Vol age Balancing Me hod o a Se en-Le el
S acked Mul icell Con e e Using Reduced
Swi ching T ansi ions
Ame M. Y. M. Ghias(1) Josep Pou(1)(2) Vassilios G. Agelidis(1) Mihai Ciobo a u(1)
(1)Aus alian Ene gy Resea ch Ins i u e & School o Elec ical Enginee ing and Telecommunica ions,
The Uni e si y o New Sou h Wales, UNSW Sydney, NSW 2052, Aus alia.
(2)Te assa Indus ial Elec onics G oup & Depa men o Elec onic Enginee ing,
Technical Uni e si y o Ca alonia, Ca alonia, Spain.
Email: ame [email p o ec ed].edu.au.
Abs ac —This pape p oposes a ol age balancing me hod o
a se en-le el s acked mul icell con e e (SMC) based on phase
disposi ion pulse-wid h modula ion (PD-PWM) using educed
swi ching ansi ions. This me hod is called op imal- ansi ion
ol age balancing me hod. The selec ion o he op imal ansi ion
sequence is pe o med by minimizing a cos unc ion and he
ansi ions ha would esul in mo e swi chings o he con e e
semiconduc o de ices a e a oided. The simula ion esul s show
a significan educ ion o he a e age swi ching equency as
compa ed o he use o he op imal-s a e ol age balancing
me hod, while main aining he balance o he FC ol ages.
Mo eo e , he p oposed PD-PWM ol age balancing me hod is
obus o unbalanced linea loads, non-linea loads and ansien s.
Index Te ms—Mul ile el con e e ; S acked mul icell con-
e e ; Capaci o ol age balancing; Pulse-wid h modula ion.
I. INTRODUCTION
In he ecen yea s, hyb id mul ile el con e e s ha e been
in oduced and a e conside ed compe i i e solu ions in high-
powe applica ions [1]. They equi e o s o e less ene gy
han he popula mul ile el opologies, i.e. he cascaded
mul i-modula con e e [2], he modula mul ile el con e e
(MMC) [3], he diode-clamped con e e (DCC) [4], and
he flying capaci o (FC) con e e [5]. Hyb id mul ile el
con e e s allow o highe ol age/powe a ings, lowe o al
ha monic dis o ion (THD), and lowe powe losses, when
compa ed wi h he con en ional wo-le el con e e [6], [7]
and also wi h some o he popula mul ile el opologies. Fig.
1 shows he s acked mul icell con e e (SMC) which is a
hyb id mul ile el opology. The SMC is capable o p o iding
a highe numbe o ol age le els wi h educed FCs han he
con en ional mul ile el FC con e e .
Like in he o he mul ile el opologies, his newly hyb id
mul ile el con e e also equi es capaci o ol age balancing
o he accep able pe o mance o he con e e . In [9]–[15]
phase-shi ed pulse wid h modula ion (PS-PWM) was applied
o he SMC, which p o ides na u al ol age balancing. How-
e e , na u al ol age balance depends on he load condi ions
and he dynamics slow down wi h di e en ypes o loads,
specially non-linea loads. Some e e ences in [9]–[12] used
a boos e o achie e as e ol age balancing dynamics. This
balance boos e consis s o a passi e RLC fil e and hus
in oduces some powe losses and makes he o e all con e e
la ge.
The e a e a ew ac i e ol age balancing me hods ound
in he echnical li e a u e [16]–[18]. In [16], a di ec o que
con ol me hod was p oposed. This me hod egula es he FC
ol age; howe e , no line- o-line ol age is shown and analyzed
in he pape . Ano he me hod was p oposed in [17] which
uses a sliding mode obse e . This me hod pe o ms e y
well and does no equi e any ol age senso s. Howe e , he
me hod i sel is complica ed and equi es a lo o compu a ions.
Finally, an ac i e ol age balancing me hod was p oposed in
[16] o hyb id con e e s such as he ac i e neu al-poin -
clamped (ANPC) con e e and he SMC. The me hod equi es
e alua ion o a cos unc ion o he selec ion o he edundan
s a es using space ec o modula ion (SVM) in a ou -le el
SMC. The au ho s sugges ed inc easing he numbe o ol age
le els o ex end he ope a ing ange o he con e e , which is
appa en ly no an op imal solu ion.
