝑝𝑢𝑚𝑝 110 kW
S opping ime 𝑡𝑠𝑡𝑜𝑝 30 s
S a up ime 𝑡𝑠𝑡𝑎𝑟𝑡 30 s
Non-wo king ime 𝑡𝑛𝑤 240 s
Cos o ene gy 2𝑐𝑔𝑟𝑖𝑑 0,05 €/kWh
Real in e es a e 3𝑖4 %
0 2,5 5,0 km
1:220 000
senso s udy case
Figu e 4.5 –Loca ion o he i adiance senso and s udy case on he CR Seg ià-Sud acili ies. Backg ound maps
ob ained om Ins i u Ca og à ic i Geològic de Ca alunya [31] and OpenS ee Map [32]. Figu e elabo a ed in QGIS
[110]
We compa ed se e al echnologies on his analysis, comp ising lead acid ba e ies (Lead), li hium-ion
ba e ies (LIB), edox low ba e ies (Flow), ul acapaci o s (Uc) and lywheels (Fw). Since many di e en
sou ces exis o ESS cos s wi h huge anges o alues, we decided o assume he cha ac e is ics om
[111], which a e lis ed on Table 4.3.
2Based on da a om OMIE [108]
3Based on da a om Banco de España [109]
85
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 4.3 –Capi al and ope a ion cos s o he analysed ene gy s o age sys ems [111]
Technology 𝑐𝑐𝑎𝑝,𝐸 [€/kWh] 𝑐𝑐𝑎𝑝,𝑃 [€/kW] 𝑐𝑜𝑝,𝑣𝑎𝑟[€/MWh] 𝑐𝑜𝑝,𝑓𝑖𝑥,0[€/kW⋅y] 𝐷[p.u.] 𝐿[y]
Lead acid 299,20 116,45 0,44 4,34 1,00 3
Li hium-ion 272,00 209,10 0,44 8,50 0,80 10
Redox low 410,55 116,45 0,44 5,01 1,00 15
Ul acapaci o 63 308,00 0,00 25,5 0,85 1,00 16
Flywheel 9 792,00 0,00 25,5 4,76 1,00 20
4.4.1 Clouds
I adiance da a comes om a sola i adiance senso loca ed besides one o he PV panels a he pumping
s a ion o he s udy case. This senso eeds he con ol o he powe con e e . The da ase u ilised was
p o ided by he Comuni a de Regan s Seg ià-Sud and con ains he senso ’s ga he ed da a o 347 days
since 28 Ma ch 2020 un il 27 July 2023 wi h a 20 o 30 s sample ime in daily sp eadshee iles.Figu e
4.6 plo s he da a ega ding powe gene a ion o he PV sys em and powe consump ion o he pump o
a PV pumping sys em in he CR Seg ià-Sud acili ies. The plo ed PV pumping sys em is cha ac e ised
by a 523 kWp PV sys em, an i adiance h eshold se a 400 W/m2and a pump wi h a nominal powe o
315 kW.
Powe (kW)
Time (h)
0
0
200
100
300
500
400
6
12
18
23
Ppump
Ppump,N
PPV G h
PPV
Figu e 4.6 –Powe gene a ion and consump ion o a PV pump sys em in he Seg ià-Sud acili ies, co esponding
o 25 h July 2022.
We obse ed a o al amoun o 4 753 cloud e en s. The longes cloud las ed Δ𝑡𝑐𝑙𝑜𝑢𝑑 =269,50minu es
and he la ges shaded adian exposu e was 𝐴𝑐𝑙𝑜𝑢𝑑 =1 030,60 Wh/m2(Table 4.4). Wi h an a e age o
14 clouds pe day (Table 4.5), we did no de ec any mon hly o annual pa e n ha would be ele an
o he s udy case. The s anda d de ia ion (SD) o bo h he numbe o clouds and he ime cloudy is
conside able.
Table 4.4 –S a is ical desc ip ion o he p ope ies o he obse ed clouds.
Concep Mean (SD) Min. Median Max.
Δ𝑡𝑐𝑙𝑜𝑢𝑑[min] 5,99 (15,5) 0,50 2,00 269,50
𝐴𝑐𝑙𝑜𝑢𝑑[Wh/m2] 14,59 (62,5) 0,01 1,24 1 030,60
𝐺𝑚𝑖𝑛[W/m2] 286,96 (86,3) 0,00 302,00 399,00
Figu e 4.7 p esen s he ank dis ibu ions o he du a ions Δ𝑡𝑐𝑙𝑜𝑢𝑑and shaded adian exposu es 𝐴𝑐𝑙𝑜𝑢𝑑,
de ined in (4.2) and (4.7) espec i ely. Rank is de ined as he complemen o he cumula i e dis ibu ion
unc ionand se es asa isualisa ion o analysingpowe lawdis ibu ionswi h a ee en ssuch as black-
ou sizes in elec ical sys ems [112]. A succinc analysis on hem sugges s ha a powe law beha iou
is p esen o bo h he adian exposu e and du a ion, he e o e sho and ain clouds a e conside ably
mo e usual han long and hick ones, as expec ed om he d y con inen al Medi e anean clima e o he
egion, wi h annual o al p ecipi a ions o 350-550 mm [113].
86
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 4.5 –S a is ical desc ip ion o he clouds da ase .
Concep Pe day (SD) To al in da a
Numbe o clouds 14 (14) 4 753
Time cloudy 1 h 22 m (1 h 30 m) 19 d 22 h
0 50 100 150 200
Du a ion ∆ cloud (min)
10−3
10−2
10−1
100
Rank
∆ cloud
0 200 400 600 800
Radian exposu e Acloud (Wh/m2)
∆ cloud
Acloud
Figu e 4.7 –Rank unc ion plo o clouds’ du a ion and shaded adian exposu e.
Al hough da a con ains clouds shading up o 277 kWh om he PV plan , hose a e a e e en s and mo e
han 90 % o he cases a e ound unde 10 kWh, which encou ages o se he ange o he s udy case o
𝐸𝑐𝑙𝑜𝑢𝑑 ∈(0,1,10)kWh.
Applying he me hodology om Sec ion 4.2, his is (4.14) and (4.15), he model ha i s he s udy case
(Figu e 4.8), wi h an 𝑅2=0,9775, is
𝑁(𝐸)=3,746𝐸−0,51,(4.27)
wi h
𝑁 he numbe o es ima ed cloud e en s pe day (day−1), analogous o (4.12), and 𝐸 he shaded
ene gy (kWh), which will also co espond o he ene gy supplied by he ESS.
Al e a ions on he sola i adiance h eshold 𝐺𝑡ℎin luence his model. In ou s udy case coe icien 𝐾lin-
ea ly g ows wi h he h eshold while exponen 𝛼ligh ly luc ua es a ound -0,47 and -0,51. The in luence
on he esul ing ESS sizing is analysed on Sec ion 4.4.4.
10−1100101
Ene gy (kWh)
100
101
Coun (day−1)
R2= 0,9775
Figu e 4.8 –Numbe o pump s opping e en s 𝑁shading a ce ain ene gy 𝐸, om da a ( ) and es ima o
𝑁
( )
4.4.2 Resul s
The ollowing sec ion analyses he esul s ob ained o m applying he de eloped me hodology (Sec ion
4.3) o he s udy case sys em (Table 4.2) o he echnologies lis ed in Table 4.3.
We con empla e a base case as well. Base case conside s no ESS ei he o s opping no sa ing clouds
and only se es as compa ison o he cloud cos s. I does no conside ei he he main enance cos s o
he pumping sys em as a esul o he e ec o wa e hamme e en s, which is ou o he scope o his
87
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
wo k. I s o al cos 𝐶𝑏𝑎𝑠𝑒 (€) is compu ed as he s opping ope a ing expenses conside ing an a e age
numbe o cloud e en s pe day: 𝐶𝑏𝑎𝑠𝑒 =𝑐𝑠𝑡𝑜𝑝𝐿𝑏𝑎𝑠𝑒𝑁. (4.28)
To be e compa e he di e en ESS echnologies, he o al cos 𝐶is no malised by he li e ime 𝐿𝐸𝑆𝑆 o
each o hem, ob aining he o al cos pe yea in €/y. Table 4.6 summa ises he esul ing op imal size
and cos s o each ESS echnology. As depic ed in Figu e 4.9, he esul s o he op imisa ion show a clea
p e e ence o edox low ba e ies and lywheels o he applica ion and s udy case o his wo k. Since
he applica ion equi es ESS wi h capaci ies ha do no exceed 10 kWh bu has o be able o deli e
𝑃𝑝𝑢𝑚𝑝 = 110 kW (Table 4.2), he op imisa ion a ou s hose echnologies wi h lowes powe ela ed
cos s, bu is no in luenced ha much by capaci y ela ed cos s. Howe e , low capaci y cos s allow o
la ge s o age, leading o less impac o clouds on he pe o mance o he sys em and hus lowe s opping
ela ed ope a ing cos s. One should no ice ha addi ional main enance and eplacemen cos s should be
accoun ed o he base case, howe e , as s a ed p e iously u he esea ch is ye o be conduc ed on
how o adequa ely eckon hem.
Table 4.6 –Sizing esul s
Technology 𝐿[y] 𝐸(1)[kWh] 𝐸(2)[kWh] 𝑃[kW]
𝑁[day−1] Cos 𝐶[€] 𝐶/𝐿[€/y]
Base case 10 0 0 0 14 21 093,19 2 109,32
Lead acid 3 1,99 0,46 110,00 2,64 16 126,88 5 375,63
Li hium-ion 10 4,88 ” ” 1,87 35 267,94 3 526,79
Redox low 15 4,51 ” ” 1,74 25 296,67 1 686,44
Ul acapaci o 16 0,17 ” ” 9,18 64 184,49 4 011,53
Flywheel 20 0,60 ” ” 4,85 34 390,07 1 719,50
4 000
2 000
Cos pe yea (€/y)
Base
Lead
LIB
Flow
Uc
Fw
0
Ccap,E Ccap,P Cop,E Cop,P Cop,s
Figu e 4.9 –Cos s pe yea o di e en echnologies and base case.
4.4.3 Feasibili y and impac assessmen
This sec ion e alua es he easibili y o implemen ing he p oposed solu ions on he eal si e, conside ing
i s pu pose and cha ac e is ics.
The speci ic objec i es a e o s udy he physical easibili y o he applica ion o di e en ene gy s o age
sys ems. I will be analysed ha he olume and mass equi ed o he ins alla ion o each ESS i wi hin
he acili ies, he equi ed powe (𝑃𝐸𝑆𝑆) is wi hin he a ed powe , he esponse ime is sui able o he
ope a ion, and he en i onmen al impac and po en ial isks o heal h and en i onmen o he ESS, aking
in o conside a ion whe e i will be loca ed wi hin he hyd aulic ins alla ions and he ac ha hyd aulic
ins alla ions a e c ucial o p o ide he wa e o he i iga ion o la ge c op ields.
88
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
I is c ucial os udy he di e en spacesandweigh s ha wouldbe dedica edand equi edby he ESS.The
possible ange o speci ic ene gy 𝑒and ene gy densi y 𝜌 o each ESS om [114] a e used. Conside ing
bo h he sized capaci y 𝐸𝐸𝑆𝑆 om Table 4.6, he possible ange o mass 𝑚and olume 𝑣a e ound
o each s o age sys em. The esul s a e p esen ed in Table 4.7, which shows ha anadium edox low
ba e ies equi ea angeo 166-497 kg and151-311 l, signi ican lyhighe mass and olumecompa ed o
o he echnologies. In addi ion, lywheels and ul acapaci o s p esen ela i ely low olume equi emen s
compa ed o o he sys ems (a ound 70 l), bu signi ican ly highe mass equi emen s (106 and 252 kg).
Lead-acid and li hium-ion ba e ies ha e simila olume and mass cha ac e is ics (less han 50 l and 80
kg), and li hium-ion ba e ies is he ESS echnology ha would equi e less space and mass.
Table 4.7 –P ope ies o he ESS echnologies [114]
Technology 𝑒[Wh/kg] 𝜌[Wh/l] 𝑚[kg] 𝑣[l]
Lead acid 30-50 50-80 49-82 31-49
Li hium-ion 75-200 200-500 27-71 11-27
Redox low 10-30 16-33 166-497 151-311
Ul acapaci o 2,5-15 10-30 42-252 21-63
Flywheel 10-30 20-80 35-106 13-53
The ESS o be ins alled mus be sui ed o deli e a speci ic amoun o powe , as calcula ed and p esen ed
p e iously in Table 4.6. Based on da a om [115, 116], i is de e mined ha since none o he e alua ed
ESS echnologies ha e a a ed powe lowe han he powe o he pump (110 kW), all o hem would be
easible in his ega d.
The esponse ime o he ESS o an e en is also c i ical in his applica ion. A delayed esponse could
esul in powe loss o he pump, po en ially inducing wa e hamme . The equi ed ime o he s udy
case is o a ew seconds, he e o e all echnologies ha e he abili y o espond in ime o his applica ion,
since hei esponse ime is in he o de o milliseconds [117].
The acili ies a e neighbou ed by 8 875 hm2o c opland and ake pa in hei i iga ion asks [22]. In
consequence, i is c ucial o ecognise and unde s and he haza ds ha he di e en ESS echnologies
en ail o bo h heal h and he en i onmen .
The e a e di e en haza ds ega ding he use o each ESS. Lead acid and edox low ba e ies may elease
hyd ogen gases du ing no mal ope a ion, which can cause se ious inju y o humans [118]. Fu he mo e,
lead acid ba e ies con ain hea y me als ha , in he e en o damage o leakage [119], would elease lead
componen s in o he soil, po en ially con amina ing wa e ese oi s o i e s, causing signi ican en i on-
men al damage. Likewise, li hium-ion ba e y cells may emi lammable gases such as hyd ogen luo ide
and hyd ogen cyanide [118]. When exposed o wa e , ai o high humidi y, as is he case o he analysed
applica ion, hey can unde go agg essi e chemical eac ions due o he co osion o hei componen s
[118, 119], p esen ing a i e isk ha could damage he equipmen s o he pumping s a ion.
I is impo an o conside hese ac o s and choose a sui able loca ion o he ESS o a oid pe sonal,
ma e ial and en i onmen al damage. When deploying elec ochemical ba e ies, i is essen ial o conside
he use o a highly en ila ed space and o he in as uc u es o p e en en i onmen al isks, such as
p ope ly isola ing he ba e y om he soil.
The inc ease o he demand o elec ochemical ESS migh cause nega i e e ec s on he en i onmen and
social aspec s o he coun ies in ol ed in he chain o p oduc ion [119]. These ba e ies a e based on
li hium, lead and anadium, he h ee o which ha e ela i ely high abundance in he ea h’s c us and
a e no conside ed a e elemen s. Howe e , hei ex ac ion induces en i onmen al and social issues,
specially in economically uns able coun ies wi h a lack o egula ion in he mining ac i i y. Ne e heless,
bo h lead acid and li hium-ion ba e ies can be ecycled, specially in case o lead acid ba e ies wi h a
ecycling e iciency up o 95 % [119].
89
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Base
Lead
LIB
Flow
Uc
Fw
0
5000
10000
15000
Cos pe yea (€/y)
Cc,E Cc,P Co,E Co,P CgCp
Figu e 4.15 –Cos s pe yea o di e en echnologies and g id connec ed case 1.
Base
Lead
LIB
Flow
Uc
Fw
0
10000
20000
Cos pe yea (€/y)
i= 2-6 %
cg id = 2-10 c€/kWh
p= 5-15 c€/kWh
Figu e 4.16 –Cos s pe yea o di e en echnologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11
€/kW) and sensi i i y o in e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝.
