Energy management system of a zero-emission vehicle charging station based on MPC

i
Equa ion Chap e 1 Sec ion 1
Mas e Thesis
Mas e in Elec onics, Robo ics and Au oma ion
Enginee ing
Ene gy managemen sys em o a ze o-emission
ehicle cha ging s a ion based on MPC
Au ho : Manuel Mo a Nie o
Supe iso : Ca los Bo dons Alba
Dep. de Ingenie ía de Sis emas y Au omá ica
Escuela Técnica Supe io de Ingenie ía
Uni e sidad de Se illa
Se illa, 2021
T abajo Fin de Más e
Más e Uni e si a io en Ingenie ía Elec ónica,
Robó ica y Au omá ica
Sis ema de ges ión de ene gía pa a una es ación
de ca ga de ehículos ce o emisiones basado en
MPC
i
T abajo Fin de Más e
Más e Uni e si a io en Ingenie ía Elec ónica, Robó ica y Au omá ica
Ene gy managemen sys em o a ze o-emission
ehicle cha ging s a ion based on MPC
Au ho :
Manuel Mo a Nie o
Supe iso :
Ca los Bo dons Alba
Ca ed á ico de Uni e sidad
Dep. de Ingenie ía de Sis emas y Au omá ica
Escuela Técnica Supe io de Ingenie ía
Uni e sidad de Se illa
Se illa, 2021
iii
T abajo Fin de Más e : Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
Au ho :
Manuel Mo a Nie o
Supe iso :
Ca los Bo dons Alba
El ibunal nomb ado pa a juzga el P oyec o a iba indicado, compues o po los siguien es miemb os:
P esiden e:
Vocales:
Sec e a io:
Acue dan o o ga le la cali icación de:
El Sec e a io del T ibunal
Fecha:

To my amiliy
To my eache s and p o esso s
ii
Acknowledgmen s
I was almos hal and a yea when I decided o s a a new Mas e o Science while I was also inishing he
Indus ial Enginee ing Mas e . I was no an easy decision bu I ha e no doub s ha I go igh . The e o e, I
would like o hank my amily o hei pa ience. They ha e been my main suppo du ing he di icul
pandemic imes.
Thanks also o all my colleagues in he labo a o y. They ha e made easie he wo k done.
Finally, I would like o exp ess my g a i ude o my ad iso Ca los. I am con inuously lea ning om him.
Manuel Mo a Nie o
S uden in Escuela Técnica Supe io de Ingenie ía, Uni e si y o Se ille
Se ille, 2021
xi
Figu a 0-2 Esquema de la mic o ed (Imagen modi ica a pa i de la o iginal de [2])
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)+100𝜂𝑒𝑧𝑇𝑠
𝑉𝑚𝑎𝑥𝑃𝑒𝑧(𝑡)𝛿𝑒𝑧(𝑡)−100 𝑇𝑠
𝜂𝑓𝑐 𝑉𝑚𝑎𝑥𝑃𝑓𝑐(𝑡)𝛿𝑓𝑐(𝑡)
(0–2)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)+𝜂𝑢𝑐,𝑐ℎ 𝑇𝑠
𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐,𝑐ℎ(𝑡)−𝑇𝑠
𝜂𝑢𝑐,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐,𝑑𝑖𝑠𝑐(𝑡)
(0–3)
Po su pa e, el balance de po encias:
𝑃𝑔𝑟𝑖𝑑(𝑡)+𝑃𝑏𝑎𝑡(𝑡)+𝑃𝑢𝑐(𝑡)+𝑃𝑓𝑐(𝑡)−𝑃𝑒𝑧(𝑡)+𝑑(𝑡)=0
(0–4)
Siendo 𝑑(𝑡) la pe u bación medible del sis ema, ob enida como la gene ación menos la demanda (incluida la
de eca ga de ehículos eléc icos).
Una ez que se iene el modelo del sis ema, se puede diseña la es a egia de con ol. El esquema de la misma
se basa en la es uc u a basada en capas je á quicas ípicas de un sis ema de con ol, donde un con olado
e cia io lle a a cabo una plani icación económica eniendo en cuen a aspec os de ope ación y deg adación de
los equipos, pa a en ia e e encias cada ho a a un con olado secunda io que ac úa en un iempo de mues eo
del o den de segundos, y que se enca ga del seguimien o de la plani icación en iada po el con olado
e cia io. Además, es e con oldo secunda io ambién se ocupa de aspec os ope aionales y elacionados con el
man enimien o de los equipos. En e o as di e encias, el con olado secunda io incluye el supe condensado
(el e cia io no lo incluye) debido a que es un disposi o capaz de ac ua de o ma ápida amo iguando los
picos de po encia en cambios b uscos.
Es a es a egia puede e se en la Figu a 0-3. Como se puede obse a , el con olado e cia io ecibe en adas
p oceden es de las p ediciones de consumo, gene ación y p ecio de la ene gía y de las medidas de los ni eles
de ene gía en sus almacenamien os. Como salida, p opo ciona la plani icación pa a el con olado secunda io.
Dicho con olado secunda io, además de la plani icación p oceden e del con olado e cia io, ecibe medidas
de la po encia gene ada y consumida eal (incluyendo la de ca ga de ehículos eléc icos) y, de nue o, de los
ni eles de almacenamien o de ene gía. Su salida son las po encias de e e encia pa a los con e ido es de
po encia que no han sido implemen ados en es e abajo.
Pa a el diseño del con olado e cia io, an o a iables lógicas como con inuas se usa án, po lo que es
necesa io con e i el sis ema a un Mixed Logical Dynamical, MLD. En es os sis emas, las a iables bina ias y
sus elaciones lógicas se de inen, pa a luego an o ma dichas elaciones en desigualdades lineales como
mues a la Tabla 0-1, y que se án añadidas como es icciones al p oblema de op imización. También se
de inen a iables mix as, compues as po ope aciones ma emá icas que in oluc an ambos ipos de a iable. El
modelo en espacio de es ados del sis ema debe queda desc i o como unción del p opio es ado, las acciones
de con ol, las a iables lógicas y las a iables mix as. Esas es úl imas se án las a iables de decisión en el

x
Figu a 0-3. Es a egia de con ol
p oblema de op imización.Una ez que se iene el sis ema MLD desc i o y con las nue as es icciones a
añadi , se iene un p oblema Mixed In ege P og amming, MIP, que al se las es icciones lineales, se á un
Mixed In ege Linea P og amming, MILP si la unción de cos e es lineal, o un Mixed In ege Quad a ic
P og amming, MIQP si la unción de cos e es cuad á ica. Como es os p oblemas son más di íciles de esol e ,
se suelen emplea écnicas conocidas como b anch and bound pa a i educiendo el núme o de casos posibles
en el p oblema de op imización.
Tabla 0-1. Relaciones lógicas en un sis ema y sus co espondien e desigualdades lineales (Tabla omada
di ec amen e de [2])
Siendo las a iables de decisión del p oblema de op imización pa a el con olado e cia io las siguien es:
x i
𝑢(𝑡𝑘)=
[
𝑃𝑏𝑎𝑡(𝑡𝑘)
𝑃𝑓𝑐(𝑡𝑘)
𝑃𝑒𝑧(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
]
𝛿(𝑡𝑘)=
[
𝛿𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)
𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)
𝛿𝑓𝑐(𝑡𝑘)
𝛿𝑒𝑧(𝑡𝑘)
𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)
𝛿𝑝𝑢𝑟(𝑡𝑘)
𝜎𝑓𝑐
𝑜𝑛(𝑡𝑘)
𝜎𝑒𝑧
𝑜𝑛(𝑡𝑘)
𝜒𝑓𝑐(𝑡𝑘)
χez(𝑡𝑘)
]
𝑧(𝑡𝑘)=
[
𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)
𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)
𝑧𝑓𝑐(𝑡𝑘)
𝑧𝑒𝑧(𝑡𝑘)
𝑃𝑠𝑎𝑙𝑒(𝑡𝑘)
𝑃𝑝𝑢𝑟(𝑡𝑘)
𝜃𝑓𝑐(𝑡𝑘)
θez(𝑡𝑘)
]
(0–5)
Y as un la go desa ollo ma emá ico cuyo de alle puede e se en la e sión comple a de es e abajo en
inglés, el p oblema MIQP que de ine al con olado secunda io iene ecogido en la siguien e caja.
min
𝑢𝐽(𝑡)=∑((−Γ𝑠𝑎𝑙𝑒
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)𝑃𝑠𝑎𝑙𝑒(𝑡𝑘|𝑡)+ Γ𝑝𝑢𝑟
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)𝑃𝑝𝑢𝑟(𝑡𝑘|𝑡))𝑇𝑠
𝑆𝐻
𝑘=1+𝐶𝐶𝑏𝑎𝑡
2 𝐶𝑦𝑐𝑙𝑒𝑠𝑏𝑎𝑡(𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘|𝑡)+𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘|𝑡))𝑇𝑠
+(𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑐ℎ 𝑃𝑏𝑎𝑡,𝑐ℎ
2(𝑡𝑘|𝑡)+𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑑𝑖𝑠𝑐 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
2(𝑡𝑘|𝑡))𝑇𝑠
+𝑇𝑠(𝐶𝐶𝑓𝑐
𝐻𝑜𝑢𝑟𝑠𝑓𝑐+𝐶𝑜𝑠𝑡𝑜&𝑚,𝑓𝑐)𝛿𝑓𝑐(𝑡𝑘|𝑡)+𝐶𝑜𝑠𝑡𝑠𝑡𝑎𝑟𝑡,𝑓𝑐 𝜎𝑓𝑐
𝑜𝑛(𝑡𝑘 |𝑡)
+𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑓𝑐 𝜃𝑓𝑐
2(𝑡𝑘|𝑡)+𝑇𝑠(𝐶𝐶𝑒𝑧
𝐻𝑜𝑢𝑟𝑠𝑒𝑧+𝐶𝑜𝑠𝑡𝑜&𝑚,𝑒𝑧)𝛿𝑒𝑧(𝑡𝑘|𝑡)
+𝐶𝑜𝑠𝑡𝑠𝑡𝑎𝑟𝑡,𝑒𝑧 𝜎𝑒𝑧
𝑜𝑛(𝑡𝑘 |𝑡)+𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑒𝑧 𝜃𝑒𝑧
2(𝑡𝑘|𝑡))
𝑠.𝑎. [𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘+1)
𝐿𝑂𝐻(𝑡𝑘+1)]=[1 0
0 1][𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)]+[0 ⋯ 0
0 ⋯ 0](2,4)𝑢(𝑡𝑘)+
[0 ⋯ 0
0 ⋯ 0](2,10)𝛿(𝑡𝑘)+[𝐾𝑏𝑎𝑡,𝑐ℎ −𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 0 0 0 0 0 0
0 0 −𝐾𝑓𝑐 𝐾𝑒𝑧 0 0 0 0]𝑧(𝑡𝑘)
[𝑦1(𝑡𝑘)
𝑦2(𝑡𝑘)]=[1 0
0 1][𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)]
𝑃𝑝𝑣
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)+𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)+𝑃𝑏𝑎𝑡(𝑡𝑘)+𝑧𝑓𝑐(𝑡𝑘)−𝑧𝑒𝑧(𝑡𝑘)−𝑃𝑙𝑜𝑎𝑑
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)=0
𝑃𝑖𝑚𝑖𝑛≤𝑃𝑖(𝑡𝑘)≤𝑃𝑖𝑚𝑎𝑥|𝑖=𝑏𝑎𝑡,𝑓𝑐,𝑒𝑧,𝑔𝑟𝑖𝑑
𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑖𝑛≤𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)≤𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑎𝑥
𝐿𝑂𝐻𝑚𝑖𝑛≤𝐿𝑂𝐻(𝑡𝑘)≤𝐿𝑂𝐻𝑚𝑎𝑥
0≤𝛿𝑖(𝑡𝑘)≤1|𝑖=𝑓𝑐,𝑒𝑧
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)=𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑠𝑎𝑙𝑒(𝑡𝑘), 𝑃𝑝𝑢𝑟(𝑡𝑘)≥0,𝑃𝑠𝑎𝑙𝑒(𝑡𝑘)≥0
𝛿𝑝𝑢𝑟(𝑡𝑘)+𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)=1
x ii
𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛 𝛿𝑝𝑢𝑟(𝑡𝑘)≤𝑃𝑝𝑢𝑟(𝑡𝑘)≤ 𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 𝛿𝑝𝑢𝑟(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 (1− 𝛿𝑝𝑢𝑟(𝑡𝑘))≤𝑃𝑝𝑢𝑟(𝑡𝑘)≤𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛 (1− 𝛿𝑝𝑢𝑟(𝑡𝑘))
𝜖+(𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛−𝜖)𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)≤𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)≤𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 (1−𝛿𝑠𝑎𝑙𝑒(𝑡𝑘))
𝑃𝑏𝑎𝑡(𝑡𝑘)=𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)−𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘), 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)≥0,𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)≥0
𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)+𝛿𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)=1
𝑃𝑏𝑎𝑡
𝑚𝑖𝑛 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)≤𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)≤ 𝑃𝑏𝑎𝑡
𝑚𝑎𝑥 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)
𝑃𝑏𝑎𝑡(𝑡𝑘)−𝑃𝑏𝑎𝑡
𝑚𝑎𝑥 (1− 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘))≤𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)≤𝑃𝑏𝑎𝑡(𝑡𝑘)−𝑃𝑏𝑎𝑡
𝑚𝑖𝑛 (1− 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘))
𝜖+(𝑃𝑏𝑎𝑡
𝑚𝑖𝑛−𝜖)𝛿𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)≤𝑃𝑏𝑎𝑡(𝑡𝑘)≤𝑃𝑏𝑎𝑡
𝑚𝑎𝑥 (1−𝛿𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘))
0≤𝛿𝑓𝑐(𝑡𝑘)+𝛿𝑒𝑧(𝑡𝑘)≤1
𝑃𝑖𝑚𝑖𝑛 𝛿𝑖(𝑡𝑘)≤𝑧𝑖(𝑡𝑘)≤𝑃𝑖𝑚𝑎𝑥 𝛿𝑖(𝑡𝑘), 𝑖=𝑓𝑐,𝑒𝑧
𝑃𝑖(𝑡𝑘)−𝑃𝑖𝑚𝑎𝑥 (1− 𝛿𝑖(𝑡𝑘))≤𝑧𝑖(𝑡𝑘)≤𝑃𝑖(𝑡𝑘)−𝑃𝑖𝑚𝑖𝑛 (1− 𝛿𝑖(𝑡𝑘)), 𝑖=𝑓𝑐,𝑒𝑧
−∞≤−𝛿𝑖(𝑡𝑘)+𝜎𝑖𝑜𝑛(𝑡𝑘)≤0, 𝑖=𝑓𝑐,𝑒𝑧
−∞≤−(1−𝛿𝑖(𝑡𝑘−1))+𝜎𝑖𝑜𝑛(𝑡𝑘)≤0, 𝑖=𝑓𝑐,𝑒𝑧
−∞≤𝛿𝑖(𝑡𝑘)+(1−𝛿𝑖(𝑡𝑘−1))−𝜎𝑖𝑜𝑛(𝑡𝑘)≤1, 𝑖=𝑓𝑐,𝑒𝑧
−∞≤−𝛿𝑖(𝑡𝑘)+𝜒𝑖(𝑡𝑘)≤0, 𝑖=𝑓𝑐,𝑒𝑧
−∞≤−𝛿𝑖(𝑡𝑘−1)+𝜒𝑖(𝑡𝑘)≤0, 𝑖=𝑓𝑐,𝑒𝑧
−∞≤𝛿𝑖(𝑡𝑘)+𝛿𝑖(𝑡𝑘−1)−𝜒𝑖(𝑡𝑘)≤1, 𝑖=𝑓𝑐,𝑒𝑧
0≤𝜒𝑓𝑐(𝑡𝑘)+𝜒𝑒𝑧(𝑡𝑘)≤1
Δ𝑃𝑖𝑚𝑖𝑛 𝜒𝑖(𝑡𝑘)≤𝜃𝑖(𝑡𝑘)≤Δ𝑃𝑖𝑚𝑎𝑥 𝜒𝑖(𝑡𝑘), 𝑖=𝑓𝑐,𝑒𝑧
Δ𝑃𝑖(𝑡𝑘)−Δ𝑃𝑖𝑚𝑎𝑥 (1−χi(𝑡𝑘))≤𝜃𝑖(𝑡𝑘)≤Δ𝑃𝑖(𝑡𝑘)−Δ𝑃𝑖𝑚𝑖𝑛 (1−𝜒𝑖(𝑡𝑘)), 𝑖=𝑓𝑐,𝑒𝑧
Po su pa e, el con olado secunda io, como se ha dicho, a a de segui la plani icación es ablecida po el
con olado e cia io, además de busca el co ec o uncionamien o de los equipos. En es e caso sólo se usa án
a iables con inuas, po lo que se iene un p oblema de p og amación cuad á ica que puede ácilmen e esol e
con la unción p opia de MATLAB denominada quadp og.
De iniendo las acciones de con ol y sus a iaciones (es as úl imas se án las ai ables de decisión del p oblema
de op imización) como:
𝑢(𝑡𝑘)=[𝑃𝐻2(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
𝑃𝑢𝑐(𝑡𝑘)]
Δ𝑢(𝑡𝑘)=[Δ𝑃𝐻2(𝑡𝑘)
Δ𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
Δ𝑃𝑢𝑐(𝑡𝑘)]=[𝑃𝐻2(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
𝑃𝑢𝑐(𝑡𝑘)]−[𝑃𝐻2(𝑡𝑘−1)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘−1)
𝑃𝑢𝑐(𝑡𝑘−1)]
(0–6)
Y, de nue o, as una la ga deducción que puede e se en la e sión comple a en inglés, el p oblema de
op imización pa a el con olado secunda io queda ecogido en la siguien e abla.
x iii
min
𝚫𝒖 12𝚫𝒖𝑇𝑯𝒒𝒑 𝚫𝐮+𝑩𝒒𝒑 𝑇𝚫𝒖
𝑠.𝑡. 𝑹 𝚫𝒖≤𝒄
Whe e: 𝑯𝒒𝒑=2(𝑻𝑇𝜶𝑻+𝝀+𝑯𝑇𝜹𝑯+𝑻𝑇𝜶𝟒𝒖𝟐𝑻+𝝀𝟒𝒖𝟐+𝑻𝑇𝜸𝑻+𝑻𝑇 𝒂𝒖𝒙𝒖
𝑇𝜸𝒃𝒂𝒕 𝒂𝒖𝒙𝒖 𝑻)
𝑩𝒒𝒑=2(𝑻𝑇𝜶(𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝑯𝑇𝜹(𝑭𝑥(𝑡)−𝒘))+2((𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))𝑇𝜶𝟒𝒖𝟐𝑻+
𝑥𝑇(𝑡𝑘)𝜶𝟒𝒙𝒖𝑻+2Δ𝑑(𝑡𝑘)𝜆4𝑥𝑢,𝑠𝑚𝑎𝑙𝑙)𝑇+2((𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)−𝒖𝒔𝒄𝒉)𝑇𝜸 𝑻)𝑇+
+2((𝒂𝒖𝒙𝒖 𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)+𝒂𝒖𝒙𝒙𝑥(𝑡𝑘)−𝑷𝒃𝒂𝒕
𝒔𝒄𝒉)𝑇𝜸𝒃𝒂𝒕 𝒂𝒖𝒙𝒖 𝑻)𝑇
𝑹=
[
𝑰𝑵𝒄𝒎,𝑵𝒄𝒎
−𝑰𝑵𝒄𝒎,𝑵𝒄𝒎
𝑻
−𝑻
𝑯
−𝑯
𝒂𝒖𝒙𝒖 𝑻
−𝒂𝒖𝒙𝒖 𝑻
𝒂𝒖𝒙𝒖
−𝒂𝒖𝒙𝒖
]
𝒄=
[
𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑎𝑥
−𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑖𝑛
𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑎𝑥−𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)
−𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑖𝑛+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)
𝟏𝑵𝒑𝒑,𝒑 𝑦𝑚𝑎𝑥−𝑭𝑥(𝑡)
−𝟏𝑵𝒑𝒑,𝒑 y𝑚𝑖𝑛+𝑭𝑥(𝑡)
𝑷𝒃𝒂𝒕
𝒎𝒂𝒙−𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)−𝒂𝒖𝒙𝒙𝑥(𝑡𝑘)
−𝑷𝒃𝒂𝒕
𝒎𝒊𝒏+𝒂𝒖𝒙𝒖𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)+𝒂𝒖𝒙𝒙𝑥(𝑡𝑘)
𝚫𝑷𝒃𝒂𝒕
𝒎𝒂𝒙+[𝑑(𝑡𝑘)−𝑑(𝑡𝑘−1)
0⋮0]
−𝚫𝑷𝒃𝒂𝒕
𝒎𝒊𝒏−[𝑑(𝑡𝑘)−𝑑(𝑡𝑘−1)
0⋮0]
]
Pa a la simulación de la mic o ed se usa, como ya se ha comen ado p e iamen e, la lib e ía Simµg id de
MATLAB/Simulink. En es a lib e ía, los componen es ípicos de una mic o ed son modelados con el obje i o
de usa esos modelos en a eas de con ol, y se implemen an en Simulink en unción de algunos pa áme os
con igu ables que pueden ob ene se de los ab ican es o a a és de écnicas de inden i icación de modelos y
pa áme os con equipos eales. Es os modelos se han alidado y usado en o os p oyec os y publicaciones.
