ene gies
A icle
New Modula ion Technique o Mi iga e Common
Mode Vol age E ec s in S a -Connec ed Fi e-Phase
AC D i es
Ma kel Fe nandez 1,∗, And es Sie a-Gonzalez 2, Endika Robles 1, Iñigo Ko aba ia 1,
Edo a Iba a 1and Jose Luis Ma in 1
1De pa men o Elec onic Technology, Uni e si y o he Basque Coun y (UPV/EHU), Plaza Ingenie o
To es Que edo 1, 48013 Bilbao, Spain; [email p o ec ed] (E.R.); [email p o ec ed] (I.K.);
[email p o ec ed] (E.I.); [email p o ec ed] (J.L.M.)
2Tecnalia Resea ch and Inno a ion, C. Mikele egi 7, 20009 Donos ia, Spain; [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 29 No embe 2019; Accep ed: 29 Janua y 2020; Published: 31 Janua y 2020
Abs ac :
S a -connec ed mul iphase AC d i es a e being conside ed o elec omo ili y applica ions
such as elec omechanical ac ua o s (EMA), whe e high powe densi y and aul ole ance is
demanded. As o h ee-phase sys ems, common-mode ol age (CMV) is an issue o mul iphase
d i es. CMV leads o sha ol ages be ween o o and s a o windings, gene a ing bea ing
cu en s which accele a e bea ing deg ada ion and p oduce high elec omagne ic in e e ences
(EMI). CMV e ec s can be mi iga ed by using app op ia e modula ion echniques. Thus, his wo k
p oposes a new Hyb id PWM algo i hm ha e ec i ely educes CMV in i e-phase AC elec ic d i es,
imp o ing hei eliabili y. All he ma hema ical backg ound equi ed o unde s and he p oposal,
i.e., ec o ans o ma ions, ec o sequences and calcula ion o analy ical exp essions o du y
cycle de e mina ion a e de ailed. Addi ionally, p ac ical de ails ha simpli y he implemen a ion
o he p oposal in an FPGA a e also included. This echnique, HAZSL5M5-PWM, ex ends he
linea ange o he AZSL5M5-PWM modula ion, p o iding a ull linea ange. Simula ion esul s
ob ained in an accu a e mul iphase EMA model a e p o ided, showing he alidi y o he p oposed
modula ion app oach.
Keywo ds: mul iphase elec ic d i es; CMV; modula ion echniques; PWM
1. In oduc ion
AC elec ic d i es a e used in a wide a ie y o indus ial applica ions such as in comp esso s [
1
],
in elec ic ehicle p opulsion sys ems [
2
,
3
] and in mo e elec ic ai c a (MEA) [
4
], among o he s.
Al hough h ee-phase sys ems domina e he AC d i e ma ke , mul iphase solu ions a e gaining
popula i y [
5
–
7
]. Mul iphase sys ems a e p e e able o applica ions whe e high aul ole ance is
equi ed [
8
], such as o MEA applica ions, whe e elec omechanical ac ua o s (EMA) o con ol
su aces, uel pumps, landing gea s, en i onmen al con ol sys ems and s a e -gene a o s need o
be ope a ed [
9
–
11
]. Apa om hei in insic aul ole ance, o he bene i s o mul iphase d i es
include a educed cu en pe phase ( educing coppe losses and inc easing e iciency) [
4
], noise
and elec omagne ic in e e ence (EMI) minimiza ion [
12
,
13
], highe powe densi y and lowe o que
ipple [
14
], making hem a ac i e o anspo elec i ica ion. Among he mul iphase opologies
a ailable in he scien i ic li e a u e, s a -connec ed i e-phase echnologies (Figu e 1) can be highligh ed,
as hey p o ide a good ade-o be ween sys em complexi y and aul ole ance [
15
,
16
]. Speci ically,
mul iphase pe manen magne synch onous machines (PMSM) a e being conside ed o ai c a s due
o hei supe io powe densi y [17,18].