Table 4.12 –PS3 sensi i i y analysis esul s o cos o ene gy, eal in e es a e and excess powe e m
𝑐𝑔𝑟𝑖𝑑[€/kWh]: 0,05 0,05 0,05 0,05 0,02 0,10
𝑖[%]: 4 4 2 6 4 4
Technology 𝑡𝑝[€/kW]: 0,05 0,15 0,11 0,11 0,11 0,11
Base case 𝐸[kWh] 0 0 0 0 0 0
𝐶/𝐿[€/y] 10 112,74 24 722,74 18 878,74 18 878,74 17 194,10 21 686,48
Lead acid 𝐸[kWh] 10,98 10,98 10,98 10,98 10,98 10,98
𝐶/𝐿[€/y] 5 995,09 7 1446,81 6 694,15 6 678,49 6 689,12 6 686,12
Li hium-ion 𝐸[kWh] 10,98 10,98 10,98 10,98 10,98 10,98
𝐶/𝐿[€/y] 4 337,99 5 628,53 5 174,10 5 058,45 4 475,39 5 673,86
Redox low 𝐸(1)[kWh] 10,98 10,98 10,98 10,98 10,98 10,98
𝐶/𝐿[€/y] 2 063,17 3 214,89 2 805,71 2 711,87 2 754,20 2 754,20
Ul acapaci o 𝐸[kWh] 0,41 0,85 0,69 0,69 0,67 0,72
𝐶/𝐿[€/y] 7 522,94 12 499,42 10 721,03 10 704,36 9 131,83 13 338,82
Flywheel 𝐸[kWh] 1,95 4,03 3,28 3,28 2,60 7,32
𝐶/𝐿[€/y] 5 244,96 7 492,88 6 745,97 6 638,39 5 447,04 8 305,19
96
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
4.5.2 PV disconnec s, pump can s op
This case conside s ha , in he e en o a cloud, he con e e will disconnec he PV om he sys em bu
he pump will be able o s op un il he cloud has passed.
Figu e 4.17 shows he wo s ages he sys em may be ound on du ing a cloud. S age 1 comp ises he
span du ing which he ESS deli e s powe o he pump, limi ed by i s own sized powe 𝑃𝐸𝑆𝑆and capaci y
𝐸𝐸𝑆𝑆. S age 2, which may no be me , co e s he s opping o he pump.
𝑡
𝑃
𝑃𝑝𝑢𝑚𝑝 Penal y
𝐸1𝐸2
G id
𝑃𝑐𝑡𝑠𝑡𝑜𝑝
𝑡1
𝑃2
21
Figu e 4.17 –S a egy 2.
The op imisa ion p oblem is de ined by a NLP consis ing in a cos unc ion o minimise (4.44) subjec
o cons ain s (4.45)-(4.52). Penal ies mus be conside ed jus once pe day, aking he highes alue i
achie es on each cloud, hus we conside only s age 1 on each cloud sa ed by he ESS (𝑁−
𝑁 imes) and
s age 1 + s age 2 on each cloud ha exceeds he capaci y o he ESS (
𝑁 imes). Ene gy consumed om
he g id co esponds o ha he ESS could no deli e . To compu e he penal y on s age 2 we equi e
o know he alue o he powe 𝑃2(see Figu e 4.17), which co esponds o he powe ha i s le om
he s opping amp a e u ilising he whole capaci y o he ba e y. Applying i ial igonome y we can
de ine such powe as a unc ion o he capaci y 𝐸2,𝐸𝑆𝑆(4.48). Also, he penal y which applies o s age 2
should be he maximum be ween wo possible ci cums ances (4.45) and (4.46).
minimise
𝐸𝐸𝑆𝑆,𝑃𝐸𝑆𝑆 𝐶(𝐸𝐸𝑆𝑆,𝑃𝐸𝑆𝑆)=𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐)(1−
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)
𝑁)+
+𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆𝑃𝑝𝑒𝑛,2(
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)
𝑁)+
+𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)+
+𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆𝑁𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝
𝑃𝐸𝑆𝑆 −1)+
+𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)(𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝
2−𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)+
+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆𝑁+𝐸2,𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆))+
+𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆+𝐸2,𝐸𝑆𝑆)+
+𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆+𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,
subjec o
(4.44)
𝑃2−𝑃𝑐≤𝑃𝑝𝑒𝑛,2 (4.45)
𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐≤𝑃𝑝𝑒𝑛,2 (4.46)
97
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐≥0 (4.47)
𝑃2=√𝑃𝑝𝑢𝑚𝑝√𝑃𝑝𝑢𝑚𝑝−2𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆
𝑡𝑠𝑡𝑜𝑝 (4.48)
𝑃𝑝𝑒𝑛,2 ≥0 (4.49)
𝑃𝐸𝑆𝑆 >0 (4.50)
𝐸1,𝐸𝑆𝑆 ≥0 (4.51)
𝐸2,𝐸𝑆𝑆 ≥0 (4.52)
Resul s
We used he Pyomo lib a y [62] o w i e he NLP and COIN-OR IPOPT [75] wi h a ole ance o 1e-4 o
sol e i . Below we analyse he esul s ob ained o m applying he de eloped me hodology o he s udy
case sys em o he echnologies lis ed in Table 4.3.
We subdi ided he cos 𝐶(4.44) in o six concep ual pa s, ela ed o capi al cos s (4.53)-(4.54) and ope -
a ional cos s (4.55)-(4.56) o he ESS, ope a ional cos s o he acili y (4.57)-(4.58) and penal ies (4.59).
These subdi isions allow o a be e unde s anding and analysis o he esul s:
𝐶𝑐𝑎𝑝,𝐸 =𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆+𝐸2,𝐸𝑆𝑆), (4.53)
𝐶𝑐𝑎𝑝,𝑃 =𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.54)
𝐶𝑜𝑝,𝐸 =𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆𝑁+𝐸2,𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)), (4.55)
𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.56)
𝐶𝑜𝑝,𝑠 =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆), (4.57)
𝐶𝑔=𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆𝐸1,𝐸𝑆𝑆𝑁(𝑃𝑝𝑢𝑚𝑝
𝑃𝐸𝑆𝑆 −1)+
+𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)(𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝
2−𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆), (4.58)
𝐶𝑝=𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐)(1−
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)
𝑁)+
+𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆𝑃𝑝𝑒𝑛,2(
𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)
𝑁), (4.59)
whe e 𝐶𝑐𝑎𝑝,𝐸 (€) is he o al capaci y capi al cos s o he ESS, 𝐶𝑐𝑎𝑝,𝑃 (€) he o al powe capi al cos s o
he ESS, 𝐶𝑜𝑝,𝐸 (€) he o al a iable ope a ional cos s o he ESS, 𝐶𝑜𝑝,𝑃 (€) he o al ix ope a ional cos s
o he ESS, 𝐶𝑜𝑝,𝑠(€) he o al s op ope a ional cos s o he PV pumping acili y, 𝐶𝑔(€) he o al cos o he
ene gy acqui ed om he g id and 𝐶𝑝𝑒𝑛(€) he penal ies o exceeding he con ac ed powe 𝑃𝑐.
We con empla e a base case as well. Base case conside s no ESS and se es as compa ison o he ESS
echnologies cos s. I s o al cos 𝐶𝑏𝑎𝑠𝑒(€) is compu ed as
𝐶𝑏𝑎𝑠𝑒 =𝑐𝑠𝑡𝑜𝑝𝐿𝑏𝑎𝑠𝑒𝑁+𝑐𝑔𝑟𝑖𝑑𝐿𝑏𝑎𝑠𝑒𝑁𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝
2+𝑐𝑝𝑒𝑛𝐿𝑏𝑎𝑠𝑒(𝑃𝑝𝑢𝑚𝑝−𝑃𝑐). (4.60)
98
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
To be e compa e he di e en ESS echnologies, he o al cos 𝐶is no malised by he li e ime 𝐿𝐸𝑆𝑆 o
each o hem, ob aining he o al cos pe yea in €/y. Table 4.13 summa ises he esul ing op imal size
and cos s o each ESS echnology. As depic ed in Figu e 4.18, he esul s o he op imisa ion show a
clea p e e ence o edox low ba e ies, ul acapaci o s and lywheels o he applica ion and s udy case
o his wo k. The esul s show he bes s a egy in such con ex is o size an ESS o s ic ly s op he pump
on e e y cloud wi hou incu ing in any excess powe penal ies.
Table 4.13 –G id connec ed sizing esul s (S a egy 2)
Technology 𝐿[y] 𝐸1[kWh] 𝐸2[kWh] 𝑃[kW]
𝑁[day−1] Cos 𝐶[€] 𝐶/𝐿[€/y]
Base case 10 0 0 0 14,0 182 975,03 18 287,50
Lead acid 3 0,00 0,46 100,00 14,0 19 366,73 6 455,58
Li hium-ion 10 ” 0,57 ” 14,0 49 341,82 4 934,18
Redox low 15 ” 0,46 ” 14,0 49 277,34 3 285,16
Ul acapaci o 16 ” 0,45 ” 14,0 64 522,13 4 032,63
Flywheel 20 ”0,45 ”14,0 54 570,14 2 728,51
Base
Lead
LIB
Flow
Uc
Fw
0
5000
10000
15000
Cos pe yea (€/y)
Ccap,E
Ccap,P
Cop,E
Cop,P
Cop,s
Cg
Cpen
Figu e 4.18 –Cos s pe yea o di e en echnologies and g id connec ed case 2.
The esul s o a ia ions o in e es a e, cos o ene gy and excess powe e m displayed in Figu e 4.19
sugges ha none o hem ha e no iceable e ec s on he esul s.
Base
Lead
LIB
Flow
Uc
Fw
0
10000
20000
Cos pe yea (€/y)
i= 2-6 %
cg id = 2-10 c€/kWh
p= 5-15 c€/kWh
Figu e 4.19 –Cos s pe yea o di e en echnologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11
€/kW) and sensi i i y o in e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝.
99
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
T ansien excess o powe
In his scena io we could conside penal ies only apply du ing s age 1, since s age 2 is a sho las ing
ansien in compa ison o he sampling a e o he egis y, hen 𝑃𝑝𝑒𝑛,2= 0 kW.
The op imisa ion esul s e eal ha he economically op imal solu ion should be no o size any ESS, since
he ope a ion cos s o he excess powe acqui ed om he g id do no su pass he capi al cos s an ESS
would in oduce. The cos pe yea would be 𝐶/𝐿= 2 205,09 €.
4.5.3 PV does no disconnec
This case conside s ha , in he e en o a cloud, he con e e will keep he PV connec ed o he sys em.
Figu e 4.20 shows he wo s ages he sys em may be ound on du ing a cloud. S age 1 comp ises he
span du ing which he ESS deli e s powe o he pump, limi ed by i s own sized powe 𝑃𝐸𝑆𝑆and capaci y
𝐸𝐸𝑆𝑆. S age 2, which may no be me , co e s he s opping o he pump.
𝑡
𝑃
𝑃𝑝𝑢𝑚𝑝 Penal y
ESS
PV
G id
𝑃𝑐𝑡𝑠𝑡𝑜𝑝
𝑡1
21
Figu e 4.20 –Conside ed beha iou wi h g id and PV connec ed.
This scena io con empla es bo h he ene gy and powe los on he PV plan due o a cloud e en . S a is-
ically conside ing hese wo a iables esul ed in a complex op imisa ion p oblem, he e o e, we used a
da a d i en app oach o analyse his scena io. The o al o 𝑁𝑐𝑙𝑜𝑢𝑑𝑠= 4 753 cloud da a poin s du ing 𝑁𝑑𝑎𝑦𝑠
347 days we e e alua ed o each ESS echnology o ind he mos economically sui able sizing ollow-
ing he subsequen me hodology. Fi s , a ange o 𝐸𝐸𝑆𝑆 ∈(0,10) kWh in s eps o 0,1 kWh, and 𝑃𝐸𝑆𝑆 ∈
(0,110) kW in s eps o 1 kW, was de ined as he possible sizing ou comes. In a combina o ial p ocedu e,
he inal cos o each sizing was analysed, hen he minimum was selec ed o each echnology. The
analysis me hodology o ind he inal cos de elops, o each cloud:
• The amoun o powe equi ed om he g id si compu ed as he di e ence o he powe shaded by
he cloud 𝑃𝑐𝑙𝑜𝑢𝑑(4.9) and he powe ha he ESS will p o ide:
𝑃𝑔=max(𝑃𝑐𝑙𝑜𝑢𝑑−𝑃𝐸𝑆𝑆,0) (4.61)
• The powe o be conside ed on he penal y compu a ion (4.29) is he di e ence be ween he powe
equi ed om he g id and he con ac ed powe 𝑃𝑐. Penal ies only apply o he conside ed ime
pe iods pe day and no o each cloud, as de ined in Sec ion 4.5.
𝑃𝑝𝑒𝑛 =max(𝑃𝑔−𝑃𝑐,0) (4.62)
A penal y will only apply i he he ene gy shaded by he cloud 𝐸𝑐𝑙𝑜𝑢𝑑 (4.8) is g ea e han he
capaci y o he ESS 𝐸𝐸𝑆𝑆, deduc ing he ene gy ha will be sa ed o s op he pump in a amp o
powe 𝐸(2)(4.11): 𝐸𝑐𝑙𝑜𝑢𝑑 >𝐸𝐸𝑆𝑆−𝐸(2) (4.63)
100
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
• The ene gy consumed om he g id esul s om he du a ion o he cloud Δ𝑡𝑐𝑙𝑜𝑢𝑑:
𝐸𝑔=𝑃𝑔Δ𝑡𝑐𝑙𝑜𝑢𝑑 (4.64)
• The ene gy used om he ESS is equi alen o ha o he cloud:
𝐸𝑢𝑠𝑒𝑑,𝐸𝑆𝑆 =min(𝐸𝑚𝑖𝑠𝑠𝑖𝑛𝑔,𝐸𝐸𝑆𝑆)(4.65)
• Capi al cos s, o capaci y 𝐶𝑐𝑎𝑝,𝐸 and powe 𝐶𝑐𝑎𝑝,𝑃, a e compu ed as:
𝐶𝑐𝑎𝑝,𝐸 =𝐸𝐸𝑆𝑆𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 (4.66)
𝐶𝑐𝑎𝑝,𝑃 =𝑃𝐸𝑆𝑆𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆 (4.67)
• Ope a ing cos s, o ene gy 𝐶𝑜𝑝,𝐸and powe 𝐶𝑜𝑝,𝑃 usage, a e compu ed as:
𝐶𝑜𝑝,𝐸 =𝐿𝐸𝑆𝑆
𝑁𝑑𝑎𝑦𝑠 ∑
𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠𝐸𝑢𝑠𝑒𝑑,𝐸𝑆𝑆,𝑖 (4.68)
𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.69)
• G id cos s a e compu ed om he ene gy used om he g id:
𝐶𝑔=𝐿𝐸𝑆𝑆
𝑁𝑑𝑎𝑦𝑠 ∑
𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠𝐸𝑔,𝑖𝑐𝑔𝑟𝑖𝑑 (4.70)
• Ope a ing cos s o s opping he pump conside ha non p oduc i e ime should be compensa ed
du ing nigh ime wi h ex a pumping ope a ions, wi h 𝑁𝑐𝑙𝑜𝑢𝑑𝑠,𝑛𝑠 he numbe o clouds such ha
𝐸𝐸𝑆𝑆 <𝐸𝑐𝑙𝑜𝑢𝑑(ns s anding o no su icien ) and conside ing 𝑐𝑠𝑡𝑜𝑝de ined in (4.23):
𝐶𝑜𝑝,𝑠 =𝐿𝐸𝑆𝑆
𝑁𝑑𝑎𝑦𝑠 ∑
𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠,𝑛𝑠𝑐𝑠𝑡𝑜𝑝 (4.71)
• Finally, he o al cos 𝐶is compu ed as he sum o he pa ial cos s:
𝐶=𝐶𝑐𝑎𝑝,𝐸+𝐶𝑐𝑎𝑝,𝑃 +𝐶𝑜𝑝,𝐸+𝐶𝑜𝑝,𝑃 +𝐶𝑔+𝐶𝑝𝑒𝑛+𝐶𝑜𝑝,𝑠 (4.72)
To be e compa e he di e en ESS echnologies, he o al cos 𝐶is no malised by he li e ime 𝐿𝐸𝑆𝑆 o
each o hem, ob aining he o al cos pe yea in €/y. Table 4.14 summa ises he esul ing op imal size
and cos s o each ESS echnology. As depic ed in Figu e 4.21, he esul s o he op imisa ion show a
clea p e e ence o edox low ba e ies and lywheels o he applica ion and s udy case o his wo k. I
did no size a lead acid ba e y, which would be a mo e expensi e solu ion han ha ing no ESS.
The esul s o a ia ions o in e es a e, cos o ene gy and excess powe e m displayed in Figu e 4.22
sugges ha , all o he pa ame e s ha e li le in luence on he esul s. I is ema kable he e ec o he
cos o ene gy on he lead acid ba e ies echnology, caused by no being sized and depending on he
g id ins ead. Since li hium-ion ba e ies a e sized o allow some penal ies, he cos o penal y ha e a
signi ican in luence on i as well as he cos o ene gy.
