P edic i e Middle Poin Modula ion:
A New Modula ion Me hod o Pa allel Ac i e Fil e s
Manuel A. Pe ales, Juan M. Ca asco, Juan A. Sánchez, Luis Te ón, Leopoldo Ga cía F anquelo.
DEPT. OF ELECTRONIC ENGINEERING. UNIVERSITY OF SEVILLE
Escuela Supe io de Ingenie os. Camino de los Descub imien os. Isla de la Ca uja.
Se ille, Spain
el: 954 48 73 74. ax: 954 48 73 73
e-mail: pe ales@g e.esi.us.es, [email p o ec ed], shanshe@g e.esi.us.es, syl@g e.esi.us.es,
leopoldo@g e.esi.us.es
Keywo ds
Ac i e il e s , Modula ion s a egies, Powe ac o co ec ion, Powe Quali y
Abs ac
When designing an Ac i e il e , using a cu en -con olled ol age sou ce in e e , he e a e wo
main asks : o gene a e an app opia e e e ence, o nulling ha monic cu en and eac i e powe ,
an , on he o he side, o gene a e a swi ching pa e n ha pe mi s o ollow he e e ence as close as
i can be done. P edic i e Middle Poin Modula ion (PMPM) is a no el modula ion echnique,
specially sui ed o Ac i e Fil e s. This me hod is de i ed om p edic i e Dead-Bea con olle ,
imp o ing i s dynamic esponse and cu en e o . Simula ion esul s con i m he alidi y o he
p oposed me hod. Expe imen al esul s will be p o ided in he inal pape .
I. In oduc ion
PWM me hods ha e became e y popula on cu en -con olled ol age sou ce in e e s (CC_VSI).
Many open-loop and closed-loop me hods ha e been desc ibed in li e a u e [1], [2], [3], [4]...,
ocused mainly on mo o con ol, o gene ically con ol o elec onic loads. When he ‘load’ is he
public g id, special conside a ions had o be aken in o accoun , as he p oblem is qui e di e en :
• S a ing ha ol age on public g id is igid, he CC-VSI ac s pu ely as a cu en sou ce.
• i is e y easy o de elop a simpli ied model o he en i e sys em, and hen use a p edic i e
con ol me hod.
• When using a Space Vec o me hod, ec o s 0 and 7 (ze o ol age ec o s) a e no
in e changeable, and should be conside ed as he o he ec o s.
Also, depending on he applica ion and opology o he in e e , a pa icula modula ion me hod
could be be e o wo se. Dealing wi h ou wi ed – h ee legged sys ems, he use o Space Vec o
modula ion ins ead o classic pulse wid h modula ion is no jus i ied in e ms o simpli ying
algo i hms, as i is necessa y o use some 3D ec o modula ion, no a simple 2D ec o modula ion.
In addi ion, in ou -wi ed sys ems each leg can be con olled sepa a ely, con e ing he con ol
p oblem in con olling h ee 1-phase in e e s
This pape p oposes a new me hod o calcula ing
commu a ion ime o each leg o a h ee phase,
ou wi e in e e , commonly used in Shun
Ac i e Fil e s, as shown in Figu e 1.
Fi s , in sec ion II, we p esen an o e iew o he
shun ac i e il e case in s udy, in o de o s a e
some conside a ions abou he modula ion
Fig. 1: 3-phase 4-wi e in e e
L
L
L
C1
C2
T1
T2
T3
T4
T5
T6
R
S
T
N
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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me hod desi ed. Then, in sec ion III we p esen he simpli ied model o he in e e connec ed as a
shun ac i e il e , and based on ha model, we p esen he basic equa ions o he new modula ion
s a egy. In sec ion IV we p esen some simula ion esul s and compa ison wi h o he me hods. In
sec ion V we show he expe imen al p o o ype, unde de elopmen by now, in which he algo i hm
will be es soon. Finally, in sec ion VI we p esen some conclusions abou modula ion s a egies o
ac i e il e s.