The solu ions discussed abo e do no analyze he e ec o
he ol age balancing p ocess on he swi ching equencies in
he powe de ices o he SMC. This pape p esen s a capaci o
ol age balancing me hod ha uses educed swi ching ansi-
ions. Phase-disposi ion pulse-wid h modula ion (PD-PWM) is
applied and ol age balance is pe o med by a p ope selec ion
o he swi ching ansi ions by using a cos unc ion. The
swi ching equencies o he powe de ices a e compa ed o he
op imal-s a e ol age balancing (OSVB) me hod [19], which
is based on op imizing he swi ching s a es independen ly and
i does no a oid he non-op imal swi ching ansi ions. The
modula ion me hod p oposed in his pape selec s he minimum
ansi ions be ween consecu i e s a es. I is he e o e called
op imal- ansi ion ol age balancing (OTVB) me hod. The
analysis shows ha by using he OTVB me hod, a significan
educ ion in he swi ching equencies can be achie ed as
compa ed o OSVB. The ol age ipples in he FCs a e also
0
x
12
x
C
11
x
C
22
x
C
21
x
C
1
C
2
C
2
dc
V
Cell1
Cell2
Cell3( )Y
11
x
s
11
x
s
12
x
s
12
x
s
22
x
s
22
x
s
21
x
s
21
x
s
32
x
s
32
x
s
31
x
s
31
x
s
x
i
21Cx
11Cx
22Cx
12Cx
2
dc
V
S age1
S age2( )Z
Fig. 1. Ci cui diag am o a 3×2SMC.
analyzed o he wo ol age balancing me hods.
The es o he pape is o ganized as ollows. Sec ion II
desc ibes he ope a ing p inciple o a se en-le el SMC and
he OSVB me hod. Sec ion III in oduces he OTVB me hod
o educing he swi ching equencies in he powe de ices.
Sec ion IV p esen s selec ed simula ion esul s o e i y he
e ec i eness o he p oposed ol age balancing me hod on a
se en-le el SMC. Also, swi ching equencies on he powe
de ices and capaci o ol age ipples a e compa ed wi h hose
p oduced by he OSVB me hod. Finally, he conclusions a e
summa ized in Sec ion V.
II. OPERATING PRINCIPLE OF THE SMC CONVERTER
Fig. 1 shows a ci cui diag am o a phase-leg o a se en-
le el SMC. I consis s o h ee cells (Y=3)o FC con e e ,
which a e in eg a ed o o m wo s ages/s acks (Z=2).I
is a 3x2 SMC opology. The con e e comp ises ou FCs,
he uppe FCs Cx12 and Cx22, a e in he S age 2, while
he lowe FCs Cx11,Cx21 a e in he S age 1, whe e he
subsc ip xis used o phase iden ifica ion x={a, b, c}. The
dc bus consis s o wo capaci o s C1and C2, each o hem is
egula ed o ope a e a a hal o he dc-link ol age (Vdc/2).
Du ing no mal ope a ion, he mean ol age o he FCs Cx11
and Cx12 has o be main ained a Vdc/6, whe eas i has o be
main ained a Vdc/3 o he FCs Cx21 and Cx22. The ou pu
ol age x0consis s o se en (3 ×2+1) ol age le els, i.e. 0,
Vdc/6,Vdc/3,Vdc/2,2Vdc/3,5Vdc/6,Vdc. The swi ch con ol
unc ion is defined as sxyz, whe e ydeno es he swi ch numbe
co esponding o a pa icula cell in he phase-leg xo he
SMC con e e y={1, ..., Y }(Y=3), and zdefines he
S age z={1, ..., Z}(Z=2). The swi ch con ol unc ions
can ake wo alues sxyz ={0,1}, meaning “0” and “1” ha
he swi ch is o and on, espec i ely. The swi ch pai s in each
phase leg (sxyz and sxyz) ope a e in a complemen a y manne .
The OSVB me hod is based on minimizing a cos unc ion
o he S age z, which is gi en as ollows [18]–[20]:
Jxs z =1
2
Y−1
j=1
Cxjz( Cxjz −V∗
Cxjz)2,(1)
whe e xiden ifies he phase, and sis he swi ching s a e
s={0, .., 7}o s age z. Fo example, Ja12 is he cos unc ion
calcula ed o phase a(x=a), a S age 2 (z=2)and
Swi ching S a e 1 (s=1), i.e. sa32 =0,sa22 =0, and
sa12 =1.jis he index used o he iden ifica ion o each FC
j={1,2}, being Cxjz a pa icula FC and V∗
Cxjz i s e e ence
ol age.