101
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Table 4.14 –G id connec ed sizing esul s (wi hou PV disconnec ion)
Technology 𝐿[y] 𝐸[kWh] 𝑃[kW] Cos 𝐶[€] 𝐶/𝐿[€/y]
Base case 10 0 0 37 504,70 3 750,47
Lead acid 3 0,00 0,0 11 251,40 3 750,47
Li hium-ion 10 7,30 70,0 28 334,70 2 833,47
Redox low 15 5,60 88,0 22 733,50 1 515,57
Ul acapaci o 16 0,10 104,0 45 213,80 2 825,86
Flywheel 20 1,30 97,0 36 795,80 1 839,79
Base
LIB
Flow
Uc
Fw
0
1000
2000
3000
Cos pe yea (€/y)
Ccap,E
Ccap,P
Cop,E
Cop,P
Cop,s
Cg
Cpen
Figu e 4.21 –Cos s pe yea o di e en echnologies and g id connec ed wi h PV.
Lead
LIB
Flow
Uc
Fw
0
1000
2000
3000
4000
Cos pe yea (€/y)
i= 2-6 %
cg id = 2-10 c€/kWh
p= 5-15 c€/kWh
Figu e 4.22 –Cos s pe yea o di e en echnologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11
€/kW) and sensi i i y o in e es a e 𝑖, cos o ene gy 𝑐𝑔𝑟𝑖𝑑and penal y 𝑡𝑝.
102
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
4.6 Aqueous ECR ba e y
Al hough o he s o age echnologies wi h highe eadiness le el may be sui able, as pa o he AGISTIN4
p ojec his chap e conside s se ing up an aqueous ECR. These low-ene gy s o age ba e ies, cu en ly
in p e-comme cial s a e (TRL-5), a e supposed o supply high-powe cha ge/discha ge cycles wi h no
signi ican deg ada ion o 1 million cycles. Allegedly, in e ms o ene gy s o ed and supplied powe , his
echnology would all in he mid g ound o a LIB and an ul acapaci o . Howe e , he a o emen ioned is
o be es ed and p o en in he p ojec on a demons a o .
Li le o no ac ual in o ma ion is a ailable abou aqueous ECR ba e ies bu a whi e pape om he de-
elope company [121], alleging he ollowing cha ac e is ics:
• Based in a solu ion o unspeci ied ino ganic chemicals dissol ed in pu e wa e .
• Speci ic ene gy up o 10,69 Wh/kg ( en hs o hund eds o Wh pe ba e y).
• Speci ic powe up o 5 kW/kg.
• P ojec ed li e o mo e han 1 million cycles.
• De e io a es as e when cha ged, so i is ad ised o keep i discha ged as much as possible and no
o e cha ging i .
• Sui ed o high powe and high cyclabili y applica ions.
4.6.1 Resul s
Applying he me hodology om 4.3 we can ob ain he capi al cos s a which an Aqueous ECR could be
conside ed. Assuming a esul o 𝐸(1) ≤0,10kWh, which is ou o he analysed domain, implies ha
he sized ESS is no p o i able, we can ind he maximum capi al cos o mee such condi ion. By sol ing
(4.26) o 𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆
𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 =−𝐿𝐸𝑆𝑆(𝑐𝑠𝑡𝑜𝑝+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐸(2))𝐷𝛼
𝐸𝑆𝑆𝐾𝛼𝐸(𝛼−1)
(1) −𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁, (4.73)
wi h 𝐸(1) =0,10kWh we ind exp ession o he maximum capi al p ices o an Aqueous ECR ba e y
on his applica ion. Table 4.15 compiles he esul s o di e en cos s o ene gy. Fo a ange o 𝐸(1)see
Figu e 4.23.
Table 4.15 –Maximum capi al cos o 𝐸(1) ≤0,1 kWh o di e en cos o ene gy alues
Cos o ene gy (€/kWh) CAPEX (€/kWmin)
0,10 40,19
0,05 20,10
0,02 8,04
4.6.2 Resul s (G id connec ed)
Applying he me hodology om 4.5 o a ange o he ESS capi al cos s we can ob ain hose a which an
Aqueous ECR could be conside ed. Table 4.16 summa ises he esul s ob ained o all o he conside ed
s a egies.
4h ps://www.agis in.eu/
103
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
0 10 20 30 40 50
Capi al cos (€/kW·min)
0,1
0,4
0,8
1,2
Ene gy E(1) (kWh)
cg id (€/kWh)
0,10
0,05
0,02
Figu e 4.23 –Op imal sizing 𝐸(1) o he Geyse Aqueous ECR ene gy s o age sys em o a ange o capi al cos
and sensi i i y o cos o ene gy 𝑐𝑔𝑟𝑖𝑑.
Table 4.16 –Maximum capi al cos o di e en excess powe e m (g id connec ed cases)
Excess powe e m (€/kW) S a egy 1 CAPEX (€/kWmin) S a egy 2 CAPEX (€/kWmin)
0,05 11,00 12,00
0,11 24,00 26,00
0,15 33,00 36,00
4.7 Conclusion
The applica ion analysed in his wo k equi es medium capaci y ( ew kWh) bu high powe (hund eds o
kW) ene gy s o age. Ou indings show ha lywheels and edox low ba e ies ob ain he lowe cos s,
bene i ing om mode a e s o age capaci y cos s bu low powe ela ed cos s, as s a ed in he NREL
li e a u e. Ul acapaci o and li hium-ion p o e o be solid echnologies bu a e penalised by capaci y
capi al cos s and powe capi al cos s espec i ely. Finally, lead acid ba e ies mani es low li e ime and
high economic and en i onmen al cos s o such an applica ion. Howe e , such economic decisions a e
subjec o he speci ic loca ion and ma ke condi ions and should be analysed acco dingly.
I should be emphasized ha he cos s used in he s udy case a e ex apola ed om da a p o ided by
NREL, which o igina es om analysing highe capaci y sys ems and could no be ep esen a i e o his
s udy case. This migh be pa icula ly ele an o he edox low and li hium-ion ba e ies, as he esul s
o he sizing me hodology a e alloca ed in he low-kWh ange, o cing an impo an ex apola ion o he
cos ange o hem, ypically in he 10-100 kWh ange. This conside a ion challenges he op imal esul s
ob ained, as high-powe , low-kWh edox low and li hium-ion ba e ies migh show a highe cos han
he ones used o he analysis.
Sensi i i y analysis e ealed ha luc ua ions o he cos o ene gy ha e a signi ican impac on he ou -
pu o he op imisa ion, since low ene gy p ices educe he economical sui abili y o an ESS. This is es-
pecially ele an o ene gy s o age echnologies wi h highe capaci y cos s such as ul acapaci o s and
lywheels.
Modi ying he h eshold alue o i adiance ha disce ns clouds om ha ing o no an e ec on he sys em
also conside ably in luences he inal decision. Highe h esholds imply a g ea e numbe o conside ed
clouds and ene gy o deli e , he e o e s o age capaci y equi emen s a e highe which bene i s ech-
nologies wi h lowe capaci y cos s.
Flow ba e ies appea o be he mos sui able op ion in e ms o space equi emen s and ins alla ion
mass, while s ill o e ing adequa e esponse pe o mance o he in ended applica ion. Howe e , when
conside ing en i onmen al impac and li e ime, lywheel s o age demons a es ad an ages.
104
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
4.7.1 Fu u e wo k
This sec ion discusses gaps we iden i ied du ing ou esea ch o wo k on u u e analysis.
Main enance cos s
S a -s op cycles and consequen induced wa e hamme damage he in as uc u e, which ansla es
in o inc eased main enance and eplacemen cos s. This cos s a e no eckoned in his s udy since we
we e no in possession o nei he hei inancial wo h no any me hod o e alua ion. Fu u e analysis
should be ca ied ou in o de o de e mine hei alue and accoun o hem in u he esea ch on his
opic.
Con ol and managemen o he ene gy s o age sys em
Al hough, as men ioned in Sec ion 4.1 o he au ho s ha e wo ked in he implemen a ion o a con ol s a -
egy on he ESS and designing an ene gy managemen sys em (EMS), we did no ind any ha conside ed
la ge ese oi -based PV pumping sys ems. Such sys ems ca y hei own challenges ela ed o high
powe usage and la ge ex ensions o he PV sys ems.
On-si e implemen a ion
Implemen ing he ESS on he eal si e, a e an ene gy managemen sys em is designed, will p o ide
u he insigh on he beha iou and pe o mance o he whole sys em ha o he wise is no possible o
app ecia e.
105
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Seconda y egula ion
Seconda y egula ion (aFRR) is a disc e iona y se ice aimed a main aining he balance be ween gen-
e a ion and demand by au oma ically co ec ing de ia ions in g id equency. The esponse ime o his
se ice anges om 20 seconds o 15 minu es.
Each day, he sys em ope a o publishes he ese e equi emen s o seconda y egula ion o each pe-
iod o he co esponding p og am o he nex day. The gene a ion uni s eligible o he se ice submi
hei o e s o he seconda y egula ion band. Once he se ice is assigned, i con inues o co e he
sys em’s needs acco ding o a minimal cos ule [134].
The se ice is compensa ed h ough wo ma ke mechanisms: a ailabili y ( egula ion band) and u iliza ion
( he ene gy p o ided).
Cu en ly, his se ice is managed a a local le el by he Spanish TSO. Howe e , i is expec ed o be
in eg a ed and s anda dized wi h he Eu opean aFRR p oduc and will be managed h ough he imple-
men a ion o he Eu opean pla o m PICASSO.
Te ia y egula ion
Te ia y egula ion (mFRR) is a balancing se ice ha ac i a es ac i e powe ese es wi h he aim o
main aining ne wo k equency and balance. The se ice is igge ed manually, wi h a maximum ac i a-
ion ime o 15 minu es, and i can be ac i a ed o a leas 30 minu es.
The ene gy p o ided by e ia y egula ion is paid a he ma ginal p ice, ollowing an alloca ion p ocess
ha akes place 15 minu es be o e he scheduled pe iod. Simila o seconda y egula ion, his p ocess is
cu en ly managed a he local le el by he TSO, bu i is expec ed o be ans e ed o he Eu opean le el
h ough he implemen a ion o he MARI pla o m [134].
Addi ionally, he P.O. 7.3 ”Regulación e cia ia” men ions he po en ial o pumping s a ions o p o ide his
se ice [135].
Replacemen ese e
The ac i a ion o he Replacemen Rese e (RR) is a balancing se ice ha ac i a es ac i e powe e-
se es wi h he goal o esol ing de ia ions be ween gene a ion and demand ha may be iden i ied a e
he day-ahead ma ke . I aims o es o e o main ain he ene gy le els equi ed o equency eco e y.
Ac i a ion can be ei he manual o au oma ic (using seconda y and e ia y egula ion ene gies), depend-
ing on he need o p epa e o imbalances o equency de ia ions. The se ice mus be ac i a ed wi hin
a maximum ime o 30 minu es and is managed h ough he Eu opean pla o m LIBRA [134].
Se ice p o ide s submi hei RR o e s o he local TSO, which, a e a alida ion p ocess, sends he
o e s o he Eu opean TSO. The Eu opean TSO hen uses he LIBRA pla o m o op imise and de e mine
ac i a ions a he local le el, as well as he in e na ional ene gy exchanges [134].
112
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
6 Real- ime ope a ion & con ol o
inno a i ei iga ioncanal-baseden-
e gy s o age sys ems
The p ope ope a ion o he i iga ion acili ies depends on he e ec i e managemen o wa e esou ces.
In he amewo k o his p ojec , his in ol es o ensu e ha he necessa y olumes o wa e o i iga ion
a e a ailable while p o iding g id se ices. Op imising he con ol o i iga ion sys ems, pa icula ly hose
in ol ing ese oi s and pumps, p esen s a complex ma hema ical challenge. In addi ion o his chal-
lenge, inco po a ing unce ain ies in wa e demand, a ailabili y, and me eo ological and g id condi ions
ep esen s a u he complex aspec o he ask.
This chap e p esen s a ma hema ical desc ip ion o he p oblem unde conside a ion, including he clas-
sical elemen s o he i iga ion sys em and he elemen s de e mined by he long- e m op imisa ion ool
desc ibed in 3. Fu he mo e, unce ain y sou ces a e iden i ied. The chap e hen in oduces he me hod-
ology employed in de eloping he plan con olle capable o ensu ing op imal ope a ion, e en in condi-
ions ha de ia e om he expec ed ope a ing scena io. Finally, he de eloped algo i hm is es ed in a
simula ion en i onmen . The esul s a e hen p esen ed and discussed.
Speci ically, his chap e is s uc u ed as ollows:
i Sec ion 6.1 p o ides an o e iew o he cu en s a e o he a in he ield, in oducing he opic and
e iewing he a ailable solu ions.
ii Sec ion 6.2 ou lines he con olle ’s objec i es and e iews he majo challenges acing he i iga ion
sys em ope a ion. I hen in oduces he ma hema ical o mula ion o he p oblem.
iii Sec ion 6.3 desc ibes he me hodology on which he op imal con olle is based and de elops he
o mula ion o de e mining he p oposed algo i hm.
i Sec ion 6.4 p o ides an analysis o he pe o mance o he con ol algo i hm de eloped on di e en
case s udies.
Sec ion 6.5 concludes he chap e wi h he conclusions d awn. I also p o ides a desc ip ion o he
nex s eps o be aken in he p ojec .
6.1 In oduc ion
The i iga ion sys em unde conside a ion in his p ojec is cu en ly comp ised o a se ies o ese oi s
connec ed by pipes, wi h wa e low acili a ed by pumps o ganised in pumping s a ions. These ese oi s
acili a e he s o age and dis ibu ion o wa e o he ields. The plan ope a o s hen use heu is ic ules o
de e mine he demand o a ce ain amoun o elec ical powe om he g id o main ain su icien wa e
in he uppe ese oi s om he lowe ese oi s.
113
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
The p ima y objec i e o his ope a ional model is o educe elec ici y cos s. To his end, ene gy demand
is scheduled o occu du ing pe iods o he day when, as s ipula ed in he con ac , he p ice pe kWh is
lowe , ypically a nigh . In addi ion, o -g id pho o ol aic panels a e being ins alled o supply an isola ed
pump, so ha when su icien powe is a ailable, he pump associa ed wi h he PV ins alla ion will pump
wa e .
Wi hin he amewo k o his p ojec , he in en ion is o exploi he po en ial pe o mance o he ese oi s
as a s o e o elec ical ene gy in he o m o wa e . This will equi e he ins alla ion o new asse s ha
allow o he bi-di ec ional low o wa e and he ex ac ion o ene gy om wa e lows o be e u ned
o he powe g id. The in oduc ion o new asse s wi hin he sys em will enable new unc ionali ies,
he eby inc easing he complexi y o plan ope a ion. This will o e ule he heu is ic ules ha ope a o s
ha e de eloped o e he yea s.
This new, la ge and mo e complica ed sys em will equi e mo e sophis ica ed con ol schemes o op i-
mallybalancewa e dis ibu ion, ene gyconsump ion, andg idsuppo . T adi ional ule-based o eac i e
con ol me hods may no longe be su icien as hey lack he lexibili y o an icipa e u u e luc ua ions
in wa e a ailabili y, elec ici y p ices and c op i iga ion equi emen s. Ins ead, ad anced op imisa ion-
based app oaches a e needed o ensu e eal- ime adap abili y and long- e m e iciency.
The op imisa ion ool, which is explained in de ail in Chap e 3, p o ides as ou pu , in addi ion o he
dimensioning o he plan elemen s, an op imal ope a ing s a egy o a speci ic scena io. Howe e , om
a con ol pe spec i e, sol ing an o line op imisa ion p oblem (wi h all da a known o es ima ed) and
implemen ing i s ou pu as a se -poin o a physical sys em is a eed o wa d app oach. This app oach
can be conside ed adequa e in cases whe e he plan model is pe ec ly known, bo h in e ms o opology
and pa ame e s, and whe e he o ecas o dis u bances is es ima ed wi h high accu acy.
In sys ems whe e unce ain y is a signi ican conce n, such as he sys em unde conside a ion in his
p ojec , howe e , achie ing op imal con ol is complica ed due o se e al in e dependen ac o s:
• Unce ain y in wa e demand: wa e equi emen s depend on soil condi ions and ex e nal en i on-
men al condi ions, c ea ing a iabili y in i iga ion needs.
• Accu a e wea he o ecas : ain all and e apo a ion a es a e inhe en ly unp edic able and ha e a
signi ican impac on he a ailabili y o wa e in ese oi s. In addi ion, he p oduc ion o pho o ol aic
ene gy is also dependen on clima ic condi ions.
• In eg a ion wi h he powe g id: wa e s o age in ese oi s se es as an ene gy ese e o suppo
he elec ici y g id. Howe e , he imes when he g id is subjec o dis u bances a e comple ely
unp edic able.