Ene gies 2020,13, 607; doi:10.3390/en13030607 www.mdpi.com/jou nal/ene gies
Ene gies 2020,13, 607 2 o 19
In gene al, AC elec ic d i es can expe ience issues due o he common-mode ol age (CMV) [
19
]
and common mode cu en s (CMC) [
20
]. CMV a ia ions a e gene a ed by he commu a ion o he
powe con e e de ices, p oducing EMI [
21
] and bea ing cu en s ha can comp omise he in eg i y
o he elec ic machine [
22
]. Such ol age a ia ions c ea e new capaci i e pa hs h ough he mo o
bea ings, leading o p ema u e aging. Capaci i e cu en s, elec os a ic discha ge machine (EDM)
cu en s, ci cula ing cu en s and o o - o-g ound cu en s can low h ough he bea ings [
23
,
24
]
(Figu e 2), and hei ha m ul e ec s depend on he ype o bea ing, size o he machine and how he
machine is used.
e
d
c
0
b
a
VCM
n
Vdc
Z
Figu e 1. CMV in a i e-phase powe sys em.
CMV
d /d a
mo o e minals
CMV mi o ed
o e he bea ings
Common Mode
Cu en s
Ci cula ing
cu en s
Sha ol age
EDM
cu en s
Capaci i e
cu en s
Ro o o g ound
cu en s
Figu e 2. Cause-and-e ec chain o common mode ol age (CMV) (adap ed om [25]).
Ope a ing a highe swi ching equencies can en ail mo e se e e CMV ela ed issues (addi ional
EMI gene a ion and la ge numbe o d /d ) [
26
]. As conside able e o s a e being ca ied ou
o widesp ead he usage o wide bandgap (WBG) de ices in AC d i es, much highe swi ching
equencies a e expec ed in he u u e, making he in es iga ion on CMV mi iga ion a popula
opic [
13
,
19
,
20
]. Thus, a wide a ie y o solu ions ha e been p oposed in he li e a u e. Such solu ions
can be classi ied as passi e o ac i e. Passi e solu ions a e hose which mi iga e o elimina e he
ha m ul e ec s gene a ed by CMV, while ac i e solu ions a e in ended o educe o o ally a oid CMV
gene a ion. Among passi e solu ions, Fa aday shielding [
27
,
28
], ce amic and hyb id bea ings [
22
,
29
],
shielded cables [
23
,
30
] and sha g ounding ings [
27
,
31
] can be highligh ed. On he o he hand,
modula ion echniques and new in e e opologies such as mul ile el in e e s [
32
], single-phase
ans o me less in e e s [
33
,
34
] and h ee-phase in e e s [
35
] among o he s [
36
] a e he mos common
ac i e solu ions. Among all hese solu ions, modula ion algo i hms can be conside ed o CMV
educ ion in s a -connec ed i e-phase AC d i es due o hei ease o implemen a ion, low cos ,
and because no addi ional ha dwa e is needed.
Ene gies 2020,13, 607 3 o 19
In [
37
], he au ho s ini ially p oposed a CMV educ ion modula ion echnique o i e-phase
in e e s, named AZSL5M5-PWM. Howe e , he p oposal has been only conside ed o passi e
loads (s a -connec ed
RL
loads) and solely alida ed in open-loop. F om he ob ained esul s, i has
been concluded ha he linea ange o he o iginal AZSL5M5-PWM is limi ed, which can p e en
he u iliza ion o his echnique in elec ic d i es whe e ope a ion close o he base speed (wi hou
en e ing in ield weakening egion) is desi able, as is he case in mos EMA sys ems. Thus, a hyb id
AZSL5M5-PWM echnique (HAZSL5M5-PWM) ha p o ides he same linea ange as con en ional
space ec o PWM (SV-PWM) is p oposed in his wo k, and i s pe o mance is e alua ed in an
EMA sys em.
This manusc ip is o ganized as ollows. Fi s o all, con en ional SV-PWM o s a -connec ed
i e-phase powe sys ems is p esen ed, whe e he ha monic p ojec ion o he s a o ol ages in o
hei co esponding o hogonal subspaces by means o Cla ke ans o ma ion is ma hema ically
jus i ied. A e ha and conside ing he hi d ha monic elimina ion cons ain , i is shown how CMV
a ia ions a e gene a ed in he mul iphase d i e. Secondly, he mos ele an educed common-mode
ol age PWM (RCMV-PWM) modula ion echniques a e b ie ly desc ibed, ocusing on hei limi a ions.