The cos unc ion in (1) is posi i ely defined and i be-
comes ze o i all he FC ol ages a e a he e e ence alues.
The e o e, he cos unc ion in (1) should be minimized. The
minimiza ion p ocess can be pe o med using a di e en ia ing
me hod, which is gi en as:
d
d Jxs z =d
d
1
2
Y−1
j=1
Cxjz( Cxjz −V∗
Cxjz)2
=
Y−1
j=1
(Δ CxjziCxjz)≤0,
(2)
whe e Δ Cxjz is he ol age de ia ion o a FC (Δ Cxjz =
Cxjz −V∗
Cxjz), and iCxjz is he cu en in each FC, which
depends on he selec ed edundan swi ching s a e and load
cu en , as shown in Table I. When he modula o defines wo
pa icula ol age le els o he ollowing swi ching pe iod a
S age z, he cos unc ion is e alua ed o all edundan swi ch-
ing s a es a ailable o hose le els. Based on he calcula ed
alues, he swi ching s a es ha p o ide he minimum alue
o he cos unc ion a e he ones selec ed and a e used o he
ga ing signals.
I should be no ed ha he op imal swi ching s a es be ween
wo consecu i e ol age le els a e selec ed independen ly one
om ano he . The OSVB me hod does no a oid he non-
op imal ansi ions, i.e. hose ansi ions ha p oduce mo e
swi ching e en s, hus esul ing in highe swi ching equencies
o he powe de ices. The OTVB p oposed in his pape
o e comes his p oblem because i a oids he use o non-
op imal ansi ions.
III. PROPOSED VOLTAGE BALANCING METHOD
The swi ching ansi ions be ween consecu i e ol age le els
o all he possible combina ions o swi ching s a es om
000{0} o 111{7}a e shown in Fig. 2. The ansi ions be ween
wo swi ching s a es shown by solid lines a e called op imum
ansi ions, as hose ansi ions in ol e changing only one bi .
The e o e, hey p oduce he minimum numbe o swi ching
e en s. On he o he hand, he ansi ions ep esen ed by
dashed lines a e non-op imal, as mo e han one bi changes
in he ansi ion be ween consecu i e le els. Fo example, a
minimum ansi ion is p oduced when swi ching be ween he
S a es 001{1}and 101{5}(see Fig. 2), while he ansi ion
be ween he S a es 001{1}and 110{6}is a non-op imal one.
Hence, i he non-op imal ansi ions a e chosen, he swi ch-
ing equencies o he powe de ices inc ease. Addi ional
swi ching e en s can be p oduced due o he ansi ions wi hin
he same ol age le el. Ne e heless, hose ansi ions can be
a oided by using saw oo h ca ie s [20].
000 {0}
x0= 0
001 {1}
111 {7}
x0= Vdc/6 x0= Vdc/3 x0= Vdc/2
Non-op imal ansi ions
01 0{2}
1 0 0 {4}
0 1 1 {3}
1 0 1 {5}
1 1 0 {6}
Fig. 2. Swi ching ansi ions be ween consecu i e ol age le els o he S age z.