Como ejemplo, el diag am Simµg id diag am o his wo k is shown in Figu a 0-4.
En el aspec o so wa e, a lo an e io lo complemen an el oolbox Yalmip con el sol e CPLEX usado en el
con olado e cia io y el sol e quadp og como una unción p opia de MATLAB pa a el con olado
secunda io. El segundo caso es sencillo y di ec o de aplica . Pa a el p ime o, an o Yalmip como CPLEX
equie en de unos pasos p e ios de ins alación y con igu ación so wa e, que son ecogidos en el ex o
comple o de es e abajo en inglés. Además, pa a usa Yalmip, que es muy adecuado pa a p oblemas de
op imización en el ámbi o del con ol au omá ico como los MPCs, es necesa io conoce que, ípicamen e, hay
que segui una se ie de pasos:
1- De ini las a iables de decisión del p oblema de op imización usando sdp a , o bin a pa a a iables
bina ias. Es as se án usadas como a iables simbólicas en la de inición del p oblema.
2- De ini la unción de cos e y es icciones siguiendo las sin axis p opia de Yalmip.
3- Decidi y es ableces cuáles an a se las en adas y salidas del p oblema de op imización.
xix
Figu a 0-4. Diag ama Simµg id comple e
4- Usa el commando op imize pa a de ine una sóla ez el p oblema como un obje o. Es e comando
ecibe como en ada, en el siguien e o den: es icciones, unción de cos e, opciones, en adas,
salidas. En las opciones, el sol e se puede cambia ; po ejemplo, pa a usa CPLEX, se debe en ia el
a gumen o sdpse ings(‘sol e ’,’cplex’) en el campo de opciones.
5- Llama al obje o que con iene el p oblema de op imización po po cionándole las en adas eque idas
pa a esol e lo.
D. Resul ados
Los con olado es han sido p obados en simulación con p uebas de un día de du ación (simulado) en di e en es
si uaciones. En p ime luga , el con olado e cia io se p ueba po sepa ado pa a comp oba su co ec o
uncionamien o, así como la e olución adecuada an o de las a iables lógicas como con inuas. Se hacen
p uebas en el modo conec ado a ed pa a días soleado y nublado, cuyos esul ados de po encias y ni el de
almacenamien o de ene gía se mues an en la Figu a 0-5 y la Figu a 0-6, espec i amen e. Los esul ados son
sa is ac o ios, buscando la maximización del bene icio económico endiendo a ed en los momen os de mayo
p ecio de la ene gía (en o no a las ho as 11 y 20). Además, se minimizan los a anques del elec olizado y la
pila, asi como se p o gen los equipos de al as ca gas de po encia y a iaciones. En el caso del día nublado, se
iene que hace un mayo uso de la ed comp ando ene gía pa a pode supli la demanda.
Como en ambas simulaciones no se obse a el uncionamien o del hid ógeno, ya que su a anque es cos oso
económicamen e y en cuan o a aspec os ope acionales, se lle an a cabo dos simulaciones más. La p ime a de
ellas, mos ada en la Figu a 0-7, se co esponde con el modo conec ado a ed en un día soleado con demanda
casi nula, como pod ía se un in de semana en el campus uni e si a io. Po an o, hay mucho exceso de
ene gía y no odo puede se almacenado en la ba e ía o endido a la ed, po lo que el elec olizado a anca y
almacena algo de ene gía.
La úl ima simulación hecha pa a el con olado e cia io sólo se co esponde con una día soleado en el caso de
mic o ed aislada, po lo que en es e caso el elec olizado , así como la ba e ía y la pila de combus ible se usa
con más ecuencia e in e cambiando más ene gía. Los esul ados puede e se en la Figu a 0-8, ob eniendo
simila es conclusiones que en los casos an e io es.
Po su pa e, pa a p oba el sis ema comple o, dos simulaciones se han lle ado cabo, ambas en modo
conec ado a ed. La p ime a de ellas co esponde a un día soleado como el que se simuló en el p ime caso del
con olado e cia io. Las po encias esul ado del con olado e cia io (a iba) y secunda io (abajo) se
mues an en la Figu a 0-9. Los ni eles de almacenamien o de ene gía, po su pa e, se mues an en la Figu a
0-10 pa a lo plani icado po el con olado e cia io (a iba) y pa a las medidas omadas di ec amen e de los

xx
Figu a 0-5. E olución de las po encias y los ni eles de almacenamien o pa a el caso conec ado a ed y día
soleado
Figu a 0-6. E olución de las po encias y los ni eles de almacenamien o pa a el caso conec ado a ed y día
nublado
equipos (abajo). Se puede e cómo el con olado secunda io a a de segui las e e encias an o de es ado
como de po encia pa a odos los equipos, a pesa de que la po encia ne a di ie e en el caso eal, y más po la
inclusión de demanda eléc ica pa a ca ga de ehículos eléc icos y demanda ex a de hid ógeno. Además,
o os aspec os como las a iaciones sua es en elec olizado y pila de combus ible ambién se cuidan.
También es impo an e des aca cómo el supe condensado abso be las a iaciones ápidas de po encia cada
ez que se p oduce un cambio b usco y cómo lo hace po poco iempo, lo que encaja con el hecho de que
enga al a po encia especí ica pe o baja ene gía especí ica.
xxi
Figu a 0-7. E olución de las po encias y los ni eles de almacenamien o pa a el caso conec ado a ed en día
soleado con demanda casi nula
Figu a 0-8. E olución de las po encias y los ni eles de almacenamien o pa a el caso de mic o ed aislada en día
soleado
La o a simulación hecha pa a el sis ema comple o se co esponde con un día nublado como el p obado pa a el
con olado e cia io. La e olución de las po encias y de los ni eles de almacenamien o de ene gía pueden
e se en la Figu a 0-11 y la Figu a 0-12, espec i amen e, como en el caso de la simulación an e io .En es e
caso es necesa io comp a más ene gía de la ed, ya que no hay an o exceso de p oducción como pa a
ende la, po lo que el bene ico económico se e á me mado en a as de cumpli con los eque imien os de la
demanda con la gene ación y almacenamien o disponibles. Conclusiones simila es se pueden saca , po lo que
se conside an sa is ac o ias las p uebas hechas y álidos los con olado es diseñados.
xxii
Figu a 0-9. E olución de las po encias en el caso conec ado a ed y día soleado. A iba: po encia plani icada
po el con olado e cia io; abajo: e e encias de po encia dadas po el con olado secunda io
Figu a 0-10. E olución de los ni eles de almacenamien o en el caso conec ado a ed y día soleado. A iba:
po encia plani icada po el con olado e cia io; abajo: e e encias de po encia dadas po el con olado
secunda io
E. Conclusiones
Una ez que los con olado es se han diseñado y los esul ados de simulación se han analizado, se puede
ecapi ula y ex ae algunas conclusiones. Además, los pun os débiles y el posible abajo u u o se desc iben
pa a mejo a la es a egia de con ol y p og esa hacia la implemen ación en la plan a eal de la mic o ed pa a
xxiii
Figu a 0-11. E olución de las po encias en el caso conec ado a ed y día nublado. A iba: po encia plani icada
po el con olado e cia io; abajo: e e encias de po encia dadas po el con olado secunda io
Figu a 0-12. E olución de los ni eles de almacenamien o en el caso conec ado a ed y día soleado. A iba:
po encia plani icada po el con olado e cia io; abajo: e e encias de po encia dadas po el con olado
secunda io
ca ga de ehículos de ce o emisiones.
Una mi c o ed pa a es ación de ca ga de ehículos de ce o emisiones se ha desc i o y modelado en es e abajo
pa a diseña una es a egia de con ol óp imo basada en écnicas de MPC. Dos con olado es se han diseñado y
p obado en simulación usando MATLAB/Simulink: un con olado e cia io pa a la op imización de aspec os
económicos, de ope ación y deg adación en un p oblema MIQP (usando Yalmip y CPLEX), que p opo ciona

xxxi
ÍNDICE DE FIGURAS
Figu e 1. G eenhouse gas emissions in mobili y sec o in EU (Sou ce: [4]) 1
Figu e 2. Pe cen ages o g eenhouse gas emissions in anspo sec o and de ailed sha e o
oad anspo (Sou ce: [6]) 2
Figu e 3. Scheme o he mic og id (Modi ied image om he o iginal o [12]) 16
Figu e 4. Con ol s a egy 19
Figu e 5. Te ia y con olle 21
Figu e 6. Seconda y con olle 29
Figu e 7. Simµg id comple e diag am 42
Figu e 8. Day-ahead ma ke ene gy p ice 47
Figu e 9. Powe e olu ion and s o age le el in he sunny and g id-connec ed case 48
Figu e 10. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and g id-connec ed
case 49
Figu e 11. Ba e y con ol, bina y and auxilia y a iables in he sunny and g id-connec ed
case 49
Figu e 12. G id con ol, bina y and auxilia y a iables in he sunny and g id-connec ed case 50
Figu e 13. Powe e olu ion and s o age le el in he cloudy and g id-connec ed case 50
Figu e 14. Hyd ogen con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed
case 51
Figu e 15. Ba e y con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed
case 51
Figu e 16. G id con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed case 52
Figu e 17. Powe e olu ion and s o age le el in he sunny and nea ly-ze o demand day and in
g id-connec ed case 52
Figu e 18. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o
demand day and in g id-connec ed case 53
Figu e 19. Ba e y con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o
demand day and in g id-connec ed case 53
Figu e 20. G id con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o demand
day and in g id-connec ed case 54
Figu e 21. Powe e olu ion and s o age le el in he sunny and islanded case 54
Figu e 22. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and islanded case 55
Figu e 23. Ba e y con ol, bina y and auxilia y a iables in he sunny and islanded case 55
Figu e 24. EVs cha ging powe demand p o ile 56
Figu e 25. Ex a hyd ogen consump ion p o ile 57
Figu e 26. Powe e olu ion in he sunny and g id-connec ed case. A he op: powe schedule
gi en by he e ia y con olle ; a he bo om: powe e e ence gi en by he seconda y
con olle 59
xxxii
Figu e 27. S o age le el in he sunny and g id-connec ed case. A he op: s o age le el
schedule gi en by he e ia y con olle ; a he bo om: eal s o age le el measu ed om he
equipmen 59
Figu e 28. Powe e olu ion in he cloudy and g id-connec ed case. A he op: powe schedule
gi en by he e ia y con olle ; a he bo om: powe e e ence gi en by he seconda y
con olle 60
Figu e 29. S o age le el in he cloudy and g id-connec ed case. A he op: s o age le el
schedule gi en by he e ia y con olle ; a he bo om: eal s o age le el measu ed om he
equipmen 60
1
1 INTRODUCTION
is well-known nowadays ha ou plane is su e ing a clima e change p ocess, whose consequences a e
expec ed o be ca as ophic i no u gen and d as ic ac ions a e aken. In ac , ecen ly, he 2021 Uni ed
Na ions F amewo k Con en ion on Clima e Change, UNFCCC, has held he 26 h Con e ence o he
Pa ies, COP26, in Glasgow [4]. The e, he 197 pa ies ag eed in educing emissions in o de o limi he
inc ease in Ea h empe a u e o 1.5 deg ees. Simila ly, he Eu opean Commission launched he Eu opean
G een Deal in 2019 [5], whose main objec i e is o each clima e neu ali y in 2050; i.e. no g eenhouse gases
would be emmi ed.
The p e ious easons explain why an impo an pa o Eu opean unds in he p og amme Ho izon Eu ope
a e COVID19 c isis a e going o be alloca ed o suppo sus ainable and g een p ojec s. In Ho izon Eu ope
P og amme [6], some p ojec opics o be ounded a e clima e change, UN’s sus ainable De elopmen Goals
( he e a e 3 in e es ing om a o al o 17: A o dable and Clean Ene gy, Sus ainable Ci ies and Communi ies,
and Clima e Ac ion), and imp o emen s and g ow h o Eu opean echnology and indus y. One o he main
a eas in his p og amme is he Pilla II (Global Challenges & Eu opean Indus ial Compe i i eness), which
has 6 Clus e s. One o hose clus e s is Clima e, Ene gy & Mobili y. Abou 53.4% o he budge will be
alloca ed o ha Pilla II, whe e 15.123 billion€ will be o Clus e 5 – Clima e, Ene gy & Mobili y (including
1.35 billion€ om Nex Gene a ion Eu ope, NGEU). In Ho izon 2020, 30% o in es men s we e des ined o
clima e change. Digi aliza ion is also p esen in Clus e 4 – Digi al, Indus y & Space, so p ojec s combining
en i onmen al sus ainabili y and digi aliza ion as a key ool will ha e high p io i y in he ollowing yea s.
As i has been old ye , an impo an opic in clima e change is mobili y. The Eu opean En i onmen Agency
showed in 2021 ha , in gene al, g eenhouse gas emissions (GHG) in mobili y sec o a e inc easing, unlike in
o he sec o s [7]. Figu e 1 shows he change in emission le els since and wi h espec o 1990, and i can be
obse ed how a ia ion, ma i ime and oad anspo emissions we e inc easing un il COVID19 c isis. This
g aph also p edic s he u u e change in emission conside ing policy measu es in EU Membe S a es (wi h
exis ing measu es, WEM) and including na ional planned policies (wi h addi ional measu es, WAM). I can be
seen ha in ma i ime and a ia ion sec o he e is a need o mo e se e e measu es, bu in oad anspo i
seems ha emissions will dec ease i planned measu es a e accomplished.
Figu e 1. G eenhouse gas emissions in mobili y sec o in EU (Sou ce: [7])
I
In oduc ion
2
Looking a g aphs in Figu e 2, one can deduce why oad anspo is he one whe e mo e ac ions a e scheduled
o be done, since is he main emisso o g eenhouse gases. Ca s a e he p incipal con ibu o s o hose
emissions in oad anspo . I is also known ha when emissions compa isons a e made pe passenge and
kilome e , a ia ion emissions a e eally high [8]. Howe e , he less en i onmen ally- iendly could be a one
passenge ca . So he g owing in e es in ze o-emissions ehicles nowadays is easonable.
Figu e 2. Pe cen ages o g eenhouse gas emissions in anspo sec o and de ailed sha e o oad anspo
(Sou ce: [1])
Mobili y emissions ep esen abou 25% o o al g eenhouse gases emissions and oad anspo a e a huge
pe cen age o i [9]. So, in spi e o encou agemen o use ail anspo o deca bonize, i is clea ha also a
change in pa adigm o oad mobili y should be ca ied ou i EU 2030 and 2050 a ge s wi h espec o
emissions wan o be eached.
In he desc ibed con ex , enewable ene gy p oduc ion and elec ic mobili y mus play a c ucial ole in he
deca bonisa ion and ene gy ansi ion. Bu bo h ha e he p oblem o in e mi ence, since he i s one depends
on me eo ological condi ions and he second one, on people beha iou as in classical ene gy consump ion.
Ene gy p oduc ion and consump ion p edic ion and ene gy s o age sys ems, ESS, help in coping wi h such
a iabili y. In 2021, Spanish Go e nmen has launched i s own Ene gy S o age S a egy, whe e ene gy s o age
sys em such as ba e ies, hyd ogen and supe capaci o s a e highly conside ed [10]. A s a egic oadmap o
encou aging ESS use is de eloped, including an ex e nal and independen oadmap o hyd ogen, which is
conside ed one he mos p omising ene gy ec o [11]. The Spanish budge o 2022 includes 2184.6 M€ o
sus ainable mobili y and 1646 M€ o ene gy ansi ion [12]. Mo eo e , enewable ene gies and sus ainable
mobili y a e he opics whe e mo e unds om NGEU will be alloca ed in Spain [13].
He e is whe e he concep o mic og id appea s. Mic og ids a e p oduc ion ene gy sys ems which a e
composed o ene gy p oduc ion and s o age equipmen o sho and medium scale consump ion [2]. They
wo k in an independen manne and can be connec ed o he main g id o o he mic og ids, helping in he
balance and s abili y p oblem o he elec ical ne wo k.
1.1 Con ex and objec i es
The en i e desc ibed abo e se e as an impulse o his wo k. The inal objec i e is o build a mic og id in he
labo a o y acili ies o be used o ze o-emissions ehicle echa ging, including bo h elec ic and hyd ogen-
based ehicles. This is a p ojec which appea s as a syne gy be ween elec ical, ene gy, elec onic and
au oma ic con ol depa men s, among o he s. Each o hese con ibu o s will p o ide hei expe ience and
a ailable equipmen . The mic og id will be composed o pho o ol aic (PV) ield, ba e ies, hyd ogen
echnology (elec olyze , me al hyd ide s o age and uel cell), ul acapaci o , connec ion wi h he main g id,
3
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
elec ic ehicle cha ging poin s and hyd ogen-based ehicle echa ging poin s.
The goal o his wo k is o de elope an e icien ene gy managemen s a egy o ha mic og id, which will be
able o decide he ene gy low be ween equipmen in e e y ime ins an . This is done using wo MPC
con olle s deciding he ene gy low in an op imal way, aking in o accoun equipmen limi a ions and
deg ada ion p oblems. The i s MPC-con olle uses ene gy consump ion, p oduc ion and p ice o ecas s
e e y hou o gi e e e ences o he second con olle , which will ac in a imescale o seconds co ec ing
powe de ia ions and coping wi h ins an aneous changes in ene gy consump ion and p oduc ion. These
de ia ions will be inc eased by an ex a hyd ogen demand o echa ging a hyd ogen ehicle a ailable in he
labo a o y and by he elec ic powe demanded by elec ic ehicle cha ging p ocess. The ou pu o he second
con olle will be used in he u u e as e e ences o he elec onic powe con e e s, which will ac in he
miliseconds scale, bu hey a e no implemen ed in his wo k.
The con olle s a e es ed in simula ion using MATLAB/Simulink wi h he model o he mic og id buil om
Simµg id, a simula ion ool de eloped by he Au oma ica y Robó ica Indus ial esea ch g oup some yea s
ago. Fo sol ing he op imiza ion p oblem, Yalmip oolbox and sol e CPLEX a e used o he i s con olle ,
and sol e quadp og wi hou Yalmip o he second con olle .
1.2 Me odology
To achie e he men ioned objec i es, he ollowing s eps ha e been ca ied ou :
 S a e-o -A e iew, especially in he g een hyd ogen and elec ic ehicle cha ging s a ion ields.
 Mic og id planning, ga he ing a ailable equipmen in o ma ion, and simula ion model se ing up.
 S udy abou mic og id con ol s a egies.
 Ins all and lea n how o use Yalmip oolbox and sol e CPLEX in MATLAB.
 MPC-con olle s ( e ia y and seconda y) design and es ing in simula ion.
 C ea ion o ex a demand o ze o-emission ca cha ging s a ion: hyd ogen and elec ic powe .
So, his epo is o ganized as ollows. This in oduc ion is ollowed by he s a e-o -a , mainly ocused on
hyd ogen echnology and elec ic ehicle cha ging p ocess in mic og ids. Sec ion 3 is he mos impo an since
i is dedica ed o con olle s design. The con ol s a egy is desc ibed and equa ions o bo h o hem ga he ed,
explaining how o implemen i in simula ion. In his sec ion, some b ie ins uc ions o including Yalmip and
CPLEX in MATLAB a e gi en, as well as some hin s o implemen he seconda y con olle wi h quadp og.
Resul s om he di e en simula ions ca ied ou a e exposed and analized in sec ion 4. Di e en scena ios a e
es ed including sunny and cloudy days. Finally, conclusions om he p e ious sec ions a e shown in sec ion
5, whe e u u e wo ks a e men ioned in o de o con inue wi h his p ojec .

5
2 STATE-OF-ART
i e a u e abou enewable ene gy has been widely de eloped and one can ead abou lo o p ojec s and
publica ions wo king on he mic og id ield. Ad an ages o p ope mic og id con ol ha e been
discussed and e o s a e ocused on his opic. The main e e ence o his wo k is [2], whe e he
concep o mic og id is desc ibe and analized, de i ing he need o con ol and de eloping some ad ances
con ol echniques using MPC. In ha con empo a y wo k one can see he huge amoun o ela ed li e a u e
which has been de eloped so a .
Building-up a mic og id is a ask which has been ex ensely done ye . Due o some o he equipmen used we e
pa o he Hylab labo a o y in he Uni e si y o Se ille, wo in e es ing wo ks a e [14] and [15]. In he i s
one, he au ho s show how Hylab mic og id was se up in o de o use i in he u u e wi h con ol pu poses. I
p e ends o co e an ini ial phase in mic og id con ol: he co ec modelling, cha ac e iza ion and building o
he mic og id. In he second one, Hylab componen s (PV panels, PEM elec olyze and uel cell, me al hyd ide
ank and ba e y) a e modelled and alida ed in he eal plan wi h he aim a conside ing dynamics and being
as simple as possible. The models a e o in e es o con ol pu poses. Some da a and pa ame e s o doing
simula ions in Simulink a e aken in his wo k om hese wo pape s.