A e ha , he p oposed Hyb id AZSL5M5-PWM modula ion echnique is p esen ed p o iding he
equi ed ools o du y cycle calcula ion, and alida ed by means o simula ion. The a ge o he
p oposed modula ion echnique is o e ec i ely educe CMV in s a connec ed mul iphase sys ems,
while he hyb idiza ion is pe o med o co e he whole ope a ion ange o he d i e. Open-loop
and de ailed i e-phase EMA simula ions a e conduc ed o pe o m he alida ion, whe e no only
CMV educ ion is e i ied, bu o he igu es such as o al ha monic dis o ion (THD) and e iciency a e
e alua ed in o de o demons a e ha he achie ed CMV educ ion does no signi ican ly penalize
o he ele an d i e igu es.
2. In luence o he SV-PWM Technique in he CMV o a S a -Connec ed Fi e-Phase AC D i e
SV-PWM is one o he mos used modula ion echniques in h ee-phase and mul iphase powe
sys ems hanks o i s easy digi al implemen a ion and op imum DC bus ol age u iliza ion. As a
s a -connec ed i e-phase sys em has ou deg ees o eedom, s a o ol ages and cu en s can be
ep esen ed in o wo sepa a ed wo-dimensional planes,
α
-
β
and
x
-
y
, and one homopola componen
by means o he ollowing ampli ude in a ian Cla ke ans o ma ion [38]:
α
β
x
y
0
=2
5
1cos(2π/5)cos(4π/5)cos(6π/5)cos(8π/5)
0sin(2π/5)sin(4π/5)sin(6π/5)sin(8π/5)
1cos(4π/5)cos(8π/5)cos(12π/5)cos(16π/5)
0sin(4π/5)sin(8π/5)sin(12π/5)sin(16π/5)
1
21
21
21
21
2
a
b
c
d
e
. (1)
The Cla ke ans o ma ion allows us o decouple he 5-dimensional ol age ec o in he
abcde
e e ence ame in o h ee o hogonal subspaces (
α
-
β
,
x
-
y
and 0). Fo a su ace-moun ed pe manen
magne synch onous machine (SM-PMSM), his decoupling is done h ough he diagonaliza ion o he
induc ance ma ix L(2).
L=
L11 L12 L13 L14 L15
L21 L22 L23 L24 L25
L31 L32 L33 L34 L35
L41 L42 L43 L44 L45
L51 L52 L53 L54 L55
. (2)
Fo SM-PMSMs, he elemen s o
L
can be conside ed in a ian wi h espec o he o o angula
posi ion, as he su ace placed magne s ha e a pe meabili y nea ha he one o he ai . The e o e,
a SM-PMSM beha es like a non-salien pole synch onous machine [
39
]. As he windings in each phase
a e manu ac u ed iden ically, he mu ual induc ances be ween any pai o phases sepa a ed wi h he
Ene gies 2020,13, 607 4 o 19
same elec ical angle a e equal, i.e.,
L12 =L15 =L21 =L23 =L51 =Ljk
(i
|j−k|=
1) o
L13 =L31 =
L25 =L52 =Ljk
(i
|j−k|=
2). Simila ly, all he sel -induc ances a e equal (
L11 =L22 =··· =L55
).
This ype o ma ix is known as a ci culan ma ix, and i has some special p ope ies [
40
]. Fo example,
i gua an ees ha
L
is o hogonally diagonalizable by a ans o ma ion ep esen ed by a 5
×
5 eal
ma ix [41,42].
The ci culan ma ices a e diagonalized by he Fou ie Ma ix [
40
,
43
]. The e o e, he Cla ke
ans o ma ion decomposes he 5-dimensional ec o s acco ding o hei ha monic componen s. In he
α
-
β
sub-space, he
h=
5
(l−
1
)±
1 ha monic componen s a e p ojec ed while, in he
x
-
y
sub-space,
he
h=
5
(l−
1
)±
3 ones a e p ojec ed, being
l∈ {
1, 3, 5, ...
}
[
41
,
44
]. The ha monic componen s
o o de
h=
5
l
a e p ojec ed in o he ze o-sequence o homopola sub-space. In Table 1, he odd
ha monics associa ed wi h each sub-space acco ding o he Cla ke ans o ma ion o (1) a e p esen ed
o a 5-phase machine.
Table 1. Sub-space ha monics mapping o a i e-phase machine.
Sub-Space Ha monics
α−βh=1, 9, 11, 19...
x−y h =3, 7, 13, 17...
ze o-sequence h=0, 5,15, 25...