TABLE I
3×2SMC CONVERTER:VOLTAGE LEVELS,SWITCHING STATES,FC
CURRENTS,AND EFFECTSONTHEFC VOLTAGES
Ou pu Swi ching S a es FC Cu en s FC ol ages
Vol age
Le el ( x0)sx3zsx2zsx1zs .#iCx2ziCx1z Cx2z Cx1z
4Vdc
2111{7}0 0 x x
3Vdc
3
110{6}0ixx↑
101{5}ix-ix↑ ↓
011{3}-ix0↓x
2Vdc
6
100{4}ix0↑x
010{2}-ixix↓ ↑
001{1}0 -ixx↓
1 0 0 0 0 {0}0 0 x x
No e: The cha ging/discha ging e ec s in he FC a e gi en
assuming ha ixis posi i e (ix>0) wi h he ollowing
no a ion:
↑Capaci o ol age inc eases
↓Capaci o ol age dec eases
x No change in he capaci o ol age
Mo eo e , he swi ching equencies o he powe de ices
can be u he educed by a oiding he non-op imal ansi-
ions be ween consecu i e le els. Howe e , a oiding he non-
op imal ansi ions will wo sen he FC ol age balance. This
e ec is shown in he example in Table II, whe e h ee cases
a e gi en. In he Case I, he con e e is swi ching om S a e
001{1} o S a e 011{3}, and in Case II he swi ching is om
S a e 001{1} o S a e 101{5}. Bo h CasesI&IIa eop imal
ansi ions, howe e none o he final s a es p o ide op imum
ol age balance, since he ol age in one o he FCs inc eases
and ends o go a beyond he e e ence alue (capaci o s
Cx2zand Cx1zin he Cases I and II, espec i ely). On he
o he hand, in he Case III he swi ching ansi ion is om S a e
001{1} o S a e 110{6}, which is a non-op imal one. Howe e ,
he S a e 110{6}is he bes om he poin o iew o ol age
balancing, since none o he ol ages in he FCs de ia es
u he om he e e ence alues. The e o e, i his s a e is
TABLE II
CASE STUDY OF OSVB METHOD
iz s
dT
*
1
6
dc
Cx z
V
V
iz s
dT
*
2
3
dc
Cx z
V
V
Case I
Non op imal
ansi ion
**
112 2
,, ,0
CxzCxzCxzCxzx
Assump ion V V i!!!
0
6
dc
x
V
0
3
dc
x
V
0 0 1 {1}
0 1 0 {2}
1 0 0 {4}
0 1 1 {3}
1 0 1 {5}
1 1 0 {6}
2Cx z
1Cx z
iz s
dT
iz s
dT
Case II
0
6
dc
x
V
0
3
dc
x
V
**
112 2
,, ,0
Cx z Cx z Cx z Cx z x
Assump ion V V i!!!
0 0 1 {1}
0 1 0 {2}
1 0 0 {4}
0 1 1 {3}
1 0 1 {5}
1 1 0 {6}
*
1
6
dc
Cx z
V
V
*
2
3
dc
Cx z
V
V
2Cx z
1Cx z
Non op imal
ansi ion
iz s
dT
iz s
dT
Case III
0
6
dc
x
V
0
3
dc
x
V
**
112 2
,, ,0
Cx z Cx z Cx z Cx z x
Assump ion V V i!!!
0 0 1 {1}
0 1 0 {2}
1 0 0 {4}
0 1 1 {3}
1 0 1 {5}
1 1 0 {6}
*
1
6
dc
Cx z
V
V
*
2
3
dc
Cx z
V
V
2Cx z
1Cx z
Non op imal
ansi ion
a oided because i p oduces addi ional swi ching ansi ions,
and ei he o he wo s a es in Case I o II a e chosen, he
ol age balancing will be less e ec i e. This can be pa ially
compensa ed by using a modula ion me hod ha chooses he
op imal sequence conside ing he wo s a es simul aneously,
and no only he op imal s a es sepa a ely. As a esul , he FC
ol age balance will imp o e.
The cos unc ion in [18], [20] is modified o selec he
ime
Le el 0
Le el 1
Le el 1i
Le el i
Le el 1i
Le el 2n
Le el 1n
0
1
21
1
i
n
21
1
i
n
1
21
1
i
n
+1
-1
3
Le el 2
n
1
Le el 2
n
1
Le el 2
n
Fig. 3. Ca ie s in PD-PWM.
Calcula ion o
Du y Cycle
Selec he
Swi ching
T ansi ion wi h
Minimum Cos
Func ion Value
o S age 1
Gene a ion
o
Ga ing
Signals
22x
s
32x
s
11x
s
21x
s
31x
s
12x
s
Modula ion
Signal ( )
mx
Du y Cycles
Measu ed FC
Vol ages in S age 1
Measu ed
Load Cu en
11
x
s
21
x
s
Selec he
Swi ching
T ansi ion wi h
Minimum Cos
Func ion Value
o S age 2
Measu ed FC
Vol ages in S age 2
Measu ed
Load Cu en
12
x
s
22x
s
32
x
s
31
x
s
Ca ie in S age 2
Ca ie in S age 1
Fig. 4. Block diag am o he p oposed OTVB me hod.