Gi en he s ochas ic na u e o he sys em, obus and s ochas ic con ol echniques can help mi iga e he
e ec s o unce ain y by inco po a ing p obabilis ic models o ain all, e apo a ion, and ag icul u al wa e
demand. Howe e , hese me hods can some imes esul in excessi ely conse a i e policies ha may
unde -u ilise a ailable esou ces.
In con as , eedback op imisa ion s uc u es o e a powe ul amewo k o enhancing con ol obus ness
and adap abili y. Unlike open-loop s a egies ha ely solely on o ecas s and p ecompu ed schedules,
eedback-based me hods con inuously inco po a e eal- ime measu emen s in o he op imisa ion p o-
cess. Such measu emen s can include ese oi le els, wea he da a and powe g id signals, allowing
he sys em o espond apidly o unexpec ed dis u bances.
Embedding op imisa ion wi hin a eedback loop enables he con olle o adjus decisions as new in o -
ma ion becomes a ailable, he eby educing he impac o modelling e o s and o ecas inaccu acies.
Feedback op imisa ion p o ides a na u al way o handle cons ain iola ions and sys em nonlinea i ies,
114
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
ensu ing sa e and e icien ope a ion e en unde highly a iable condi ions. When coupled wi h p edic-
i e s a egies like Model P edic i e Con ol (MPC), eedback op imisa ion enables an icipa o y ye eac-
i e decision-making, balancing long- e m planning wi h sho - e m esponse - an essen ial ea u e o
mode n, mul i-objec i e i iga ion sys ems.
MPC echniques p o ide an e ec i e amewo k by explici ly conside ing u u e sys em dynamics wi hin a
eceding ho izon op imisa ion p oblem. MPC con inuously upda es i s decisions based on new measu e-
men s and o ecas s, op imising he ope a ion o pumps and ese oi s. By le e aging p edic i e models
and cons ain s, MPC can schedule wa e ans e s and pumping ope a ions in a way ha minimises en-
e gy cos s, p e en s sho ages, and s a egically aligns wa e s o age wi h pe iods o excess enewable
ene gy gene a ion. Howe e , i should be no ed ha his me hodology s ill elies on an accu a e model
o he exis ing plan o be op imised.
In ecen yea s, he e has been a g owing in e es in he ac ha many nume ical op imisa ion algo i hms,
specially i s o de i e a i e algo i hms, can be in e p e ed as dynamical sys ems. Acco ding o his in e -
p e a ion, i is possible o cons uc an ex ended dynamical sys em consis ing o plan dynamics and he
dynamics o an algo i hm o sol ing an op imisa ion p oblem. The e o e, his sys em will au onomously
d i e he plan o an op imal ope a ing poin . In he con ex o his no ion, a echnique known as Online
Feedback Op imisa ion (OFO) has been in oduced in he li e a u e.
The key idea o OFO is o implemen op imisa ion algo i hms as eedback con olle s, which a e connec ed
wi h a physical plan o o m a closed loop. The e o e, OFO-based con olle s employs eal- ime mea-
su emen s o adap con ol ac ions as and when equi ed. Mo eo e , OFO s a egies demand minimal
model in o ma ion, making i pa icula ly bene icial in si ua ions whe e accu a e models a e challenging
o acqui e. The ime e olu ion o he plan s a e con e ging o he solu ion o an op imisa ion p oblem
ollows he ollowing s uc u e:
• The se o eal- ime measu emen s a e collec ed in he cen al con olle .
• The con olle upda es he con ol ac ions by sol ing an i e a ion o he op imisa ion p oblem.
• The new con ol ac ions a e dispa ched o he sys em by upda ing he se -poin s o he con ollable
de ices.
• A e a wai ing pe iod du ing which he as es ansien s disappea and he sys em measu emen s
a e aken again. Then, he p ocess is epea ed as he sys em con e ges o he solu ion o he op i-
misa ion p oblem.
I is impo an o no e ha wi hin he OFO amewo k, he plan is conside ed a cons ain en o ce ou ine,
i.e. gi en an inpu , he physical sys em will p oduce an ou pu ha sa is ies he inpu -ou pu ela ionship.
As a consequence, he e is no need o e alua e he (possibly nonlinea ) unc ions desc ibing he sys em’s
beha iou , he eby educing he compu a ional cos . This ea u e p o ides OFO-based con ol s uc u es
wi h a high deg ee o scalabili y, making i an a ac i e op ion o la ge-scale and complex sys ems.
Fu he mo e, eedback he measu emen se , ins ead o being model dependen , inhe en ly includes he
e ec o exogenous dis u bances and he co esponding con ol ac ions a e upda ed wi hou he need o
o ecas hem.
Gi en hese ad an ages, he applica ion o OFO-based con olle in combina ion wi h he de eloped
classical op imisa ion ools on his i iga ion sys em is a p omising app oach o achie ing an op imal ade-
o be ween wa e a ailabili y, economic e iciency, and g id in eg a ion.
115
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
6.2 P oblem de ini ion
Conside a non-linea dynamic sys em which is he ein e e ed o as he plan . The beha iou o he
sys em unde conside a ion is de e mined by he ollowing equa ions:
𝑑
𝑑𝑡𝜁= (𝜁,u),
y=g(𝜁)+d,(6.1)
whe e 𝜁 ∈ℜ𝑛deno es he column ec o comp ising he 𝑛s a es o he sys em, u∈ℜ𝑝and y∈ℜ𝑞
a e espec i ely he con ol ac ions and he measu able ou pu s o he plan . The ec o ield (⋅)and he
map g(⋅)desc ibe he dynamic e olu ion o he plan and he ou pu measu emen p ocess, espec i ely.
In addi ion, in his plan , a se o dis u bances is conside ed o be p esen which a e ep esen ed by he
column ec o d∈ℜ𝑤. No e ha hese dis u bances a e conside ed o a ec he sys em in an addi i e
manne .
One o he p ima y assump ions ega ding his plan is ha , gi en a cons an inpu uand a cons an
dis u bance d, he plan exhibi s asymp o ically s able beha iou . This implies ha ansien s dissipa e
apidly, leading o a as con e gence o he ope a ing poin owa ds a s a iona y s a e. Fu he mo e,
i is assumed ha a unique s eady-s a e is eached o a gi en inpu : 𝜁𝑠𝑠 =h𝑠(u), which implies he
ollowing:
0= (𝜁𝑠𝑠,u)= (h𝑠(u),u). (6.2)
I can be concluded ha a di ec consequence o his is he exis ence o a s a iona y mapping be ween
dis u bance- ee measu emen s and con ol ac ions, as ollows:
y𝑠=h(u)∶=g(h𝑠(u)), (6.3)
He e, i is necessa y o conside ha h(⋅)is con inuously di e en iable in u.
In he sys em p e iously desc ibed, conside he p oblem o de e mining he alues o he se -poin s,
which a e bounded by a easible se , in o de o minimise a gi en cos unc ion while sa is ying ce ain
cons ain s on he se o ou pu signals. This can be ma hema ically exp essed as ollows:
minimise
u𝜙(y,u)
subjec o h(u)+d−y=0
y∈𝒴
u∈𝒰,
(6.4)
whe e 𝜙(⋅)deno es a scala unc ion ha encompasses he objec i e o be minimised. The objec i e in
ques ion may be dependen ei he on he inpu s uo he ou pu s y, o indeed on bo h ypes o a iable.
𝒴and 𝒰a e used o deno e, espec i ely, he se s o admissible s eady-s a e alues o he measu ed
a iables and he con ol ac ions. Finally, h(⋅)is he s eady-s a e inpu -ou pu (p obably non-linea ) map
o he dynamic plan , and ddeno es he dis u bance ec o .
The undamen al p oblem is he e o e o s ee he ope a ing poin o he plan o a s a e ha sa is ies all
cons ain s while minimising he cos unc ion alue.
116
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Figu e 6.1 –Online Feedback op imisa ion s uc u e based on g adien low.
6.3 Me hodology
This sec ion ou lines he p ocedu e o ob aining he eedback con ol law ha sol es p oblem (6.4), de-
sc ibed in he p e ious sec ion.
The objec i e o he algo i hm is o d i e he ope a ing poin o he plan o a poin he minimises he unc-
ion 𝜙(y,u)which is a unc ion o he plan ou pu yand inpu u. Conside ing ha bo h he ma hema ical
model o he s a iona y mapping and he dis u bances a e known, hen he cos unc ion can be educed
as ollows:
𝜙(u)∶=𝜙(h(u)+d,u). (6.5)
Fo a momen , assume ha he minimisa ion p oblem 6.4 is uncons ained. In his case, he op imum can
be eached by means o a simple g adien low algo i hm [136]:
𝑑
𝑑𝑡u=−∇𝑢
𝜙(u)
=−∇𝑢h(u)⊤∇𝜙(h(u)+d,u)⊤,(6.6)
whe e ∇𝑢h(u)is a consequence o he chain ule applied o 𝜙(h(u)+d,u). No e ha ∇𝑢h(u)is he
Jacobian ma ix o he unc ion h(⋅)a u. This ma ix will be e e ed o as H om he e on in. This ma ix
ma ix p o ides an indica ion o he sensi i i y o he ou pu s o he inpu s.
P oblem (6.6) can be sol ed in a closed loop wi hou he need o addi ional in o ma ion un il an equilib-
ium poin (𝜁⋆,u⋆)is eached. This s a iona y poin o he plan sa is ies ∇𝜙(h(u)+d,u)⊤=0, hus, i is
a c i ical poin o he cos unc ion 𝜙(⋅).
An al e na i e p oposi ion is o ecognise in (6.6) ha he exp ession h(u)+dco esponds o he se o
measu emen s o he plan , i.e. y. In his case, he algo i hm (6.6) is ew i en in an open loop o m, as
ollows: 𝑑
𝑑𝑡u=−∇𝑢h(u)⊤∇𝜙(y,u)⊤.(6.7)
The new algo i hm (6.7) equi es knowledge o he se o measu emen s y, bu a oids he need o com-
pu e he plan model h(⋅)and hus a oids he need o know explici ly he dis u bances d. The p ima y
bene i o his app oach is ha i acili a es he cons uc ion o a closed-loop sys em, whe ein he plan
(6.1) is go e ned by algo i hm (6.7) as he con olle . The con olle is e e ed o as Online Feedback
Op imisa ion [137, 138]. The in e connec ion o hese wo sys ems is illus a ed in Figu e 6.1.
117
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
The in eg al con ol na u e o (6.7) gua an ees he con e gence o a s eady-s a e op imal poin [139]. In
o de o a oid la ge excu sions in con ol ac ions, a gain (𝜖) wi h a small posi i e alue is added o he
con olle . The e o e, he whole in e connec ed sys em is exp essed as ollows:
𝑑
𝑑𝑡𝜁= (𝜁,u)
y=g(𝜁)+d
𝑑
𝑑𝑡u=−𝜖H⊤∇𝜙(y,u)⊤.
(6.8)
Due o i s eedback na u e, he OFO app oach is obus o model inaccu acy and dis u bance e ec s.
The e o e, he e is no need o a o ecas o dis u bance beha iou o comp ehensi e knowledge o he
plan ; only an es ima ion o sensi i i y is equi ed.
Now ha he uncons ained OFO ope a ion has been e iewed, le ’s e u n o he o iginal p oblem and
conside he cons ain s on he con ol ac ions and ou pu s o he plan . A a ie y o s a egies can be
employed o inco po a e he cons ain s in he cons uc ion o he OFO-based con ol algo i hm:
1. G adien me hods wi h penal y e ms
2. G adien me hods wi h ba ie unc ions
3. P ojec ed g adien lows [140, 141]
4. P imal-Dual saddle poin s [142, 143]
The i s wo me hods ha e he disad an age o modi ying he objec i e unc ion, so hey can only con-
e ge o a alue close o he op imum. Fu he mo e, i should be no ed ha he use o penal y-based
me hods does no ensu e ha he solu ion will sa is y he cons ain s.
P imal-Dual saddle poin me hods ha e demons a ed excellen pe o mance in con e ging o an op imal
solu ion o con ex-de ini e p oblems. Gene ally, hese algo i hms consis o a g adien descen in he
p imal p oblem and a g adien ascen in he dual p oblem. Con olle s based on hese algo i hms ha e
e en been es ed expe imen ally [142, 144]. Howe e , i he objec i e unc ion o cons ain s a e non-
con ex, con e gence o a saddle poin canno be gua an eed. This equi es he addi ion o egula isa ion
e ms o bo h he p imal and dual p oblems. While his ensu es con e gence o he low, he saddle
poin s o he new p oblem will no longe co espond o hose o he o iginal p oblem.
Finally, p ojec ed g adien lows en o ce inequali y cons ain s by u ilising p ojec ion mechanisms. Clas-
sical p ojec ed g adien descen is based on he Euclidean minimum no m, which is used o p ojec he
esul o each i e a ion on o he easible egion. In he in e io o he easible se , he e o e, ajec o ies ol-
low he g adien di ec ion, whe eas a he bounda y hey ollow he s eepes easible di ec ion. I should
be no ed ha hese me hods a e discon inuous sys ems by de ini ion and he e o e equi e non-smoo h
analysis echniques.
Fo he pu poses o his s udy, i was decided ha an algo i hm o he p ojec ed g adien low ype would
be bes sui ed o acili a ing he in eg a ion o he p oblem’s inequali y cons ain . Speci ically, he al-
go i hm p esen ed in [141] has been adop ed, which unc ions by p ojec ing he g adien i e a ion on a
linea isa ion o he easible se a he cu en poin .
The 𝑘- h i e a ion o he in eg al eedback con olle , o mula ed in disc e e ime, can be exp essed as
ollows:
u[𝑘+1]=u[𝑘]+𝜖𝜎(u[𝑘],y[𝑘]), (6.9)
118
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
whe e 𝜖>0is a small ixed s ep-size, and 𝜎(u,y)is de ined as:
𝜎(u,y)∶=a g min
w‖w+G−H−∇𝜙(y[𝑘],u[𝑘])‖2
G
subjec o A(u[𝑘]+𝜖w)≤b
C(y[𝑘]+𝜖Hw)≤d,(6.10)
whe e Gis a con inuous me ic on he easible se .
The exp ession (6.10) de e mines he esul ing ec o om p ojec ing he con ol ac ion ha educes
he objec i e unc ion on o he linea isa ion o he easible sea ch egion. No e ha he cons ain s a e
e alua ed a he poin o which he sys em is expec ed o e ol e in he linea ised space, a he han a
he cu en poin .
The emaining issue o be add essed in he implemen a ion o he algo i hm conce ns he de e mina ion
o he plan sensi i i y ma ix H. I is impo an o no e ha his ma ix is no cons an unless he plan can
be cha ac e ised by a linea ime-in a ian (LTI) sys em, howe e , in ealis ic en i onmen s, he Jacobian
ma ix is s a e o ime dependen . A salien ea u e o con olle s ha a e based on OFO echniques is
ha , due o he eedback s uc u e, hey exhibi a high deg ee o obus ness agains inaccu acies in he
alues o he sensi i i y ma ix [145]. Howe e , imp o ed es ima ion o he alues o his ma ix lead o
enhanced con e gence o he sys em o he desi ed ope a ing poin . The e o e, i is highly desi able o
ha e a good es ima e o he inpu -ou pu sensi i i y.
In cases whe e a model o he plan is a ailable, he mos di ec app oach is o e alua e he de i a i e a
he desi ed ope a ing poin , he eby ob aining he sensi i i y ma ix analy ically. A mo e di ec app oach,
o online p ocedu e, would be o pe u b each o he con ol ac ions sequen ially and de e mine hei
e ec on he ou pu s. This would be equi alen o applying he ini e di e ence me hod o he Jacobian
ma ix. In sys ems whe e such me hods a e no applicable, i is su icien o de e mine a ma ix wi h 0, 1
and -1, depending on whe he he inpu has a ze o e ec on he ou pu , whe he i is di ec ly p opo ional
o in e sely p opo ional. Each o hese me hods p o ides a alue o he sensi i i y a an ope a ing poin .
I is he e o e desi able ha his ma ix be upda ed online by compa ing he expec ed a ia ion wi h ha
ob ained a each s ep.
6.3.1 De elopmen o OFO-based con olle o pump-based
i iga ion plan s
The i s s ep in he OFO-based con olle o mula ion is o iden i y he con ol a iables and he measu ed
a iables. In pump-based i iga ion sys ems, we conside ha he con ol ac ions can be:
1. Elec ical powe supplied o he pump 𝑝𝑒, o pumping di ec ly connec ed o he main g id.
2. Elec ical powe supplied o he pump 𝑝𝑒and mechanical speed o he mo o 𝑛a hose s a ions
equipped wi h equency egula ing asse s.