II. CC-VSI used as Shun Ac i e Fil e
When using an CC-VSI o build a shun ac i e il e , he e a e some conside a ions ha should be
aken in o accoun , ela ed o modula ion me hod. The main cha ac e is ics ha make his necessa y
a e:
• The shape o he e e ence cu en o be ollowed is no sinusoidal a all. I has, indeed, all he
ha monics o he load, and uses o ha e e y sha pen slopes.
• The load, as commen ed be o e, is he public g id, which is mos ly a ol age sou ce and a li le
se ies impedance.
• I is e y impo an o ack he e e ence as quick as i can be possible, because he
compensa ion e ec i eness depends on i .
• The e ec i eness o compensa ion lays on he wo sides - he gene a ion o he e e ence and he
acking o his e e ence- o he p oblem. The e o e a balanced solu ion mus be p o ided
be ween a pe ec –bu slow- e e ence gene a o and a quick acking me hod ha makes
impossible o calcula e he app op ia e e e ence.
The en i e sys em can be ep esen ed as in igu e 2. In his pic u e we can see he public g id, ha
will be conside ed as a non-ideal ol age sou ce, wi h i s se ies impedance; also, he load will be a
hy is o ec i ie , wi h a high 5 h , 7 h and 11 h ha monic, and low powe ac o (a ound 0.87); The
il e i sel will be implemen ed wi h he CC-VSI, di ided in o e e ence gene a o and e e ence
acking.
The pe o mance o a modula ion echnique can be measu ed in so many di e en ways [3], and
depending on he applica ion designed, some c i e ia had o be conside ed mo e impo an han
o he s. Fo he Ac i e Fil e (AF) applica ion, he mos impo an c i e ion could be a as esponse,
because he shape o he e e ence o be ollowed is e y sha p in ce ain egions and e y la in
o he egions. Also, i is e y impo an o educe high equency ha monics gene a ed by he
in e e , as he AF is designed o educe THD o a load.
Fig. 2: Gene al block diag am
Z
L
LOAD
REFERENCE
GENERATION
(DSP)
MODULATION
TECHNIQUE
3-PHASE 4-WIRE
V-SOURCE
INVERTER
+
-
D
Q
Q
i
S
i
L
i
F
N
Public G id (3-phase + neu al)
Ac i e Fil e
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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The p oblem is e y di icul o a o d, because he e e ence gene a o is no o ally decoupled om
he acking me hod, and he e a e many e ec s ha had o be aken in o accoun , as he e ec o
dead imes, he e ec o o he sys ems in e e ing wi h ou il e , o he public g id impedance,
among o he s. The e o e, an app oxima ion should be con enien , a leas as a s a ing poin .
III. P edic i e Middle Poin Modula ion
App oxima ed model
In o de o e alua e he pe o mance o di e en modula ion me hods, a Simulink model o he en i e
sys em was buil . The ollowing conside a ions ha e been made:
• Sou ce (ne ) impedance is much less han he se ies induc ance o he Ac i e Fil e .
• Capaci o ol ages s ay cons an on a sample ime
• Sou ce ol ages also emains cons an on a sample ime
• Each phase is decoupled om he o he wo, and i s cu en depends only on he posi ion o i s
swi ches and on he ol age o he ne on i s phase.
Really, he ou h conside a ion could be de i ed om he second one, as he DC-LINK is he only
poin o connec ion be ween phases. Using his simpli ica ions, he sys em was linea ized pe phase
using he basic scheme shown in Figu e 2. Fo his scheme, he main equa ions ha gi es cu en on
phase , depending on he posi ion o swi ches T1 and T2 a e s a ed in Eq.1
whe e V is he line ol age(phase o neu al) , nulling he e ec o sou ce impedance, i is phase
cu en o he il e , and VC1 and VC2 a e ol ages ac oss he upside and downside capaci o s.
