POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
No el Speed and Cu en Senso FDI Schemes wi h
an Imp o ed AFTC o Induc ion Mo o D i es
Mohamed BOUAKOURA, Nas eddine NAIT-SAID,
Mohamed-Said NAIT-SAID, Adel BELBACH
LSP-IE’2000 Labo a o y, Elec ical Enginee ing Depa men , Facul y o Technology, Uni e si y o Ba na 2,
Rue Chahid Mohamed El-Hadi Boukhlou , 05000 Ba na, Alge ia
bouak[email p o ec ed], n_nai [email protected], medsnai said@yahoo. , adel.belbac[email p o ec ed]
DOI: 10.15598/aeee. 16i1.2573
Abs ac . This pape ocuses on speed and cu en sen-
so Faul s De ec ion and Isola ion (FDI) in an Induc-
ion Mo o (IM) d i e. The e ec o senso s aul s
on he IM ec o con ol is p esen ed, hen, new de ec-
ion and isola ion app oaches a e sugges ed. Speed sen-
so aul s a e de ec ed when an e o be ween only wo
poin s om speed da a exceeds a ce ain h eshold. An
algo i hm based on RMS cu en s is de eloped o de ec
and isola e any aul y cu en senso . This equi es
h ee cu en senso s, each pe phase. Besides, open
ci cui aul s o in e e powe swi ches a e aken in o
accoun oo. To ensu e con inuous unc ionali y o he
d i e, we concei ed an Ac i e Faul Tole an Con olle
(AFTC) wi h smoo he econ igu a ion ea u e. Simu-
la ions in Ma lab/Simulink a e ca ied ou o show he
e iciency o he sugges ed schemes.
Keywo ds
Ac i e aul ole an con ol, cu en senso , in-
e e powe swi ch, MRAS, RMS alue, speed
senso .
1. In oduc ion
Faul Tole an Con ol (FTC) is a echnique imple-
men ed in many c i ical and high a ailabili y sys ems.
I s main pu pose is o mi iga e aul s and ensu e a
con inuous unc ionali y o a sys em wi h aul y ele-
men s a he han o al ailu e. The i s FTC was
implemen ed in ai c a s [1]. A e ha , i has been
b oadened o many o he ields, such as powe plan s
[2], anspo a ion [3], [4] and [5], and wind ene gy con-
e sion sys ems [6], [7] and [8]. To con ol any p ocess,
accu a e eedback in o ma ion is equi ed, and his one
is p o ided by senso s. Thus, in his pape , we in es-
iga e pa icula ly speed and cu en senso aul s in
an induc ion mo o d i e. The choice was aken since
induc ion mo o d i es a e in ol ed in mos p opulsion
and ac ion applica ions [9].
Faul ole an echniques a e di ided in o wo ypes:
passi e FTCs and ac i e FTCs. The i s ones in ol e
obus con olle s such as H_∞[10] and [11] and slid-
ing mode con olle s [12], [13] and [14], i.e. he aul y
elemen emains in eg a ed in he sys em whe e he
con olle abso bs i s e ec . Ne e heless, his ech-
nique has a limi ed e ec i eness because i ole a es
only low se e i y aul s [15] and [16]. Ac i e FTCs
(AFTC), o econ igu able FTCs, a e mo e sui able o
se e e aul s since he aul y componen is eplaced au-
oma ically by a heal hy one o i s signal is gene a ed
by a ma hema ical model based on o he a ailable sen-
so s. AFTC necessi a es a Faul De ec ion and Isola-
ion (FDI) mechanism.
In some pape s, ha dwa e edundancy is conside ed
o aul de ec ion [17] and [18], whe eas in o he s an-
aly ical edundancy is p e e ed. This las ely on es i-
ma o s and obse e s, o example; in [19] an ex ended
Kalman il e is conside ed as a speed i ual senso .
Alkaya and Eke applied a Luenbe ge obse e wi h a
DC mo o o de ec speed senso aul s [20]. MRAS is
also a widely used me hod o speed es ima ion. I is
p esen ed by Wang e al. as a subs i u e o he aul y
speed senso [21]. Usually, when i is ha d o model
a p ocess, signal p ocessing and machine lea ning ap-
p oaches a e e ec i e. In [22], wa ele analysis has a
undamen al ole in FTC scheme. In [23] he au ho s
conside ed he s a o cu en signa u e as a eliable
ool o de ec eccen ici y aul s o induc ion mo o s.
Fuzzy logic was an e icien ool used by Kamal e al.
o es ima e senso aul s in a wind-diesel hyb id sys em
[24] and also in [25] o de elop a mo e e icien con ol
o an induc ion mo o .
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 1
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
Many esea che s deal wi h senso s aul s. In [7],
[26] and [27] senso s mal unc ion causes signi ican loss
o he con olle pe o mance. Hence, his issue was a
mo i a ion o FTC design. This pape co e s se e al
con ibu ions o speed and cu en senso aul s diag-
nosis and ole ance in induc ion mo o d i es. Fi s ,
he e ec o senso s aul s on he IM ec o con ol
(IFOC) is p esen ed. Then, we p opose new de ec-
ion and isola ion s a egies based on signal p ocessing.
Las men ioned a e e ec i e and easy o implemen . To
handle hese aul s, an imp o ed AFTC scheme is de-
eloped wi h smoo he econ igu a ion ea u e a sen-
so aul momen .