The numbe o possible swi ching s a es o space ec o s is 2
5
, whe e 30 a e ac i e ec o s and
wo a e ze o ec o s (Figu e 3). Ac i e ec o s can be classi ied depending on hei magni ude as:
•
La ge ec o s, whe e
|Vl|=
4
/
5
VDC cos(π/
5
)
, which co espond o he ou e decagon o Figu e 3.
•Medium ec o s, whe e |Vm|=2/5VDC, which co espond o he middle decagon o Figu e 3.
•
Small ec o s, whe e
|Vs|=
4
/
5
VDC cos(
2
π/
5
)
, which co espond o he inne decagon o
Figu e 3.
(11100)
(01000)
(10100)
(11000)
(11101)
(11010)
(11001)
(10000)
(01001)
(10001)
(11011)
(10101)
(10010)
(00001)
(10011)
(00011)
(10111)
(01011)
(01101)
(11110)
(01100)
(01110)
(00100)
(01010)
(10110)
(01111)
(00110)
(00101)
(00010)
(00111)
1
2
3
4
5
6
7
8
9
10
α
β
(a)
y
x
(10101)
(00100)
(10001)
(10100)
(10111)
(11100)
(10110)(10000)
(00110)
(10010)
(11110)
(10011)
(11000)
(00010)
(11010)
(01010)
(11011)
(01110)
(00111)
(11101)
(00101)
(01101)
(00001)
(01100)
(11001)
(01111)
(01001)
(00011)
(01000)
(01011)
1
2
3
4
5
6
7
8
9
10
(b)
Figu e 3.
Fi e-phase SV-PWM:
α
-
β
and
x
-
y
planes wi h hei co esponding space ec o s and swi ching
s a es (a ‘1’ in a swi ching s a e ep esen s ha he op swi ch o a gi en phase is ac i a ed, while a ‘0’
ep esen s ha i s complemen a y swi ch is ac i a ed). (a)α-β ec o plane. (b)x-y ec o plane.
Fo an
n
-phase sys em,
n−
1 ac i e ec o s mus be applied a each commu a ion pe iod in
o de o achie e a sinusoidal ou pu [
45
]. Thus, ou ac i e ec o s mus be used in a s a -connec ed
Ene gies 2020,13, 607 5 o 19
i e-phase sys em. Al hough a ious possible ac i e ec o combina ions a e possible o p oduce a
gi en ou pu ol age ec o , he mos common al e na i e consis s on using wo la ge and wo medium
adjacen ec o s. As an illus a i e example, Figu e 3shows he ec o s used o syn hesize a gi en
e e ence ol age ec o loca ed in he i s sec o o he
α
-
β
plane, being he ollowing he applica ion
sequence ha minimizes swi ching losses: 00000, 10000, 11000, 11001, 11101, 11111, 11101, 11001,
11000, 10000, 00000. I he hi d ha monic componen needs o be elimina ed, he applica ion- ime a io
be ween medium and la ge ec o s mus sa is y (3), as wi h his a io he sum o he applied ec o s in
he x-yplane is ze o (Figu e 3) [46].
la ge
medium
=1.618. (3)
As a esul , he maximum achie able ou pu ol age ollowing his modula ion app oach is:
Vomax =4
5cos π
5cos π
10=0.6155VDC, (4)
and he CMV gene a ed in he i e-phase sys em is:
VCM( ) = 1
5[Va0( ) + Vb0( ) + Vc0( ) + Vd0( ) + Ve0( )]. (5)
When using SV-PWM and applying he ec o sequence ha co esponds o he i s sec o o he
α
-
β
plane, he CMV wa e o m o Figu e 4is ob ained. F om (5), i can be deduced ha all la ge and
sho ec o s gene a e CMV le els o
±
0.3
VDC
, while CMV le els a e o
±
0.1
VDC
o medium ec o s
and o
±
0.5
VDC
o null ec o s. When e alua ing he impac o he CMV, he di e ence be ween he
maximum and minimum CMV le els (
∆CMV
, Figu e 4) mus be conside ed, and he numbe o CMV
a ia ions o each commu a ion pe iod (NCMV) mus also be aken in o accoun .