swi ching ansi ions be ween wo s a es o di e en ol age
le els and is gi en as:
Jxi z−i+1 z=Jx,i zdiz +Jx,i+1 zdi+1 z,(3)
whe e xiden ifies he phase (x={a, b, c}),iis he fi s s a e,
i+1is he second s a e, diz [0,1] is he du y cycle o he
fi s s a e o he S age z, and di+1 z[0,1] is he du y cycle o
he second s a e o he S age z. As shown in Fig. 3, he du y
cycle o an ou pu ol age le el o he S age zusing PD-PWM
can be ob ained as ollows:
o 2 i
n−1−1≤ mx ≤2i+1
n−1−1:
diz =(i+1)−(n−1) mx +1
2,
(4)
and o 2 i−1
n−1−1≤ mx ≤2i
n−1−1:
diz =(n−1) mx +1
2−(i−1),
(5)
whe e nis he numbe o le el and mx is he modula ion
signal ha anges in he in e al [-1,1] unde linea ope a ion
mode. When mx is posi i e z=2, o he wise, z=1. The
cos unc ion o he ansi ions be ween wo di e en ol age
le els is posi i ely defined, and i all he FC ol ages a e
egula ed a hei e e ence alue, i becomes ze o. Hence, in
o de o achie e ol age balance, his cos unc ion needs o be
minimized a any swi ching pe iod using di e en ia ion. Thus,
di e en ia ing (3), he ollowing exp ession is ob ained:
d
d jxi z−i+1 z=
Y−1
j=1
Δ Cxjz(iCxjz,idiz +iCxjz,i+1di+1 z)≤0,
(6)
whe e iCxjz,i and iCxjz,i+1 a e he capaci o cu en s o he
co esponding s a es o he S age z. They depend on he
load cu en s and he edundan swi ching s a es, as shown
in Table I. Δ Cxjz a e he ol age de ia ions o he FCs
(Δ Cxjz = Cxjz −V∗
Cxjz).
When he modula o defines wo pa icula ol age le els
o he ollowing swi ching pe iod a he S age z, he cos
unc ion is e alua ed o all he edundan op imum swi ching
ansi ions a ailable o hose le els. Based on he calcula ed
alues, he swi ching ansi ion ha p o ides he minimum
alue o he cos unc ion is selec ed. In o de o a oid
addi ional swi ching e en s, all he non-op imal ansi ions
a e dis ega ded in he selec ion p ocess. Once he op imal
swi ching ansi ion is selec ed, he wo consecu i e swi ching
s a es a e de e mined, which define he ga ing signals o he
SMC. Fig. 4, shows a block diag am o he implemen a ion
o he p oposed ol age balance me hod.
IV. PERFORMANCE EVALUATION
In his sec ion, he p oposed ol age balancing me hod is
applied o a se en-le el SMC in MATLAB/Simulink [21]
using PLECS Blockse [22]. In he simula ions, he dc ol age
is Vdc = 100Vand a linea RL Y-connec ed load (R=
44Ω,L =6mH)is connec ed o he con e e ou pu . The
alue o he FCs is C= 400μF. The undamen al and he
ca ie equencies a e =50Hz and s=2kHz espec i ely.
The con e e is es ed wi h unbalanced load, non-linea load
and unde ansien s.
The dynamic beha io o he p oposed ol age balancing
me hod is shown in Fig. 5. In his es , an unbalanced condi ion
is in oduced in he linea RL load (Ra=8.8Ω,R
b=
79.2Ω,R
c= 44Ω). The line- o-line ol age ab and he capac-
i o ol ages ( Ca 11, Cb12, Cb 21, and Cb22) a e shown in
Fig. 5(a). In he simula ion, he ini ial capaci o ol ages we e
VCa11 =4V, VCa 12 =22V, VCb 21 =26V, VCb22 =50V
and egula ed o he desi ed ol ages, i.e. 16.67 V, 16.67 V,
33.33 V, and 33.33V espec i ely. One can obse e ha he
capaci o ol ages each hei nominal alues in abou 20 ms.
Once in he s eady-s a e condi ion, he modula ion index m
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.240.24
-100
-50
0
50
100
Time (s)
Vol age (V)
ab
Ca11
Ca12
Ca21
Ca22
(a)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.240.24
-4
-2
0
2
4
Time (s)
Cu en (A)
ia
ib
ic
(b)
Fig. 5. The SMC is ope a ed using he p oposed OTVB me hod unde unbalanced linea load. A s ep change in he modula ion index om m=0.4 o m=0.9
occu s a 80ms and a 160ms a non-linea load is added: (a) line- o-line ol age ( ab) and FC ol ages ( Ca11,
Ca12,
Ca21,and Ca22)(b) ou pu cu en s
(ia,i
b,and ic).