In bo h cases, he elec ical powe shall emain in s eady s a e wi hin es ablished ope a ing limi s:
𝑝𝑒≤𝑝𝑒≤𝑝𝑒,(6.11)
whe e 𝑢deno es he minimum alue ha 𝑢can each, whe eas 𝑢is used o iden i y i s maximum alue.
Whe e applicable, he o a ional speed o he pump mus also be o ced o emain wi hin he limi s o
s eady s a e ope a ion: 𝑛≤𝑛≤𝑛. (6.12)
119
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Tu bine
Pump
Rese oi 1
Rese oi 0
I iga ion
Pipe Hyd o
Powe
PV
Ba e y
G id
CP
Figu e 6.2 –Rela ionship be ween o line and online op imisa ion ools.
The cons ain s de ined in equa ions (6.11) and (6.12) a e o he box-cons ain ype and can be o mu-
la ed linea ly in a compac o m as ollows:
Au ≤b,(6.13)
whe e he column ec o ug oups he con ol ac ions. The ma ix Acon ains only 1 and -1 o he signs
o he inequali ies, and he column ec o bcon ains he p e iously de ined uppe and lowe limi s o
ope a ion.
The dis u bances ha a e conside ed unknown in his p oblem a e he lows demanded o i iga ion.
Wi h ega d o he sys em’s ou pu s, i is essen ial o closely moni o he le el o he ese oi s, 𝑧, (o he
olume o wa e con ained 𝑊), and he s a e o cha ge o he ba e ies 𝑆𝑂𝐶. I may also be ad isable o
conside measu eso wa e lows. All hese a iables, alongwi h hei espec i eminimumand maximum
limi s, ep esen a se o box cons ain s ha can be exp essed as a linea inequali y cons ain , in he same
way as equa ion (6.13).
I is impo an o no e ha in his p oblem he objec i e is no exac ly o each an op imal ope a ing poin ,
bu o de e mine an op imal wa e use planning. Fo ha eason, he OFO-based con olle is conside ed
o in e ac wi h he long e m o line op imise p esen ed in Sec ion 3.3 h ough he objec i e unc ion.
Figu e 6.2 de ails he in e connec ion be ween hese wo ools.
Speci ically, he sys em is conside ed o ollow he op imal s a egy coming om he o line op imise .
Howe e , his op imisa ion depends on a wea he o ecas and a wa e demand o ecas , which may be
inaccu a e. The e o e, he objec i e o he OFO-based con olle will be o keep sys em ope a ion as close
as possible o he op imal s a egy, while co ec ing any de ia ions caused by condi ions ha di e om
hose p edic ed du ing o line op imisa ion.
120
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Figu e 6.3 –Model o he simples es case.
6.4 Pe o mance assessmen
Thissec ion p esen s he esul so he applica iono hecon olalgo i hmde elopedusing heme hodol-
ogy desc ibed abo e on a case s udy. The objec i e o he p esen s udies is o analyse he unc ionali ies
o he p oposed con olle .
6.4.1 S udy case
To da e, only one case s udy has been analysed. This i iga ion plan model is a simple sys em ha allows
o s aigh o wa d e alua ion o he con olle ’s pe o mance.
The sys em consis s o wo ese oi s, one posi ioned a a highe le el han he o he , connec ed by a
pipe. I is assumed ha he i iga ion sys em akes wa e om a i e , so he olume o he modelled
lowe ese oi is much la ge han he uppe ese oi . The pumping s a ion, which is connec ed o he
main g id, is loca ed adjacen o he lowe ese oi . A schema ic o he sys em is shown g aphically in
Figu e 6.3 and Table 6.1 lis s he main sys em pa ame e s.
Table 6.1 –Pa ame e s o he simple es case.
Pa ame e Value
Maximum olume o he downs eam ese oi 106m3
Minimum olume o he downs eam ese oi 0m3
Maximum heigh o downs eam ese oi 1m
Minimum heigh o downs eam ese oi 0m
Maximum olume o he ups eam ese oi 600m3
Minimum olume o he ups eam ese oi 400m3
Maximum heigh o ups eam ese oi 80m
Minimum heigh o ups eam ese oi 60m
Linea p essu e loss coe icien o he pipe 0.05 s2
m5
Pump coe icien A 120m
Pump coe icien B 0,002 𝑠2
𝑚5
Pump e iciency 72%
Pump maximum powe 16kW
The ini ial olume o he downs eam ese oi is 105𝑚3, while he ups eam ese oi 2 has a olume o
500𝑚3a he beginning o he simula ion. Finally, i is conside ed ha he pump is inac i e. The i iga ion
wa e consump ion p o ile has been andomly gene a ed.
The o line op imisa ion ool, which de e mines heop imalconsump ionp o ileo he pump, is conside ed
o upda e i s e e ences e e y hou . The OFO-based con olle upda es he con ol ac ions e e y minu e,
in his i s s udy only he powe consumed by he pump.
121
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
G id
connec ion
G id
connec ion
PV sys em
Pump sys em
PV sys em
Pump sys em
AC g id DC g id
Figu e 7.2 –AC s DC in e connec ions.
pass h ough he p ima y g id. This also has implica ions on he low o ene gy, and i is no possible o
di ec ly con ol which ene gy is deli e ed o he g id and which is ed o he pumping sys em. Based on
hese ac s, i is in e es ing o conside connec ing hese wo sys ems wi h DC. The di e ence be ween
hese wo schemes is shown in Figu e 7.2.
The DC con igu a ion main ains he wo essen ial con e e s o he pumping and PV sys ems while in-
e connec ing hem using a DC mic og id. I includes an addi ional con e e o in e connec his sys em
o he p incipal AC g id. This con igu a ion’s main ad an age is he possibili y o ope a ing in islanded
mode. The pumping sys em can be ed di ec ly om he PV sys em wi hou bypassing he elec ical
ene gy h ough he p incipal g id. E en i he g id is down, he sys em could s ill ope a e. The main dis-
ad an age is i s highe ini ial cos and i s complexi y. Howe e , i s highe p ice can e en ually compensa e
o mo e hou s o ope a ion in islanded mode, i.e., wi hou buying ene gy om he p incipal g id, and he
possibili y o o e ing g id se ices om he con e e connec ing his sys em o he p incipal g id. This
con igu a ion makes i easie o p o ide g id se ices om he main con e e . I is sui able o ope a ing
in islanded mode and is conside ed a alid op ion o his applica ion.
7.3 Con ol a chi ec u es o he con e e connec ed o
he p ima y g id
On he DC g id in e connec ion s a egy, he e a e a leas h ee con e e s. The i s one, he DC/DC
con e e o he PV sys em, pe o ms he MPPT algo i hm; he second one is he AC/DC con e e o he
pumping sys em, which egula es he equency o he pumping sha and i s ol age. The con ol o be
applied a he hi d con e e mus s ill be de ined. This sec ion’s main subjec is an ini ial discussion on
which possible con ol a chi ec u es can be applied o his con e e .
The li e a u e con ains con ol s a egies and a chi ec u es o ul il di e en equi emen s. Some o he
mos common s a e-o - he-a con ol a chi ec u es and unc ionali ies a e highligh ed he e. Speci ically,
h ee con olle s a e p esen ed: PQ con ol, DC ol age con ol, and AC g id- o ming con ol.
PQ con ol, o AC g id- ollowing con ol, elies on a Phase-Locked Loop (PLL) o synch onize wi h he g id
ol age. This elemen eads he g id’s ol age and akes ou he angle so he con e e ’s in e nal angle
e e ence o a es a he same angle as he g id. I ope a es in he synch onous 𝑑𝑞0 e e ence ame and
egula es he ou pu cu en o independen ly con ol he ac i e (P) and eac i e (Q) powe deli e ed o
he g id. This con ol s a egy is ypically used in sys ems whe e he s ong g id p o ides a s able ol age
e e ence. Thus, i depends on he p esence o an ex e nal AC ol age sou ce o unc ion co ec ly. The
same happens on he DC side; i elies on a s able DC g id ol age o be connec ed, as his con olle
canno o m he DC side ol age.
128
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
dc
dc
dc
DC Vol age Loop
AC Vol age suppo
kV
ac
Figu e 7.3 –Example o a DC ol age con ol a chi ec u e.
+
+
+
uq
PI
PIu
+
+
C
+
+
1
s
AC Vol age Loop
_
_
u
q
d
ω0 ac
C
ω0 ac
uq*
uqd
u = 0
d*
ω0
_
Sync honiza ion Loop
kP
P
ω
1
τs+1
Figu e 7.4 –Example o an AC g id- o ming con ol a chi ec u e wi h d oop con ol.
An al e na i e, ha does no equi e a s able DC ol age o be connec ed wi h, is he DC ol age con ol
scheme (see Figu e 7.3), as his con olle is used o egula e he ol age o he DC link by adjus ing he
ac i e powe exchange on he AC side o he con e e . This con ol scheme is usually implemen ed in
𝑑𝑞0and equi es a PLL o synch onize wi h he AC g id ol age. Thus, i also depends on he p esence
o an ex e nal AC ol age sou ce o unc ion co ec ly. An al e na i e con ol a chi ec u e ha does no
equi e an ex e nal AC ol age sou ce is AC g id- o ming con ol.
AC g id- o ming con ol, o en implemen ed h ough i ual synch onous machine models, d oop con ol,
o powe -angle egula ion, eplaces he PLL wi h an in e nal ol age and equency e e ence (see Fig-
u e ?? o example). This allows he con e e o egula e bo h ol age ampli ude and equency, making
i sui able o ope a ion in islanded sys ems, weak g ids, o black-s a condi ions. G id- o ming con ol
enables he VSC o ac as he sys em’s ol age sou ce. I can emula e ine ia and damping, acili a ing
load sha ing and sys em s abili y in in e e -domina ed ne wo ks. I is essen ial o no e ha a s able DC
ol age is equi ed on he DC side, as his con ol s a egy can o m he AC ol age bu no he DC. Di -
e en con ol a chi ec u es ha e been p oposed in he li e a u e [146, 147] o o e come his limi a ion,
one o which is p esen ed nex .
7.3.1 Dual-Po con ol
The p e iously discussed con ol a chi ec u es canno p o ide g id- o ming unc ionali ies o bo h AC and
DC sides. In he li e a u e, se e al p oposed con ol a chi ec u es [146, 147] exis ha can p o ide his
se ice on bo h sides. One p oposed in [147] is he one depic ed in Figu e 7.5. The gene al scheme is
e y simila o a adi ional AC g id- o ming con ol, which includes an AC ol age ec o con ol wi h a
cascaded g id cu en con ol. The main di e ence comes in he synch oniza ion loop, whe e a di e en
scheme is used ins ead o a classical PLL. This scheme uses he DC ol age o synch onize he con e e
wi h he g id angle.
129
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
+
+
+
uq
PI
PIu
+
+
C
k
dp
+
+
1
s
AC Vol age Loop
_
_
u
q
d
ω0 ac
C
ω0 ac
uq*
uqd
u = 0
d*
ω0
_dc
dc
Dual Po loop
p
k
dp
i
Figu e 7.5 –Dual-Po con ol a chi ec u e.
Geyse
s o age
G id
connec ion
G id
connec ion
G id
connec ion
Geyse
s o age
G id
connec ion
PV sys em
Pump sys em
PV sys em
PV sys em
PV sys em
Pump sys em
Pump sys em
Pump sys em
Wi hou s o age Wi h s o age
Wi hou DC/DC
con e e
Wi h DC/DC
con e e
Figu e 7.6 –Schemes o he analysed AGI con igu a ions.
7.4 Discussion on possible AGI con igu a ions
Fou di e en con igu a ions can be analysed based on p e ious discussions on he elemen s o be in-
cluded in he sys em. This depends on whe he o ins all s o age and i he PV sys em consis s o a
DC/DC con e e o is di ec ly connec ed o he DC g id. Figu e 7.6 ep esen s hese ou con igu a ions.
These con igu a ions a e nex analysed based on which con ol a chi ec u e is included in he con e e
in e connec ing he sys em wi h he g id.
Conside ing he con igu a ion wi hou he DC/DC con e e complica es he op ion o ope a ing he PV
sys em ollowing an MPPT. Depending on he con ol scheme con igu ed in he main con e e , some
limi ed MPPT can be p o ided. I is limi ed in he sense ha he DC ol age le el on he DC g id canno
a y up and down wi hou limi s, as o he con e e s a e connec ed o his DC g id, such as he pump
s a ion con e e . Mo eo e , e y low o high le els on he DC side can cause unde - and o e -modula ion
p oblems on he con e e . The con e e schemes ha could p o ide limi ed MPPT a e he DC ol age
and Dual-Po con ol. The main limi a ion o he DC ol age con ol is ha i can o e only limi ed g id
se ice, i.e., only he ones equi ing eac i e powe . The o he con ol scheme, AC g id- o ming, can no
p o ide MPPT as i can no egula e he DC ol age. Howe e , i will be possible o o e g id se ices.
130
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Ceq
P
ac +
_
}
%idc dc
AC side
elec ic scheme
DC side
elec ic scheme
Figu e 7.7 –VSC elec ic scheme model.
VVV
}
a,b,c
PLL
P
Q
*
*
τ s+1
1
θ
q
calc.
τ s+1
1
P
τ s+1
1
Q
i
τ s+1
1
i
ia,b,c iq
id
*
*
iq
id
P
Q
a b c
qd0
abc
qd0
abc d
Figu e 7.8 –Con olled cu en sou ce model.
Including a DC/DC con e e wi h he PV sys ems ensu es he possibili y o including MPPT. In his case, i
he cen al con olle is equipped wi h DC ol age con ol, simila ly o he p e ious case, he g id se ices
o p o ide a e limi ed.
A possibili y is o include some ba e y s o age. This can help o smoo h ansien s and enhance he
ope a ion in s and-alone mode.
When conside ing he di e en con ols o apply o he main con e e , a gene al, impo an conside a ion
is o s udy how he pe u ba ions p opaga e be ween he AC and DC sys ems.
7.5 Models o s udy he connec ion o he p ima y g id
Di e en models ha e been implemen ed o p ope ly s udy he connec ion o he p ima y g id, emula ing
he DC g id con igu a ion. The main con e e is modelled as a wo-le el VSC con e e . The elec ic
model includes he AC elec ical side wi h i s ans o me /RL- il e , and he con ol inpu s a e applied ia
a con olled ol age sou ce. The DC side is modelled as a con olled cu en sou ce, ensu ing he powe
balance be ween he AC and DC sides and including a capaci o . The model scheme used is depic ed in
Figu e 7.7.
The pumping sys em has been modelled wi h a wo-le el VSC con e e and a con olled cu en sou ce.
The pumping sys em is connec ed o he DC side ia a con e e wi h he same scheme as he one used
o he main con e e (Figu e 7.7). The con olled cu en sou ce is modelled as in Figu e 7.8.
Finally, he s o age has been modelled as a cons an capaci o , and he PV sys em has been modelled as
a cu en sou ce.
These elemen s a e modelled in di e en ways. Th ee di e en ypes o models a e included. These a e
desc ibed nex .
131
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
7.5.1 S eady-s a e Model
The s eady-s a e model is used o calcula e he powe low scena io. I can calcula e s eady-s a e pe o -
mance indices, such as ol age d oop be ween lines, powe dis ibu ion inside he DC g id, e c. Mo eo e ,
i will be help ul o calcula e he linea model’s linea iza ion poin and p ope ly ini ialize he MATLAB-
Simulink model.
To sol e he powe low in his case, i has o be conside ed ha he algo i hm used has o accoun
o AC and DC g ids. Gene ally, wo di e en me hods exis , ca ego ized in o sequen ial and uni ied
app oaches. Sequen ial me hods in ol e sol ing AC and DC equa ions s ep-by-s ep, as seen in [148,
149, 150]. Uni ied me hods simul aneously sol e he AC and DC sys ems, as demons a ed in e e ence
[151]. One ad an age o he sequen ial me hod is i s compa ibili y wi h exis ing AC-based powe low
so wa e, allowing o he in eg a ion o DC sys ems wi hou equi ing ex ensi e p og am modi ica ions,
unlike he uni ied app oach, which necessi a es changing he en i e implemen a ion o sol e bo h AC and
DC sys ems simul aneously.
An al e na i e app oach, sui able o small-sized sys ems, is o include all non-linea equa ions con o m-
ing o he powe low scena io and sol e hem wi h a non-linea sol e . This is badly scaled i he sys em
needs o be inc eased, bu i has he ad an age ha i can be ully con igu ed. Conside ing ha he sys em
in his case is small, his app oach is used o sol e he powe low.
