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Resonance damping o LCL fil e s ia inpu
admi ance equency shaping
Jo ge Pé ez, San iago Cób eces,
Daniel Piza o, F ancisco Ja ie Rod íguez Sánchez
Depa amen o de Elec ónica
Uni e sidad de Alcalá
Email: jo [email p o ec ed]
Robe G iñó
Ins . o Indus ial and Con ol Enginee ing.(IOC)
Uni e si a Poli ècnica de Ca alunya (UPC)
Email: [email p o ec ed]
Abs ac —This pape p esen s a no el ac i e damping ech-
nique o cu en -con olled g id-connec ed powe con e e s
h ough LCL fil e s. Based on H∞syn hesis algo i hms, a
g id cu en con olle is ob ained so ha he g id-connec ed
powe con e ed-based applica ion admi ance esembles a gi en
equency e e ence. By defining a low esis i e admi ance as he
e e ence, conside ed applica ion esonance is e ec i ely damped,
educing g id cu en oscilla ions unde g id ol age a ia ions
and a oiding hei associa ed s abili y p oblems. P esen ed g id
cu en con olle senses only he PCC g id ol age and cu en ,
and is expe imen ally es ed in bo h ime and equency domains.
Addi ionally, he e ec i eness o p esen ed damping me hod is
p o ed unde di e en g id impedance scena ios.
I. INTRODUCTION
Pulsewid h modula ed (PWM) powe elec onic con e e s
a e usually connec ed o he g id h ough inpu fil e s in o de
o ensu e low THD sinusoidally shaped g id cu en s [1].
Rega ding g id cu en con ol applica ions, one o he mos
common opologies is he LCL fil e [2], which has be e
fil e ing capabili y han simple opologies as, o example,
he L fil e , bu also inc eases con ol complexi y [3]. Tha
is due o he p esence o wo complex conjuga e poles in he
con olled plan , which esonan ly inc eases i s open-loop gain
(i.e., i s admi ance alue).
This esonance will gene a e cu en oscilla ions (a he
esonan equency) unde changes in he sys em ope a ing
poin (e.g., PCC ol age pe u ba ions). These oscilla ions can
be mo e o less du able o e ime and high in magni ude
depending on how damped he esonance is. Mo eo e , hey
can become uns able in p esence o non-dissipa i e closed-
loop sys ems [4] and weak g ids [5].
Damping echniques o esonan sys ems ha e ecei ed
significan a en ion by he specialized li e a u e. They can be
so ed in wo big g oups; ac i e damping [2], [3], [5]–[10],
whe e he sys em con olle is modified o damp he esonance,
and passi e damping [1], [11]–[14], whe e passi e elemen s,
commonly esis ances, a e added o he fil e o displace he
esonan poles. Passi e damping is a simple solu ion bu
comes a he cos o ex a powe loss and educ ion o he
high- equency a enua ion capabili y [13]. Ac i e damping
echniques o e come passi e damping d awbacks, bu i s e -
ec i eness, howe e , is limi ed by he swi ching equency,
VSC
PCC
LCL il e
+
-
+
-
+
-
Powe
con olle
Cu en con olle
Fig. 1. One-line equi alen diag am o he conside ed sys em. In blue he
measu ed a iables, in g een he cu en con olle and in ed he inpu
admi ance o be shaped.
and addi ional passi e componen s may s ill be needed o
damp high- equency esonance [11].
This pape p oposes a new ac i e damping echnique o
g id-connec ed powe elec onic con e e s h ough LCL fil e s
by di ec ly shaping, in he equency domain, he closed-
loop inpu admi ance o he conside ed applica ion. A model-
e e ence app oach is adop ed, whe e designe defines he
desi ed admi ance a he esonan equency and an H∞syn-
hesis algo i hm ob ain he (sub)op imal con olle ha makes
he closed-loop inpu admi ance ma ch he gi en e e ence
[17]. The sys em esonance will be e ec i ely damped, hen,
by defining a pu ely esis i e admi ance as he e e ence.
The es o he pape is o ganized as ollows. Sec ion II
models he plan o he conside ed applica ion and in oduce
he esonan beha iou o he LCL fil e . Sec ion III de elop
he p oposed sys em con ol, s a ing wi h he con olle ob-
jec i es and ending up wi h i s design. Sec ion IV discuss
he esul s o he p oposed con olle , expe imen ally es ed in
bo h ime and equency domains. Addi ionally, i shows how
obus he con olle is, ega ding bo h s and-alone s abili y
and damping capabili y unde di e en g id condi ions. The
pape ends wi h a b ie discussion o i s conclusions.