Mic og ids wi h hyb id ene gy s o age sys ems seem o be adequa e o aking ad an ages o di e en
echnologies. In his con ex , hyd ogen is ge ing mo e and mo e impo ance. Elec olyze s a e chemical
de ices which use DC cu en and wa e in o de o p oduce hyd ogen, so i he DC elec ici y comes om
enewable ene gies, he p ocess will be g een. Then, hyd ogen is s o ed in anks o la e use in uel cells,
whe e i is again con e ed o DC cu en o supply he mic og id.
The use o g een hyd ogen is ex ensi e and i is expec ed o be g ea e in nex yea s. Hyd ogen can be used
[11] as aw ma e ial in e ine ies, s eel p oduc ion o chemical indus ies, in sec o ial in eg a ion abso bing and
s o ing ene gy excess om enewable ene gies o being mixed in gas in as uc u es, as uel cell combined
wi h ba e ies in mobili y (ca s, ehicles o hea y-du y anspo s) whe e an in e se elec olysis p ocess is
needed o p oduce elec ici y and he unique esidual p oduc is wa e . O he uses such as powe supply o
hea ing in buildings a e being in es iga ed.
As he e a e impo an echnological de elopmen s in ields like uel cells o elec olyze s which make g een
hyd ogen easible, and ad an ages and uses a e eally in e es ing, companies, go e nmen s and esea ch
cen e s ha e been pu ing an in ensi e e o on imp o ing hese echnologies. In pa icula , he e a e
d awbacks which ha e no allowed g een hyd ogen o be ully de eloped [16]. In ha way, i is necessa y o
make g een hyd ogen echnology mo e cos ly and ene gy e icien . The p ocess om elec ici y- o-hyd ogen
has an e iciency o abou 50% [10].
So we a e now in a con ex whe e lo s o p ojec s a e being de eloped in o de o demons a e in eal plan s he
easibili y o g een hyd ogen p oduc ion ia wa e elec olysis o di e en uses. The cu en si ua ion is he
de elopmen o PEM (some imes alkaline) elec olyze s-based plan s in he MW-scale p oduc ion, wi h he
goal o eaching GW by 2030. In Eu ope g een hyd ogen seems o be a end in No h-Wes e n coun ies such
as Ne he lands, No he n Ge many o No way, which a e mo e in ensi e in g een hyd ogen p oduc ion,
ypically aking elec ici y om wind sou ces ins ead o sola ones. The mos impo an and p esen p ojec s in
Eu ope a e summa ized in Table 1. As hey a e p ojec s in cou se, some da a a e no a ailable ye and e en
he e is no an o icial websi e.
In Spain he e is a ecen ly in ensi e ac i i y because o he s a egy adop ed by Spanish Go e nmen , which
has published a Hyd ogen oadmap [11]. This plan elies on g een hyd ogen p oduc ion and s o age (as o he
s o age me hods as de ailed in [10]) in o de o eco e om COVID-19 c isis. I can be obse ed a change
wi h espec o Eu opean p ojec s in he ene gy sou ce. Clima ological condi ions in Spain made possible mo e
sola - o-hyd ogen p oduc ion han in No h Eu ope, so he go e nmen aims a posi ioning Spain in he op o
L
S a e-o -A
6
P ojec
Loca ion
Desc ip ion / Goal
Cap.
MW
P od.
ons
Sou ce
Main use (5)
Da e
(2)
Companies
[17]
H24ALL
Spain
Cons uc a high-p essu e alkaline
elec olyze which can wo k in a 100
MW g een H2 p oduc ion plan
P oduce a 3 €/kgH2
100
- (1)
- (1)
Mobili y, e ining,
syn he ic uel
p oduc ion, powe
gene a ion
Jan
2021
Repsol, 14 pa ne s
om Belgium,
Denma k,
Ge many, No way,
Spain, Tu key
[18]
FCH2RAIL
Belgium,
Ge many,
Spain,
Po ugal
Ze o-emissions ains ed by ae ial
g id and a uel cell sys em (wi h bo h
H2 uel cell and ba e ies)
Al e na i e o diesel ains and in
zones whe e i is di icul o elec i y
T ying o ake ad an ages o uel cell
hea o he ain ai -condi ioning
- (3)
- (3)
- (3)
Fuel Cell o ains
Jan
2021
Toyo a, Ren e,
ADIF, CAF,
pa ne s om
Belgium, Ge many,
Spain and Po ugal
[19] Lingen
G een
Hyd ogen
Ge many
G een H2 p oduc ion
Imp o e elec olyze e iciency
50
9000
yea
Wind
Re ine y
No
2020
BP, Ø s ed
[20]
No H2
Ne he lands
G een H2 p oduc ion
1, 4,
+10
GW
(4)
1·109
yea
O sho e
wind
Indus y
Feb
2020
Gasuine,
G oningen
Seapo s, Shell
Nede land,
Equino , RWE
[21]
Djewels
Ne he lands
De elopmen o a high p essu e
alkaline elec olyze
20
3000
yea
Wind o
sola
Me hanol
p oduc ion
Jan
2020
Nou yon, Gasuine,
McPhy, BioMCN,
DeNo a, Hinicio
[22] ITM
Linde
Elec olysis
GmbH
Ge many
G een H2 p oduc ion wi h he la ges
PEM elec olyze in he wo ld (24
MW)
24
- (1)
- (1)
Indus y
(6) 2nd
hal
2022
Join en u e
be ween Linde and
ITM Powe
[23] G een
Hyd ogen
F ance
G een H2 p oduc ion in a new
elec olyze plan
200
28000
yea
Wind o
sola
Indus y and
mobili y
Jan
2021
Ai Liquide, H2V
No mandy
[24]
MassHylia
F ance
G een H2 p oduc ion
Op imal managemen in he
in eg a ion be ween di e en sola
ields and he H2 uses
40
5 day
Sola
Bio e ine y
(7) Jan
2021
To al, Engie
[25]
Hyb idge
Ge many
S udying g een H2 p oduc ion wi h
bo h PEM and alkaline elec olyze s
T ying o adap gas anspo a ion
in as uc u es o H2
100
- (1)
Wind o
sola
Mobili y, hea ing,
e c.
(6)
2023
Amp ion, Open
G id Eu ope
[26] BP
Ro e dam
Re ine y
Ne he lands
G een H2 p oduc ion
250
45000
yea
O sho e
wind
Re ine y
(8)
2022
BP, Nou yon, Po
o Ro e dam
[27]
REFHYNE
Ge many
G een H2 p oduc ion wi h PEM
elec olyze
10
1300
yea
Wind o
sola
Re ine y. Explo ing
indus y, powe
gene a ion, hea ing,
mobili y
(9) Jan
2018
Shell, ITM Powe
[28]
H2Fu u e
Aus ia
G een H2 p oduc ion wi h PEM
elec olyze
6
1200
m3/h
Wind o
sola
S eel p oduc ion
plan
Jan
2017
No
2019
(P od)
Ve bund,
oes alpine,
Siemens, Aus ian
Powe G id, TNO,
K1-MET
[29]
ELEMENT
ONE
Ge many
Powe - o-gas pilo plan
Focus on elec ici y and gas g ids
connec ion, especially in he s o age
wi h gas ansmission in as uc u es
100
- (1)
Wind
Me hane
p oduc ion
(indus y), mobili y
(10)
Oc
2018
TenneT, Gasunie,
Thyssengas
[30]
OYSTER
- (1)
G een H2 p od. wi h compac PEM
elec olyze s (in eg a ed o sho e)
which adap o ough condi ions
MW
- (1)
O sho e
wind
- (1)
Jan
2021
Elemen Ene gy,
ITM Powe ,
Ø s ed, Siemens
Gamesa Renewable
Ene gy
(1) No a ailable da a
(2) P ojec announcemen da a, no necessa ily p oducing H2 a ha ime
(3) I is no hyd ogen p oduc ion, bu hyd ogen applica ion
(4) 1 GW in 2027, 4 GW in 2030, +10 GW in 2040
(5) Bu in mos cases no limi ed o
(6) Da e scheduled o s a p oduc ion
(7) S a cons uc ion in 2022 and p oduc ion in 2024
(8) Now in easibili y s udy. Decision will be made in 2022
(9) I is ope a ing since middle 2021
(10) To s a in 2022
Table 1. Main cu en Eu opean p ojec s o g een H2 p oduc ion and uses
7
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
P ojec
Loca ion
Desc ip ion / Goal
Cap.
MW
P od.
ons
Sou ce
Main use (4)
Da e
(2)
Companies
[11] [31]
H2PORTS
Valencia
Hyd ogen s a ion and H2 supply
managemen in he po
- (3)
- (3)
- (3)
Fuel o ope a ing
machines in he
po
Jan
2019
Au o idad Po ua ia
de Valencia,
Fundación
Valenciapo ,
Cen o Nacional del
Hid ógeno, MSC
Te minal Valencia,
G upo G imaldi,
Hys e -Yale, A ena,
Balla d Powe
Sys ems Eu opa,
Enagás
[11]
SUN2HY
Mós oles
(Mad id)
H2 p oduc ion wi h elec o-ca alysis
(PEC echnologies, di ec con e sion
om sola and wa e o H2) and eal
implemen a ion in he i s plan
(Pue ollano) o his ype wi hou
g id connec ion
- (1)
- (1)
Sola
- (1)
2019
Enagás, Repsol
[11]
SEAFUEL
Tene i e
G een H2 p oduc ion wi h wind
ene gy and sea wa e
- (1)
- (1)
Wind
Hyd ogen ehicles
2017
9 pa ne s and 6
associa e membe s,
including companys
o all a eas. Enagás
is an associa e
membe
[11] HIGGS
Pa icipan s
esea ch
cen e s
In e na ional p ojec o H2 injec ion
in high p essu e na u al gas ne wo ks
- (3)
- (3)
- (3)
T anspo a ion o
di e en uses
Jan
2020
Fundación
Hid ógeno de
A agón, Redexis,
Tecnalia, DVGW,
HSR, ERIG
[11] [32]
GREEN
HYSLAND
Mallo ca
The i s p ojec o a Medi e anean
coun y which will be unded by
Eu opean unds and i is expec ed o
be he i s H2 hub in Sou he n
Eu ope
7.5
300
yea
Sola
Buses, en -a-ca
ehicles, powe ,
hea
Jan
2021
Acciona, Enagás y
Cemex, Balea es
Go e nmen ,
IDAE, Redexis,
FHa, Islas Balea es
Uni e si y
[11] [33]-
As Pon es
(A Co uña)
The Spanish Go . wan s o c ea e a
hub he e o p oduce g een H2
100
10000
yea
Wind
Indus y, mobili y
Jan
2021
Endesa
[11] [34]
GREEN
SPIDER
As u ias
G een H2 p oduc ion o be used o
local consump ion and in o de o
expo o Ge many and Ne he lands
350
- (1)
Wind (250
MW) and
sola (100
MW)
S eel p oduc ion
Feb
2021
Na u gy, Enagás
[11] [35]-
Pue ollano
(Ciudad
Real)
The bigges g een H2 p oduc ion
(PEM elec olyze ) plan o
indus ial use in Eu ope
The nex p ojec will be in Palos de
la F on e a (Huel a). Be ween bo h
hey ge 800 MW elec olysis (20%
o na ional goal o 2030)
Ibe d ola has also cons uc ed h ee
hyd ogen s a ions (5 MW
elec olyze s in each one) in
Valencia, Alican e and Mu cia whose
g een H2 is used in hea y anspo
20
- (1)
Sola
NH3 and e ilize
p oduc ion
S a
in
2021
Ibe d ola, Fe ibe ia
[11] -
Huesca
G een H2 p oduc ion and g id
connec ion
- (1)
- (1)
- (1)
Mobili y ( oad and
ail)
2020
Fundación
Hid ógeno de
A agón
[11] [36]
E-FUELS
BILBAO
Bilbao
(Vizcaya)
Use o g een H2 + CO2 om Pe ono
oil e ine y in o de o ob ain
syn he ic uels
I will allow s eel o conc e e
ac o ies o " euse" he CO2 p oduced
and become ca bon-neu al
- (3)
50
syn h.
uels
ba els
day
Wind and
CO2
cap u ed
Syn he ic uels o
ehicles, ucks o
planes combus ion
engines
Jun
2020
Repsol, Pe ono ,
Saudi A amco, En e
Vasco de la Ene gía
(EVE)
[37] The m.
Powe Plan
Ba anco de
Ti ajana
Ba anco de
Ti ajana
(G an
Cana ias)
Ins all enewable ene gy o eed
elec olyze s (ene gy excess will be
used o suppo he g id). I is a g een
H2 p oduc ion plan
7
- (1)
Sola
- (1)
Feb
2021
Endesa

15
3 CONTROL STRATEGY DESIGN
n his sec ion, he con olle s a e designed using MPC echniques. Fi s , he sys em is b ie ly desc ibed and
he gene al sys em s a e space model is de i ed. Then, he con ol s a egy is explained, desc ibing he
de ails o seconda y and e ia y con olle s wi h he o mula ion o hei en i e op imiza ion p oblems.
Finally, he so wa e ools employed o he simula ions a e desc ibed wi h some hin s o use hem.
3.1 Sys em desc ip ion and modeling
As i has al eady been commen ed in sec ion 1, he sys em o be con olled is a mic og id composed o
equipmen om di e en esea ch g oups o Escuela Técnica Supe io de Ingenie ía de Se illa. These
componen s a e:
- PV ield o 4 kW
- Lead-acid Ba e y bank o 48 V and capaci y o 367 Ah
- PEM Elec olyze o 1 kW and 0.23 Nm3/h
- Me al Hyd ide S o age Tank o 7 Nm3
- PEM Fuel Cell o 1.5 kW
- Ul acapaci o o 63 F
- Consume load
- Elec ic ehicle cha ge and hyd ogen echa ging poin
- Connec ion o he elec ical g id
Fo he componen s desc ip ion and ope a ion de ails, as well as hei equa ions, he eade is e e ed o he
e e ence [2]. All he componen s will be connec ed o an AC bus h ough powe con e e s, as can be seen in
he scheme o Figu e 3. In pa icula , DC-AC in e e s a e necessa y o he PV panels, uel cell, ba e y and
ul acapaci o , and an AC-DC ec i ie o he elec olyze . Mo eo e , o he g id, a ans o me and an AC-
AC con e e a e needed. This las con e e , as well as he ones o ba e y and ul acapaci o , mus be
bidi ec ional [76]. Anyway, powe elec onics and he ze o-emissions ehicles cha ging poin s a e ou o he
scope o his wo k and a e expec ed o be ea ed in he u u e. In ac , he designed con olle s in his wo k
ob ain a he end he powe e e ences o be sen o he powe con e e s, assuming ha he e exis s low-le el
con olle s in he men ioned con e e s [2]. The EVs and hyd ogen-based ehicles a e ea ed as an ex a
powe consump ion ollowing a speci ic demand o powe o hyd ogen depending on he ehicle, so he e is
no V2G implemen a ion in his wo k. In Figu e 3, he di ec ion o he cu en and hyd ogen can also be seen.
The modelling o such sys ems can be done ega ding as componen s dynamics and he ene gy balance [2].
Howe e , aking in o accoun ha gene a ion, s o age sys ems such as he elec olyze and he uel cell, and
consump ion ac s as e han second-scale (which is ypically he as es sampling ime in an EMS), only
dynamics he dynamics o ba e ies, hyd ogen ank and ul acapaci o a e conside ed.
Al hough equa ions desc ibed in [2] o ba e y, hyd ogen ank and ul acapaci o dynamics a e used in he
Simulink mic og id implemen a ion, he linea ized e sion a e going o be used o con ol pu poses. The
con en ion o powe a iables will be he same o his wo k and he same as [2]: posi i e i p o iding powe
o he bus and nega i e i consuming powe om he bus. Selec ing he le el o ene gy in he s o age sys ems,
i.e. ba e y SOC, Le el o Hyd ogen (LOH) and ul acapaci o SOC, as he s a e a iables in
I
Con ol s a egy design
16
Figu e 3. Scheme o he mic og id (Modi ied image om he o iginal o [2])
pe cen age (%), he disc e e- ime linea equa ions a e [2]:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)−𝜂𝑏𝑎𝑡𝑇𝑠
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡𝑃𝑏𝑎𝑡(𝑡)
(3–1)
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)−100𝜂𝐻2𝑇𝑠
𝑉𝑚𝑎𝑥𝑃𝐻2(𝑡)
(3–2)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)−𝜂𝑢𝑐 𝑇𝑠
𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐(𝑡)
(3–3)
Whe e is he cu en ime ins an , 𝑇𝑠 is he sampling ime in hou s (h), 𝐶𝑚𝑎𝑥,𝑏𝑎𝑡 and 𝐶𝑚𝑎𝑥,𝑢𝑐 a e he
maximum ba e y and ul acapaci o capaci ies in kWh, espec i ely, 𝑉𝑚𝑎𝑥 is he me al hyd ide ank maximum
olume in Nm3, and 𝑃𝑖(𝑡)|𝑖=𝑏𝑎𝑡,𝐻2,𝑢𝑐 a e he ba e y, hyd ogen and ul acapaci o powe in kW, espec i ely.
𝜂𝑖|𝑖=𝑏𝑎𝑡,𝐻2,𝑢𝑐 a e he e iciencies in hose sys ems in pe cen age (%) o he ba e y and ul acapaci o and in
Nm3/kWh o he hyd ogen. These e iciencies can be b oken down depending on he sign o 𝑃𝑖 as ollows:
𝜂𝑖= {𝜂𝑐ℎ 𝑖𝑓 𝑃𝑖<0 (𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔)
1
𝜂𝑑𝑖𝑠𝑐 𝑖𝑓 𝑃𝑖≥0 (𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔), 𝑖=𝑏𝑎𝑡,𝐻2,𝑢𝑐
(3–4)
Bu , i he p oblem is s a ed in e ms o con inuous and bina y a iables (see nex subsec ions), on can conside
ha :
𝑃𝑏𝑎𝑡(𝑡)=𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡)−𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡)
(3–5)
𝑃𝐻2(𝑡)=𝑃𝑓𝑐(𝑡)−𝑃𝑒𝑧(𝑡)
(3–6)
𝑃𝑢𝑐(𝑡)=𝑃𝑢𝑐,𝑑𝑖𝑠𝑐(𝑡)−𝑃𝑢𝑐,𝑐ℎ(𝑡)
(3–7)
Whe e he subsc ip s meaning a e: ch (cha ging), disc (discha ging), c ( uel cell) and ez (elec olyze ). I mus
be ema ked ha 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡), 𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡), 𝑃𝑓𝑐(𝑡), 𝑃𝑒𝑧(𝑡), 𝑃𝑢𝑐,𝑑𝑖𝑠𝑐(𝑡) and 𝑃𝑢𝑐,𝑐ℎ(𝑡) a e always posi i e
alues.
The equa ions (3–1), (3–2) and (3–3) can be ew i en as:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)+𝜂𝑏𝑎𝑡,𝑐ℎ 𝑇𝑠
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡)−𝑇𝑠
𝜂𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑏𝑎𝑡𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡)
(3–8)
17
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)+100𝜂𝑒𝑧𝑇𝑠
𝑉𝑚𝑎𝑥𝑃𝑒𝑧(𝑡)𝛿𝑒𝑧(𝑡)−100 𝑇𝑠
𝜂𝑓𝑐 𝑉𝑚𝑎𝑥𝑃𝑓𝑐(𝑡)𝛿𝑓𝑐(𝑡)
(3–9)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)+𝜂𝑢𝑐,𝑐ℎ 𝑇𝑠
𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐,𝑐ℎ(𝑡)−𝑇𝑠
𝜂𝑢𝑐,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐,𝑑𝑖𝑠𝑐(𝑡)
(3–10)
Being 𝛿𝑒𝑧(𝑡) and 𝛿𝑓𝑐(𝑡) wo bina y a iables which indica e he ene gized s a e o he elec olyze and he
uel cell, espec i ely. I he elec olyze is wo king a ime ins an , 𝛿𝑒𝑧(𝑡) will be ‘1’; i no wo king, 𝛿𝑒𝑧(𝑡)
will be ‘0’ (and he same o he uel cell). They will be u he desc ibed and o mula ed in nex subsec ions.
Looking a equa ions (3–8), (3–9) and (3–10) and aking in o accoun he sign con en ion, one can see ha i
he s o age sys em is cha ging (o he elec olyze ac i e o he hyd ogen case), he ene gy le el will inc ease.
On he con a y, i he s o age sys em is discha ging (o he uel cell is wo king o he hyd ogen case), he
ene gy le el will dec ease. Those ene gy le els a e de ined, as i has al eady been said in pe cen ages, as he
coe icien be ween he ac ual capaci y and he maximum capaci y o each s o age de ice.