To compu e he s eady-s a e solu ion o he sys em, we sol e a non-linea cons ained op imisa ion p ob-
lem. The p oblem is o mula ed as:
minimise
x (x)
subjec o g(x)=0.(7.1)
Whe e:
•x∈ℝ𝑛is he ec o o sys em a iables, ini ialized wi h x0, which includes ol ages magni udes,
ol age angles and powe s.
•𝑓(x)is an auxilia y objec i e unc ion used o egula ize o selec among mul iple easible solu ions.
The implemen a ion may e u n ze o o a mino no m-based penal y.
•g(x)=0 ep esen s he nonlinea equali y cons ain s imposed by he powe low equa ions and
con e e s eady-s a e condi ions.
The e a e no o he cons ain s imposed besides g(x)=0.
• No linea inequali y cons ain s (Ax ≤b),
• No linea equali y cons ain s (Aeqx=beq),
• No explici uppe o lowe bounds on a iables (l𝑏=−∞,u𝑏=+∞).
The p oblem is sol ed using MATLAB’s mincon unc ion wi h he in e io -poin algo i hm:
x∗= mincon (𝑓,x0,A,b,Aeq,beq,l𝑏,u𝑏,g,op ions).
The solu ion x∗con ains he s eady-s a e ope a ing poin o he sys em.
132
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
7.5.2 Linea Model
Small-signal s udies in ol e analysing he sys em a ound i s ope a ing poin ia a linea model. Gen-
e ally, he models used a e non-linea ; hese models need o be linea ized a ound he ope a ion poin ,
which can be calcula ed based on he s eady-s a e analysis, i.e., sol ing he AC/DC powe - low p e i-
ously o mula ed.
Small-signal s udies p o ide aluable insigh s in o he sys em’s dynamic s abili y and con ol pe o -
mance. Howe e , building hese linea models is challenging, and some mis akes can be made du ing
he p ocess. The e o e, e i ying he models by compa ing he esul s ob ained in he linea model wi h
he non-linea one is essen ial.
The s eps ollowed wi h he linea model conside he ollowing:
1. Compu a ion o he sys em’s ope a ion poin ia an AC/DC powe low.
2. Linea iza ion poin calcula ion.
3. Cons uc ion o all he linea models included in he AC/DC sys em.
4. In eg a e all he linea models.
5. Linea model alida ion.
6. Linea model analysis.
The compu a ion o he comple e linea model o he sys em can be di ided in o sub-linea models. Once
all he sub-linea models a e compu ed, hey can be in e connec ed using linea algeb a. One sub-linea
model is connec ed o ano he i he ou pu o his sub-linea model is he inpu o ano he one, and ice
e sa. Nex , he mos c i ical sub-linea models a e included.
l-ci cui
The s a e-space model o an AC 𝑟𝑙-ci cui connec ing an AC node 𝑥 o an AC node 𝑦can be ep esen ed
as:
• S a e ec o : Δ𝑥(𝑡)=[Δ𝑖𝑞
𝑥𝑦,Δ𝑖𝑑
𝑥𝑦]𝑇
• Inpu ec o : Δ𝑢(𝑡)=[Δ𝑣𝑞
𝑥,Δ𝑣𝑑
𝑥,Δ𝑣𝑞
𝑦,Δ𝑣𝑑
𝑦]𝑇
• Ou pu ec o : Δ𝑦(𝑡)=[Δ𝑖𝑞
𝑥𝑦,Δ𝑖𝑑
𝑥𝑦]𝑇
𝐴=[−𝑅
𝐿−𝜔0
𝜔0−𝑅
𝐿];𝐵=[1
𝐿0−1
𝐿0
01
𝐿0 −1
𝐿];𝐶=[ℐ2𝑥2];𝐷=[02𝑥4], (7.2)
whe e 𝑣𝑞,𝑑
𝑥and 𝑣𝑞,𝑑
𝑦a e he 𝑞𝑑 ol ages a he AC nodes 𝑥and 𝑦, espec i ely; 𝑖𝑞,𝑑
𝑥𝑦 is he cu en lowing
om node 𝑥 o node 𝑦and 𝑅and 𝐿a e he 𝜋-sec ion line esis ance and induc ance, espec i ely. This
model can ep esen he con e e ’s AC side elec ical scheme and a Thé enin equi alen model.
133
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
𝑞𝑑-angle Ro a ion
All he blocks linked o he AC sys em a e ep esen ed in he con e e local 𝑞𝑑- ame, which is gi en
by i s angle e e ence es ima ed by i s PLL. To p ope ly in e connec hese subsys ems, i is necessa y o
ans o m he inpu s o he di e en blocks om he global ame (AC g id) o he local ame (con e e
local 𝑞𝑑- ame). This is done wi h a o a ion ma ix (7.4), which akes in o accoun he PLL de ia ion (Δ𝑒𝜃)
while i is es ima ing he g id equency (𝜔𝑔).
[Δ𝑥𝑞
𝑙
Δ𝑥𝑑
𝑙]=𝑇𝑔−𝑙⎡
⎢
⎣Δ𝑥𝑞
𝑔
Δ𝑥𝑑
𝑔
Δ𝑒𝜃⎤
⎥
⎦,(7.3)
𝑇𝑔−𝑙 =[cos(𝑒𝜃0) −sin(𝑒𝜃0) −sin(𝑒𝜃0)𝑥𝑞
0𝑔−cos(𝑒𝜃0)𝑥𝑑
0𝑔
sin(𝑒𝜃0)cos(𝑒𝜃0)cos(𝑒𝜃0)𝑥𝑞
0𝑔−sin(𝑒𝜃0)𝑥𝑑
0𝑔], (7.4)
Δ𝑒𝜃=(Δ𝜔𝑃𝐿𝐿(𝑠)−Δ𝜔𝑔), (7.5)
whe e 𝑇𝑔−𝑙 is he ans o ma ion ma ix, Δ𝑥𝑞
𝑙and Δ𝑥𝑑
𝑙a e he s a e ans o med a iables in he local
ame, Δ𝑥𝑞
𝑔and Δ𝑥𝑑
𝑔a e he s a e a iables in he global ame, 𝑒𝜃0is he angle di e ence in he s eady-
s a e ope a ion poin be ween he global and he local ame and 𝑥𝑞
0𝑔and 𝑥𝑑
0𝑔a e he a iables o be
ans o med a he ope a ion poin exp essed in he global ame. The ou pu s ha e o be ans o med
om he local ame o he global ame using (7.7), as:
[Δ𝑥𝑞
𝑔
Δ𝑥𝑑
𝑔]=𝑇𝑙−𝑔⎡
⎢
⎣Δ𝑥𝑞
𝑙
Δ𝑥𝑑
𝑙
Δ𝑒𝜃⎤
⎥
⎦,(7.6)
𝑇𝑙−𝑔 =[cos(𝑒𝜃0)sin(𝑒𝜃0) −sin(𝑒𝜃0)𝑥𝑞
0𝑙+cos(𝑒𝜃0)𝑥𝑑
0𝑙
−sin(𝑒𝜃0)cos(𝑒𝜃0) −cos(𝑒𝜃0)𝑥𝑞
0𝑙−sin(𝑒𝜃0)𝑥𝑑
0𝑙], (7.7)
whe e 𝑥𝑞
0𝑙and 𝑥𝑑
0𝑙a e he a iables o be ans o med and exp essed in he local ame a he s eady-s a e
linea iza ion poin .
Phase-Locked Loop
The PLL con olle ep esen a ion in s a e-space o m is included nex .
• S a e ec o : Δ𝑥(𝑡)=[Δ𝑥𝑝𝑙𝑙]
• Inpu ec o : Δ𝑢(𝑡)=[Δ𝑣𝑑
𝑔,𝑐]
• Ou pu ec o : Δ𝑦(𝑡)=[Δ𝜔𝐼𝑃𝐶]
𝐴=[0];𝐵=[1];𝐶=[−𝑘𝑃𝐿𝐿
𝑖];𝐷=[−𝑘𝑃𝐿𝐿
𝑝], (7.8)
whe e 𝑣𝑑
𝑔,𝑐 is he 𝑑componen o he g id ol age seen by he con e e , 𝜔𝐼𝑃𝐶 is he PLL’s es ima ed
equency. The p opo ional and in eg al PLL pa ame e s a e 𝑘𝑃𝐿𝐿
𝑝and 𝑘𝑃𝐿𝐿
𝑖. No e ha all a iables
used in his block e e o he con e e angle (𝑣𝑑
𝑔,𝑐).
134
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Con e e angle di e ence
F om he ob ained 𝜔𝑐 equency and he e e ence equency 𝜔𝑔𝑟𝑖𝑑, he angle di e ence used o apply he
e e ence change be ween global and local a iables can be ep esen ed in s a e-space o m as:
• S a e ec o : Δ𝑥(𝑡)=[Δ𝜃𝑒]
• Inpu ec o : Δ𝑢(𝑡)=[Δ𝜔𝑐,Δ𝜔𝑔𝑟𝑖𝑑]𝑇
• Ou pu ec o : Δ𝑦(𝑡)=[Δ𝜃𝑒]
𝐴=[0];𝐵=[1 −1];𝐶=[1];𝐷=[01𝑥2], (7.9)
whe e Δ𝜔𝑐is he equency es ima ed by he PLL, Δ𝜔𝑔𝑟𝑖𝑑 is he AC g id e e ence equency, and 𝜃𝑒is
he di e ence angle be ween he g id e e ence and he con e e .
G id cu en con ol
The s a e-space ep esen a ion o his con olle can be ep esen ed as:
• S a e ec o : Δ𝑥(𝑡)=[Δ𝑥𝑞,Δ𝑥𝑑]𝑇
• Inpu ec o : Δ𝑢(𝑡)=[Δ𝑖𝑞
𝑠∗,Δ𝑖𝑑
𝑠∗,Δ𝑖𝑞,𝑐
𝑠,Δ𝑖𝑑,𝑐
𝑠]𝑇
• Ou pu ec o : Δ𝑦(𝑡)=[Δ𝑣𝑞,𝑐
𝑑𝑖𝑓𝑓,Δ𝑣𝑑,𝑐
𝑑𝑖𝑓𝑓]𝑇
𝐴=[02𝑥2];𝐵=[1 0 −1 0 0 0
0 1 0 −1 0 0];
𝐶=[𝑘𝑖−𝑖𝑠0
0 𝑘𝑖−𝑖𝑠];𝐷=[𝑘𝑝−𝑖𝑠0 −𝑘𝑝−𝑖𝑠𝜔0𝐿𝑒𝑞 1 0
0 𝑘𝑝−𝑖𝑠−𝜔0𝐿𝑒𝑞 −𝑘𝑝−𝑖𝑠0 1](7.10)
whe e 𝑖𝑞,𝑑
𝑠∗a e he cu en e e ences, 𝑖𝑞,𝑑,𝑐
𝑠a e he di ci cui cu en s exp essed in he con e e local
ame and, 𝑣𝑞,𝑑,𝑐
𝑑𝑖𝑓𝑓 a e he ol ages applied a he AC ci cui in he con e e local ame. The p opo ional
and in eg al con ol pa ame e s a e 𝑘𝑝−𝑖𝑠and 𝑘𝑖−𝑖𝑠,𝜔0is he nominal g id equency, and 𝐿𝑒𝑞is he equi -
alen induc ance o he AC ci cui .
7.6 Ini ial Resul s
The p e iously discussed con ols and models ha e been implemen ed in he case s udy shown in Fig-
u e 7.9. The main con e e con ol selec ed o hese ini ial esul s is he dual-po con ol depic ed in
Figu e 7.5. The PV sys em is modelled as a cu en sou ce whe e he injec ed cu en depends on he DC
ol age. The Geyse s o age is modelled as a supe cap ha includes an a e age DC/DC con e e model
con olling he supe cap’s ol age le el. The pump sys em is modelled as a ol age sou ce con e e
imposing a ol age and equency and a con olled load as depic ed in Figu e 7.8.
The PV sys em powe is 275 kW, he pump sys em powe is 160 kW, and he Geyse s o age is con-
side ed o gi e 100 kW o 1 minu e. Thus, he supe cap is dimensioned o 18,75 F. The main con e e
powe is 320 kVA, and i is connec ed a 400 V. The connec ion o he main g id is done ia a ans o me
135
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Geyse
s o age
G id
connec ion
PV sys em
Pump sys em
V / θ1
1
Vdc
1
Vdc
2
Vdc
3
Vdc
4
Figu e 7.9 –Ini ial case s udy scheme.
Table 7.1 –Main con e e pa ame e s.
Pa ame e Symbol Value Uni s
Resis ance il e R 0,01 pu
Impedance il e X 0,1 pu
DC side condense C 1e-3 F
Cu en con ol p opo ional gain 𝑘𝑐
𝑝0,16 V/A
Cu en con ol in eg al gain 𝑘𝑐
𝑖5 V/A
Vol age con ol in eg al gain 𝑘𝑐
𝑖2 A/V
Vol age con ol p opo ional gain 𝑘𝑐
𝑝3 A/V
Synch oniza ion in eg al gain 𝑘𝑑𝑝
𝑖0,1 ad/(V·s)
Synch oniza ion p opo ional gain 𝑘𝑑𝑝
𝑝1 ad/V
ha ele a es he ol age om 400 V o 25 kV. The g id’s SCR is conside ed o be 2. Thus, emula ing a
ela i ely weak g id. The DC ol age le el o he DC g id is 800 V. The main con e e ’s pa ame e s a e
gi en in Table 7.1
7.6.1 Powe low solu ion
The case s udy p esen ed conside s he ollowing scena io. The PV sys em injec s ull powe o he DC
g id, i.e., is injec ing 275 kW, and he pump sys em is wo king a ull powe , i.e., abso bing 160 kW om
he DC g id. The powe low is sol ed conside ing he main con e e injec s 0 a o he AC g id. The
solu ion o he powe low is sol ed as explained in Sec ion 7.5.1 and he esul s a e gi en in Table 7.2.
F om he solu ion o he powe low, i can be seen ha he scena io conside ed is well de ined, as all
ol ages a e se a a easonable le el. Mo eo e , i can be concluded ha he algo i hm o sol e he
powe low is well designed. The solu ion is eached in 3 i e a ions.
Table 7.2 –Powe low solu ion.
Pa ame e Value Uni s
𝑉1401,96 V
𝜃16,42 deg ee
𝑃𝑉𝑆𝐶 112,63 kW
𝑄𝑉𝑆𝐶 0 k a
𝑉𝑑𝑐
1800 V
𝑉𝑑𝑐
2799,79 V
𝑉𝑑𝑐
3800,34 V
𝑉𝑑𝑐
4800 V
136
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
Figu e 7.10 –Linea and non-linea models compa ison.
7.6.2 Small-Signal analysis
The linea model o he case s udy is compu ed. The linea model will gi e impo an in o ma ion abou
he sys em s abili y and con ol pe o mance. Fi s ly, o ensu e he linea model’s alidi y, he linea model
is compa ed wi h he non-linea model when a small pe u ba ion is made. In his case, a 1% ol age
change in he connec ion o he main g id is simula ed. The compa ison is shown in Figu e 7.10.
Nex , he sys em’s eigen alues a e compu ed. These a e shown in Tab. 7.3. All eigen alues ha e a
nega i e eal pa ; he e o e, he sys em is s able. Mo eo e , all he eigen alues ha e a damping highe
han 5 %, which indica es ha , in gene al, he sys em dynamics will espond app op ia ely.
7.6.3 PV s ep change
The sys em is checked when a sudden s ep change in he gene a ed powe in he PV sys em occu s. This
can emula e a loss o gene a ions due o an unexpec ed cloud ha co e s he PV panels. The gene a ed
powe is changed om ull (275 kW) o 0 kW.
The main con e e e minals’ ac i e and eac i e powe s magni udes a e shown in Figu e 7.11. The con-
e e can adjus he new ope a ion poin by adjus ing he amoun o ac i e and eac i e powe deli e ed
o he g id. As shown, a he ini ial poin , he con e e injec s app oxima ely 100 kW, while a e he
dis u bance, i abso bs a ound 200 kW.
137
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[40] S.P. Adhau, R.M. Moha il, and P.G. Adhau. Mini-hyd o powe gene a ion on exis ing i iga ion
p ojec s: Case s udy o indian si es. Renewable and Sus ainable Ene gy Re iews, 16(7):4785–
4795, Sep embe 2012.
[41] Alessand o Mo abi o and Pa ick Hend ick. Pump as u bine applied o mic o ene gy s o age and
sma wa e g ids: A case s udy. Applied Ene gy, 241:567–579, May 2019.