Modula ion S a egy
The e a e many me hods o modula e a signal using Pulse Wid h Modula ion echniques. A iangula
wa e o m is commonly used, which is compa ed wi h he signal o be modula ed, and he compa ison
decides wha swi ch has o be u ned on. The p esen me hod is a a ia ion o he classical
suboscila ion me hod known as p edic i e Dead-Bea con olle [5]. In ha me hod, he in e e
ol age is chosen in o de o null cu en e o a he end o he sample pe iod. Tha me hod p esen s
some disad an ages o using in Ac i e Fil e s:
• The e e ence is eached a he end o he pe iod, so he delay is, a leas , one sample ime.
• The e o is no dis ibu ed symme ically, so he in eg al e o is no ze o.
Now, we will y o minimise wo pa icula pe o mance c i e ia, specially impo an o ac i e
il e s, as s a ed be o e:
• The cu en e o , measu ed as he in eg al o he di e ence be ween cu en e e ence and ac ual
cu en .
• The delay be ween e e ence and cu en , measu ed as he ime in which he cu en equals he
e e ence.
Fig. 3: Simpli ied Sys em Model
Eq 1.
L
C1
C2
V
T2
T1 Vc1
Vc2
I
)(:,
:,
221
121
V Vc
d
di
LonTo T
V Vc
d
di
Lo TonT
+−=⋅
−=⋅
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 3
F om his poin , we calcula e commu a ion ime, using linea ized equa ions, in o de o minimise
bo h delay ime and cu en in eg al e o . The a ge is o ge an a e age cu en , du ing a sample
ime, equal o he e e ence we a e acking.
In Figu e 3 is shown he e olu ion o cu en on a sample ime, in a ypical iangula PWM
suboscilla ion me hod.
whe e:
1, 2 : pe iods when he uppe and lowe swi ch
a e connec ed, espec i ely.
T: Commu a ion pe iod.
ia , ib , ic: wa e o ms o he cu en in he h ee
in e als o a commu a ion pe iod, (no ha ing in
coun dead imes)
I0: Ini ial cu en , measu ed a he beginning o a
commu a ion pe iod.
I1 ,I2 ,I3: Final cu en s a he end o each
in e al.
The a e age cu en in he in e al could be calcula ed as ollows :
whe e 1 and 2 a e he ime whe e swi ches T1 and T2 a e u ned on, espec i ely.
Le us conside ha ol age o e capaci o s a e balanced, so VC1 a e equal o VC2. Then, a e age
cu en can be calcula ed as:
Finally, i we wan IAV o be equal o he cu en e e ence, being I0 ac ual (measu ed) cu en , hen 2
can be calcula ed as:
The e a e some ad an ages di ec ly de i ed om he use o his modula ion:
• The a e age cu en o e he sample ime is equal o he e e ence calcula ed.
• The e e ence, i sel , is eached a he middle o he sampling ime. Tha ea u e gi es he name
o he me hod (P edic i e Middle Poin Modula ion,
PMPM).
Eq. 2
Eq. 3
11
1
122
1
2
2
2
1
011
1
1
2
1
0
2/
000
2/
0
)··(;)·()(
;)··(;)·()(
;)·()(
·
2
212
V VcII V VcI i
V VcII V VcI i
V VcI i
d id id id iIT
LL
c
LL
b
L
a
c
T
b
aAV
−+=+−=
+−=−+=
+−=
⋅+⋅+⋅=⋅= ∫∫∫∫
[]
Vc V VcT
L
II AV ⋅⋅−−⋅⋅
⋅
+= 20 2)(
2
1
Vc
TV Vc
II
Vc
L
AV ⋅
⋅−
+−⋅= 2
)(
)( 02 Eq. 4
d iiI
T
e )·(
0
∫−=
ε
Eq. 5
I
e
I
0
I
1
I
2
I
3
2
/2
2
/2
1
T
i
i
c
( )
i
b
( )
i
a
( )
Fig. 4: Cu en e olu ion
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 4
• he in eg al e o , de ined in Eq. 5, is null, supposing all magni udes ixed o e one commu a ion
pe iod, because is null on each pe iod.