Fo he sake o simplici y, one can de ine he cons an s:
𝐾𝑏𝑎𝑡,𝑐ℎ=𝜂𝑏𝑎𝑡,𝑐ℎ
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡
(3–11)
𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐=1
𝜂𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑏𝑎𝑡
(3–12)
𝐾𝑒𝑧=𝜂𝑒𝑧
𝑉𝑚𝑎𝑥
(3–13)
𝐾𝑓𝑐=1
𝜂𝑓𝑐 𝑉𝑚𝑎𝑥
(3–14)
𝐾𝑢𝑐,𝑐ℎ=𝜂𝑢𝑐,𝑐ℎ
𝐶𝑚𝑎𝑥,𝑢𝑐
(3–15)
𝐾𝑢𝑐,𝑑𝑖𝑠𝑐=1
𝜂𝑢𝑐,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑢𝑐
(3–16)
Wi h all ha ing uni s o (kWh)-1. Wi h hese de ini ios, he dynamics equa ions s a e as ollows:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)+𝐾𝑏𝑎𝑡,𝑐ℎ 𝑇𝑠 𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡)−𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 𝑇𝑠 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡)
(3–17)
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)+100 𝐾𝑒𝑧 𝑇𝑠 𝑃𝑒𝑧(𝑡) 𝛿𝑒𝑧(𝑡)−100 𝐾𝑓𝑐 𝑇𝑠 𝑃𝑓𝑐(𝑡) 𝛿𝑓𝑐(𝑡)
(3–18)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)+𝐾𝑢𝑐,𝑐ℎ 𝑇𝑠 𝑃𝑢𝑐,𝑐ℎ(𝑡)−𝐾𝑢𝑐,𝑑𝑖𝑠𝑐 𝑇𝑠 𝑃𝑢𝑐,𝑑𝑖𝑠𝑐(𝑡)
(3–19)
Finally, he ene gy balance mus be o mula ed as i is done in equa ion (3–20).
𝑃𝑝𝑣(𝑡)+𝑃𝑔𝑟𝑖𝑑(𝑡)+𝑃𝑏𝑎𝑡(𝑡)+𝑃𝑢𝑐(𝑡)+𝑃𝑓𝑐(𝑡)−𝑃𝑒𝑧(𝑡)−𝑃𝑙𝑜𝑎𝑑(𝑡)−𝑃𝑒𝑣(𝑡)=0
(3–20)
Whe e he subsc ip s mean: p (pho o ol aic) and e (elec ic ehicle). 𝑃𝑝𝑣(𝑡), 𝑃𝑓𝑐(𝑡), 𝑃𝑒𝑧(𝑡), 𝑃𝑙𝑜𝑎𝑑(𝑡) and
𝑃𝑒𝑣(𝑡) a e always posi i e alues, and 𝑃𝑔𝑟𝑖𝑑(𝑡), 𝑃𝑏𝑎𝑡(𝑡) and 𝑃𝑢𝑐(𝑡) can ha e posi i e o nega i e sign,
depending on he de ined sign c i e ion.
I he o al ne powe , de ined as he gene a ion minus he consump ion powe , is conside ed as a measu able
dis u bance d, he ollowing can be s a ed:
Con ol s a egy design
18
𝑑(𝑡)=𝑃𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛(𝑡)−𝑃𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛(𝑡)=𝑃𝑝𝑣(𝑡)−(𝑃𝑙𝑜𝑎𝑑(𝑡)+𝑃𝑒𝑣(𝑡))
(3–21)
And he equa ion (3–20) emains as ollows:
𝑃𝑔𝑟𝑖𝑑(𝑡)+𝑃𝑏𝑎𝑡(𝑡)+𝑃𝑢𝑐(𝑡)+𝑃𝑓𝑐(𝑡)−𝑃𝑒𝑧(𝑡)+𝑑(𝑡)=0
(3–22)
On he one hand, om equa ion (3–22), all he e ms will be decision a iables in he op imiza ion p oblem o
be sol e ia MPC echniques, excep o 𝑑(𝑡), which will be measu ed and aken as inpu s o he con olle s.
On he o he hand, o equa ions (3–8), (3–9) and (3–10), some pa ame e s a e needed. They a e ga he ed in
Table 4, aken om [2], [14], [15] and [79].
Pa ame e
Rep esen a ion
Uni
Value
Ba e y cha ging e iciency
𝜂𝑏𝑎𝑡,𝑐ℎ
%
90
Ba e y discha ging e iciency
𝜂𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
%
95
Maximum ba e y capaci y
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡
kWh
17.6
Elec olyze e iciency
𝜂𝑒𝑧
Nm3/kWh
0.23
Fuel cell e iciency
𝜂𝑓𝑐
kWh/ Nm3
1.32
Maximum hyd ogen capaci y
𝑉𝑚𝑎𝑥
Nm3
7
Ul acapaci o cha ging e iciency
𝜂𝑢𝑐,𝑐ℎ
%
97
Ul acapaci o discha ging e iciency
𝜂𝑢𝑐,𝑑𝑖𝑠𝑐
%
99
Maximum ul acapaci o capaci y
𝐶𝑚𝑎𝑥,𝑢𝑐
kWh
0.14
Table 4. Pa ame e s o dynamics equa ions
3.2 Con olle design
Once he sys em model has al eady been o mula ed, MPC echniques can be used in o de o sol e he EMS
in he mic og id. MPC allows aking ca e o he sys em h ough cons ain s and he cos unc ion. This can be
used, among o he s, o ope a ional, economical and sa e y easons o o e e ence acking, depending on he
con olle . A de ailed desc ip ion o MPC can be seen in [2], [80] and [81]. In his case, as i is p oposed in [2],
which will be he main e e ence o all he con olle s design, wo con olle s a e designed.
On he one hand, he i s con olle , known as e ia y con olle , is in ended o do he scheduling pa e e y
hou , aking p edic ions and ene gy s o age le el measu emen s om he eal plan as inpu s and calcula ing
he scheduled sys em s a e and powe , which will be sen o he seconda y con olle and a pa o i will be as
eedback o his e ia y con olle in o de o calcula e inc emen al ac ions. The ene gy consump ion,
p oduc ion and p ice p edic ions a e simula ed e e y sample ime o he ollowing 24 hou s/sampling imes
(one day), bu he e is no a p edic o implemen a ion, since i is ou o he scope o his wo k.
On he o he hand, he seconda y con olle is dedica ed o ollow he schedule calcula ed by he e ia y one,
ying o co ec powe de ia ions. Fo ha eason, he sampling ime is in he second-scale (1 second) in o de
o ca ch e en s such as new ehicle cha ging (since nei he EVs no hyd ogen-based ehicles demand a e no
included in he o ecas ). Again, s o age le el measu emen s a e inpu s o he con olle , as well as he
scheduled ou pu s o he e ia y con olle and he eal gene a ion and demand measu emen s, including EVs
cha ging powe . The esul o his con olle is he powe which mus be sen o he powe con e e s o all he
equipmen . These ou pu s a e used as eedback o his seconda y con olle oo, en e ing as inpu s o powe
a ia ions compu a ions.
An impo an di e ence be ween he wo con olle s is ha in he e ia y one he ul acapaci o is no
19
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
included. This is due o ul acapaci o s ha e high speci ic powe bu low speci ic ene gy, and hey ac quickly,
so hey a e su iable o co ec ing powe de ia ions. As hey a e expec ed o ac mo e ins an aneously, i makes
no sense o include he ul acapaci o in an hou ly-ahead schedule MPC. In ac , ul acapaci o s helps he
seconda y con olle in so ening he a ia ions espec o he schedule gi en by he e ia y con olle .
As i is well-know, MPC con ol calcula es he op imal solu ion o he p edic ion ho izon, bu only he i s
ime ins an ac ions a e applied, ecalcula ing again o he en i e p edic ion ho izon in he nex ime ins an .
This is known as eceding ho izon s a egy [80] and [81]. Fo he e ia y con olle a p edic ion ho izon o 24
hou s is aken, while o he seconda y con olle , 15 seconds a e enough. As he con ol ho izon can be lowe
han he p edic ion ho izon (see [80] and [81] o u he de ails), o he seconda y con olle a 5 seconds
con ol ho izon has been selec ed in o de o accele a e compu a ions. A scheme o he adop ed con ol
s a egy is shown in Figu e 4. The le e Γ is used o ep esen ene gy p ice, and he subsc ip s mean: p ed
(p edic ion), meas (measu emen s), sch (schedule) and e ( e e ence).
Figu e 4. Con ol s a egy
This con ol s a egy coincides wi h he ypical hie a chical con ol laye s, whe e he e ia y con olle can be
seen as an economic planne , he seconda y con olle as a supe iso o sending powe e e ences and he
p ima y con ole s, no implemen ed he e and ac ing in he o de o miliseconds, a e in cha ge o ol age and
equency de ia ions co ec ion.
3.2.1 Mixed Logical Dynamical Sys ems
Fo he e ia y con olle design, bo h con inuous and logical a iables will be used. The heo y o MPC is
de eloped o con inuous a iables, bu i can be ex ended o hyb id sys ems, esul ing in he so-called Mixed
Logical Dynamical, MLD, sys ems. The idea o hese sys ems is o mix he ini e s a e machines echniques
wi h he classical con inuous con ol heo y [80]. This opic can be use ul o modeling when a sys em is
swi ched on/o , when i is in a ini e s a e ( o example, cha ging o discha ging), and so on.
To cons uc a MLD sys em, wo s eps mus be done [2]:
1. Con e any ela ion which in ol es logical a iables 𝛿 𝜖 {0,1} in o linea inequali ies, which will be
added as cons ain s o he MPC p oblem o mula ion. These ans o ma ions a e ga he ed in Table 5,
di ec ly aken om [2]. The deduc ion o all he ela ionships a e based on he wo k done by [82] and
is well-explained in chap e 10 o he book [80]. The ela ion P7 includes he de ini ion o he mixed
p oduc in an auxilia y a iable, z, whe e bo h con inuous and disc e e a iables a e in ol ed.

Con ol s a egy design
20
Table 5. Logical ela ions in a sys em and hei co esponding linea inequali ies (Table di ec ly aken
om [2]). Nomencla u e: 𝛿 (bina y a iable), S (s a emen ep esen ed by 𝛿), a ( ec o o pa ame e s),
x (con inuous a iable), 𝜖>0 (small ole ance)
2. Modi y he classical s a e space model de ini ion and w i e he dynamical equa ions as:
𝑥(𝑡+1)=𝐴𝑥(𝑡)+𝐵1𝑢(𝑡)+𝐵2𝛿(𝑡)+𝐵3𝑧(𝑡)
(3–23)
𝑦(𝑡)=𝐶𝑥(𝑡)+𝐷1𝑢(𝑡)+𝐷2𝛿(𝑡)+𝐷3𝑧(𝑡)
(3–24)
And he sys ems cons ain s can be eo de as:
𝐸1𝑢(𝑡)+𝐸2𝛿(𝑡)+𝐸3𝑧(𝑡)+𝐸4𝑥(𝑡)≤𝐸5
(3–25)
Once he MLD sys em is a ailable, he op imiza ion MPC p oblem u ns in o a Mixed In ege P og amming,
MIP [80]. Since he cons ain s a e linea , he p oblem o sol e will be a Mixed In ege Linea P og amming,
MILP, i he cos unc ion is linea , o a Mixed In ege Quad a ic P og amming, MIQP, i he cos unc ion is
quad a ic. The e exis s b anch and bound echniques which a oid o sol e he Linea P og amming, LP, o
he Quad a ic P og amming, QP, o any combina ion o logical a iable, educing he numbe o p oblems o
be sol ed in he bina y ee.
3.2.2 Te ia y con olle
As i has al eady been desc ibed, his con olle akes ca e e e y hou o powe planning ega ding o ecas s in
ene gy p ice, sola gene a ion and consump ion (excep om EVs cha ging powe ) o he ollowing 24 hou s
[2]. The objec i e is bo h economical and ope a ional. On he one hand, he con olle aims a minimizing cos
o ene gy pu chase and equipmen uses and a maximizing he e enue o selling ene gy o he g id. This
schedule plays a c ucial ole he e, since he e a e impo an penal ies i he scheduled g id powe (pu chased
o sold) is no inally accomplished. Accu a e o ecas s help in his ask. On he o he hand, he componen s
a e conside ed wi h he objec i e o ex end hei li e imes and no o damage hem. Bo h physical limi s and
ab up ope a ing changes a e aken in o accoun .
The scheme o he e ia y con olle is depic ed in Figu e 5. As i has al eady been commen ed, he ou pu o
he con olle gi es e e y hou he powe and s a e scheduled o he mic og id componen s wi hou he
ul acapaci o , which will be used in he seconda y con olle . F om hose ou pu s, he hyd ogen ela ed a e
sen as inpu s o he nex ime ins an o his e ia y con olle wi h he goal o powe a ia ion compu a ions
o p o ec hyd ogen equipmen . The SOC and LOH measu emen s a e also aken as inpu om he componen s
blocks in he simula ion and will be aken om eal measu emen s in he u u e plan implemen a ion. The
o he inpu s a e he men ioned p edic ions.
21
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
As in classical MPC, a MIQP op imiza ion p oblem mus be o mula ed. This akes he o m p esen ed in
equa ions (3–26)-(3–34). The p oblem is composed by he cos unc ion (3–26), sys em model cons ain (3–
27)-(3–28), powe balance cons ain (3–29), physical cons ain s (3–30)-(3–32) and all he MLD cons ain s
de i ed om he inclusion o bina y a iables (3–33)-(3–34). The sys em model, he cos unc ion and MLD
cons ain s a e going o be de ailed in he ollowing and he whole MIQP p oblem will be summa ized a he
end.
Figu e 5. Te ia y con olle
min
𝑢𝐽(𝑡)=∑(𝐽𝑔𝑟𝑖𝑑(𝑡𝑘|𝑡)+𝐽𝑏𝑎𝑡(𝑡𝑘|𝑡)+𝐽𝐻2(𝑡𝑘|𝑡))
𝑆𝐻
𝑘=1
(3–26)
𝑠.𝑡. 𝑥(𝑡𝑘+1)=𝐴𝑥(𝑡𝑘)+𝐵1𝑢(𝑡𝑘)+𝐵2𝛿(𝑡𝑘)+𝐵3𝑧(𝑡𝑘)
(3–27)
𝑦(𝑡𝑘)=𝐶𝑥(𝑡𝑘)+𝐷1𝑢(𝑡𝑘)+𝐷2𝛿(𝑡𝑘)+𝐷3𝑧(𝑡𝑘)
(3–28)
𝑃𝑝𝑣
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)+𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)+𝑃𝑏𝑎𝑡(𝑡𝑘)+𝑃𝑓𝑐(𝑡𝑘)𝛿𝑓𝑐(𝑡𝑘)−𝑃𝑒𝑧(𝑡𝑘)𝛿𝑒𝑧(𝑡𝑘)−𝑃𝑙𝑜𝑎𝑑
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)=0
(3–29)
𝑃𝑖𝑚𝑖𝑛≤𝑃𝑖(𝑡𝑘)≤𝑃𝑖𝑚𝑎𝑥|𝑖=𝑏𝑎𝑡,𝑓𝑐,𝑒𝑧,𝑔𝑟𝑖𝑑
(3–30)
𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑖𝑛≤𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)≤𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑎𝑥
(3–31)
𝐿𝑂𝐻𝑚𝑖𝑛≤𝐿𝑂𝐻(𝑡𝑘)≤𝐿𝑂𝐻𝑚𝑎𝑥
(3–32)
0≤𝛿𝑖(𝑡𝑘)≤1|𝑖=𝑓𝑐,𝑒𝑧
(3–33)
𝐸1𝑢(𝑡𝑘)+𝐸2𝛿(𝑡𝑘)+𝐸3𝑧(𝑡𝑘)+𝐸4𝑥(𝑡𝑘)≤𝐸5
(3–34)
The ime no a ion is chosen indica ing ha is he cu en ime ins an and 𝑡𝑘 co esponds o k ins an s a e he
cu en ime ( +k). The no a ion (𝑡𝑘|𝑡) e e s o he p edic ion made in ins an o he ime ins an +k. The
supe sc ip schedule (sch) has no been included he e o simplici y. Now, he e ms in equa ions (3–26)-(3–
34) a e going o be b oken down.
Con ol s a egy design
22
The i s s ep is o know well he model o he sys em. Vec o s o con ol a iable, u, bina y a iables, 𝛿, and
auxilia y a iables, z,a e de ined in (3–35) and con ain he decision a iables. The a iables in ec o u ha e
al eady been de ined and he a iables in ec o 𝛿 and z will be de ined in he ollowing.
𝑢(𝑡𝑘)=
[
𝑃𝑏𝑎𝑡(𝑡𝑘)
𝑃𝑓𝑐(𝑡𝑘)
𝑃𝑒𝑧(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
]
𝛿(𝑡𝑘)=
[
𝛿𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)
𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)
𝛿𝑓𝑐(𝑡𝑘)
𝛿𝑒𝑧(𝑡𝑘)
𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)
𝛿𝑝𝑢𝑟(𝑡𝑘)
𝜎𝑓𝑐
𝑜𝑛(𝑡𝑘)
𝜎𝑒𝑧
𝑜𝑛(𝑡𝑘)
𝜒𝑓𝑐(𝑡𝑘)
χez(𝑡𝑘)
]
𝑧(𝑡𝑘)=
[
𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘)
𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘)
𝑧𝑓𝑐(𝑡𝑘)
𝑧𝑒𝑧(𝑡𝑘)
𝑃𝑠𝑎𝑙𝑒(𝑡𝑘)
𝑃𝑝𝑢𝑟(𝑡𝑘)
𝜃𝑓𝑐(𝑡𝑘)
θez(𝑡𝑘)
]
(3–35)
As he s a e, x, and ou pu o he sys em, y, a e de ined by he same ec o s:
𝑥(𝑡𝑘)=𝑦(𝑡𝑘)= [𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)]
(3–36)
Wi h hese de ini ions, he s a e space model o he sys em can be ob ained om he subsec ions 3.1 and 3.2.1,
so equa ions (3–27) and (3–28) a e ans o med in equa ions (3–37) and (3–38) as:
[𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘+1)
𝐿𝑂𝐻(𝑡𝑘+1)]=[1 0
0 1][𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)]+[0 ⋯ 0
0 ⋯ 0](2,4)𝑢(𝑡𝑘)+[0 ⋯ 0
0 ⋯ 0](2,10)𝛿(𝑡𝑘)
+[𝐾𝑏𝑎𝑡,𝑐ℎ −𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 0 0 0 0 0 0
0 0 −𝐾𝑓𝑐 𝐾𝑒𝑧 0 0 0 0]𝑧(𝑡𝑘)
(3–37)
[𝑦1(𝑡𝑘)
𝑦2(𝑡𝑘)]=[1 0
0 1][𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)]
(3–38)
Then, as is shown in equa ion (3–26), he cos unc ion is di ided in h ee e ms: g id, ba e y and hyd ogen
(which is again di ided in o uel cell and elec olyze ). The i s e m, co esponding o he g id, aims a
maximizing he p o i in he ene gy exchange wi h he g id. The e ms Γ𝑠𝑎𝑙𝑒
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡) and Γ𝑝𝑢𝑟
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡) in €/kWh
a e assumed o be he same and equal o he ene gy p ice o ecas ing. Taking ca e wi h uni s, he g id cos
unc ion is:
𝐽𝑔𝑟𝑖𝑑(𝑡𝑘|𝑡)=(−Γ𝑠𝑎𝑙𝑒
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)𝑃𝑠𝑎𝑙𝑒(𝑡𝑘|𝑡)+ Γ𝑝𝑢𝑟
𝑝𝑟𝑒𝑑(𝑡𝑘|𝑡)𝑃𝑝𝑢𝑟(𝑡𝑘|𝑡))𝑇𝑠
(3–39)
Fo di iding 𝑃𝑔𝑟𝑖𝑑 in o 𝑃𝑠𝑎𝑙𝑒and 𝑃𝑝𝑢𝑟, i is necessa y o de ine 𝛿𝑠𝑎𝑙𝑒 and 𝛿𝑝𝑢𝑟, wo bina y a iables which will
be ac i e when selling o o pu chasing om he main g id, espec i ely. So, he ollowing ela ions mus be
conside ed:
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)=𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑠𝑎𝑙𝑒(𝑡𝑘), 𝑃𝑝𝑢𝑟(𝑡𝑘)≥0,𝑃𝑠𝑎𝑙𝑒(𝑡𝑘)≥0
(3–40)
𝛿𝑝𝑢𝑟(𝑡𝑘)+𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)=1
(3–41)
𝑃𝑝𝑢𝑟(𝑡𝑘)=𝑃𝑔𝑟𝑖𝑑(𝑡𝑘) 𝛿𝑝𝑢𝑟(𝑡𝑘)
(3–42)
23
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
𝑃𝑠𝑎𝑙𝑒(𝑡𝑘)=−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘) 𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)
(3–43)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)≤0↔𝛿𝑠𝑎𝑙𝑒=1
(3–44)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)>0↔𝛿𝑝𝑢𝑟=1
(3–45)
Bu equa ions (3–43) and (3–45) a e no necessa y i equa ions (3–40) and (3–41) a e used. Mo eo e ,
equa ion (3–42) can be ans o med in equa ions (3–46)-(3–49), and equa ion (3–44) in equa ions (3–50)-(3–
51), using he equi alences o Table 5.