Fig. 6. Swi ching equency o he powe de ices using he OTVB me hod.
Fig. 7. Swi ching equency a io (OTVB/OSVB) o he powe de ices.
Fig. 8. FC ol age ipples a io OTVB/OSVB.
changes om 0.4 o 0.9. a 80 ms, and la e a 160 ms a non-
linea load consis ing o a h ee-phase diode ec ifie wi h a
dc-side load made o a capaci o and a esis o o 30μF and
88Ω, espec i ely, is added. I should be no ed ha du ing
hese ansien s he capaci o ol ages o he SMC a e no
a ec ed. Hence, he p oposed ol age balance me hod p o es
o be obus no only unde s eady-s a e ope a ing condi ions
wi h unbalanced and non-linea load bu also unde ansien s.
Fig. 6 shows he a e age swi ching equency o he powe
de ices using he OTVB me hod. All possible ela i e cu en
phase angles and modula ion indices ha e been conside ed.
In o de o achie e he maximum ampli udes o he ou pu
ol age undamen als unde linea mode, a ze o sequence has
been added o he modula ion signals o he con e e . The ze o
sequence is gi en by -( mx max+ mx min)/2, whe e mx max
and mx min a e he maximum and minimum alues o he
modula ion signals o he con e e , espec i ely. As i can
be no iced in Fig. 6, he ou pu cu en phase angle does no
significan ly a ec he swi ching equency.
Fig. 7 shows he swi ching equency a io o bo h ol age
balancing s a egies, i.e. OTVB o e OSVB, o all modula ion
indices and load powe ac o s. I can be ema ked ha wi h he
OTVB me hod he e is a educ ion o he swi ching equency
o abou 5%on a e age o high modula ion indices. Such a
educ ion in he swi ching equency is significan ly la ge o
low modula ion indices.
Fig. 8 shows he FC ol age ipples a io OTVB o e OSVB.
I can be no ed ha wi h he OTVB me hod he e is an inc ease
in he ol age ipples o abou 50%on a e age o high
modula ion indices. Such an inc ease in he ol age ipples
becomes smalle o low modula ion indices.
In summa y, using he OTVB me hod a educ ion o abou
5%o he swi ching equencies in he powe de ices o
high modula ion indices can be achie ed a he expense o
inc easing he FC ol age ipples.
V. CONCLUSION
This pape has p esen ed a ol age balancing me hod o a
se en-le el SMC using a educed swi ching ansi ion. This
me hod is based on calcula ing a cos unc ion conside ing he
FC ol age de ia ions and he ou pu cu en s. The p oposed
cos unc ion e alua es minimum swi ching ansi ions, i.e.
he wo consecu i e s a es be ween consecu i e ol age le els.
Only he minimum swi ching ansi ions a e e alua ed and
he one ha gi es he lowe alue o he cos unc ion is
selec ed. The p oposed me hod has been implemen ed in a
se en-le el SMC and es ed agains unbalanced loads, non-
linea loads and ansien s. I pe o ms e y well in egula ing
he FC ol ages o he desi ed le els. The esul s ha e been
compa ed wi h a modula ion me hod ha does no a oid non-
op imal ansi ions and op imizes swi ching s a es ins ead o
ansi ions, i.e. OSVB. Simula ion esul s ha e been p esen ed
ha show ha o high modula ion indices, he a e age swi ch-
ing equencies o he de ices a e educed by abou 5% when
using he p oposed OTVB me hod. This educ ion comes a
he cos o inc easing he FC ol age ipples. Hence, he e is a
adeo be ween swi ching equency educ ion and inc eased
FC ol age ipples.
ACKNOWLEDGMENT
This wo k has been suppo ed by he Uni e si y o New
Sou h Wales, Aus alia Ene gy Resea ch Ins i u e and he
School o Elec ical enginee ing and Telecommunica ions.
I has also been suppo ed by he Minis e io de Economia y
Compe i i idad o Spain unde p ojec ENE2012-36871-C02-
01.
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