[42] Na id Mousa i, Ganesh Ko hapalli, Da yoush Habibi, Cho on K. Das, and Ali Baniasadi. A
no el pho o ol aic-pumped hyd o s o age mic og id applicable o u al a eas. Applied Ene gy,
262:114284, Ma ch 2020.
[43] Na id Mousa i, Ganesh Ko hapalli, Da yoush Habibi, Mehdi Khiadani, and Cho on K. Das. An im-
p o ed ma hema ical model o a pumped hyd o s o age sys em conside ing elec ical, mechanical,
and hyd aulic losses. Applied Ene gy, 247:228–236, Augus 2019.
[44] Nicholas Gilmo e, Thomas B i z, E ik Maa ensson, Ca lo O begoso-Jo dan, Sebas ian Sch ode ,
and Ma ino Male ba. Con inen al-scale assessmen o mic o-pumped hyd o ene gy s o age using
ag icul u al ese oi s. Applied Ene gy, 349:121715, No embe 2023.
[45] Se gi Cos a-Dilmé, J. Ca los Oli es-Camps, Paula Muñoz-Peña, Pau Ga cía-Mo illa, O iol Gomis-
Bellmun , and Edua do P ie o-A aujo. Redesign o la ge-scale i iga ion sys ems o lexible ene gy
s o age. In 2024 IEEE PES Inno a i e Sma G id Technologies Eu ope (ISGT EUROPE), pages 1–5.
IEEE, Oc obe 2024.
[46] Li Wang, Dong-Jing Lee, Jian-Hong Liu, Zan-Zia Chen, Zone-Yuan Kuo, Jin-Shi Hsu, Cheng-Mei
Chen, Shen-Syi Chiu, Ming-Hua Tsai, Wei-Taw Lin, and Yun-Chung Lee. Economic analysis o
ins alling mic o hyd o powe plan s in chia-nan i iga ion associa ion o aiwan using wa e o i i-
ga ion canals. In 2008 IEEE Powe and Ene gy Socie y Gene al Mee ing - Con e sion and Deli e y
o Elec ical Ene gy in he 21s Cen u y, pages 1–5. IEEE, July 2008.
[47] Li Wang, Dong-Jing Lee, Jian-Hong Liu, Zan-Zia Chen, Zone-Yuan Kuo, Huei-Yuan Jang, Jiunn-Ji
You, Jin-Tsang Tsai, Ming-Hua Tsai, Wey-Tau Lin, and Yeun-Jong Lee. Ins alla ion and p ac ical
ope a ion o he i s mic o hyd o powe sys em in aiwan using i iga ion wa e in an ag icul u e
canal. In 2008 IEEE Powe and Ene gy Socie y Gene al Mee ing - Con e sion and Deli e y o
Elec ical Ene gy in he 21s Cen u y, pages 1–6. IEEE, July 2008.
[48] Ila ia Bu e a and Robe o Bales a. Es ima ion o he hyd opowe po en ial o i iga ion ne wo ks.
Renewable and Sus ainable Ene gy Re iews, 48:140–151, Augus 2015.
[49] F ançois P e os and G Guicha d. Réalisa ion e exploi a ion d’une mic ocen ale: modali és d’un
pa ena ia du able en e l’asco des i igan s de la c au e la socié é du canal de p o ence. In ICID
Con e ence, Special Session ‘I iga ion and Ene gy’, Mon pellie , F ance, 2015.
[50] Deme io An onio Zema, Angelo Nico a, Vincenzo Tambu ino, and San o Ma cello Zimbone. A
simple me hod o e alua e he echnical and economic easibili y o mic o hyd o powe plan s in
exis ing i iga ion sys ems. Renewable Ene gy, 85:498–506, Janua y 2016.
[51] Tommaso B azzini, Edga Lo enzo-Saez, Vicen Sales Ma ínez, Es he López Pé ez, Ma V. O ega-
Reig, and Guille mo Palau-Sal ado . Is small-scale hyd opowe ene gy eco e y a iable al e na-
i e o clima e change mi iga ion and adap a ion? he case o he adi ional i iga ion sys em in
alencia (spain). Ene gy Repo s, 12:736–749, Decembe 2024.
[52] MiguelC espo Chacón, JuanAn onio Rod íguez Díaz, Jo ge Ga cía Mo illo, and AonghusMcNabola.
Hyd opowe ene gy eco e y ini iga ion ne wo ks: Valida iono ame hodology o lowp edic ion
and pump as u bine selec ion. Renewable Ene gy, 147:1728–1738, Ma ch 2020.
144
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[53] MiguelC espo Chacón, JuanAn onio Rod íguez Díaz, Jo ge Ga cía Mo illo, and AonghusMcNabola.
Es ima ing egional po en ial o mic o-hyd opowe ene gy eco e y in i iga ion ne wo ks on a
la ge geog aphical scale. Renewable Ene gy, 155:396–406, Augus 2020.
[54] San oshkuma M. Hunachal, G. A unkuma , Sushil Si sa , P. R. Shanka , Raja Shi gaonka , and
Bhushan Khandzode. I iga ion wa e as a enewable ene gy sou ce in pico hyd opowe gene a-
ion. In 2020 In e na ional Con e ence on Renewable Ene gy In eg a ion in o Sma G ids: A Mul-
idisciplina y App oach o Technology Modelling and Simula ion (ICREISG), pages 27–31. IEEE,
Feb ua y 2020.
[55] A. Me ida Ga cía, J. Gallaghe , M. C espo Chacón, and A. Mc Nabola. The en i onmen al and
economicbene i s o ahyb idhyd opowe ene gy eco e yand sola ene gysys em(pa -p ), unde
a ying ene gy demands in he ag icul u al sec o . Jou nal o Cleane P oduc ion, 303:127078,
June 2021.
[56] Angel V. Me cedes Ga cia, F ancisco Ja ie Sánchez-Rome o, P. Ampa o López-Jiménez, and
Modes o Pé ez-Sánchez. A new op imiza ion app oach o he use o hyb id enewable sys ems
in he sea ch o he ze o ne ene gy consump ion in wa e i iga ion sys ems. Renewable Ene gy,
195:853–871, Augus 2022.
[57] William E. Ha , Jean-Paul Wa son, and Da id L. Wood u . Pyomo: modeling and sol ing ma h-
ema ical p og ams in py hon. Ma hema ical P og amming Compu a ion, 3(3):219–260, Augus
2011.
[58] Ze F iedman, Jack Ingalls, John D. Sii ola, and Jean-Paul Wa son. Block-o ien ed modeling o
supe s uc u e op imiza ion p oblems. Compu e s & Chemical Enginee ing, 57:10–23, Oc obe
2013.
[59] Jo ge Nocedal and S ephen J. W igh . Nume ical op imiza ion, pages 1–664. Sp inge Se ies in
Ope a ions Resea ch and Financial Enginee ing. Sp inge Na u e, 2006.
[60] Se gi Cos a-Dilmé, J. Ca los Oli es-Camps, Paula Muñoz-Peña, Pau Ga cía-Mo illa, O iol Gomis-
Bellmun , and Edua do P ie o-A aujo. Mul i-physics ope a ion and sizing op imisa ion in pyomo:
Applica ion o la ge i iga ion sys ems. In 2024 Open Sou ce Modelling and Simula ion o Ene gy
Sys ems (OSMSES), pages 1–6. IEEE, Sep embe 2024.
[61] Da iush Fooladi anda and Joshua A. Taylo . Ene gy-op imal pump scheduling and wa e low.
IEEE T ansac ions on Con ol o Ne wo k Sys ems, 5(3):1016–1026, Sep embe 2018.
[62] Michael L. Bynum, Gab iel A. Hackebeil, William E. Ha , Ca l D. Lai d, Be hany L. Nicholson,
John D. Sii ola, Jean-Paul Wa son, and Da idL. Wood u . Pyomo–op imiza ion modeling in py hon,
olume 67. Sp inge Science & Business Media, hi d edi ion, 2021.
[63] The Ma hWo ks Inc. S a is ics and machine lea ning oolbox, 2023.
[64] Pauli Vi anen, Ral Gomme s, T a is E. Oliphan , Ma Habe land, Tyle Reddy, Da id Cou na-
peau, E geni Bu o ski, Pea u Pe e son, Wa en Weckesse , Jona han B igh , S é an J. an de Wal ,
Ma hew B e , Joshua Wilson, K. Ja od Millman, Nikolay Mayo o , And ew R. J. Nelson, E ic Jones,
Robe Ke n, E ic La son, C J Ca ey, İlhan Pola , Yu Feng, E ic W. Moo e, Jake Vande Plas, Denis
Laxalde, Jose Pe k old, Robe Cim man, Ian Hen iksen, E. A. Quin e o, Cha les R. Ha is, Anne M.
A chibald, An ônio H. Ribei o, Fabian Ped egosa, Paul an Mulb eg , and SciPy 1.0 Con ibu o s.
SciPy 1.0: Fundamen al Algo i hms o Scien i ic Compu ing in Py hon. Na u e Me hods, 17:261–
272, 2020.
[65] Ahmed S. Zamzam, Emiliano Dall’Anese, Changhong Zhao, Josh A. Taylo , and Nicholas D.
Sidi opoulos. Op imal wa e –powe low-p oblem: Fo mula ion and dis ibu ed op imal solu ion.
IEEE T ansac ions on Con ol o Ne wo k Sys ems, 6(1):37–47, Ma ch 2019.
145
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[66] Juan I. Pé ez, José R. Wilhelmi, and Luis Ma o o. Adjus able speed ope a ion o a hyd opowe plan
associa ed o an i iga ion ese oi . Ene gy Con e sion and Managemen , 49(11):2973–2978,
No embe 2008.
[67] H. Ramos and A. Bo ga. Pumps as u bines: an uncon en ional solu ion o ene gy p oduc ion.
U ban Wa e , 1(3):261–263, Sep embe 1999.
[68] Maxime Binama, Wen-Tao Su, Xiao-Bin Li, Feng-Chen Li, Xian-Zhu Wei, and Shi An. In es iga ion
on pump as u bine (pa ) echnical aspec s o mic o hyd opowe schemes: A s a e-o - he-a
e iew. Renewable and Sus ainable Ene gy Re iews, 79:148–179, No embe 2017.
[69] Omp akash K. Gup a and A. Ra ind an. B anch and bound expe imen s in con ex nonlinea in ege
p og amming. Managemen Science, 31(12):1533–1546, 1985.
[70] Pie e Bonami, Lo enz T. Biegle , And ew R. Conn, Gé a d Co nuéjols, Ignacio E. G ossmann,
Ca l D. Lai d, Jon Lee, And ea Lodi, F ançois Ma go , Nicolas Sawaya, and And eas Wäch e .
An algo i hmic amewo k o con ex mixed in ege nonlinea p og ams. Disc e e Op imiza ion,
5(2):186–204, 2008. In Memo y o Geo ge B. Dan zig.
[71] Roge Fle che and S en Ley e . Sol ing mixed in ege nonlinea p og ams by ou e app oxima-
ion. Ma hema ical P og amming, 66:327–349, Augus 1994.
[72] I. Quesada and I.E. G ossmann. An LP/NLP based b anch and bound algo i hm o con ex MINLP
op imiza ion p oblems. Compu e s & Chemical Enginee ing, 16(10):937–947, 1992. An In e na-
ional Jou nal o Compu e Applica ions in Chemical Enginee ing.
[73] Kuma Abhishek, S en Ley e , and Je Linde o h. FilMINT: An Ou e App oxima ion-Based Sol e
o Con ex Mixed-In ege Nonlinea P og ams. INFORMS Jou nal on Compu ing, 22(4):555–567,
2010.
[74] F ancisco Díaz-González, And eas Sumpe , and O iol Gomis-Bellmun . Ene gy S o age in Powe
Sys ems. Wiley, Ma ch 2016.
[75] R. Lougee-Heime . The common op imiza ion in e ace o ope a ions esea ch: P omo ing open-
sou ce so wa e in he ope a ions esea ch communi y. IBM Jou nal o Resea ch and De elopmen ,
47(1):57–66, Janua y 2003.
[76] Se gi Cos a-Dilmé, J. Ca los Oli es-Camps, Pau Ga cía-Mo illa, Ca la Cin o Campmany, O iol
Gomis-Bellmun , and Edua do P ie o-A aujo. Redesign o la ge-scale i iga ion sys ems o lexi-
ble ene gy s o age. unpublished, 2025.
[77] REE. Reeda a, 2025. h ps://www. ee.es/es/da os/aldia.
[78] Ted G. Eschenbach. Spide plo s e sus o nado diag ams o sensi i i y analysis. In e aces,
22(6):40–46, Decembe 1992.
[79] Se gi Cos a-Dilmé, Pau Ga cía-Mo illa, O iol Gomis-Bellmun , and Edua do P ie o-A aujo. Ene gy
s o age sizing o clouds shading o e sola pho o ol aic pumping sys ems. unpublished, 2025.
[80] Giuseppe Todde, Lelia Mu gia, Paola An onia Deligios, Ri a Hogan, Isaac Ca elo, Madalena Mo -
ei a, An onio Pazzona, Luigi Ledda, and Luis Na a e. Ene gy and en i onmen al pe o mances
o hyb id pho o ol aic i iga ion sys ems in Medi e anean in ensi e and supe -in ensi e oli e o -
cha ds. Science o The To al En i onmen , 651:2514–2523, Feb ua y 2019.
[81] Ramazan Senol. An analysis o sola ene gy and i iga ion sys ems in u key. Ene gy Policy,
47:478–486, Augus 2012.
[82] P.C. Pande, A.K. Singh, S. Ansa i, S.K. Vyas, and B.K. Da e. Design de elopmen and es ing o a
sola PV pump based d ip sys em o o cha ds. Renewable Ene gy, 28(3):385–396, Ma ch 2003.
146
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[83] Ali A. Hamza and Azmi Z. Taha. Pe o mance o subme sible p sola pumping sys ems unde
condi ions in he sudan. Renewable Ene gy, 6(5–6):491–495, July 1995.
[84] Olga V. Shepo alo a, Alexande T. Beleno , and Se gei V. Chi ko . Re iew o pho o ol aic wa e
pumping sys em esea ch. Ene gy Repo s, 6:306–324, No embe 2020.
[85] Olga V. Shepo alo a and Alexande T. Beleno . In es iga ion o dc mo o s mechanical cha ac e -
is ics wi h powe ed by compa able capaci y p a ay. Ene gy P ocedia, 119:990–994, July 2017.
[86] Z.Abidin Fi a oglu and Bulen Yesila a. New app oaches on he op imiza ion o di ec ly coupled p
pumping sys ems. Sola Ene gy, 77(1):81–93, 2004.
[87] Daniele Fiaschi, Robe o G aniglia, and Giampaolo Man ida. Imp o ing he e ec i eness o so-
la pumping sys ems by using modula cen i ugal pumps wi h a iable o a ional speed. Sola
Ene gy, 79(3):234–244, Sep embe 2005.
[88] R.H. Almeida, J.R. Ledesma, I.B. Ca êlo, L. Na a e, G. Fe a a, and L. An ipodi. A new pump
selec ion me hod o la ge-powe p i iga ion sys ems a a a iable equency. Ene gy Con e sion
and Managemen , 174:874–885, Oc obe 2018.
[89] Hicham Ka mouni, Mohamed Chouiekh, Saad Mo ahhi , Hassan Qjidaa, Mohamed Ouazzani Jamil,
and Mhamed Sayyou i. Op imiza ion and implemen a ion o a pho o ol aic pumping sys em us-
ing he sine–cosine algo i hm. Enginee ing Applica ions o A i icial In elligence, 114:105104,
Sep embe 2022.
[90] Wissem Nemouchi, Youssou Am ane, Hichem Nemouchi, and Najib Lakhda Bouce a. Ene gy
managemen o op imal design o p /wind/diesel sys em o wa e pumping i iga ion in semi-a id
clima e. Ene gy Con e sion and Managemen , 304:118216, Ma ch 2024.
[91] Vic o L S ee e , E Benjamin Wylie, and Kei h W Bed o d. Fluid mechanics. Mc G aw Hill Educa-
ion, Dec 1997.
[92] E Benjamin Wylie and Vic o Lyle S ee e . Fluid ansien s. Mc G aw Hill Inc., 1978.
[93] And ew F. Colombo and B yan W. Ka ney. Ene gy and cos s o leaky pipes: Towa d comp ehen-
si e pic u e. Jou nal o Wa e Resou ces Planning and Managemen , 128(6):441–450, No embe
2002.
[94] Jalil Emadi and Abbas Solemani. Maximum wa e hamme sensi i i y analysis. Wo ld Acad. Sci.