−∞≤𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 𝛿𝑝𝑢𝑟(𝑡𝑘)≤0
(3–46)
0≤𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛 𝛿𝑝𝑢𝑟(𝑡𝑘)≤∞
(3–47)
−∞≤𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)+𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛 (1− 𝛿𝑝𝑢𝑟(𝑡𝑘))≤0
(3–48)
0≤𝑃𝑝𝑢𝑟(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)+𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 (1− 𝛿𝑝𝑢𝑟(𝑡𝑘))≤∞
(3–49)
𝜖≤𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)−(𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛−𝜖)𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)≤∞
(3–50)
−∞≤𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)+𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥 𝛿𝑠𝑎𝑙𝑒(𝑡𝑘)≤𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥
(3–51)
The nex e m in he cos unc ion is ela ed wi h he ba e y. Assuming ha he pa ame e s in Table 6 a e
known [2], he ba e y cos unc ion can be w i en as in equa ion (3–52). Bo h e ms ha e economic goals and
he second one is ela ed wi h he ac ha ba e ies su e a high cu en a io. One mus ake ca e o uni s
again; i.e. powe a iables in kW and sampling ime in hou s.
Pa ame e
Rep esen a ion
Uni
Value
Ba e y capi al cos
𝐶𝐶𝑏𝑎𝑡
€/kWh
125
Ba e y li e cycles
𝐶𝑦𝑐𝑙𝑒𝑠𝑏𝑎𝑡
-
3000
Ba e y cha ging deg ada ion cos
𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑐ℎ
€/kW2h
10−3
Ba e y discha ging deg ada ion cos
𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑑𝑖𝑠𝑐
€/kW2h
10−3
Table 6. Pa ame e s o ba e y cos unc ion (Taken om [2])
𝐽𝑏𝑎𝑡(𝑡𝑘|𝑡)=𝐶𝐶𝑏𝑎𝑡
2 𝐶𝑦𝑐𝑙𝑒𝑠𝑏𝑎𝑡(𝑃𝑏𝑎𝑡,𝑐ℎ(𝑡𝑘|𝑡)+𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐(𝑡𝑘|𝑡))𝑇𝑠
+(𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑐ℎ 𝑃𝑏𝑎𝑡,𝑐ℎ
2(𝑡𝑘|𝑡)+𝐶𝑜𝑠𝑡𝑑𝑒𝑔𝑟,𝑑𝑖𝑠𝑐 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
2(𝑡𝑘|𝑡))𝑇𝑠
(3–52)
As o he ba e y SOC dynamical model exposed in equa ion (3–37), he a iables 𝑃𝑏𝑎𝑡,𝑐ℎ and 𝑃𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
appea in his cos unc ion. Simila o he case o bina y and auxilia y a iables o he g id, bina y a iables
𝛿𝑏𝑎𝑡,𝑐ℎ and 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 a e in oduced o indica e ha he ba e y is cha ging (𝛿𝑏𝑎𝑡,𝑐ℎ equal o ‘1’ and 𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
equal o ‘0’) o discha ging (𝛿𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 equal o ‘1’ and 𝛿𝑏𝑎𝑡,𝑐ℎ equal o ‘0’). Mo eo e , as in he case o he
g id, he ollowing ela ions mus be ul illed:
Con ol s a egy design
30
he QP p oblem does no use heses ec o componen s as decision a iables. Inc emen al con ol ac ions,
de ined in equa ion (3–104) oo, will be composed o he decision a iables. The meaning o a iables in hese
ec o s is easily in e p e ed.
𝑢(𝑡𝑘)=[𝑃𝐻2(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
𝑃𝑢𝑐(𝑡𝑘)]
Δ𝑢(𝑡𝑘)=[Δ𝑃𝐻2(𝑡𝑘)
Δ𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
Δ𝑃𝑢𝑐(𝑡𝑘)]=[𝑃𝐻2(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
𝑃𝑢𝑐(𝑡𝑘)]−[𝑃𝐻2(𝑡𝑘−1)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘−1)
𝑃𝑢𝑐(𝑡𝑘−1)]
(3–104)
As de ined in equa ion (3–104), he ba e y powe and powe a ia ion e ms a e no included in he con ol
ac ions ec o s. This is due o he ac ha equa ions (3–97) and (3–98) a e going o be included in he QP
p oblema by eplacing 𝑃𝑏𝑎𝑡 a iable by:
𝑃𝑏𝑎𝑡(𝑡𝑘)=−𝑃𝑝𝑣
𝑚𝑒𝑎𝑠(𝑡𝑘)−𝑃𝐻2(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)− 𝑃𝑢𝑐(𝑡𝑘)+𝑃𝑙𝑜𝑎𝑑
𝑚𝑒𝑎𝑠(𝑡𝑘)+𝑃𝑒𝑣
𝑚𝑒𝑎𝑠(𝑡𝑘)
(3–105)
And de ining he dis u bance a iable as in equa ion (3–21) in subsec ion 3.1, equa ion (3–105) emains as
ollows:
𝑃𝑏𝑎𝑡(𝑡𝑘)=−𝑃𝐻2(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)− 𝑃𝑢𝑐(𝑡𝑘)−𝑑(𝑡𝑘)
(3–106)
Wi h his conside a ion, cons ain s ela ed o he ba e y o (3–99) and (3–100) will need u he de elopmen
o be included in he op imiza ion p oblem. This will be explained a he end o his sec ion. Mo eo e ,
conside ing ha no bina y a iables a e going o be used, he sys em model o be included in he p oblem is he
one in equa ions (3–1), (3–2) and (3–3); i.e.:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)−𝜂𝑏𝑎𝑡𝑇𝑠
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡𝑃𝑏𝑎𝑡(𝑡)
(3–107)
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)−100𝜂𝐻2𝑇𝑠
𝑉𝑚𝑎𝑥𝑃𝐻2(𝑡)
(3–108)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)−𝜂𝑢𝑐 𝑇𝑠
𝐶𝑚𝑎𝑥,𝑢𝑐𝑃𝑢𝑐(𝑡)
(3–109)
And aking in o accoun equa ion (3–106) o eplacing 𝑃𝑏𝑎𝑡, he ba e y equa ion model is ans o med in o:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)−𝜂𝑏𝑎𝑡𝑇𝑠
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡(−𝑃𝐻2(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)− 𝑃𝑢𝑐(𝑡𝑘)−𝑑(𝑡𝑘))
(3–110)
I model cons an s de ini ions a e ecapped om subsec ion 3.1 (equa ions (3–11)-(3–16)):
𝐾𝑏𝑎𝑡,𝑐ℎ=𝜂𝑏𝑎𝑡,𝑐ℎ
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡
(3–111)
𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐=1
𝜂𝑏𝑎𝑡,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑏𝑎𝑡
(3–112)
𝐾𝑒𝑧=𝜂𝑒𝑧
𝑉𝑚𝑎𝑥
(3–113)
𝐾𝑓𝑐=1
𝜂𝑓𝑐 𝑉𝑚𝑎𝑥
(3–114)

31
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
𝐾𝑢𝑐,𝑐ℎ=𝜂𝑢𝑐,𝑐ℎ
𝐶𝑚𝑎𝑥,𝑢𝑐
(3–115)
𝐾𝑢𝑐,𝑑𝑖𝑠𝑐=1
𝜂𝑢𝑐,𝑑𝑖𝑠𝑐 𝐶𝑚𝑎𝑥,𝑢𝑐
(3–116)
And new de ini ions a e included, assuming a mean alue be ween he wo a ailable ones o he cons an o
each de ice:
𝐾𝑏𝑎𝑡=𝜂𝑏𝑎𝑡
𝐶𝑚𝑎𝑥,𝑏𝑎𝑡=𝐾𝑏𝑎𝑡,𝑐ℎ+𝐾𝑏𝑎𝑡,𝑑𝑖𝑠𝑐
2
(3–117)
𝐾𝐻2=𝜂𝐻2
𝑉𝑚𝑎𝑥=𝐾𝑓𝑐+𝐾𝑒𝑧
2
(3–118)
𝐾𝑢𝑐=𝜂𝑢𝑐
𝐶𝑚𝑎𝑥,𝑢𝑐=𝐾𝑢𝑐,𝑐ℎ+𝐾𝑢𝑐,𝑑𝑖𝑠𝑐
2
(3–119)
The sys em model equa ions emain as ollows:
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡+1)=𝑆𝑂𝐶𝑏𝑎𝑡(𝑡)−𝐾𝑏𝑎𝑡 𝑇𝑠 𝑃𝑏𝑎𝑡(𝑡)
(3–120)
𝐿𝑂𝐻(𝑡+1)=𝐿𝑂𝐻(𝑡)−100 𝐾𝐻2 𝑇𝑠 𝑃𝐻2(𝑡)
(3–121)
𝑆𝑂𝐶𝑢𝑐(𝑡+1)=𝑆𝑂𝐶𝑢𝑐(𝑡)−𝐾𝑢𝑐 𝑇𝑠 𝑃𝑢𝑐(𝑡)
(3–122)
As he s a e, x, and ou pu o he sys em, y, a e de ined by he same ec o s:
𝑥(𝑡𝑘)=𝑦(𝑡𝑘)= [𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)
𝑆𝑂𝐶𝑢𝑐(𝑡𝑘)]
(3–123)
The s a e space model o he sys em o equa ions (3–95) and (3–96) is ans o med in equa ions (3–124) and
(3–125) as:
[𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘+1)
𝐿𝑂𝐻(𝑡𝑘+1)
𝑆𝑂𝐶𝑢𝑐(𝑡𝑘+1)]=[𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)
𝑆𝑂𝐶𝑢𝑐(𝑡𝑘)]+[𝐾𝑏𝑎𝑡 𝐾𝑏𝑎𝑡 𝐾𝑏𝑎𝑡
−𝐾𝐻20 0
0 0 −𝐾𝑢𝑐]𝑢(𝑡𝑘)+[𝐾𝑏𝑎𝑡
00]𝑑(𝑡𝑘)
(3–124)
[𝑦1(𝑡𝑘)
𝑦2(𝑡𝑘)
𝑦3(𝑡𝑘)]=[𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)
𝑆𝑂𝐶𝑢𝑐(𝑡𝑘)]
(3–125)
So, iden i ying e ms:
𝐴=[1 0 0
0 1 0
0 0 1]
𝐵=[𝐾𝑏𝑎𝑡 𝐾𝑏𝑎𝑡 𝐾𝑏𝑎𝑡
−𝐾𝐻20 0
0 0 −𝐾𝑢𝑐]
𝐸=[𝐾𝑏𝑎𝑡
00]
(3–126)
𝐶= [1 0 0
0 1 0
0 0 1] 𝐷=[0 0 0
0 0 0
0 0 0]
Con ol s a egy design
32
Following e e ence [2], dis u bances can be included as a componen o he s a e, ob aining he augmen ed
s a e, 𝑥(𝑡𝑘):
𝑥(𝑡𝑘)=[𝑥(𝑡𝑘)
𝑑(𝑡𝑘)]
(3–127)
So, he augmen ed s a e space model is ans o med in:
𝑥(𝑡𝑘+1)=[𝑥(𝑡𝑘+1)
𝑑(𝑡𝑘+1)]=[𝐴 𝐸
0 𝐼][𝑥(𝑡𝑘)
𝑑(𝑡𝑘)]+[𝐵0]𝑢(𝑡𝑘)
(3–128)
𝑦(𝑡𝑘)=[𝐶 0][𝑥(𝑡𝑘)
𝑑(𝑡𝑘)]
(3–129)
Whe e 𝐼 means he iden i y ma ix o p ope dimensions. Mo eo e , i he inc emen al powe ec o Δ𝑢,
de ined in equa ion (3–104), is wan ed o be used as decision a iable, he inc emen al s a e space model mus
be used, aking in o accoun ha he new s a e will be composed as ollows:
𝑥(𝑡𝑘)=[𝑥(𝑡𝑘)
𝑢(𝑡𝑘−1)]
(3–130)
Being he inc emen al con ol ac ion:
Δ𝑢(𝑡𝑘)=𝑢(𝑡𝑘)−𝑢(𝑡𝑘−1)
(3–131)
The inc emen al s a e space model emains as:
𝑥(𝑡𝑘+1)=[𝑥(𝑡𝑘+1)
𝑑(𝑡𝑘+1)
𝑢(𝑡𝑘)]=[𝐴 𝐸 𝐵
0 𝐼 0
0 0 𝐼][ 𝑥(𝑡𝑘)
𝑑(𝑡𝑘)
𝑢(𝑡𝑘−1)]+[𝐵0𝐼]Δ𝑢(𝑡𝑘)
(3–132)
𝑦(𝑡𝑘)=[𝐶 0 0][𝑥(𝑡𝑘)
𝑑(𝑡𝑘)
𝑢(𝑡𝑘−1)]
(3–133)
And in compac o m, whe e ma ices 𝑀, 𝑁 and 𝑄 a e easily iden i iable:
𝑥(𝑡𝑘+1)=𝑀𝑥(𝑡𝑘)+𝑁Δ𝑢(𝑡𝑘)
(3–134)
𝑦(𝑡𝑘)=𝑄𝑥(𝑡𝑘)
(3–135)
Once he inc emen al model has been deduced, he op imiza ion p oblem in (3–94)-(3–103) mus be ew i en
as a quad a ic p og amming p oblem in he o m o gene ic equa ion (3–136). This allows o di ec ly using he
sol e quadp og in MATLAB. The cos unc ion in equa ion (3–94) and he cons ain s in equa ions (3–99)-(3–
103) mus be ans o med o ha e he s uc u e o he ones in equa ion (3–136). Powe balance (equa ions (3–
97) and (3–98)) ha e al eady been included in he sys em model, and his sys em model (equa ions (3–95) and
(3–96)) will be implici ly included in bo h he cos unc ion and he ou pu cons ain s.
min
𝒖 12𝚫𝒖𝑇𝑯𝒒𝒑 𝚫𝐮+𝑩𝒒𝒑 𝑇𝚫𝒖
𝑠.𝑡. 𝑹 𝚫𝒖≤𝒄
(3–136)
The i s ask is o con e he cos unc ion. As poin ed in equa ion (3–94), he cos unc ion is gi en by:
33
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
𝐽(𝑡)=∑‖𝑢(𝑡𝑘−1)‖𝜶
2
𝑁𝑐
𝑘=1 +∑‖Δ𝑢(𝑡𝑘−1)‖𝝀2
𝑁𝑐
𝑘=1 +∑‖𝑦(𝑡𝑘)−𝑤(𝑡𝑘)‖𝜹2
𝑁𝑝
𝑘=1
(3–137)
B eaking down hese e ms, i esul s in:
𝐽(𝑡)=∑(𝛼1𝑃𝐻2
2(𝑡𝑘−1)+𝛼2𝑃𝑔𝑟𝑖𝑑
2(𝑡𝑘−1)+𝛼3𝑃𝑢𝑐
2(𝑡𝑘−1)+𝜆1Δ𝑃𝐻2
2(𝑡𝑘−1)
𝑁𝑐
𝑘=1 +𝜆2Δ𝑃𝑔𝑟𝑖𝑑
2(𝑡𝑘)+𝜆3Δ𝑃𝑢𝑐
2(𝑡𝑘−1))
+∑(𝛿1(𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)−𝑆𝑂𝐶𝑏𝑎𝑡
𝑠𝑐ℎ(𝑡𝑘|𝑡))2
𝑁𝑝
𝑘=1
+𝛿2(𝐿𝑂𝐻(𝑡𝑘)−𝐿𝑂𝐻𝑠𝑐ℎ(𝑡𝑘|𝑡))2+𝛿3(𝑆𝑂𝐶𝑢𝑐(𝑡𝑘)−𝑆𝑂𝐶𝑢𝑐
𝑠𝑐ℎ(𝑡𝑘|𝑡))2)
(3–138)
Bu o he p oblem ans o ma ion in equa ion (3–136), he ma icial o m is ad isable. De ailing hese
ma ices, he cos unc ion emains as:
𝐽(𝑡)
=[𝑢𝑇(𝑡𝑘) 𝑢𝑇(𝑡𝑘+1) ⋯ 𝑢𝑇(𝑡𝑘+𝑁𝑐−1)] 𝜶 [𝑢(𝑡𝑘)
𝑢(𝑡𝑘+1)
⋮
𝑢(𝑡𝑘+𝑁𝑐−1)]
+[Δ𝑢𝑇(𝑡𝑘) Δ𝑢𝑇(𝑡𝑘+1) ⋯ Δ𝑢𝑇(𝑡𝑘+𝑁𝑐−1)] 𝝀 [Δ𝑢(𝑡𝑘)
Δ𝑢(𝑡𝑘+1)
⋮
Δ𝑢(𝑡𝑘+𝑁𝑐−1)]
+[(𝑦(𝑡𝑘+1)−𝑤(𝑡𝑘+1))𝑇⋯(𝑦(𝑡𝑘+𝑁𝑝)−𝑤(𝑡𝑘+𝑁𝑝))𝑇] 𝜹 ([𝑦(𝑡𝑘+1)
⋮
𝑦(𝑡𝑘+𝑁𝑝)]
−[𝑤(𝑡𝑘+1)
⋮
𝑤(𝑡𝑘+𝑁𝑝)])
(3–139)
Whe e he cos unc ion weigh ing ma ices a e de ined as:
𝜶=
[
[𝛼1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝛼𝑚]⋯ 0
⋮ ⋱ ⋮
0 ⋯ [𝛼1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝛼𝑚]
]
(3–140)
Con ol s a egy design
34
𝝀=
[
[𝜆1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝜆𝑚]⋯ 0
⋮ ⋱ ⋮
0 ⋯ [𝜆1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝜆𝑚]
]
(3–141)
𝜹=
[
[𝛿1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝛿𝑝]⋯ 0
⋮ ⋱ ⋮
0 ⋯ [𝛿1⋯ 0
⋮ ⋱ ⋮
0 ⋯ 𝛿𝑝]
]
(3–142)
Whe e 𝑚 and 𝑝 indica es o he numbe o con ol ac ions (in his case, h ee) and o he numbe o ou pu s
(in his case, h ee again), espec i ely.
Deno ing:
𝒖=[𝑢(𝑡𝑘)
𝑢(𝑡𝑘+1)
⋮
𝑢(𝑡𝑘+𝑁𝑐−1)]
𝚫𝒖=[Δ𝑢(𝑡𝑘)
Δ𝑢(𝑡𝑘+1)
⋮
Δ𝑢(𝑡𝑘+𝑁𝑐−1)]
(3–143)
𝒚=[𝑦(𝑡𝑘+1)
⋮
𝑦(𝑡𝑘+𝑁𝑝)]
𝒘=[𝑤(𝑡𝑘+1)
⋮
𝑤(𝑡𝑘+𝑁𝑝)]
The cos unc ion emains as:
𝐽(𝑡)=𝒖𝑇𝜶 𝒖+𝚫𝒖𝑇𝝀 𝚫𝒖+(𝒚−𝒘)𝑇𝜹 (𝒚−𝒘)
(3–144)
As he decision a iable is 𝚫𝒖, bo h he ec o 𝒖 and y mus be ew i en as a unc ion o 𝚫𝒖.