II. DYNAMIC MODELLING
This pape conside s a g id cu en con ol o a shun
con e e connec ed o he g id h ough an LCL fil e (see
Fig. 1). The sys em is modelled in s a iona y (i.e., αβ)
e e ence ame, which allows e ec i e con olle ope a ion
e en unde unbalanced condi ions. Addi ionally, as αβ axes
a e uncoupled, he o iginal MIMO con ol p oblem is educed
o he con ol o wo iden ical SISO p oblems. Fo he sake
o no a ion simplici y, only one o he con olled channels is
conside ed in his pape o bo h plan modelling and con olle
design.
G id cu en idynamic o conside ed sys em is ep esen ed
in he Laplace domain as ollows:
I(s)=G(s)·U(s)+Gd(s)·Vs(s),(1)
whe e I(s),U(s)and Vs(s)a e he g id injec ed cu en ,
he VSC a e age ou pu ol age and PCC ol age, espec-
i ely. T ans e unc ions G(s)and Gd(s)a e he open-loop
command- o-ou pu and inpu open loop admi ance, espec-
i ely, which will ollow he nex dynamic exp essions i an
ideal PCC ol age (i.e., Lg=0) is conside ed:
G(s)=−Zc(s)
ZL1(s)·Zc(s)+ZL2(s)·(ZL1(s)+Zc(s)),(2)
Gd(s)= ZL1(s)+Zc(s)
ZL1(s)·Zc(s)+ZL2(s)·(ZL1(s)+Zc(s)),(3)
whe e Zc(s)=1/(sC),ZL1(s)=sL1+R1and ZL2(s)=
sL2+R2a e he capaci o , con e e -side coil and g id-side
coil impedances, espec i ely.
Bo h G(s)and Gd(s)ha e a pai o complex conjuga e
poles which will p oduce an inc ease o hei espec i e gains
a he esonance equency ω es =(L1+L2)/(L1·L2·C)
ad/s. O main impo ance in he s abili y o he conside ed
applica ion is he esonance in Gd(s)( e e o Fig. 7 o see
i s equency domain ep esen a ion), as i may cause high
cu en oscilla ions and e en sys em ins abili y unde PCC
ol age changes. Tha p oblem is inc eased i he sys em is
connec ed o a weak g id (i.e., wi h high g id impedance) [5].
The esonance mus be p ope ly damped in o de o assu e he
co ec and obus ope a ion o he sys em.
III. SYSTEM CONTROL
A. Con ol objec i es
The main objec i e o his pape is he design o a g id
cu en con olle ha , in addi ion o ack a gi en e e ence
i∗, can e ec i ely damp he sys em esonance. In o de o do
so, his pape p oposes he equency shaping o wo closed
loop ans e unc ion, acking ans e unc ion T(s)and
closed-loop admi ance Y(s), which ela e he g id cu en
e e ence i∗and he PCC ol age s o he ob ained g id
cu en , espec i ely.
Fig. 1 shows, in g een, he in eg a ion o he p oposed
con olle Kin he sys em. I has h ee inpu s: he measu ed
PCC ol age s, he sensed g id cu en iand i s co esponding
e e ence i∗. E en hough he con olle is ob ained as a
MIMO sys em in he syn hesis p ocess, is in e es ing o di ide
i s ans e ma ix in ows: K(s)=[KsK e Ki]T. Con-
olle ac ua ion udynamic can be exp essed in he Laplace
domain as ollows:
U(s)=Ks(s)·Vs(s)+K e (s)·I∗(s)+Ki(s)·I(s).(4)
Subs i u ing exp essions (4), (2) and (3) in (1) gi es he closed
loop g id cu en dynamic in he Laplace domain:
I=(1−GKi)−1GK e
  
T(s)
I∗+(1−GKi)−1(Gd+GKs)
 
Y(s)
Vs,
(5)
whe e (s and-alone) sys em s abili y depends only on he
sys em open-loop ans e unc ion L=−GKi.