S1
Tsw
S3
S5
SV-PWM
00000 11000
10000 11001111011111111101110011100010000 00000
S7
S9
CMV [V]
Tsw
0.5Vdc
-0.5Vdc
0.3Vdc
-0.3Vdc
0.1Vdc
-0.1Vdc
ΔCMV
Tsw
Tsw
Sha ol age [V]
Bea ing cu en [A]
Figu e 4. CMV wa e o m o SV-PWM echnique (adap ed om [23]).
Ene gies 2020,13, 607 6 o 19
3. RCMV-PWM Techniques
As ze o ec o s a e esponsible o gene a ing he maximum CMV le els (Figu e 4), mos o he
RCMV-PWM echniques a oid he applica ion o hese ec o s o educe
∆CMV
and
NCMV
. In [
38
],
an ex ension o he h ee-phase ac i e ze o s a e PWM (AZS-PWM) [
47
] modula ion echnique o he
i e-phase scena io is p oposed. This echnique eplaces ze o ec o s by applying wo ac i e ec o s
wi h he opposi e phase a he same ime. In his wo k, his echnique will be named AZSL2M2-PWM
as, apa om he ac i e ec o s ha subs i u e ze o ec o s, wo la ge (L2) and wo medium (M2)
ec o s a e used a each modula ion pe iod. This echnique shows a good ha monic pe o mance and
DC bus u iliza ion, being i s linea ange 0
≤m≤
1. Howe e ,
∆CMV
is no g ea ly educed, as only
±
0.5
VDC
CMV le els a e a oided (Table 2). Simila ly, a modula ion algo i hm ha employs ou la ge
ac i e ec o s in conjunc ion wi h wo ac i e ec o s wi h opposi e phases (AZSL4-PWM) is p oposed
in [
38
]. This echnique has he same linea ange as SV-PWM and AZSL2M2-PWM, and conside ably
educes ∆CMV, as only applies la ge ec o s. None heless, NCMV emains as o SV-PWM (Table 2).
M5-PWM [
48
] and L5-PWM [
49
] echniques comple ely elimina e
∆CMV
and
NCMV
by only using
odd o e en medium (M5-PWM), o odd o e en la ge (L5-PWM) ac i e ec o s. Howe e , his is
achie ed a he cos o in oducing addi ional powe losses, signi ican ly educing he linea ange up
o 0.5257 o M5-PWM (Table 2), and gene a ing high ha monic dis o ion o L5-PWM, making hem
inapp op ia e o many indus ial applica ions. Au ho s in [
48
,
49
] also p opose a ian s ha use en
medium (M10-PWM) o en la ge (L10-PWM) ec o s. These echniques enhance he linea ange by
inc easing he a ailable ec o s, bu do no educe
∆CMV
and
NCMV
as much as wi h M5-PWM and
L5-PWM (Table 2).
Table 2. Summa y o he mos ele an ea u es o SV-PWM and RCMV-PWM echniques.
Modula ion ∆CMV [V] NCMV ∆CMV Reduc ion [%] NCMV Reduc ion [%] CM Wa e o m Linea Range
SV-PWM VDC 10 - -
0.5VDC
-0.5VDC
0.3VDC
0.1VDC
-0.1VDC
-0.3VDC
0≤m≤1
AZSL2M2-PWM 0.6VDC 6−40% −40%
0.3VDC
0.1VDC
-0.1VDC
-0.3VDC
0≤m≤1
AZSL4-PWM 0.2VDC 10 −80% 0%
0.1VDC
-0.1VDC
0≤m≤1
M5-PWM 0 0 −100% −100%
-0.3VDC
0≤m≤0.5257
M10-PWM 0.6VDC 2−40% −80%
0.3VDC
-0.3VDC
0≤m≤0.618
L5-PWM 0 0 −100% −100%
0.1VDC
0≤m≤0.8507
L10-PWM 0.2VDC 6−80% −40%
0.1VDC
-0.1VDC
0≤m≤1
AZSL5M5-PWM 0.4VDC 2−60% −80%
0.1VDC
-0.3VDC
0≤m≤0.8507
Among he e iewed echniques, AZSL2M2-PWM and L10-PWM bes sui o indus ial
applica ions, as hey keep he linea ange wi h a easonable THD while e ec i ely educing
∆CMV
. Howe e ,
NCMV
educ ion by means o such modula ion algo i hms is limi ed. Thus, a new
RCMV-PWM echnique ha u he educes
NCMV
while keeping an ex ended linea ange is p oposed
in he ollowing sec ion.