Fo 𝒖, aking in o accoun :
Δ𝑢(𝑡𝑘)=𝑢(𝑡𝑘)−𝑢(𝑡𝑘−1)
(3–145)
The ollowing sequence can be w i en:
𝑢(𝑡)=Δ𝑢(𝑡)+𝑢(𝑡−1)
𝑢(𝑡+1)=Δ𝑢(𝑡+1)+Δ𝑢(𝑡)+𝑢(𝑡−1)
𝑢(𝑡+2)=Δ𝑢(𝑡+2)+Δ𝑢(𝑡+1)+Δ𝑢(𝑡)+𝑢(𝑡−1)
…
𝑢(𝑡+𝑗)=Δ𝑢(𝑡+𝑗)+Δ𝑢(𝑡+𝑗−1)+⋯+Δ𝑢(𝑡)+𝑢(𝑡−1)
…
𝑢(𝑡+𝑁𝑐−1)=Δ𝑢(𝑡+𝑁𝑐−1)+Δ𝑢(𝑡+𝑁𝑐−2)+⋯+Δ𝑢(𝑡)+𝑢(𝑡−1)
(3–146)
Tha is, in ma ix o m:
35
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
[𝑢(𝑡𝑘)
𝑢(𝑡𝑘+1)
⋮
𝑢(𝑡𝑘+𝑁𝑐−1)]
=
[
𝐼𝑚,𝑚 0 ⋯ 0
𝐼𝑚,𝑚 𝐼𝑚,𝑚 ⋯ 0
⋮ ⋮ ⋱ ⋮
𝐼𝑚,𝑚 𝐼𝑚,𝑚 ⋯ 𝐼𝑚,𝑚
]
[Δ𝑢(𝑡𝑘)
Δ𝑢(𝑡𝑘+1)
⋮
Δ𝑢(𝑡𝑘+𝑁𝑐−1)]+[𝐼𝑚,𝑚
𝐼𝑚,𝑚
⋮
𝐼𝑚,𝑚]𝑢(𝑡𝑘−1)
(3–147)
Whe e 𝐼𝑚,𝑚 is he iden i y ma iz o size 𝑚. De ining:
𝑻=
[
𝐼𝑚,𝑚 0 ⋯ 0
𝐼𝑚,𝑚 𝐼𝑚,𝑚 ⋯ 0
⋮ ⋮ ⋱ ⋮
𝐼𝑚,𝑚 𝐼𝑚,𝑚 ⋯ 𝐼𝑚,𝑚
]
𝟏𝑵𝒄𝒎,𝒎=[𝐼𝑚,𝑚
𝐼𝑚,𝑚
⋮
𝐼𝑚,𝑚]
(3–148)
The ec o 𝒖 can be ep esen ed as:
𝒖=𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)
(3–149)
On he o he side, om he inc emen al model (equa ions (3–134)and (3–135)), ecu si ely, one has [80]:
𝑦(𝑡𝑘)=𝑄𝑥(𝑡𝑘)=𝑄(𝑀𝑥(𝑡𝑘−1)+𝑁Δ𝑢(𝑡𝑘−1))
=𝑄[𝑀(𝑀𝑥(𝑡𝑘−2)+𝑁Δ𝑢(𝑡𝑘−2))+𝑁Δ𝑢(𝑡𝑘−1)]
=𝑄{𝑀[𝑀(𝑀𝑥(𝑡𝑘−3)+𝑁Δ𝑢(𝑡𝑘−3))+𝑁Δ𝑢(𝑡𝑘−2)]
+𝑁Δ𝑢(𝑡𝑘−1)}=⋯=𝑄𝑀𝑘𝑥(𝑡)+∑𝑄𝑀𝑘−𝑖−1𝑁Δ𝑢(𝑡𝑖)
𝑘−1
𝑖=0
(3–150)
W i ing equa ion (3–150) in ma ix o m:
𝒚=𝑭𝑥(𝑡)+𝑯𝚫𝒖
(3–151)
Whe e 𝑥(𝑡) is he inc emen al and augmen ed s a e in he cu en ime ins an , and he ma ices a e:
𝑭=[𝑄𝑀
𝑄𝑀2
⋮
𝑄𝑀𝑁𝑝]
𝑯=[𝑄𝑁 0 ⋯ 0
𝑄𝑀𝑁 𝑄𝑁 ⋯ 0
⋮ ⋮ ⋱ ⋮
𝑄𝑀𝑁𝑝−1𝑁 𝑄𝑀𝑁𝑝−2𝑁 ⋯ 𝑄𝑀𝑁𝑝−𝑁𝑐𝑁]
(3–152)
The e o e, he cos unc ion in equa ion (3–144) can be ew i en as:
𝐽(𝑡)=(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))𝑇𝜶 (𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝚫𝒖𝑇𝝀 𝚫𝒖
+(𝑯𝚫𝒖+(𝑭𝑥(𝑡)−𝒘))𝑇𝜹 (𝑯𝚫𝒖+(𝑭𝑥(𝑡)−𝒘))
(3–153)
Re-o ganizing e ms:
𝐽(𝑡)=𝚫𝒖𝑇(𝑻𝑇𝜶𝑻+𝝀+𝑯𝑇𝜹𝑯)𝑇𝚫𝒖
+2((𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))𝑇𝜶𝑻+(𝑭𝑥(𝑡)−𝒘)𝜹𝑯)𝚫𝒖
(3–154)

Con ol s a egy design
36
So, looking a cons unc ion in he gene ic o m op imiza ion p oblem o equa ion (3–136), i is easy o
iden i y e ms:
𝑯𝒒𝒑=2(𝑻𝑇𝜶𝑻+𝝀+𝑯𝑇𝜹𝑯)
𝑩𝒒𝒑=2(𝑻𝑇𝜶(𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝑯𝑇𝜹(𝑭𝑥(𝑡)−𝒘))
(3–155)
Once he cos unc ion has been ans o ma ed, he nex s ep is o do he same wi h he cons ain s. Res ic ions
in equa ions (3–99)-(3–103), excep om hose o 𝑃𝑏𝑎𝑡 and Δ𝑃𝑏𝑎𝑡, can be summa ized in ec o o m as:
𝑢𝑚𝑖𝑛≤𝑢(𝑡𝑘)≤𝑢𝑚𝑎𝑥
(3–156)
Δ𝑢𝑚𝑖𝑛≤Δ𝑢(𝑡𝑘)≤Δ𝑢𝑚𝑎𝑥
(3–157)
𝑦𝑚𝑖𝑛≤𝑦(𝑡𝑘)≤𝑦𝑚𝑎𝑥
(3–158)
Whe e:
𝑢𝑚𝑖𝑛=[𝑃𝐻2
𝑚𝑖𝑛
𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛
𝑃𝑢𝑐
𝑚𝑖𝑛]
𝑢𝑚𝑎𝑥=[𝑃𝐻2
𝑚𝑎𝑥
𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥
𝑃𝑢𝑐
𝑚𝑎𝑥]
(3–159)
Δ𝑢𝑚𝑖𝑛=[ Δ𝑃𝐻2
𝑚𝑖𝑛
Δ𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛
Δ𝑃𝑢𝑐
𝑚𝑖𝑛]
Δ𝑢𝑚𝑎𝑥=[ Δ𝑃𝐻2
𝑚𝑎𝑥
Δ𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥
Δ𝑃𝑢𝑐
𝑚𝑎𝑥]
(3–160)
𝑦𝑚𝑖𝑛=[𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑖𝑛
𝐿𝑂𝐻𝑚𝑖𝑛
𝑆𝑂𝐶𝑢𝑐
𝑚𝑖𝑛]
𝑦𝑚𝑎𝑥=[𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑎𝑥
𝐿𝑂𝐻𝑚𝑎𝑥
𝑆𝑂𝐶𝑢𝑐
𝑚𝑎𝑥]
(3–161)
Expanding hese cons ain s in he whole p edic ion and con ol ho izons, one ob ains he ollowing:
𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑖𝑛≤𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)≤𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑎𝑥
(3–162)
𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑖𝑛≤𝚫𝒖≤𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑎𝑥
(3–163)
𝟏𝑵𝒑𝒑,𝒑 y𝑚𝑖𝑛≤𝑭𝑥(𝑡)+𝑯𝚫𝒖≤𝟏𝑵𝒑𝒑,𝒑 𝑦𝑚𝑎𝑥
(3–164)
Hence, looking a es ic ion o m in equa ion (3–136), he ma ix 𝑹 and ec o 𝒄 de ini ions a e:
𝑹=
[
𝑰𝑵𝒄𝒎,𝑵𝒄𝒎
−𝑰𝑵𝒄𝒎,𝑵𝒄𝒎
𝑻
−𝑻
𝑯
−𝑯
]
𝒄=
[
𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑎𝑥
−𝟏𝑵𝒄𝒎,𝒎 Δ𝑢𝑚𝑖𝑛
𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑎𝑥−𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)
−𝟏𝑵𝒄𝒎,𝒎 𝑢𝑚𝑖𝑛+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1)
𝟏𝑵𝒑𝒑,𝒑 𝑦𝑚𝑎𝑥−𝑭𝑥(𝑡)
−𝟏𝑵𝒑𝒑,𝒑 y𝑚𝑖𝑛+𝑭𝑥(𝑡)
]
(3–165)
Now, wi h he gene ic p oblem w i en in he igh o m o use quadp og like ano he QP p oblems, ba e y
powe and inc emen al powe cons ain s and cos unc ion e ms a e going o be added o he o mula ed
37
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
p oblem. In he i s place, he ba e y powe cons ain s a e gi en by:
𝑃𝑏𝑎𝑡
𝑚𝑖𝑛≤𝑃𝑏𝑎𝑡(𝑡𝑘)≤𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
(3–166)
Remembe ing he powe balance gi en by equa ion (3–167) and he de ini ions gi en by equa ion (3–168):
𝑃𝑏𝑎𝑡(𝑡𝑘)=−𝑃𝐻2(𝑡𝑘)−𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)−𝑃𝑢𝑐(𝑡𝑘)−𝑑(𝑡𝑘)
(3–167)
𝑢(𝑡𝑘)=[𝑃𝐻2(𝑡𝑘)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘)
𝑃𝑢𝑐(𝑡𝑘)]
𝑥(𝑡𝑘)=
[
𝑆𝑂𝐶𝑏𝑎𝑡(𝑡𝑘)
𝐿𝑂𝐻(𝑡𝑘)
𝑆𝑂𝐶𝑢𝑐(𝑡𝑘)
𝑑(𝑡𝑘)
𝑃𝐻2(𝑡𝑘−1)
𝑃𝑔𝑟𝑖𝑑(𝑡𝑘−1)
𝑃𝑢𝑐(𝑡𝑘−1)
]
(3–168)
Equa ion (3–167) can be w i en as:
𝑃𝑏𝑎𝑡(𝑡𝑘)=[−1 −1 −1]𝑢(𝑡𝑘)+[0 0 0 −1 0 0 0]𝑥(𝑡𝑘)
(3–169)
Expanding o all he ime ins an s o he con ol ho izon:
𝑷𝒃𝒂𝒕=𝒂𝒖𝒙𝒖𝒖+𝒂𝒖𝒙𝒙𝑥(𝑡𝑘)
(3–170)
Being:
𝑷𝒃𝒂𝒕=[𝑃𝑏𝑎𝑡(𝑡)
𝑃𝑏𝑎𝑡(𝑡+1)
⋮
𝑃𝑏𝑎𝑡(𝑡+𝑁𝑐−1)]
𝒂𝒖𝒙𝒙=[[0 0 0 −1 0 0 0]
[0 0 0 −1 0 0 0]
⋮
[0 0 0 −1 0 0 0]]
(3–171)
𝒂𝒖𝒙𝒖=[[−1 −1 −1]0 ⋯ 0
0[−1 −1 −1]⋯ 0
⋮ ⋮ ⋱ ⋮
0 0 ⋯ [−1 −1 −1]]
De ining:
𝑷𝒃𝒂𝒕
𝒎𝒊𝒏=
[
𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
⋮
𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
]
𝑁𝑐,1
𝑷𝒃𝒂𝒕
𝒎𝒂𝒙=
[
𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
⋮
𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
]
𝑁𝑐,1
(3–172)
W i ing ec o 𝑢 as a unc ion o Δ𝑢, as poin ed in equa ion (3–149), he es ic ion (3–166) can be w i en as:
𝑷𝒃𝒂𝒕
𝒎𝒊𝒏≤𝒂𝒖𝒙𝒖(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝒂𝒖𝒙𝒙𝑥(𝑡𝑘)≤𝑷𝒃𝒂𝒕
𝒎𝒂𝒙
(3–173)
The e o e, adding wo mo e ows o ma ix 𝑹 and o he wo ows o ec o 𝒄 o equa ion (3–165), he ba e y
powe cons ain is added o he op imiza ion p oblem.
In he same way, he ba e y inc emen al powe cons ain can be added. This cons ain is w i en as:
Con ol s a egy design
38
Δ𝑃𝑏𝑎𝑡
𝑚𝑖𝑛≤Δ𝑃𝑏𝑎𝑡(𝑡𝑘)≤Δ𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
(3–174)
Following a simila p ocedu e, he inc emen al ba e y powe , assuming ha he dis u bance is cons an in he
whole con ol ho izon, can be exp essed as:
Δ𝑃𝑏𝑎𝑡(𝑡𝑘)=𝑃𝑏𝑎𝑡(𝑡𝑘)−𝑃𝑏𝑎𝑡(𝑡𝑘−1)
=[−1 −1 −1]Δ𝑢(𝑡𝑘)−[𝑑(𝑡𝑘)−𝑑(𝑡𝑘−1)
0⋮0]
(3–175)
De ining:
𝚫𝑷𝒃𝒂𝒕
𝒎𝒊𝒏=
[
Δ𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
Δ𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
⋮
Δ𝑃𝑏𝑎𝑡
𝑚𝑖𝑛
]
𝑁𝑐,1
𝚫𝑷𝒃𝒂𝒕
𝒎𝒂𝒙=
[
Δ𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
Δ𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
⋮
Δ𝑃𝑏𝑎𝑡
𝑚𝑎𝑥
]
𝑁𝑐,1
(3–176)
The cons ain (3–174) can be w i en as:
𝚫𝑷𝒃𝒂𝒕
𝒎𝒊𝒏≤𝒂𝒖𝒙𝒖𝚫𝒖−[𝑑(𝑡𝑘)−𝑑(𝑡𝑘−1)
0⋮0]≤𝚫𝑷𝒃𝒂𝒕
𝒎𝒂𝒙
(3–177)
The p ocedu e consis s again o adding wo ows o bo h he ma ix 𝑹 and he ec o 𝒄 in equa ion (3–165).
The nex s ep is o add a e m in he cos unc ion which penalizes bo h he ba e y powe and he ba e y
inc emen al powe . This e m is gi en by:
∑(𝛼4𝑃𝑏𝑎𝑡
2(𝑡𝑘−1)+𝜆4Δ𝑃𝑏𝑎𝑡
2(𝑡𝑘−1))
𝑁𝑐
𝑘=1
(3–178)
Recalling ha :
𝑃𝑏𝑎𝑡(𝑡𝑘)=[−1 −1 −1]𝑢(𝑡𝑘)+[0 0 0 −1 0 0 0]𝑥(𝑡𝑘)
(3–179)
The i s e m o (3–178) can be exp essed as:
𝛼4𝑃𝑏𝑎𝑡
2(𝑡𝑘)=𝑃𝑏𝑎𝑡(𝑡𝑘)𝑇𝛼4𝑃𝑏𝑎𝑡(𝑡𝑘)
=
(
𝑢𝑇(𝑡𝑘)[−1
−1
−1]+𝑥𝑇(𝑡𝑘)
[
000
−1
000
]
)
𝛼4([−1 −1 −1]𝑢(𝑡𝑘)
+[0 0 0 −1 0 0 0]𝑥(𝑡𝑘))
=𝑢𝑇(𝑡𝑘)𝛼4𝑢2𝑢(𝑡𝑘)+2𝑥𝑇(𝑡𝑘)𝛼4𝑥𝑢𝑢(𝑡𝑘)+𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 Δ𝑢
(3–180)
Whe e:
39
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
𝛼4𝑢2=[𝛼4𝛼4𝛼4
𝛼4𝛼4𝛼4
𝛼4𝛼4𝛼4]
𝛼4𝑥𝑢=
[
000
−1
000
]
𝛼4[−1 −1 −1]
(3–181)
Wi h a simila p ocedu e, one can de elop he ollowing o he second e m in (3–178):
𝜆4Δ𝑃𝑏𝑎𝑡
2(𝑡𝑘)=Δ𝑃𝑏𝑎𝑡(𝑡𝑘)𝑇𝜆4Δ𝑃𝑏𝑎𝑡(𝑡𝑘)=
=Δ𝑢𝑇(𝑡𝑘)𝜆4𝑢2Δ𝑢(𝑡𝑘)+2Δ𝑥𝑇(𝑡𝑘)𝜆4𝑥𝑢Δ𝑢(𝑡𝑘)
+𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 Δ𝑢
(3–182)
Ex ending he weigh ing e ms 𝛼4𝑢2, 𝛼4𝑥𝑢, 𝜆4𝑢2 and 𝜆4𝑥𝑢in o de o implemen a ma ix o m:
𝜶𝟒𝒖𝟐=
[
𝛼4𝑢2 0 ⋯ 0
0 𝛼4𝑢2 ⋯ 0
⋮ ⋮ ⋱ ⋮
0 0 ⋯ 𝛼4𝑢2
]
𝜶𝟒𝒙𝒖=[𝛼4𝑥𝑢 𝛼4𝑥𝑢 ⋯ 𝛼4𝑥𝑢]
(3–183)
𝝀𝟒𝒖𝟐=
[
𝝀4𝑢2 0 ⋯ 0
0 𝝀4𝑢2 ⋯ 0
⋮ ⋮ ⋱ ⋮
0 0 ⋯ 𝝀4𝑢2
]
𝝀𝟒𝒙𝒖=[𝝀4𝑥𝑢 𝝀4𝑥𝑢 ⋯ 𝝀4𝑥𝑢]
(3–184)
The exp ession o (3–138) can be exp essed in ma ix o m as:
(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))𝑇𝜶𝟒𝒖𝟐(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))
+2𝑥𝑇(𝑡𝑘)𝜶𝟒𝒙𝒖(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝚫𝒖𝑇𝝀𝟒𝒖𝟐𝚫𝒖
+2Δ𝑥𝑇(𝑡𝑘)𝝀𝟒𝒙𝒖𝚫𝒖+𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 Δ𝑢
(3–185)
Knowing ha :
2Δ𝑥𝑇(𝑡𝑘)𝝀𝟒𝒙𝒖𝚫𝒖=2Δ𝑑(𝑡𝑘)𝜆4𝑥𝑢,𝑠𝑚𝑎𝑙𝑙 𝚫𝒖 = 2(𝑑(𝑡𝑘)−𝑑(𝑡𝑘−1)) 𝜆4𝑥𝑢,𝑠𝑚𝑎𝑙𝑙 𝚫𝒖
(3–186)
Whe e:
𝜆4𝑥𝑢,𝑠𝑚𝑎𝑙𝑙=[𝝀4𝝀4⋯ 𝝀4]1,𝑁𝑐𝑚
(3–187)
The exp ession (3–185) emains as:
(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))𝑇𝜶𝟒𝒖𝟐(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))
+2𝑥𝑇(𝑡𝑘)𝜶𝟒𝒙𝒖(𝑻 𝚫𝒖+𝟏𝑵𝒄𝒎,𝒎 𝑢(𝑡𝑘−1))+𝚫𝒖𝑇𝝀𝟒𝒖𝟐𝚫𝒖
+2Δ𝑑(𝑡𝑘)𝜆4𝑥𝑢,𝑠𝑚𝑎𝑙𝑙 𝚫𝒖 +𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 Δ𝑢
(3–188)
The las exp ession can be ew i en as ollows:
Con ol s a egy design
46
[91]. In his case, e sion 12.10 o Windows 64 bi s (CC438ML) was downloaded wi h he “Quick
S a Guide Mul ipla o m Mul ilingual (CC437ML)”.
3- I you do no ha e ins alled a so wa e om IBM called “IBM Download Di ec o ”, hey equi e you
o ins all i . To do ha , ollow he ins uc ions o h ps://www-
03.ibm.com/isc/esd/dswdown/dldi ec o /ins alla ion_en.h ml.
4- Du ing de IBM Download Di ec o downloading, Ja a 8 mus be also downloaded. I can be done in
he webpage h ps://ja a.com/es/download/.
5- Once IBM Dowload Di ec o and Ja a 8 ha e been ins alled, one mus p oceed wi h ILOG CPLEX
Op imiza ion S udio ins alla ion.
6- Du ing he a o emen ioned ins alla ion, Mic oso Visual C++ 2015 Redis ibu able Upda e 3 is
equi ed o be ins alled. The execu able o ha can be ob ained by simply clicking in
h ps://www.mic oso .com/es-es/download/con i ma ion.aspx?id=53587.
7- Finish he ILOG CPLEX Op imiza ion S udio ins alla ion.
8- Finally, ollowing he ins uc ions in [92], one mus w i e in MATLAB a he beginning o each ime
CPLEX is going o be used wi h Yalmip:
>> addpa h(genpa h('C: P og am Files MATLAB R2020b oolbox YALMIP'));
% To be able o use YALMIP
>> addpa h(genpa h('C: P og am Files IBM ILOG CPLEX_S udio1210 cplex m
a lab x64_win64')); % To be able o use CPLEX
>> addpa h(genpa h('C: P og am Files IBM ILOG CPLEX_S udio1210 cplex e
xamples s c ma lab')); % To suppo na iga ional links o examples in
he online help om wi hin a MATLAB session
9- Finally, he command yalmip es can be used again and he use can check in he able i CPLEX has
co ec ly been ins alled.
Once bo h Yalmip and CPLEX a e ins alled, he impo an pa is o lea n how o use Yalmip. The e is an
ex ensi e o icial and public u o ial webpage whe e lo o esou ces and examples can be ound [93]. As can
be deduced om [86] and [93], o use Yalmip, he op imiza ion p oblem mus be de ined and hen used
ollowing hese s eps:
6- De ine he op imiza ion decision a iables using sdp a , o bin a o bina y a iables. They will be
used as symbolic a iables in he p oblem de ini ion. An in e es ing u o ial on how o de ine hem
can be ound in [94].
7- De ine he cos unc ion and cons ain s ollowing Yalmip sin ax.
8- Decide and es ablish wha a e going o be he inpu s and ou pu s o he op imiza ion p oblem.