Eng. Technol, 73:416–419, 2011.
[95] Josh A. Taylo , Richa d Pe yman, Aimy Bazylak, and B yan Ka ney. Sa ely landing wa e ne -
wo ks du ing powe ou ages wi h ene gy s o age. In 2018 56 h Annual Alle on Con e ence on
Communica ion, Con ol, and Compu ing (Alle on), pages 346–350. IEEE, Oc obe 2018.
[96] Madhumi a Das and Ra an Mandal. A compa a i e pe o mance analysis o di ec , wi h ba e y,
supe capaci o , and ba e y-supe capaci o enabled pho o ol aic wa e pumping sys ems using
cen i ugal pump. Sola Ene gy, 171:302–309, Sep embe 2018.
[97] S. O s-G au, P. Gonzalez-Al ozano, F ancisco J. Gimeno-Sales, I. Balbas e-Pe al a, C. I. Ma inez
Ma quez, M. Gasque, and S. Segui-Chile . Pho o ol aic wa e pumping: Compa ison be ween
di ec and li hium ba e y solu ions. IEEE Access, 9:101147–101163, 2021.
[98] Tehuan Chen, Zhigang Ren, Chao Xu, and Ryan Lox on. Op imal bounda y con ol o wa e ham-
me supp ession in luid ansmission pipelines. Compu e s & Ma hema ics wi h Applica ions,
69(4):275–290, Feb ua y 2015.
147
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[99] J.K. Roy, P.K. Roy, and P. Basak. Wa e hamme p o ec ionin wa e supplysys em: A new app oach
wi h p ac ical implemen a ion. In 2011 In e na ional Con e ence on Communica ion and Indus ial
Applica ion, pages 1–6. IEEE, Decembe 2011.
[100] Packiam Pe iasamy, N.K. Jain, and I.P. Singh. A e iew on de elopmen o pho o ol aic wa e pump-
ing sys em. Renewable and Sus ainable Ene gy Re iews, 43:918–925, Ma ch 2015.
[101] A. Mohammedi, N. Mezzai, D. Rekioua, and T. Rekioua. Impac o shadow on he pe o mances o
a domes ic pho o ol aic pumping sys em inco po a ing an mpp con ol: A case s udy in bejaia,
no h alge ia. Ene gy Con e sion and Managemen , 84:20–29, Augus 2014.
[102] L. Na a e, J. Fe nández-Ramos, F. Ma ínez-Mo eno, L.M. Ca asco, R.H. Almeida, and I.B. Ca êlo.
Solu ions o adap ing pho o ol aics o la ge powe i iga ion sys ems o ag icul u e. Sus ainable
Ene gy Technologies and Assessmen s, 29:119–130, Oc obe 2018.
[103] Uni e sidad Poli écnica de Mad id. MASLOWATEN. Especi icaciones Técnicas pa a Sis emas de
Riego Fo o ol aico, 2018. A ailable online: h ps://maslowa en.eu (accessed on 30/01/2024).
[104] An on Be gan , Je nej Mazij, and U oš Ka adžić. Design o wa e hamme con ol s a egies in
hyd opowe plan s. Applied Enginee ing Le e s: Jou nal o Enginee ing and Applied Sciences,
3(1):27–33, 2018.
[105] G. Remenie as. Disposi i simple pou édui e la célé i é des ondes Élas iques dans les condui es
en cha ge. La Houille Blanche, 38(sup1):172–196, Janua y 1952.
[106] Jinzhe Gong, Ma k L. S ephens, Ma in F. Lambe , Aa on C. Zecchin, and Angus R. Simpson. P es-
su e su ge supp ession using a me allic-plas ic-me allic pipe con igu a ion. Jou nal o Hyd aulic
Enginee ing, 144(6), June 2018.
[107] Michał Kub ak. Wa e hamme mi iga ion by in e nal ubbe hose. A chi es o Ci il Enginee ing,
pages 275–288, Ma ch 2024.
[108] OMIE: Ope ado del Me cado Ibé ico de Ene gía - Polo Español. OMIEDa a Resul ados del Me -
cado. www.omie.es/es, 2024.
[109] Banco de España. Se ies: S a is ical Bulle in. h ps://www.bde.es/wbe/en/publicaciones/in
o macion-es adis ica/bole in-es adis ico/, 2024.
[110] QGIS De elopmen Team. QGIS Geog aphic In o ma ion Sys em. QGIS Associa ion,
[111] Chad Augus ine and Na han Blai . S o age Fu u es S udy: S o age Technology Modeling Inpu
Da a Repo . NREL, May 2021.
[112] Benjamin A. Ca e as, Ede Ba is a Tchawou Tchuisseu, José M. Reynolds-Ba edo, Damià Gomila,
and Pe e Cole . E ec s o demand con ol on he complex dynamics o elec ic powe sys em
blackou s. Chaos: An In e disciplina y Jou nal o Nonlinea Science, 30(11), No embe 2020.
[113] Ja ie Ma ín Vide. El Clima i el elleu. Geog a ia Gene al dels Països Ca alans. Enciclopèdia Ca a-
lana, Ba celona, 1992.
[114] Haisheng Chen, Thang Ngoc Cong, Wei Yang, Chunqing Tan, Yongliang Li, and Yulong Ding.
P og ess in elec ical ene gy s o age sys em: A c i ical e iew. P og ess in Na u al Science,
19(3):291–312, Ma ch 2009.
[115] Behnam Zake i and Sanna Sy i. Elec ical ene gy s o age sys ems: A compa a i e li e cycle cos
analysis. Renewable and Sus ainable Ene gy Re iews, 42:569–596, Feb ua y 2015.
[116] Md Mus a izu Rahman, Abayomi Olu emi Oni, Eskinde Gemechu, and Ami Kuma . Assessmen
o ene gy s o age echnologies: A e iew. Ene gy Con e sion and Managemen , 223:113295,
No embe 2020.
148
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[117] Cho on K. Das, Oc a ian Bass, Ganesh Ko hapalli, Thai S. Mahmoud, and Da yoush Habibi.
O e iew o ene gy s o age sys ems in dis ibu ion ne wo ks: Placemen , sizing, ope a ion, and
powe quali y. Renewable and Sus ainable Ene gy Re iews, 91:1205–1230, Augus 2018.
[118] E nes Moa and Yun Go. La ge-scale ene gy s o age sys em: sa e y and isk assessmen . Sus ain-
able Ene gy Resea ch, 10, 09 2023.
[119] A.R. Dehghani-Sanij, E. Tha umalingam, M.B. Dusseaul , and R. F ase . S udy o ene gy s o age
sys ems and en i onmen al challenges o ba e ies. Renewable and Sus ainable Ene gy Re iews,
104:192–208, Ap il 2019.
[120] Ci cula 1/2025, de 28 de ene o, de la Comisión Nacional de los Me cados y la Compe encia, po
la que se modi ica la Ci cula 3/2020, de 15 de ene o, po la que se es ablece la me odología pa a
el cálculo de los peajes de anspo e y dis ibución de elec icidad. BOE-A-2025-2044, Janua y
2025.
[121] Geyse Ba e ies Oy. Geyse ba e y: In oduc ion o a powe -dense ba e y o hea y-du y appli-
ca ions, 2021. [Whi e pape ]. A ailable online: h ps://www.geyse ba e ies.com/ echnolo
gy (accessed on 29/01/2024).
[122] AGISTIN P ojec Conso ium. D2.1: Ene gy S o age In eg a ion Requi emen s, Incen i es and Con-
s ain s: EU-wide Analyses. Technical Repo D2.1, Ho izon Eu ope P og am, Eu opean Commis-
sion, Decembe 2023. G an Ag eemen Numbe : 101096197, Lead Pa icipan : EPRI, Submi ed:
25/12/2023.
[123] EU ACER. ACER webina on amendmen s o he Eu opean elec ici y g id connec ion ne wo k
codes. Online, July 2023. A ailable onlien: h ps://www.you ube.com/wa ch? =p P4qSX10&a
b_channel=EUACER.
[124] Xing Luo, Jihong Wang, Ma k Doone , and Jona han Cla ke. O e iew o cu en de elopmen in
elec ical ene gy s o age echnologies and he applica ion po en ial in powe sys em ope a ion.
Applied Ene gy, 137:511–536, 2015.
[125] F ancisco Díaz-González, And eas Sumpe , O iol Gomis-Bellmun , and Robe o Villa á ila-Robles.
A e iew o ene gy s o age echnologies o wind powe applica ions. Renewable and Sus ainable
Ene gy Re iews, 16(4):2154–2171, 2012.
[126] En ique Loba o, Lukas Sig is , and Luis Rouco. Use o ene gy s o age sys ems o peak sha ing in
he spanish cana y islands. In 2013 IEEE Powe & Ene gy Socie y Gene al Mee ing, pages 1–5,
2013.
[127] E.B. P asas i, M. Aouad, M. Joseph, M. Zangeneh, and K. Te heiden. Op imiza ion o pumped hy-
d o ene gy s o age design and ope a ion o o sho e low-head applica ion and g id s abiliza ion.
Renewable and Sus ainable Ene gy Re iews, 191:114122, 2024.
[128] Jan Figgene , Benedik Tepe, Fabian Rücke , Ilka Schoenebe ge , Ch is ophe Hech , And eas
Jossen, and Di k Uwe Saue . The in luence o equency con ainmen ese e lexibiliza ion on
he economics o elec ic ehicle lee ope a ion. Jou nal o Ene gy S o age, 53:105138, 2022.
[129] K ishnakuma R. Vasude an, Vigna K. Ramachanda amu hy, Goma hi Venugopal, J.B. Ekanayake,
and S.K. Tiong. Va iable speed pumped hyd o s o age: A e iew o con e e s, con ols and ene gy
managemen s a egies. Renewable and Sus ainable Ene gy Re iews, 135:110156, 2021.
[130] C Nicole , O B aun, N Ruchonne , J. Hell, A Béguin, and F A ellan. Simula ion o pump- u bine
p o o ype as mode ansi ion o g id s abili y suppo . Jou nal o Physics: Con e ence Se ies,
813(1):012040, ma 2017.
149
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[131] An o Joseph, Raghu Sel a aj, Thanga Raj Chelliah, and S. V. Appa Sa ma. S a ing and b aking
o a la ge a iable speed hyd ogene a ing uni subjec ed o con e e and senso aul s. IEEE
T ansac ions on Indus y Applica ions, 54(4):3372–3382, July 2018.
[132] Edua do Sánchez-Díez, Edga Ven osa, Massimo Gua nie i, And ea T o ò, C is ina Flox, Rebeca
Ma cilla, F ancesca Soa i, Pe Mazu , Es ibaliz A anzabe, and Raquel Fe e . Redox low ba e ies:
S a us and pe spec i e owa ds sus ainable s a iona y ene gy s o age. Jou nal o Powe Sou ces,
481:228804, 2021.
[133] And ea T o ò, Vi o Di No o, Joseph Epoupa Mengou, Chia a Gamaba o, and Massimo Gua nie i.
Fas esponse o kw-class anadium edox low ba e ies. IEEE T ansac ions on Sus ainable En-
e gy, 12(4):2413–2422, 2021.
[134] Red Eléc ica de España. Guía desc ip i a: Se p o eedo de se icios de balance, Janua y 2024.
Accessed: 2025-01-29.
[135] Comisión Nacional de los Me cados y la Compe encia. Resolución de 3 de oc ub e de 2024, de la
Comisión Nacional de los Me cados y la Compe encia, po la que se modi ican los p ocedimien os
de ope ación eléc icos 14.1 y 14.4 pa a la adap ación de la liquidación al ISP cua o-ho a io. Bo-
le ín O icial del Es ado, 248:131410–131478, Oc obe 2024. Re e ence: BOE-A-2024-20995,
Accessed: 2025-01-29.
[136] Da id G. Luenbe ge and Yinyu Ye. Linea and Nonlinea P og amming. Sp inge Publishing Com-
pany, Inco po a ed, 2015.
[137] Ad ian Hauswi h, Alessand o Zana di, Sa e io Bolognani, Flo ian Dö le , and Gab iela Hug. On-
line op imiza ion in closed loop on he powe low mani old. In 2017 IEEE Manches e Powe Tech,
pages 1–6, 2017.
[138] Miguel Picallo, Dominic Liao-McPhe son, Sa e io Bolognani, and Flo ian Dö le . C oss-laye de-
sign o eal- ime g id ope a ion: Es ima ion, op imiza ion and powe low. Elec ic Powe Sys ems
Resea ch, 212:108378, 2022.
[139] Ma cello Colombino, Emiliano Dall’Anese, and And eyBe ns ein. Online op imiza ionasa eedback
con olle : S abili y and acking. IEEE T ansac ions on Con ol o Ne wo k Sys ems, 7(1):422–432,
2020.
[140] Ad ian Hauswi h, Sa e io Bolognani, Gab iela Hug, and Flo ian Dö le . P ojec ed g adien de-
scen on iemannian mani olds wi h applica ions o online powe sys em op imiza ion. In 2016
54 h Annual Alle on Con e ence on Communica ion, Con ol, and Compu ing (Alle on), pages
225–232, 2016.
[141] V. Häbe le, A. Hauswi h, L. O mann, S. Bolognani, and F. Dö le . Non-con ex eedback op i-
miza ion wi h inpu and ou pu cons ain s. IEEE Con ol Sys ems Le e s, 5(1):343–348, 2020.
[142] Lukas O mann, Ad ian Hauswi h, I o Cadu , Flo ian Dö le , and Sa e io Bolognani. Expe i-
men al alida ion o eedback op imiza ion in powe dis ibu ion g ids. Elec ic Powe Sys ems
Resea ch, 189:106782, 2020.
[143] J. C. Oli es-Camps, A. Rod íguez del Nozal, J. M. Mau icio, and J. M. Maza-O ega. A model-less
con ol algo i hm o dc mic og ids based on eedback op imiza ion. In e na ional Jou nal o Elec i-
cal Powe & Ene gy Sys ems, 141:108087, 2022.
[144] E.A. Rod íguez-Gonzalez, J.C. Oli es-Camps, F.P. Ga cía-Lopez, A. Rod íguez Del Nozal, J.M.
Mau icio, and J.M. Maza-O ega. Expe imen al alida ion o a eal- ime dis ibu ed model-less
con ol o dc mic og ids. In 2022 In e na ional Con e ence on Sma Ene gy Sys ems and Tech-
nologies (SEST), pages 1–6, 2022.
150
D6.3 Technical-economic sizing, ope a ion and con ol ools o i iga ion
sys em mode nisa ion in o ene gy s o age sys ems
[145] Ma cello Colombino, John W. Simpson-Po co, and And ey Be ns ein. Towa ds obus ness gua -
an ees o eedback-based op imiza ion. In 2019 IEEE 58 h Con e ence on Decision and Con ol
(CDC), pages 6207–6214, 2019.
[146] Jaume Gi ona-Badia, Vinícius Albe naz Lace da, Daniel Wes e man Spie , Edua do P ie o-A aujo,
and O iol Gomis-Bellmun . Resou ce-awa e g id- o ming synch oniza ion con ol: Design, analy-
sis and alida ion. IEEE T ansac ions on Ene gy Con e sion, pages 1–12, 2024.
[147] I ina Subo ić and Dominic G oß. Uni e sal dual-po g id- o ming con ol: B idging he gap be-
ween g id- o ming and g id- ollowing con ol. IEEE T ansac ions on Powe Sys ems, 39(6):6861–
6875, 2024.
[148] M.E. El-Hawa y and S.T. Ib ahim. A new app oach o AC-DC load low analysis. Elec ic Powe
Sys ems Resea ch, 33(3):193–200, 1995.
[149] Ugu A i oglu. The powe low algo i hm o balanced and unbalanced bipola mul i e minalACDC
sys ems. Elec ic Powe Sys ems Resea ch, 64(3):239–246, 2003.
[150] Je Bee en, S ijn Cole, and Ronnie Belmans. A sequen ial AC/DC powe low algo i hm o ne -
wo ks con aining mul i- e minal VSC HVDC sys ems. In IEEE PES Gene al Mee ing, pages 1–7,
2010.
[151] M. M. El-ma sa awy and R. M. Ma hu . A new, as echnique o load- low solu ion o in e-
g a ed mul i- e minal DC/AC sys ems. IEEE T ansac ions on Powe Appa a us and Sys ems, PAS-
99(1):246–255, 1980.
[152] Fnn guideline: G id o ming beha iou o h dc sys ems and dc-connec ed ppms. Technical guide-
line, Fo um Ne z echnik/Ne zbe ieb (FNN), VDE, 2023.
151