Ene gies 2020,13, 607 7 o 19
4. P oposed RCMV-PWM Technique
4.1. Ac i e Ze o S a e L5M5 PWM Technique (AZSL5M5-PWM)
The main pa o he p oposed RCMV-PWM echnique, named ac i e ze o s a e L5M5
PWM (AZSL5M5-PWM), is based on he AZSL2M2-PWM echnique [
38
]. Howe e , and unlike
AZSL2M2-PWM, he p oposed scheme only uses odd o e en ec o s o u he educe he CMV
ol age a ia ions. Fo example, i odd ec o s a e only conside ed, his leads o he sec o dis ibu ion
o Figu e 5a. Thus, i e medium ec o s and i e la ge ec o s a e exclusi ely used o syn hesize
he e e ence ol age (Figu e 5), and CMV a ies be ween
−
0.3
VDC
and 0.1
VDC
(i only e en
ec o s a e used, CMV a ies be ween
−
0.1
VDC
and 0.3
VDC
). Consequen ly,
∆CMV =
0.4
VDC
and
NCMV =2 (Table 2).
(11100)
(01000)
(11001)
(10000)
(00001)
(10011)
(01110)
(00100)
(00010)
(00111)
1
2
5
3
4
0 < VoMAX < 0.5236VDC
(a)
1
2
5
3
4
0 < VoMAX < 0.5236VDC
(11000)
(01100)
(00110)
(00011)
(10001)
(11101)
(01111)
(11110)
(10111)
(11011)
(b)
Figu e 5.
Sec o dis ibu ion o AZSL5M5-PWM modula ion scheme in he
α
-
β
plane. (
a
) AZSL5M5-PWM
implemen ed wi h odd ec o s. (b) AZSL5M5-PWM implemen ed wi h e en ec o s.
Fo he sake o simplici y, all he ollowing analyses a e conduc ed conside ing he AZSL5M5-PWM
a ian which exclusi ely uses odd ec o s. The p ocedu e is analogous o e en ec o s.
The applica ion ime o each ec o can be easily calcula ed by sol ing he ollowing sys em:
V∗
α
V∗
β
V∗
x
V∗
y
=
Vm αVllαVl αVmlα
Vm βVllβVl βVmlβ
Vm x Vllx Vl x Vmlx
Vm y Vlly Vl y Vmly
δ1
δ2
δ3
δ4
, (6)
whe e
V∗
α
,
V∗
β
,
V∗
x
and
V∗
y
a e he e e ence ol age p ojec ions in he
α
-
β
and
x
-
y
planes,
δ1
,
δ2
,
δ3
and
δ4
a e he du y cycles o each ec o , and he 4
×
4 ma ix is composed o he magni udes o he
ec o s o be applied in each sec o , whe e
Vm
e e s o he modulus o he medium ec o on he
igh side o he e e ence ec o (
V e
) (Figu e 6,
Â
),
Vml
e e s o he modulus o he medium ec o
on he le (Figu e 6,
Ã
), and
Vll
and
Vl
e e o he modulus o he la ge ec o s on bo h le and
igh sides, espec i ely (Figu e 6,Áand À). Consequen ly, a 4 ×4 ma ix should be de ined o each
sec o . In gene al,
V∗
x
and
V∗
y
a e se o ze o in o de o cancel he ol age hi d ha monic. F om (6),
Ene gies 2020,13, 607 8 o 19
i is possible o explici ly de e mine he alues o he du y cycles
δ1
,
δ2
,
δ3
and
δ4
wi h espec o he
e e ence ol ages V∗
αand V∗
β:
δ1=α1V∗
α/VDC +β1V∗
β/VDC =−a1sin 2sπ
5V∗
α/VDC +a1cos 2sπ
5V∗
β/VDC,
δ2=α2V∗
α/VDC +β2V∗
β/VDC =−a2sin 2(s−1)π
5V∗
α/VDC +a2cos 2(s−1)π
5V∗
β/VDC,
δ3=α3V∗
α/VDC +β3V∗
β/VDC =a2sin 2sπ
5V∗
α/VDC −a2cos 2sπ
5V∗
β/VDC,
δ4=α4V∗
α/VDC +β4V∗
β/VDC =a1sin 2(s−1)π
5V∗
α/VDC −a1cos 2(s−1)π
5V∗
β/VDC,
(7)
whe e being
s={1, 2...5}
he co esponding sec o in he
αβ
plane, and being
a1= ( −5+√5)/q2(5+√5)and a2=q(10/(5+√5).