9- Use he command op imize o de ine only one ime he p oblem as an objec . This command ecei es
as inpu , in his o de : cons ain s, cos unc ion, op ions, inpu s, ou pu s. In he op ions, he sol e can
be changed; o example, o use CPLEX, one mus sen he a gumen sdpse ings(‘sol e ’,’cplex’) in
he op ions ield.
10- Call he op imiza ion p oblem objec gi ing he equi ed inpu s o sol e i .
As an example, when using he e ia y con olle , he op imiza ion p oblem is c ea ed a he beginning only
one ime (s eps 1-4 om abo e) o educe compila ion o e head. Then, e e y sampling ime (i.e. e e y hou ),
he con olle inpu s (p edic ion, cu en s a e and p e ious con ol ac ions) a e sampled and sen o he
op imiza ion p oblem. Once he sol e has inished, he con ol ac ions a e ob ained in ec o u, 𝛿 and z. In
[95] he e is an in e es ing u o ial on how o use Yalmip o sol e MPC p oblems.

47
4 RESULTS
he con olle s a e es ed in simula ion in di e en scena ios. Fi s , simula ions a e ca ied o he e ia y
con olle and hen, o he whole sys em using bo h con olle s. These simula ions include bo h sunny
and cloudy days. All he simula ions ha e he same du a ion: 86400 seconds o one day. Mo eo e , he
sunny esul s a e also shown o islanded mode in he e ia y con olle ; i.e. wi h he mic og id no connec ed
o he main g id. Fo e e y simula ion, demand and gene a ion powe (o ne powe powe p edic ion in he
case o e ia y con olle ) p o iles a e going o be shown, as well as p ice p edic ion o he e ia y con olle
and EVs cha ging powe and ex a hyd ogen demand o he seconda y con olle . The esul s wil be
ep esen ed in he o m o g aphs con aining he powe exchange and he ene gy s o age le els. When bina y
a iables a e in ol ed, hey will be shown oo in o de o check he igh ope a ion.
4.1 Te ia y con olle
Fo he e ia y con olle , ou simula ions ha e been done. Th ee o hem a e in g id-connec ed mode o
sunny day, cloudy day and sunny day wi h nea ly-ze o demand. The las o hese h ee is due o he ac ha
he mic og id can be loca ed in an o ice o uni e si y place whe e he e is no ac i i y on weekends, bu sola
powe is gene a ed anyway. The o he simula ion is done o he islanded mode o a sunny day. Cloudy days
(almos no gene a ion) o days wi h almos no demand a e no conside ed he e because he s o age le el has
some limi s and o being in islanded mode he e mus be bo h gene a ion and demand. A solu ion in his case
can be he changing o g id-connec ed mode when he o ecas s p edic low gene a ion o low demand.
Fo his con olle , he ne powe (gene a ion minus demand) p edic ion is di ec ly ep esen ed. A common
da a o all he simula ions in g id-connec ed case is he ene gy p ice, which is aken om [96] and in his case
om 15 h No embe 2021. This day-ahead ma ke ene gy p ice can be seen in Figu e 8.
Figu e 8. Day-ahead ma ke ene gy p ice
T
Resul s
48
Ano he hing ha mus be commen ed is he physical cons ain s alues in o de o check in his sec ion ha
he op imiza ion p oblem is wo king p ope ly. They a e he same o he ou simula ions. The e a e mainly
h ee ypes o hese cons ain s: o he ou pu , o he con ol ac ions and o he inc emen al con ol ac ions.
The ou pu s a e cons ained as ollows:
- Ba e y: 𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑎𝑥=90%, 𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑖𝑛=20%
- Hyd ogen s o age: 𝐿𝑂𝐻𝑚𝑎𝑥=90% , 𝐿𝑂𝐻𝑚𝑖𝑛=10%
On he o he hand, he con ol ac ions, i.e., he powe e e ences, a e subjec ed o he ollowing cons ain s:
- Ba e y powe : 𝑃𝑏𝑎𝑡
𝑚𝑎𝑥=2.5 𝑘𝑊, 𝑃𝑏𝑎𝑡
𝑚𝑖𝑛=−2.5 𝑘𝑊, Δ𝑃𝑏𝑎𝑡
𝑚𝑎𝑥=1 𝑘𝑊/𝑠, Δ𝑃𝑏𝑎𝑡
𝑚𝑖𝑛=−1 𝑘𝑊/𝑠
- Fuel cell powe : 𝑃𝑓𝑐
𝑚𝑎𝑥=1.2 𝑘𝑊, 𝑃𝑓𝑐
𝑚𝑖𝑛=0.1 𝑘𝑊, Δ𝑃𝑓𝑐
𝑚𝑎𝑥=0.02 𝑘𝑊/𝑠, Δ𝑃𝑓𝑐
𝑚𝑖𝑛=−0.02 𝑘𝑊/𝑠
- Elec olyze powe : 𝑃𝑒𝑧
𝑚𝑎𝑥=0.9 𝑘𝑊, 𝑃𝑒𝑧
𝑚𝑖𝑛=0.1 𝑘𝑊, Δ𝑃𝑒𝑧
𝑚𝑎𝑥=0.02 𝑘𝑊/𝑠, Δ𝑃𝑒𝑧
𝑚𝑖𝑛=
−0.02 𝑘𝑊/𝑠
- G id powe : 𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥=2.5 𝑘𝑊, 𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛=−2.5 𝑘𝑊, Δ𝑃𝑔𝑟𝑖𝑑
𝑚𝑎𝑥=1 𝑘𝑊/𝑠, Δ𝑃𝑔𝑟𝑖𝑑
𝑚𝑖𝑛=−1 𝑘𝑊/𝑠
I is ema kable ha he inc emen al con ol ac ions cons ain s mus be mul iplied by he sample ime in o de
o be p ope ly applied.
Once all is p epa ed, i s ly, a simula ion in he g id-connec ed and sunny case is analised. In Figu e 9, he
powe e olu ion and he s o age le el can be seen. In he i s pa o he day, when he e is no gene a ion, he
demand is co e ed by pu chasing ene gy o he g id, since he ene gy p ice is no oo high. Then, since he
hou 6, he gene a ion becomes g ea e han demand and he excess o ene gy is sold o he g id because he
ene gy p ice has inc eased. As he con olle conside s he p edic ions o he ollowing 24 hou s, i an icipa es
he ac ha ene gy p ice will be high be ween 18 and 21 hou s whe e demand is g ea e han gene a ion, so a
hou 12, i is decided o s o e some ene gy excess in he ba e y o la e use. Finally, in he hou s o high
ene gy p ice, bo h he uel cell and he ba e y a e used o cope wi h he demand and o sell some ene gy o he
g id. As he wo ene gy s o age sys ems a e nea i s lowe limi is in he hou 21, he g id is again used o ul ill
he demand ega ding as he ene gy p ice is dec easing. As can be obse ed, he elec olyze and uel cell a e
no easily s a ed due o deg ada ion easons and, when s a ed (in his case he uel cell), i wo ks a a cons an
ope a ing poin . I is ema kable ha all he physical cons ain s a e accomplished and can be seen bo h in he
powe and in he s o age le el g aphs.
Figu e 9. Powe e olu ion and s o age le el in he sunny and g id-connec ed case
49
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
Only o his i s simula ion, bina y and auxilia y a iables a e going o be ep esen ed and explained o show
ha hey wo k as desi ed. In Figu e 10, he hyd ogen case can be obse ed. On he le side, i s appea s he
hyd ogen powe , hen he bina y a iables o he ene gized s a e (only ac i e in he h ee ime ins an s when
he uel cell wo ks), and inally, he auxilia y a iable which esul om he mul iplica ion o he wo p e ious
ones. On he igh side, he i s g aph indica es he ime ins an when he uel cell has been ac i a ed (hou 18),
he hi d g aph he ime ins an when he uel cell is ac i e and was ac i e he p e ious ime ins an , and he
second g aph shows he powe a ia ion in he ime ins an o he p e ious g aph.
Figu e 10. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and g id-connec ed case
As in he case o he le side o Figu e 10, Figu e 11 and Figu e 12 ep esen he con ol a iable, he bina y
a iable indica ing he ba e y cha ge/discha ge mode o he sale o/pu chase om he maing g id,
espec i ely, and he co esponding auxilia y a iables. I can be easily checked ha he ela ions a e ul illed
co ec ly.
Figu e 11. Ba e y con ol, bina y and auxilia y a iables in he sunny and g id-connec ed case
Resul s
50
Figu e 12. G id con ol, bina y and auxilia y a iables in he sunny and g id-connec ed case
The second simula ion is done again in g id-connec ed mode bu o a cloudy day. Resul s showing he powe
scheduled and he s o age le el can be seen in Figu e 13. Du ing all he day, demand is g ea e han
gene a ion, so ene gy mus be supplied om he g id o om he s o age sys ems. Almos all he day, he g id
is used o pu chase powe , excep o he hou s 18-21, when he ene gy p ice is eally high. In his ime, bo h
uel cell and ba e y a e used o sell ene gy and hen o ob ain an economical bene i . Fo his eason and due o
he p ice and ne powe o ecas a e a ailable o he ollowing 24 hou s, a hou 12, he EMS decides o
pu chase mo e ene gy om he g id, in o de o ha e enough ene gy o selling a hou s 18-21. As in he
p e ious simula ion, he uel cell ope a es wi hou a ia ions and all he desc ibed cons ain s a e ul illed.
Figu e 13. Powe e olu ion and s o age le el in he cloudy and g id-connec ed case
Hyd ogen con ol, bina y and auxilia y a iables a e depic ed in Figu e 14 o his simula ion. They a e sel -
explained g aphs looking he desc ip ion made o hese a iables in he p e ious simula ion. In he same way,
hese a iables a e ep esen ed o he ba e y in Figu e 15 and o he g id in Figu e 16.
51
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
Figu e 14. Hyd ogen con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed case
Figu e 15. Ba e y con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed case
F om he wo desc ibed simula ion, one can obse e ha he elec olyze has no been ac i a ed. This is due o
he ac ha s a ing he elec olyze is mo e expensi e han using he ba e y o he g id and has mo e
deg ada ion aspec s. Fo ha eason, a new scena io is simula ed whe e he demand is nea ze o du ing all he
day. This can co espond wi h a weekend day in an o ice o uni e si y campus, when he e is no ac i i y bu
gene a ion can be p oduced. A sunny day is assumed, so he ne powe is posi i e in he majo i y o he day.
The powe and s o age le els can be obse ed in Figu e 17. In ha case, he su plus o ene gy is sold o he
g id in he hou s when he ene gy p ice is highe (mainly in hou s 5-12 and 17-22). As a lo o ene gy is
p oduced and he e is no demand, bo h he ba e y and he elec olyze a e s o ing ene gy a a ound hou 10.
P e iously, he ba e y discha ged some ene gy which was sold o he g id, in o de o be eady o he

Resul s
52
Figu e 16. G id con ol, bina y and auxilia y a iables in he cloudy and g id-connec ed case
cha ging phase. Finally, be ween hou s 17 and 22, he e is nei he gene a ion no consump ion, bu he EMS
decides o sell ene gy o he g id using he ba e y and he uel cell due o he high ene gy p ice. Again, all he
cons ain s a e accomplished and he hyd ogen equipmen wo k a cons an ope a ing poin s.
Figu e 17. Powe e olu ion and s o age le el in he sunny and nea ly-ze o demand day and in g id-connec ed
case
Again, he hyd ogen, ba e y and g id con ol, bina y and auxilia y a iables a e shown in Figu e 18, Figu e 19
and Figu e 20. In he case o hyd ogen, in pa icula o he elec olyze , a iables can now be checked, as hey
wo k as i was expec ed and he elec olyze had no been ac i a ed in he p e ious simula ions.
53
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
Figu e 18. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o demand day and in
g id-connec ed case
Figu e 19. Ba e y con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o demand day and in g id-
connec ed case
Fi nally, one simula ion o he islanded case is ca ied ou . In islanded mode, he mic og id is expec ed o be
au onomous. Bu in o de o each his au onomy, bo h gene a ion and demand mus occu because he ene gy
s o age de ices a e no endless. In he case o g id-connec ed, al hough i is no ecommendable, he g id can
gi e mo e lexibili y. So, when he o ecas s p edic days wi h sca ci y o gene a ion o demand, he g id could
change o g id-connec ed mode, bu his is no conside ed in his wo k. Ano he op ion is o o e size he
ene gy s o age de ices conside ing hese special days. In bo h solu ions, he mic og id analysis en e s in week
simula ions and plani ica ion and his is ou o he scope o his wo k.
Resul s
54
Figu e 20. G id con ol, bina y and auxilia y a iables in he sunny and nea ly-ze o demand day and in g id-
connec ed case
In o de o do he simula ions wi h he same ne powe p edic ions as in he sunny and g id-connec ed case, he
ou pu cons ain s mus me modi ied in o de o enla ge hem. This allows s o ing mo e ene gy in he s o age
de ices as well as ob aining mo e ene gy om hem. The new ou pu cons ain s o his simula ion a e:
- Ba e y: 𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑎𝑥=95%, 𝑆𝑂𝐶𝑏𝑎𝑡
𝑚𝑖𝑛=10%
- Hyd ogen s o age: 𝐿𝑂𝐻𝑚𝑎𝑥=100% , 𝐿𝑂𝐻𝑚𝑖𝑛=0%
In Figu e 21, powe and s o age le el e olu ion a e ep esen ed. Bo h a he beginning and a he end o he
day he e is no gene a ion and he demand is co e ed using he uel cell and he ba e y. In he cen al pa o
he day, he gene a ion is enough o co e he demand and ene gy can be e en s o ed in he o m o hyd ogen
and in he ba e y. In his case, whe e he hyd ogen is mo e equen ly used han in he g id-connec ed case,
Figu e 21. Powe e olu ion and s o age le el in he sunny and islanded case
55
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
one can see ha he elec olyze and uel cell s a ups a e minimized. Mo eo e , bo h de ices wo k a cons an
ope a ing poin s. These wo las ac s a e possible due o a ia ions a e abso bed by he ba e y, which su e s
less han hyd ogen de ices. Finally, as in o he simula ions, all he cons ain s a e ul illed.
Finally, hyd ogen and ba e y con ol, bina y and auxilia y a iables a e depic ed in Figu e 22 and Figu e 23,
espec i ely. In his simula ion hyd ogen ac i i y is g ea e han in p e ious cases, so hese a iables
unc ioning can be be e obse ed.
Figu e 22. Hyd ogen con ol, bina y and auxilia y a iables in he sunny and islanded case
Figu e 23. Ba e y con ol, bina y and auxilia y a iables in he sunny and islanded case
Conclusions
62
5.2 Limi a ions and u u e wo k
As well as all he ad an ages which a e ex ac ed om he esul s analysis, he e a e also some d awbacks.
Fi s ly, as i was commen ed du ing his epo , when in islanded mode, he mic og id planning should be done
wi h a longe ime ho izon ( o example a week) in o de o be e size he equipmen o o be e plan he
powe exchanges wi h o he mic og ids o he main g id assuming ha he islanded mode can be ans o med
in o a connec ed one. I his aspec is no aken in o accoun , he e could be scena ios in islanded mode whe e
he ene gy s o age sys ems a e ull and he e is a su plus o ene gy p oduc ion. This si ua ion can also occu in
g id-connec ed mode, bu he g id gi es he mic og id mo e lexibili y, al hough i is no ecommended due he
economical penal ies i he schedule g id powe exchange is no ul illed.
One impo an aspec o imp o e he pe o mance o he con ol s a egy is he ac ha a seconda y con olle
wi h bo h con inuous and logical a iables can be de eloped. In his wo k, o simplici y and o sho e
simula ions du a ion, a seconda y con olle wi h only con inuous a iables is designed. Al hough i is a
comple e con olle , which conside s a lo o equipmen limi i a ions and some pe o mance equi emen s, i
does no allow conside ing he s a up p ocess o he hyd ogen echnology (elec olyze and uell cell) in o de
o minimize i . So, in some o he simula ions o he seconda y con olle , one can see ha his aspec has no
been aken in o accoun in his wo k.
Ano he aspec which can be conside ed in he u u e o imp o ing his applica ion is o be e manage he EV
demand. New EVs powe demand p o iles can be added and es ed, o e en demand models based on
Gaussian dis ibu ions can be de eloped. Mo eo e , implemen ing a V2G s a egy will inc ease he mic og id
lexibili y and his will need a speci ic EV cha ging managemen including bo h bina y and con inuous
a iables, as done in he wo k o [3].
Finally, as i was men ioned a he beginning o his epo , his p ojec is wan ed o be ca ied ou in a eal
plan . Bu o his ma e ializa ion, some mo e asks ha e o be done. Among o he s, he ene gy consump ion,
p oduc ion and p ice o ecas s mus be implemen ed wi h some p edic ions models, he powe elec onics
con e e s mus be conside ed and con olled, and mo e scena ios should be p o en. Fu he mo e, as some o
he equipmen was used in olde p ojec s, new expe imen s should be made in o de o check ha hei model
pa ame e s emain as conside ed.

63
REFERENCES
[1]
Eu opean En i onmen Agency. (2019, Decembe ) Sha e o anspo g eenhouse gas emissions. Da a
Visualiza ion. [Online]. h ps://www.eea.eu opa.eu/da a-and-maps/da iz/sha e-o - anspo -ghg-
emissions-2/# ab-dashboa d-01
[2]
Ca los Bo dons, Félix Ga cía-To es, and Miguel A. Ridao, Model P edic i e Con ol o Mic og ids.
Spain: Sp inge , 2020.
[3]
Paulo R.C. Mendes, Luis Val e de Iso na, Ca los Bo dons, and Julio E. No mey-Rico, "Ene gy
managemen o an expe imen al mic og id coupled o a V2G sys em," Jou nal o Powe Sou ces -
ELSEVIER, ol. 327, pp. 702-713, Augus 2016.
[4]
Uni ed Na ions F amewo k Con en ion on Clima e Change. (2021, No embe ) COP26 Reaches
Consensus on Key Ac ions o Add ess Clima e Change. [Online]. h ps://un ccc.in /news/cop26- eaches-
consensus-on-key-ac ions- o-add ess-clima e-change
[5]
Eu opean Commission. A Eu opean G een Deal. [Online]. h ps://ec.eu opa.eu/in o/s a egy/p io i ies-
2019-2024/eu opean-g een-deal_en
[6]
Eu opean Commission, "Ho izon Eu ope - The EU Resea ch & Inno a ion P og amme 2021-27,"
P esen a ion 2021.
[7]
Eu opean En i onmen Agency. (2021, No embe ) G eenhouse gas emissions om anspo in Eu ope.
[Online]. h ps://www.eea.eu opa.eu/ims/g eenhouse-gas-emissions- om- anspo
[8]
Eu opean En i onmen Agency, "T anspo and en i onmen epo 2020. T ain o plane?," 19, 2020.
[9]
Eu opean En i onmen Agency. (2021, Ma ch) Mo o ised anspo : ain, plane, oad o boa - which is
g eenes ? News. [Online]. h ps://www.eea.eu opa.eu/highligh s/mo o ised- anspo - ain-plane- oad
[10]
Sec e a ía de Es ado de Ene gía. Vicep esidencia Cua a del Gobie no de España, "Es a egia de
almacenamien o ene gé ico," Minis e io pa a la T ansición Ecológica y el Re o Demog á ico (MITERD),
Mad id, 2021.
[11]
Vicep esidencia Cua a del Gobie no de España, "Hoja de u a del hid ógeno: Una apues a po el
hid ógeno eno able," Minis e io pa a la T ansición Ecológica y el Re o Demog á ico (MITERD),
Mad id, 2020.
[12]
Gobie no de España. (2021, Oc obe ) La Moncloa. P esupues os Gene ales del Es ado 2022. [Online].
h ps://www.lamoncloa.gob.es/consejodeminis os/Paginas/enlaces/071021-enlace-pge.aspx
[13]
Gobie no de España. (2021, Ap il) La Moncloa. Ped o Sánchez: "El Plan de Recupe ación es el plan
económico más ambicioso de la his o ia ecien e de España". [Online].
h ps://www.lamoncloa.gob.es/p esiden e/ac i idades/Paginas/2021/130421-sanchez_ ecupe acion.aspx
[14]
Luis Val e de, Felipe Rosa, and Ca los Bo dons, "Design, Planning and Managemen o a Hyd ogen-
Re e ences
64
Based Mic og id," IEEE T ansac ions on Indus ial In o ma ics, ol. 9, no. 3, pp. 1398-1404, Augus
2013.
[15]
Luis Val e de, Felipe Rosa, Alejand o J. Del Real, Alicia A ce, and Ca los Bo dons, "Modeling,
simula ion and expe imen al se -up o a enewable hyd ogen-based domes ic mic og id," In e na ional
Jou nal o Hyd ogen Ene gy - Else ie , ol. 38, no. 27, pp. 11672 - 11684, July 2013.