The con olle design ollows a model- e e ence app oach;
ha is, a con olle K(s)is ob ained in o de o make he
closed-loop ans e unc ions Y(s)and T(s) esemble wo
gi en model e e ences, Y e (s)and T e (s). By defining
a plain low admi ance e e ence a he sys em esonance
equency, oscilla ions can be e ec i ely damped and, as a
esul , de i ed s abili y p oblems a e a oided.
As i is shown in Fig. 1, g id cu en e e ence i∗is
gene a ed by an ou e loop powe con olle , whose objec i e
may be, o example, main ain he DC-bus ol age DC equal
o a gi en e e ence ∗
DC e en unde changes o he load RL
(i.e., he sys em ac s as an ac i e ec ifie ) [15]. I s design is
ou o he scope o his wo k, which is cen ed in he inne
cu en con olle design.
B. Con olle design
Con olle K(s)is ob ained h ough an H∞syn hesis
algo i hm, whose inpu is he gene alized plan P[16]. I is
jus a i ual MIMO plan wi h he s uc u e showed below:
z
z
z
=Pw
w
w
u
u
u,(6)
whe e w
w
wis called he exogenous inpu s ec o o he sys em,
z
z
zis he so-called ou pu e o signals, u
u
uis he ac ua ion
ec o ha will be compu ed o he con olle and
is he
measu emen s ou pu ec o .
H∞syn hesis p ocess will compu e a (sub)op imal con-
olle K, which minimizes he infini y no m1o he closed-
loop sys em N ha esul s om he eedback in e connec ion
o Pand K, and ela es exogenous inpu ec o w
w
wand e o
ec o z
z
z=Nw
w
w:
min
KN(K)∞=min
K
z
z
z2
w
w
w2
≤γ(7)
Fig. 2 shows he conside ed i ual plan P(in ed) used o
ob aining he con olle K(in blue) and he esul ing closed-
loop sys em N.Pis o med by he open-loop plan s Gand
Gd(in o ange) and a se o added elemen s only necessa y o
he syn hesis p ocess (in pu ple) which a e explained below.
T e (s)and Y e (s)a e he desi ed ( e e ence model) ack-
ing and admi ance ans e unc ions. Thei ou pu s, i and iy,
1The infini y no m o a MIMO sys em H(s)in he equency domain is
defined as H(s)∞
supω¯σ(H(jω)), whe e ¯σ(H(jω)) is he maximum
singula alue o H(jω). Fo SISO sys ems ha is simplified o H(s)∞

supω|H(jω)|
s
*
i
i
i
y
e
y
i
e
w
u
z
N
*
i
s
i
u
d
G
G
e
T
e
Y
u
W
W
y
W
P
K
i
s
*
i
u
s
Fig. 2. S uc u e used o he H∞syn hesis. In ed he gene alized plan
P(s). W apped inside o i , in o ange he open loop plan G(s)and open
loop admi ance Gd(s), and in pu ple he e e ences and weigh s added o
he syn hesis. Finally, he ob ained con olle is ep esen ed in g een.
ma k he e e ence cu en s due o acking and admi ance
con ol e ec s, espec i ely. G id cu en iis sub ac ed om
bo h e e ence cu en s, gi ing wo di e en e o s: e o
acking and ey o admi ance con ol. Bo h con olle objec-
i es (i.e., admi ance and acking shaping) can be achie ed
by means o minimizing hese wo e o s. Bu , as bo h e o s
depend on he g id cu en , hey can no minimized a he
same equencies (i.e., ican no be equal o bo h i and iy
a he same equency). Addi ionally, con ol bandwid h mus
be limi ed by means o con ol e o uminimiza ion. To
handle his ade-o , h ee equency-weigh s (W (s),Wy(s)
and Wu(s) espec i ely) mul iplies each signals. Ou pu and
inpu signal ec o s o gene alized plan Pdefined in Fig. 2
a e hen:
z
z
z=⎡
⎣
W ·e
Wy·ey
Wu·u
⎤
⎦
=⎡
⎣
s
i∗
i
⎤
⎦w
w
w= s
i∗u
u
u=u(8)
As syn hesized con olle Kshould minimize z
z
z, inc easing
one weigh a a gi en equency (while se ing he o he wo
ela i ely low) should esul in he minimiza ion o i s inpu a
ha equency. Following his design c i e ion, and gi en he
con olle objec i es s a ed in he p e ious subsec ion, sui able
equency-weigh s a e ep esen ed in Fig. 3. As i is shown,
acking o cu en e e ence i∗is only desi ed a he g id
undamen al equency, 60 Hz in his applica ion, meanwhile
admi ance shaping is desi ed, mainly, a supe -synch onous
equencies, which is he loca ion o he LCL-fil e esonance
(a sub-synch onous admi ance shaping is also conside ed o
damp possible low equency g id oscilla ion). Finally, con ol
bandwid h is limi ed a high equencies. Laplace exp essions
o he selec ed weigh s a e showed below:
W (s)=K
s2+2ζnω1s+ω2
1
s2+2ζdω1s+ω2
1
,(9)
whe e K is he ini ial acking gain, ω1is he undamen al
equency in ad/s and ζdand ζnwill define bo h maximum
102101100101102103104
100
50
0
50
100
Magni ude (dB)
Admi ance
shaping a ea Admi ance
shaping a ea
Re e ence
acking a ea
Con ol
s opband
F equency (Hz)
Fig. 3. Magni ude o he selec ed weigh s in he equency domain. The
equency spec um is di ided in a eas acco ding o he con olle objec i e
in ha ange.