Rega ding he p ac ical implemen a ion o he p oposed echnique, he 2
×
4 ma ix
Ms
can be
de ined as in (8), whe e he elemen s o such ma ix can be p ecalcula ed o each sec o and s o ed
in o look-up ables (LUT). In his way, he compu a ional bu den and implemen a ion complexi y o
he algo i hm a e g ea ly educed. Table 3summa izes he alues o Ms o each sec o s={1, 2...5}.
Ms=
α1β1
α2β2
α3β3
α4β4
. (8)
Table 3. Values o Msdepending on he αβ plane sec o .
Sec o 1 (M1) Sec o 2 (M2) Sec o 3 (M3) Sec o 4 (M4) Sec o 5 (M5)
0.691 −0.224
0 1.176
1.118 −0.363
0 0.726
0.427 0.588
−1.118 0.363
0.691 0.951
−0.691 0.224
−0.427 0.588
−0.691 −0.951
−0.691 0.951
−0.427 −0.588
−0.691 −0.224
0.691 −0.951
−1.118 −0.363
0.427 −0.588
0−0.726
1.118 0.363
0−1.176
0.691 0.224
(11100)
(01000)
(11000)
(11101)
(11001)(10000)
(10001)
(11011)
(00001)
(10011)
(00011)
(10111)
(11110)
(01100)
(01110)
(00100)
(01111)
(00110)
(00010)
(00111)
16 25
29
24
8
28
12
3014
4
10 15
2
723
319
1
27
17
6
5
2
1
4
3
V e
Figu e 6.
AZSL5M5-PWM modula ion ec o sequence (
À
–
Å
) o sec o 1 when only odd ec o s
a e applied.
The main di e ence o he AZSL5M5-PWM echnique o e he AZSL2M2-PWM one is ha ,
he e a e no s ic ly phase-opposi e ec o pai s, as only odd/e en ec o s can be used (Figu e 6).
To sol e his p oblem, h ee ac i e ec o s ( wo medium and one la ge) a e used o eplace a ze o ec o .
Ene gies 2020,13, 607 9 o 19
Fi s , he la ge ec o on he igh side o he sec o (Figu e 6,
À
) is applied du ing
0/
3, and each
medium ec o (Figu e 6,Äand Å) is applied du ing 0/3.
Since he applied ec o sequence has a g ea impac on he CMV and on he swi ching losses,
a sequence wi h minimum commu a ions has been chosen o each sec o . Fo ins ance, when he
e e ence ol age ec o lays in sec o 1, he nex ec o sequence is applied: 11001, 11100, 10000, 01000,
00100, 00010, 01000, 10000, 11100 and 11001 (Figu e 6). Odd ec o a ian AZSL5M5-PWM ec o
sequences depending on he e e ence ol age sec o a e gi en in Table 4. I is impo an o no e ha ,
o AZSL5M5-PWM, mo e han one commu a ion is p oduced a each ec o change.
Table 4. AZSL5M5-PWM ec o sequences (odd ec o s).
AZSL5M5-PWM Vec o Sequence
Sec o 1 11001 11100 10000 01000 00100 00010 01000 10000 11100 11001
Sec o 2 11100 01110 01000 00100 00010 00001 00100 01000 01110 11100
Sec o 3 01110 00111 00100 00010 00001 10000 00010 00100 00111 01110
Sec o 4 00111 10011 00010 00001 10000 01000 00001 00010 10011 00111
Sec o 5 10011 11001 00001 10000 01000 00100 10000 00001 11001 10011
As he
α
-
β
plane is di ided in o i e sec o s ins ead o en (Figu e 5), he linea ange o
AZSL5M5-PWM is sligh ly educed, being he maximum achie able ou pu ol age:
VoMAX =4
5cos π
5cos π
5=0.5236VDC. (9)
Fo applica ions whe e achie ing ull linea ange is manda o y, an hyb id modula ion ha
ex ends AZSL5M5-PWM’s linea ange is p oposed in he ollowing.