[16]
Ibe d ola. G een hyd ogen: an al e na i e ha educes emissions and ca es o ou plane . [Online].
h ps://www.ibe d ola.com/sus ainabili y/g een-hyd ogen
[17]
Repsol. (2021, Janua y) Repsol joins in e na ional conso ium o de elop cu ing-edge enewable
hyd ogen echnology. [Online].
h ps://www. epsol.com/imagenes/global/en/PR27012021_h24all_ cm14-207089.pd
[18]
CORDIS EU Resea ch Resul s. Eu opean Commission. (2021, Janua y) Fuel Cell Hyb id Powe Pack o
Rail Applica ions. [Online]. h ps://co dis.eu opa.eu/p ojec /id/101006633
[19]
bp. (2020, No embe ) bp y Ø s ed c ean uno de los mayo es p oyec os eu opeos de hid ógeno eno able
con base en Alemania. [Online]. h ps://www.bp.com/es_es/spain/home/no icias/no as-de-
p ensa/bp_y_o s ed_c ean_uno_de_los_mayo es_p oyec os_eu opeos_de_hid ogeno_ eno able_con_ba
se_en_alemania.h ml
[20]
No H2. (2020, Feb ua y) No H2. Kicks a ing he g een hyd ogen economy. [Online].
h ps://www.no h2.eu/en/
[21]
Djewels. (2020, Janua y) Djewels. Pionee ing he Eu opean enewable eFuels ma ke . [Online].
h ps://djewels.eu/
[22]
ITM Powe . (2021, Janua y) Sale o Linde o Wo ld’s La ges PEM Elec olyse . [Online].
h ps://www.i m-powe .com/news/sale- o-linde-o -wo ld-s-la ges -pem-elec olyse
[23]
FuelCellsWo ks. (2021, Janua y) G een Hyd ogen: Ai Liquide Elec olysis wi h H2V. [Online].
h ps:// uelcellswo ks.com/news/g een-hyd ogen-ai -liquide-elec olysis-wi h-h2 /
[24]
To al. (2021, Janua y) To al and Engie pa ne o de elop F ance's la ges si e o he p oduc ion o g een
hyd ogen om 100% enewable elec ici y. [Online]. h ps://www. o al.com/media/news/p ess-
eleases/ o al-and-engie- o-de elop- ance-s-la ges -si e-o -g een-hyd ogen
[25]
Hyb idge. Hyb idge P ojec . [Online]. h ps://www.hyb idge.ne /P ojec /Plan/
[26]
Po o Ro e dam. (2019, Ap il) BP, Nou yon and Po o Ro e dam pa ne on g een hyd ogen s udy.
[Online]. h ps://www.po o o e dam.com/en/news-and-p ess- eleases/bp-nou yon-and-po -o -
o e dam-pa ne -on-g een-hyd ogen-s udy
[27]
REFHYNE. (2018, Janua y) REFHYNE. Clean Re ine y Hyd ogen o Eu ope. [Online].
h ps:// e hyne.eu/
[28]
H2Fu u e. (2017, Janua y) H2Fu u e P ojec . [Online]. h ps://www.h2 u u e-p ojec .eu/
[29]
Tenne . (2018, Oc obe ) Gasunie, TenneT and Thyssengas e eal de ailed, g een ‘sec o coupling’ plans
using powe - o-gas echnology. [Online]. h ps://www. enne .eu/news/de ail/gasunie- enne -and-
hyssengas- e eal-de ailed-g een-sec o -coupling-plans-using-powe - o-gas- ec/
65
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
[30]
CORDIS EU Resea ch Resul s. Eu opean Commission. (2021, Janua y) O sho e hyd ogen om
sho eside wind u bine in eg a ed elec olyse . [Online]. h ps://co dis.eu opa.eu/p ojec /id/101007168
[31]
CORDIS EU Resea ch Resul s. Eu opean Commission. (2019, Janua y) Implemen ing Fuel Cells and
Hyd ogen Technologies in Po s. [Online]. h ps://co dis.eu opa.eu/p ojec /id/826339
[32]
CORDIS EU Resea ch Resul s. Eu opean Commision. (2021, Janua y) “GREEN HYSLAND –
Deploymen o a H2 Ecosys em on he Island o Mallo ca”. [Online].
h ps://co dis.eu opa.eu/p ojec /id/101007201
[33]
El pe iódico de la ene gía. (2021, Janua y) Endesa inicia á la plan a de hid ógeno en As Pon es en 2023
con seis pa ques eólicos asociados. [Online]. h ps://elpe iodicodelaene gia.com/endesa-inicia a-la-
plan a-de-hid ogeno-en-as-pon es-en-2023-con-seis-pa ques-eolicos-asociados/
[34]
La Voz de As u ias. (2021, Feb ua y) Un p oyec o de hid ógeno e de p e ende c ea 1.500 empleos en
As u ias. [Online]. h ps://www.la ozdeas u ias.es/no icia/as u ias/2021/02/01/p oyec o-hid ogeno-
e de-p e ende-c ea -1500-empleos-as u ias/00031612179984619649320.h m
[35]
Ibe d ola. (2020) Ibe d ola cons ui á la mayo plan a de hid ógeno e de pa a uso indus ial en Eu opa.
[Online]. h ps://www.ibe d ola.com/conocenos/lineas-negocio/p oyec os-emblema icos/pue ollano-
plan a-hid ogeno- e de
[36]
Repsol. (2020, June) Repsol desa olla á en España dos g andes p oyec os de educción de emisiones.
[Online]. h ps://www. epsol.com/es/sala-p ensa/no as-p ensa/2020/ epsol-desa olla a-en-espana-dos-
g andes-p oyec os-de- educcion-de-emisiones.csh ml
[37]
Cana ias7. (2021, Feb ua y) Endesa con empla dos p oyec os dehid ógeno e de y el paso de cen ales a
bi-combus ible en Cana ias. [Online]. h ps://www.cana ias7.es/economia/endesa-con empla-p oyec os-
20210201130152-n .h ml
[38]
In e gia. (2017) P oducción de hid ógeno y uso en Vehículo de Hid ógeno – p oyec o LIFE REWIND.
[Online]. h ps://www.in e gia.es/po olio/hid ogeno-li e- ewind/
[39]
Enagás. (2020, Decembe ) Enagás y Na u gy impulsan en León la mayo plan a de hid ógeno e de de
España. [Online].
h ps://www.enagas.es/enagas/es/Comunicacion/No asP ensa/17_12_2020_Acue do_Na u gy_en_La_R
obla
[40]
Lib eMe cado. (2020, Decembe ) Amo ebie a acoge á la p ime a plan a de hid ógeno e de de España.
[Online]. h ps://www.lib eme cado.com/2020-12-17/espana-plan a-hid ogeno- e de-au obuses-
6690259/
[41]
H. Gö gün, "Dynamic modelling o a p o on exchange memb ane (PEM) elec olyze ," In e na ional
Jou nal o Hyd ogen Ene gy, ol. 31, pp. 29-38, Janua y 2006.
[42]
T. Yigi and O. F. Selame , "Ma hema ical modeling and dynamic Simulink simula ion o high-p essu e
PEM elec olyze sys em," In e na ional Jou nal o Hyd ogen Ene gy, ol. 41, pp. 13901-13914, Augus
2016.
[43]
P. F agiacomo and M. Geno ese, "Modeling and ene gy demand analysis o a scalable g een hyd ogen
p oduc ion sys em," In e na ional Jou nal o Hyd ogen Ene gy, ol. 44, pp. 30237-30255, No embe
2019.
Re e ences
66
[44]
M. Ca mo, D. L. F i z, J. Me gel, and D. S ol en, "A comp ehensi e e iew on PEM wa e elec olysis,"
In e na ional Jou nal o Hyd ogen Ene gy, ol. 38, pp. 4901-4934, Ap il 2013.
[45]
B. Han, S. M. S een III, J. Mo, and F. Zhang, "Elec ochemical pe o mance modeling o a p o on
exchange memb ane elec olyze cell o hyd ogen ene gy," In e na ional Jou nal o Hyd ogen Ene gy,
ol. 40, pp. 7006-7016, June 2015.
[46]
E. N. Pis ikopoulos G. S. Ogume em, "Pa ame ic op imiza ion and con ol o a sma P o on
Exchange," Jou nal o P ocess Con ol, ol. 91, pp. 37-49, July 2020.
[47]
R. Abou ni, A. Aziz, N. Benazzi, M. Elha yani, K. Kassmi S. Dahbi, "Op imised hyd ogen p oduc ion by
a pho o ol aic-elec olysis sys em DC/DC con e e and wa e low con olle ," In e na ional Jou nal o
Hyd ogen Ene gy, ol. 41, pp. 20858-20866, Decembe 2016.
[48]
M. Schalenbach, M. Ca mo, D. L. F i z, J. Me gel, and D. S ol en, "P essu ized PEM wa e elec olysis:
E iciency and gas c osso e ," In e na ional Jou nal o Hyd ogen Ene gy, ol. 38, pp. 14921-14933,
No embe 2013.
[49]
F. Ma angio, M. San a elli, and M. Calì, "Theo e ical model and expe imen al analysis o a high p essu e
PEM wa e elec olyse o hyd ogen p oduc ion," In e na ional Jou nal o Hyd ogen Ene gy, ol. 34,
pp. 1143-1158, Feb ua y 2009.
[50]
R. Ga cía-Val e de, N. Espinosa, and A. U bina, "Simple PEM wa e elec olyse model and
expe imen al alida ion," In e na ional Jou nal o Hyd ogen Ene gy, ol. 37, pp. 1927-1938, Janua y
2012.
[51]
S. Dahbi e al., "Managemen o excess ene gy in a pho o ol aic/g id sys em by p oduc ion o clean
hyd ogen," In e na ional Jou nal o Hyd ogen Ene gy, ol. 43, pp. 5283-5299, Ma ch 2018.
[52]
C. Bo dons, F. Rosa L.Val e de, "Powe Managemen using Model P edic i e Con ol in a hyd ogen-
based mic og id," in 38 h annual con e ence on IEEE, 2012, pp. 5669-5676.
[53]
I. Yahyaoui, J. E. No mey-Rico, C. de P ada, F. Tadeo Á. Se na, "P edic i e Con ol o hyd ogen
p oduc ion by elec olysis in an o sho e pla o m using enewable ene gies," In e na ional Jou nal o
Hyd ogen Ene gy, ol. 42, pp. 12865-12876, Ap il 2017.
[54]
Félix Ga cía-To es and Ca los Bo dons, "Op imal economic dispa ch o enewable ene gy mic og ids
wi h hyb id s o age using Model P edic i e Con ol," in IECON 2013 - 39 h Annual Con e ence o he
IEEE Indus ial Elec onics Socie y, Vienna, Aus ia, 2013, pp. 7932 - 7937.
[55]
Félix Ga cía-To es and Ca los Bo dons, "Op imal Economical Schedule o Hyd ogen-Based Mic og ids
Wi h Hyb id S o age Using Model P edic i e Con ol," IEEE T ansac ions on Indus ial Elec onics,
ol. 62, no. 8, pp. 5195-5207, Augus 2015.
[56]
Félix Ga cía-To es, Luis Val e de, and Ca los Bo dons, "Op imal Load Sha ing o Hyd ogen-Based
Mic og ids Wi h Hyb id S o age Using Model-P edic i e Con ol," IEEE T ansac ions in Indus ial
Elec onics, ol. 63, no. 8, pp. 4919 - 4928, Ma ch 2016.
[57]
B. Flamm, C. Pe e , F. N. Büchi, and J. Lyge os, "Elec olyze modeling and eal- ime con ol o
op imized p oduc ion o hyd ogen gas," Applied Ene gy, ol. 281, no. 116031, Janua y 2021.
[58]
P. Manca ella, "G een Hyd ogen: A Tale F om Two Coun ies," IEEE Sma G id eNewsle e . Sma
67
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
G id - G een Hyd ogen, Feb ua y 2021.
[59]
S. M. Bhaga a hy and J. Thaku , "G een Hyd ogen: Challenges o Comme cializa ion," IEEE Sma
G id eNewsle e . Sma G id - G een Hyd ogen, Janua y 2021.
[60]
V. Soo ia achchi, "G een Hyd ogen and T anspo a ion Indus y – An O e iew o High-Speed
Railways," IEEE Sma G id eNewsle e . Sma G id - G een Hyd ogen, Feb ua y 2021.
[61]
D. Houseman, "Cu ailmen o Renewables and Hyd ogen," IEEE Sma G id eNewsle e . Sma G id -
G een Hyd ogen, Feb ua y 2021.
[62]
Me yem Gizem Sü e and Hüseyin Tu an A a , "S a e o a o hyd ogen usage as a uel on a ia ion,"
Eu opean Mechanical Science, ol. 2(1), pp. 20-30, 2018.
[63]
Wes küs e 100. Wes küs e 100. [Online]. h ps://www.wes kues e100.de/en/
[64]
ENABLEH2. ENABLEH2 H2020 P ojec . [Online]. h ps://www.enableh2.eu/
[65]
Fede al Minis y o Educa ion and Resea ch o Ge many. Kope nikus P ojec : P2X. [Online].
h ps://www.kope nikus-p ojek e.de/en/p ojec s/p2x
[66]
Sun i e. e-Fuel. [Online]. h ps://www.sun i e.de/en/e- uel
[67]
Ze oA ia. The is p ac ical ue ze o emission a ia ion powe ain. [Online]. h ps://www.ze oa ia.com/
[68]
EMEC. The Eu opean Ma ine Ene gy Cen e LTD. HyFlye P ojec s. [Online].
h p://www.emec.o g.uk/p ojec s/hyd ogen-p ojec s/hy lye /
[69]
AIRBUS. (2020) ZEROe. Towa ds he wo ld’s i s ze o-emission comme cial ai c a . [Online].
h ps://www.ai bus.com/inno a ion/ze o-emission/hyd ogen/ze oe.h ml
[70]
Skai. Alaka'i. Hyd ogen-Powe ed VTOL Ai c a . [Online]. h ps://www.skai.co/
[71]
Deu sches Zen um ü Lu - und Raum ah (DLR). (2021, Janua y) P ojec BALIS – DLR is de elop-
ing and es ing uel cells in he megawa ange o ai anspo . [Online].
h ps://www.dl .de/con en /en/a icles/news/2021/01/20210121_balis-p ojec - unding.h ml
[72]
HES Ene gy Sys ems. Elemen One P ess Release. [Online]. h ps://www.hes.sg/elemen -one-p
[73]
Ahmad Ba ou aji, Tabbi Wilbe o ce, Mohamad Ramadan, and Abdul Ghani Olabi, "Comp ehensi e
in es iga ion on hyd ogen and uel cell echnology in he a ia ion and ae ospace sec o s," Renewable and
Sus ainable Ene gy Re iews, ol. 106, pp. 31-40, 2019.
[74]
Zehua Dai, Li Wang, and Shanshui Yang, "Fuel Cell Based Auxilia y Powe Uni in Mo e Elec ic
Ai c a ," in IEEE T anspo a ion Elec i ica ion Con e ence and Expo, Asia-Paci ic (ITEC Asia-
Paci ic), 2017.
[75]
Na han G ay, Shane McDonagh, Richa d O’Shea, Bea ice Smy h, and Je y D Mu phy, "Deca bonising
ships, planes and ucks: An analysis o sui able low-ca bon uels o he ma i ime, a ia ion and haulage
sec o s," Ad ances in Applied Ene gy, ol. 1, no. 100008, 2021.
[76]
Azha Ul-Haq, Ca lo Ceca i, and Essam A. Al-Amma , "Modeling o a Pho o ol aic-Powe ed Elec ic
Vehicle Cha ging S a ion wi h Vehicle- o-G id Implemen a ion," Ene gies, ol. 10, no. 1, Decembe

Re e ences
68
2016.
[77]
Qiongjie Dai, Jicheng Liu, and Qiushuang Wei, "Op imal Pho o ol aic/Ba e y Ene gy S o age/Elec ic
Vehicle Cha ging S a ion Design Based in Mul i-Agen Pa icle Swa m Op imiza ion Algo i hm,"
Sus ainabili y, ol. 11, no. 7, Ap il 2019.
[78]
Semen Uimonen and Ma i Leh onen, "Simula ion o elec ic Vehicle Cha ging S a ions Load P o iles in
O ice Buildings Based on Occupancy Da a," Ene gies, ol. 13, no. 21, Oc obe 2020.
[79]
Maxwell Technologies, "125V Hea y T anspo Module Da ashee ," Ul acapaci o da ashee .
[80]
Edua do F. Camacho and Ca los Bo dons, Model P edic i e Con ol, 2nd ed.: Sp inge , 2007.
[81]
J. M. Maciejowski, P edic i e Con ol wi h Cons ain s.: P en ice Hall, 2000.
[82]
Albe o Bempo ad and Man ed Mo a i, "Con ol o sys ems in eg a ing logic, dynamics, and
cons ain s," Au oma ica, no. 35, p. 407 427, Sep embe 1998.
[83]
P oyec o AGERAR. Simug id - P oyec o AGERAR. [Online]. h p://ins i ucional.us.es/age a /simug id/
[84]
Ma hwo ks. Simscape Elec ical - MATLAB & Simulink. [Online].
h ps://es.ma hwo ks.com/p oduc s/simscape-elec ical.h ml
[85]
UL. HOMER - Hyb id Renewable and Dis ibu ed Gene a ion Sys em Design So wa e. [Online].
h ps://www.home ene gy.com/index.h ml
[86]
Johan Lö be g, "YALMIP: A oolbox o modeling and op imiza ion in MATLAB," in Compu e Aided
Con ol Sys ems Design, 2004 IEEE In e na ional Symposium on, 2004.
[87]
Johan Lö be g. Sol e s - YALMIP. [Online]. h ps://yalmip.gi hub.io/allsol e s/
[88]
IBM. ILOG CPLEX Op imiza ion S udio - IBM. [Online]. h ps://www.ibm.com/p oduc s/ilog-cplex-
op imiza ion-s udio
[89]
Johan Lö be g. (2016, Sep embe ) Ins alla ion - YALMIP. [Online].
h ps://yalmip.gi hub.io/ u o ial/ins alla ion/
[90]
Ma hWo ks. View o change sea ch pa h - MATLAB pa h - Ma hWo ks. [Online].
h ps://es.ma hwo ks.com/help/ma lab/ e /pa h.h ml
[91]
Xa ie Node . (2020, July) CPLEX Op imiza ion S udio is ee o s uden s and academics! [Online].
h ps://communi y.ibm.com/communi y/use /da ascience/blogs/xa ie -node 1/2020/07/09/cplex- ee- o -
s uden s?Communi yKey=ab7de0 d-6 43-47a9-8261-33578a231bb7& ab=
[92]
IBM. (2019) Se ing up CPLEX o MATLAB - IBM Documen a ion. [Online].
h ps://www.ibm.com/docs/en/icos/12.10.0? opic=ma lab-se ing-up-cplex
[93]
Johan Lö be g. (2016, Sep embe ) YALMIP. [Online]. h ps://yalmip.gi hub.io/ u o ials/
[94]
Johan Lö be g. (2016, Sep embe ) sdp a - YALMIP. [Online].
h ps://yalmip.gi hub.io/command/sdp a /
69
Ene gy managemen sys em o a ze o-emission ehicle cha ging s a ion based on MPC
[95]
Johan Lö be g. (2016, Sep embe ) Model p edic i e con ol - Basics - YALMIP. [Online].
h ps://yalmip.gi hub.io/example/s anda dmpc/
[96]
OMIE - Ibe ian Ma ke Ope a o . (2021, No embe ) OMIE. [Online]. h ps://www.omie.es/en
[97]
Ja ie San aolaya Sánchez, "Diseño de Bancada y Sis ema de Con ol pa a la In eg ación de Pila de
Combus ible en un Vehículo," Uni e sidad de Se illa, Se illa, P oyec o Fin de Ca e a 2017.
71
NOMENCLATURE
ENGREEN: Labo a o y o Enginee ing o Ene gy and En i onmen al Sus ainabili y
MPC: Model P edic i e Con ol
UNFCC: Uni ed F amewo k Con en ion on Clima e Change
COP26: 26 h Con e ence o he Pa ies
UN: Uni ed Na ions
NGEU: Nex Gene a ion Eu ope
GHG: G eenhouse Gas
EU: Eu opean Union
ESS: Ene gy S o age Sys em
M€: Million o eu os
PV: Pho o ol aic
PEM: Polyme Elec oly e Memb ane
DC: Di ec Cu en
MW/GW: Mega/Giga-Wa s
H2: Hyd ogen
PEC: Pho oelec ochemical
CO2: Ca bone dioxide
BoP: Balance o Plan
MPPT: Maximum Powe Poin T acking
O2: Oxygen
PMS: Powe Managemen S a egy
SOC: S a e o Cha ge
MHL: Me al Hyd ide Le el
MIQP: Mixed-In ege Quad a ic P og amming
MILP: Mixed-In ege Linea P og amming
PID: P opo ional, In eg al and De i a i e
PLC: P og ammable Logic Con olle
PWM: Pulse-Wid h Modula ion
FC: Fuel Cell
APU: Auxilia y Powe Uni
EV: Elec ic Vehicle
PHEV: Plug-in Hyb id Elec ic Vehicle