)(
sW
)(
y
sW
)(
usW
)(
e
sT
)(
e
sY
)('sG
)(
dsG
)(zG
)(sG
()sK
()zK
syn hesis
()sP
1
)(()zz'
GzG
Disc e ize h ough
ZOH me hod
Add compu a ional
delay
Make con inuous
h ough Tus in
app oxima ion
Con inuous plan
wi h delay and
ZOH dynamics
sis
Disc e ize h ough
Tus in me hod
Con inuous open
loop model
C
o
n
i
n
u
o
u
s
o
p
e
n
l
o
o
p
m
o
d
e
l
Design
speci ica ions
Fig. 4. Flux diag am o he inne con olle Ksyn hesis and disc e iza ion
p ocess
gain peak and wid h o he weigh esonance;
Wy(s)=Ky
s2+2ζdω1s+ω2
1
s2+2ζnω1s+ω2
1
·1
(1/ωy)s+1 (10)
whe e an ini ial weigh Ky>K
is defined, ζdand ζnchange
posi ions o define a complemen a y no ch o he acking
weigh esonance and an addi ional pole is defined a high
equency ωy o delimi he admi ance shaping egion;
Wu(s)=Ku
(1/ωu1)s+1
(1/ωu2)s+1,(11)
whe e a ze o in he equency ωu1will inc ease he ini ial low
ac ua ion weigh Ku, and a pole a e y high equency ωu2
is added jus o ulfil H∞syn hesizing me hod equi emen s.
As o he e e ence model, a acking e e ence T e =1is
se , which will esul in pe ec cu en acking a undamen al
equency (i.e., I(jω1)≈I∗(jω1)), meanwhile a low esis i e
admi ance o Y e =0.1Ω
−1is conside ed, which will esul
in a p ope ly damped LCL esonance.
Syn hesized con olle K(s)is ob ained in Laplace con inu-
ous domain. In o de o be implemen ed in a digi al pla o m,
AC p og ammable
Powe supply
DSP-FPGA
Con ol pla o m
VSC
LCL l e
Fig. 5. Pic u e o expe imen al se -up.
TABLE I. EXPERIMENTAL SETUP PARAMETERS
Sn17.5kVA L13.4mH
Vg120 VR128.8mΩ
ω12π60 ads−1L21.7mH
V∗
DC 700 VR218.6mΩ
Tsw 400 μsC18 μF
Ts200 μsCDC 4.7mF
i mus be p e iously disc e ized. The disc e iza ion p ocess
is summed up in Fig. 4. I is impo an o poin ou ha
he ob ained con olle , and hen he close-loop admi ance,
akes in o accoun he phase lag in oduced by bo h PWM
modula ion and compu a ional delay. Fo mo e in o ma ion
abou he disc e iza ion p ocess o he admi ance and acking
shaping o powe con e e s e e o [17].
IV. RESULTS
P oposed algo i hm has been es ed in bo h simula ions
and an expe imen al se -up. The la e consis o an AC
p og ammable powe supply Pacific Sma Sou ce 345-AMX,
emula ing he g id, and a 17.5kVA wo-le el VSC connec ed
o i h ough an LCL fil e . Passi e loads RLa e connec ed
o he DC-side o es he pla o m unde di e en ope -
a ing poin s. Con ol algo i hm is implemen ed on a Texas
Ins umen s DSP TMS320DSK6713. Table I sums up se -up
pa ame e s, whe e Tsis he sampling pe iod o he con ol
algo i hm and Tsw is he con e e ’s IGBTs swi ching pe iod.