• I is e y as and simple o calcula e 2. In ac , we calcula e 2·Vc, and hen compa e wi h T·Vc
o gene a e pulses, in o de o a oid di ision in eal ime calcula ions.
IV. Simula ion Resul s
Many simula ions we e pe o med wi h he linea ized model o he shun AF, in o de o p o e
he alidi y o he me hod. Basically, a Bang-Bang me hod and he new PWM me hod a e o be
compa ed. The elec ion o he Bang-Bang me hod as a e e ence o compa ison is mo i a ed by i s
simplici y and i s ela i ely good esul s. I can be demons a ed ha Bang-Bang me hod is he as e
me hod, in e m o calcula ion and one o he be e in e ms o con ollabili y. Nex , we p esen
Fig 5: Simula ion esul s o Bang-Bang a 10kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in
seconds
,
y
-axis in am
p
e es
);
(
b
)
Sou ce Cu en S
p
ec um.
(
x-axis in Hz
,
y
-axis in
p
e cen o 1s ha monic
)
(
a
)
(
b
)
Fig. 6: Simula ion esul s o Bang-Bang a 20kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in
seconds
,
y
-axis in am
p
e es
);
(
b
)
Sou ce Cu en S
p
ec um.
(
x-axis in Hz
,
y
-axis in
p
e cen o 1s ha monic
)
(
a
)
(
b
)
0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58
-40
-30
-20
-10
0
10
20
30
40
01000 2000 3000 4000 5000 6000 7000 8000 9000
0
1
2
3
4
5
6
7
8
9
02000 4000 6000 8000 10000 12000 14000 16000 18000
0
0.5
1
1.5
2
2.5
0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58
-40
-30
-20
-10
0
10
20
30
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 5

simula ion esul s o an ac i e il e applied o a hy is o ec i ie , cha ac e ised using ac ual
measu es o he cu en .
Figu e 5 and 6 p esen s esul s o simula ion using Bang-Bang me hod , a 10kHz and 20kHz o
commu a ing equency. Wa e o ms o load (uncompensa ed) and sou ce (compensa ed) cu en s,
and he FFT o he compensa ed cu en a e shown:
Figu e 7 and 8 shows he same cu es, using PMPM me hod. I can be app ecia e ha ipple
dec eases d ama ically, and Spec um is concen a ed on he commu a ion equency.
I should be no ed ha no all he spec um g aphics ha e he same scale, in o de o gain p ecision,
al hough his could leads o con usion.
In Table I, he main esul s a e shown. he THD was calcula ed only wi h he i s 30 ha monics, o m
100Hz o 1500Hz, because he in e es o an ac i e il e is ocused on low o de ha monics.
Fig. 7: Simula ion esul s o PMPM a 10kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds,
y
-axis in am
p
e es
);
(
b
)
Sou ce Cu en S
p
ec um.
(
x-axis in Hz
,
y
-axis in
p
e cen o 1s ha monic
)
(
a
)
(
b
)
Fig. 8: Simula ion esul s o PMPM a 20kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds,
y
-axis in am
p
e es
);
(
b
)
Sou ce Cu en S
p
ec um.
(
x-axis in Hz
,
y
-axis in
p
e cen o 1s ha monic
)
(
a
)
(
b
)
0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58
-30
-20
-10
0
10
20
30
01000 2000 3000 4000 5000 6000 7000 8000 9000 10000
0
1
2
3
4
5
6
7
8
9
0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58
-30
-20
-10
0
10
20
30
00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 2
x 104
0
0.5
1
1.5
2
2.5
3
3.5
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 6
Table I: Simula ion Resul s
Me hod THD (<1500 Hz) 5 h Ha m.