4.2. Hyb idiza ion o he P oposed Modula ion Algo i hm
Th ee ope a ion a eas ha e been di e en ia ed in Figu e 7 o ca y ou he hyb id modula ion
algo i hm and ex end he linea ange o AZSL5M5-PWM. The AZSL5M5-PWM hyb id a ian
(HASZL5M5-PWM) ha uses odd ec o s (whi e a ea) has been chosen as he main modula ion
scheme. When
V e
s eps o e he bounda ies o he whi e pen agon, wo hings may occu . On he one
hand,
V e
migh emain wi hin he shadowed bounda ies. In such case, AZSL5M5-PWM wi h e en
ec o s would be applied. On he o he hand, i
V e
is ou o he limi s o AZSL5M5-PWM wi h e en
o odd ec o s, SV-PWM can be used o ul ill he emaining a ea, ma ked wi h lines. This modi ica ion
ex ends he linea ange o AZSL5M5-PWM up o 26.8%. Fu he a ian s wi h g ea e CMV educ ion
could also be conside ed i a ull ange RCMV-PWM echnique, such as AZSL2M2-PWM, is used
ins ead o SV-PWM.
(11100)
(01000)
(11001)
(10000)
(00001)
(10011)
(01110)
(00100)
(00010)
(00111)
16
25
8
28
14
4
2
7
19
1
(11000)
(11101)
(10001)
(11011)
(00011)
(10111)
(11110)
(01100)
(01111)
(00110)
29
24
12
30
10 15
23
3
27
17
Figu e 7.
HAZSL5M5-PWM. Whi e: AZSL5M5-PWM wi h odd ec o s; shadowed: AZSL5M5-PWM
wi h e en ec o s; lines: SV-PWM.
Ene gies 2020,13, 607 16 o 19
Au ho Con ibu ions:
M.F. concep o he a icle, w i ing, p oposed modula ion echnique de elopmen ,
open-loop and closed-loop models simula ions and analysis. A.S-G. EMA model de elopmen and suppo on
closed-loop model simula ions. E.R. IGBT and he mal model de elopmen , suppo on open-loop simula ions
and e iew. I.K. suppo on modula ion echnique de elopmen , concep ual suppo , e iew and supe ision. E.I.
simula ion pla o m de elopmen , e iew and supe ision. J.L.M. e iew. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
This wo k has been suppo ed in pa by he Go e nmen o he Basque Coun y wi hin he und o
esea ch g oups o he Basque Uni e si y sys em IT978-16 and in pa by he Go e nmen o he Basque Coun y
wi hin he esea ch p og am ELKARTEK as he p ojec ENSOL (KK-2018/00040).
Con lic s o In e es : The au ho s decla e no con lic o i ne es .
Abb e ia ions
The ollowing abb e ia ions a e used in his manusc ip :
AC Al e na ing cu en
AZS-PWM Ac i e Ze o-S a e Pulse Wid h Modula ion
AZSL2M2-PWM Ac i e Ze o-S a e Two La ge Two Medium
AZSL4-PWM Ac i e Ze o-S a e Fou La ge
AZSL5M5-PWM Ac i e Ze o-S a e Fi e La ge Fi e Medium
CMC Common mode cu en
CMV Common mode ol age
DC Di ec cu en
EDM Elec ic discha ge machining
EMA Elec omechanical ac ua o
EMI Elec omagne ic in e e ences
FEM Fini e elemen me hod
GaN Gallium ni ide
HVDC High- ol age di ec cu en
IGBT Insula ed ga e bipola ansis o
L5-PWM Fi e La ge Pulse Wid h Modula ion
L10-PWM Ten La ge Pulse Wid h Modula ion
M5-PWM Fi e Medium Pulse Wid h Modula ion
M10-PWM Ten Medium Pulse Wid h Modula ion
MEA Mo e Elec ic Ai c a s
PI P opo ional In eg al
PMSM Pe manen Magne Synch onous Machine
PWM Pulse Wid h Modula ion
RCMV-PWM Reduced Common Mode Vol age Pulse Wid h Modula ion
SiC Silicon Ca bide
SV-PWM Space Vec o Pulse Wid h Modula ion
THD To al Ha monic Dis o ion
VSI Vol age Sou ce In e e
WBG Wide Bandgap
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