A pic u e o he expe imen al se -up is shown in Fig. 5.
A. F equency domain esul s
Fig. 6 shows heo e ical acking ans e unc ion T(ob-
ained ollowing (5)), which is equal o i s e e ence T e a
he undamen al equency, as was specified in he design p o-
cess. Fig. 7 shows he admi ance shaping esul s. Theo e ical
admi ance Yis equal o he gi en e e ence Y e a bo h
sub and supe -synch onous equencies as i was specified.
F equency (Hz)
M
agn
i
u
d
e
(dB)
100101102103
−10
−5
0
5
T e T
Fig. 6. Ob ained acking ans e unc ion Tand i s e e ence T e .
F equency (Hz)
−200
−150
−100
−50
0
Magni ude (dB)
Y e GdYYiden
Phase (deg)
100101102103
−180
−90
0
90
180
Fig. 7. Admi ance equency esul s. Open-loop admi ance Gdis shown in
black. Admi ance e e ence model Y e is shown on blue colo . The closed
loop syn hesised admi ance ( heo e ical) Yis shown on pu ple. Red c osses
show he expe imen ally measu ed admi ance Yiden .
Yiden is an expe imen al admi ance measu emen ob ained by
adding a h ee phase con olled sinusoidal signal o he ol age
gene a ed by he AC powe supply and analysing, in s eady-
s a e, he cu en esponse o he con e e a ha equency.
O main impo ance is he esonance equency o Gd, whe e
mo e poin s o Yiden a e aken, which p o es he good ac i e
damping capabili ies o he p oposed me hod.
B. Sys em obus ness
Fig. 8 shows he ob ained sys em sensi i i y unc ion S=
(1 −GKi)−1. I s infini y no m S∞is a good in e se
indica o o he design s and-alone obus ness [16], ha is,
how much plan pa ame e s may change un il he designed
sys em becomes uns able. A commonly design c i e ion o
obus con olle is o syn hesize loops wi h S∞<6dB,
which will assu e a gain ma gin bigge han 6dB and a phase
ma gin bigge han 30o. This c i e ion is ulfilled, as i can be
seen in Fig. 8, which p o es he design obus ness.
The e ec s o g id impedance on he p esen ed ac i e
damping echnique a e es ed below. Conside ing a non-ideal
induc ance Lga he PCC, he g id cu en is modified as
ollows:
I(s)=G(s)·U(s)+G
d(s)·Vg(s),(12)

F equency (Hz)
M
agn
i
u
d
e
(dB)
100101102103
−80
−60
−40
−20
0
20
S
Fig. 8. Ob ained sensi i i y unc ion S. Blue dash-do ed line ma ks he
accep ed 6dB sensi i i y gain limi o obus sys ems.
Lg(p.u)
F equency(Hz)
|Y|(-1)
Lg(p.u)
F equenc
y
(Hz)
Fig. 9. E ec o modi ying he g id induc ance Lgon he ob ained close
loop admi ance modulus |Y(s)|.
whe e Vg(s)=Vs(s)+(s·Lg)·I(s)and
G(s)=−Zc(s)
ZL1(s)·Zc(s)+Zg(s)·(ZL1(s)+Zc(s)),(13)
G
d(s)= ZL1(s)+Zc(s)
ZL1(s)·Zc(s)+Zg(s)·(ZL1(s)+Zc(s)) (14)
He e Zg(s)=s(Lg+L2)+R2is he new g id-side impedance.
Subs i u ing exp essions (4), (13) and (14) in (12) gi es he
new closed loop inpu admi ance Y(s)seen om he PCC:
Y(s)= I(s)
Vs(s)=G(s)·Ks(s)+G
d(s)
1−(G(s)·Ki(s)+s·Lg·Gd(s))
(15)
Fig. 9 shows closed loop inpu admi ance modulus |Y(s)|in
he equency domain unde changes o he g id induc ance
Lg∈[0.05,1] p.u 2. P esen ed damping echnique is e ec i e
e en unde high g id induc ances (i.e., weak g ids), as i
is shown in he minimum modulus inc ease o e he gi en
admi ance e e ence o 0.1Ω
−1.