Bang Bang a 10kHz 11.96 % 3.4%
Bang Bang a 20kHz 3.96% 2.3%
PMPM a 10kHz 3.7% 2.07%
PMPM a 20kHz 2.25% 1.32%
I should be no ed ha he THD is always g ea e in Bang-Bang han in PMPM, e en doubling he
equency. The 5 h ha monic is shown as i is he g ea es ha monic in he load, and he smalle i
emains in he compensa ed cu en , he be e is he me hod o acking he e e ence.
V. Expe imen al Model
An expe imen al model is being cons uc ed o inally alida e he simula ion esul s ob ained. I is
based on a p e ious wo k o he au ho s [6], and basically consis on a h ee-phase IGBT ol age
Sou ce In e e , connec ed hough a 380/220 au o ans o me . The DSP boa d, in his case, was
composed by wo DSP-based boa ds. The i s o hem, based on he TMS320C31 om Texas
Ins umen s, is used o calcula e an app op ia e e e ence, in eal ime (20kHz). The second one is
based on he TMS320F243, o m Texas Ins umen s, which is a ixed-poin DSP wi h PWM
modula o s buil in. In Figu e 9 a gene ic o e iew o he ins alla ion is shown, and in Figu e 10 a
pic u e o he digi al sys em is shown, ma king he mo e impo an pa s o i .
Fig. 9: Expe imen al model
Fig. 10: Digi al Con ol Boa ds
DSP
BOARD
iL
iL
R
S
T
N
LOAD
Swi ching Signals
iLs
iL
iF
iFs
iF
V
Vs
V
220V-50Hz
220:127
iF
V s
VDC
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 7
VI. Conclusions
When dealing wi h non sinusoidal wa e o ms, specially wi h locally high slopes, no all he
modula ion me hods shows good esul s. In he pa icula case o ac i e il e s, an ex a ca e ha e o
be aken in choosing he modula ion me hod, as i con ibu es d ama ically o he success o no o he
il a ion.
The main cha ac e is ics o a modula ion me hod o be selec ed, in his a ea, will be a as esponse
and a minimal e o in acking a e e ence, e en al hough he elec ical e iciency will be less han in
o he me hods.
A new me hod o modula ion, specially sui ed o Shun Ac i e il e s bu use ul in any g id-
connec ed applica ion, is p esen ed. Simula ion esul s con i ms heo e ical conclusions, showing a
e y good and as esponse.
An expe imen al model is being inished, and soon we will be able o p esen expe imen al esul s, o
con i m he alidi y o he modula ion me hod p esen ed.
Re e ences
1. Joachim Hol z. “Pulsewid h Modula ion Techniques o Con olled AC D i es” Con e ence held on Ma ch,
3- 2000, in he E.S.I. Se illa.
2. M. A. Dzieniakowski, M. P. Kazmie kiwski, “Sel - uned uzzy PI Cu en Con olle o PWM_VSI”. P oc.
EPE Con . 1995. pp 1308-1313.
3. Ma ian P. Kazmie kowski, Luigi Malesani, “Cu en Con ol Techniques o Th ee-Phase Vol age Sou ce
PWM Con e e s: A Su ey. IEEE T ans. on Ind. Elec, Oc .1998. Vol 45, no 5, pp 691-703
4. Michael M. Bechm F ede Blaabje g, John K. Pede sen, “Random Modula ion Techniques wi h Fixed
Swi ching equency o Th ee-Phase Powe Con e e s. IEEE T ans. on Powe Elec. July 2000, Vol 15, no
4, pp 753-761.
5. T. Kawaba a, T. Miyashi a, Y. Yamamo o, “Dead Bea Con ol o h ee-phase PWM in e e ”, IEEE T ans.
Powe Elec onics, Jan. 1990 Vol 5, pp 21-28.
6. J.M. Ca asco, M. Pe ales, B. Ruiz, E.Gal án, L.G. F anquelo, “ DSP Con ol o an Ac i e Powe Line
Condi ioning sys em”. EPE’97, ISBN 90-75815-02-6
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P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales
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EPE 2001 - G az P. 8