C. Time domain esul s
Fig. 10 shows expe imen al ime domain e olu ion o he
sys em a e he in oduc ion o a DC-load o 4.2 kW. Fig.
2Lgis exp essed in pe uni alues o he con e e nominal impedance
Zn=(
√3Vg)2/Sn.
G id ol age
G id cu en
DC-bus ol .
Zoom 1
Zoom 1 Zoom 2
G id ol age G id ol age
G id cu en G id cu en
DC-bus ol . DC-bus ol .
+250V
-250V
+30A
-30A
+780V
+580V
+250V
-250V
+30A
-30A
+780V
+580V
+250V
-250V
+30A
-30A
+780V
+580V
5ms/di 50ms/di
0ms
-5000ms
-3165ms-3215ms-3390ms-3890ms
Zoom 2
Fig. 10. Connec ion o a 4.2kW DC-load wi h a null eac i e e e ence. Top
shows he comple e ansien . Zoom 1 ocuses on he cu en s and DC- ol age
e olu ion a e he connec ion. Zoom 2 shows g id cu en s and ol ages in
s eady-s a e.
G id ol age
G id cu en
DC-bus ol .
Zoom 1
Zoom 1
+250V
-250V
+60A
-60A
+720V
+680V
+250V
-250V
+60A
-60A
+720V
+680V
20ms/di
-790000us
-1290000us
-1084000ms
G id ol age
G id cu en
DC-bus ol .
50ms/di
-1284000us
Fig. 11. Response unde g id balanced ol age dip when DC-bus is loaded
wi h 4.2kW. All phases all o 60% o i s alue keeping hei phase un ouched.
Top iew shows he comple e ansien in g id ol ages, cu en s and DC-bus
ol age. Lowe iew ocuses on he dip ini ial edge.
11 shows he esponse o he sys em unde a balanced dip
o 60% o he nominal g id ol age alue. Bo h expe imen s
show good cu en acking pe o mance. O main impo ance
is he cu en esponse unde he g id dip: as can be seen, no
oscilla ion a equency ω es can be app ecia ed on i , which
p o es again he good ob ained esonance damping.
V. CONCLUSION
This wo k p esen s a no el ac i e damping echnique o
cu en -con olled g id-connec ed powe con e e s h ough
esonance fil e s like he LCL. Resonance damping will esul
in smalle cu en oscilla ions unde PCC ol age a ia ions
and, as a consequence, will imp o e sys em s abili y in con-
nec ion o weak g ids.
P esen ed ac i e damping echnique is based on equency
shaping o he closed-loop inpu admi ance o he conside ed
applica ion, and only needs g id cu en and g id ol age mea-
su emen s (i.e., no addi ional LCL fil e senso s a e needed).
This is achie ed by a model- e e ence app oach, whe e, a e
designe specifies a desi ed admi ance e e ence, an H∞
syn hesis algo i hm will ob ain he (sub)-op imal con olle
ha shapes he sys em admi ance, in he equency domain, o
ollow he gi en e e ence. By defining a esis i e admi ance
e e ence he esonance can be e ec i ely damped, and ela ed
s abili y p oblems a e a oided. Cu en con ol design o
achie e his goal is explained.
Expe imen al es o he ob ained con olle a e done and
hei esul s a e shown. P oposed me hod shows good cu en
acking and esonance damping capabili ies. The la e is
p o ed expe imen ally in bo h equency and ime domains.
Mo eo e , damping echnique is demons a ed ( heo e ically)
e ec i e e en unde ex emely high g id impedance, wi h bo h
good phase and gain ma gins.
Fu u e wo ks will s udy he esonance damping and s abili y
obus ness unde fil e and g id modelling unce ain ies, and
how hey a e a ec ed by he addi ion o di e en con ol
measu emen s (like fil e capaci o ol age o con e e side
cu en ).
ACKNOWLEDGEMENT
This wo k o he Uni e si y o Alcala g oup was sup-
po ed in pa by he spanish esea ch p ojec s CONPOSITE
(ENE2014-57760-C2-2-R Minis e io de Economía y Com-
pe i i idad) and PRICAM (S2013/ICE-2933 Conseje ía de
educación, ju en ud y depo e de la Comunidad de Mad id).
The wo k o Robe G iñó was suppo ed in pa by he
Spanish Resea ch P ojec DPI2013-41224-P.
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