This pape is o ganized as ollows: Sec ion 2. is
dedica ed o he de ec ion and isola ion o speed and
cu en senso aul s. Sec ion 3. p esen s an ex-
ension o cu en senso FDI algo i hm o de ec and
isola e in e e leg open swi ches aul s. The main im-
p o emen s on he AFTC a e explained in Sec. 4.
Sec ion 5. concludes he pape .
Rema k 1. No e ha in Fig. 2, Fig. 5, Fig. 6, Fig. 8,
Fig. 11 and Fig. 12 he ec angle wi h ounded angles
ep esen s a condi ional es . I s ou pu is bina y, so
i equals “1” i he condi ion is e i ied, o he wise i
equals “0”.
2. Speed and Cu en Senso
Faul Diagnosis
Be o e we p esen he FDI algo i hms, we show he
in luence o speed and cu en senso aul s on he pe -
o mance o he IM d i e wi h indi ec ield-o ien ed
con ol. We chose i since i is one o he mos pe o -
man and widesp ead echnique.
The in e mi en aul in speed senso s o DC gen-
e a o ype o al e na o s is usually caused by o o
eccen ici y [28] and [29] o he a i ion o b ushes o
bea ings. Whe eas o se aul s may be caused by he
a ia ion o elec ical pa ame e s o he senso in some
ope a ing condi ions. In o a y encode s, an insu i-
cien ligh sou ce (LED) o a mal unc ion o he pho-
o ansis o p oduces unce ain measu emen [8] and
[29]. The mechanical sliding in bo h ypes o speed
senso s (encode , gene a o ) causes ab up changes in
measu emen .
Since IFOC con ols mo o cu en s, he las men-
ioned a e usually measu ed by a leas wo cu en
senso s, bu some imes hey a e es ima ed om speed
and DC bus ol age. To inc ease he eliabili y o he
d i e we p e e o measu e phase cu en s ins ead o
es ima ing hem elying on o he senso s.
Cu en senso aul s a e less se e e han hose o
speed senso , ye , hey al e he con olle pe o -
mance. The causes o cu en senso mal unc ion a e
ela ed o i s physical s uc u e. In some unc ioning
condi ions, he change in ma e ial p ope ies and also
he deg ada ion a e a long ime o use p oduces sen-
so aul s. Cu en senso s based on Hall e ec a e no
linea wi h espec o magne ic lux densi y, so hey
may be sa u a ed i he measu ed cu en exceeds he
nominal suppo ed alue, which engende s a bias in
measu emen [30] and [31]. A disconnec ion o he elec-
ical link o b eakdown o he senso is an o igin o he
o al loss o eedback in o ma ion.
Rema k 2. In all simula ions in his sec ion, a ed
load oque Tl = 6.1[Nm] is applied a = 1 [s] and
each aul is ac i a ed a = 1.5[s].
2.1. Speed Senso Faul s E ec on
IFOC
In his pape , he in es iga ed aul s a e: in e mi en
aul , o se aul , and o al loss aul . Each one is
pe o med in Ma lab as ollows:





In e mi en aul : Ω = Ω + δ,
O se aul : Ω = Ω + γ,
To al loss: Ω = Ω ×0,
(1)
whe e γis he o se alue, γ= 10 ad·s−1, and δis
a andom numbe wi h a mean alue equal o 0 and a
a iance equal o 10 ad·s−1.
Figu e 1 shows phase cu en , o o luxes on “dq”
e e ence ame, and speed o each speed senso aul .
Speed senso aul s ha e a clea impac on he ec-
o con ol. The in e mi en aul causes signi i-
can o que ipples which cause he changes in speed
(Fig. 1(a)). Rega ding o se aul (Fig. 1(b)), i is
ea ed almos as a load o que by he ec o con ol.
So he phase cu en s ise ins an ly. Howe e , he e -
ec o he aul on he ac ual speed is no elimina ed
since he o se alue added o he ac ual speed makes
he speed alue p o ided by he aul y senso equal o
he e e ence. To al loss aul is he mos isky be-
cause he speed becomes no longe con olled. Thus,
we limi ed he s a o elec ic speed “ωs” and he cu -
en “Isq” o p e en speed di e gence. S a o cu en s
ise o wo imes he a ed cu en a he aul momen
and o o luxes do no ollow hei e e ences a e he
aul (Fig. 1(c)). The To que ipple a e inc eases o
Temax −min ≈5.8Nm.
2.2. Speed Senso Faul s De ec ion
Mos o en, he speed a ia ion due o a senso aul is
as e han i s a ia ion due o a o que load, change
in speed e e ence o aul s in o he componen s o he
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 2
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
-5
0
5
Ia [A]
0
0.5
1
Ro o Flux
[Wb]
5
6
7
To que
[Nm]
1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6
Time [s]
99.5
100
100.5
Speed
[Rad·s-1]
Fi dFi q
(a) In e mi en aul .
-10
0
10
Ia [A]
-2
0
2
Ro o Flux
[Wb]
-5
0
5
10
To que
[Nm]
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Time [s]
80
100
120
Speed
[Rad·s-1]
Fi d
Fi q
(b) O se aul .
-10
0
10
Ia [A]
-2
0
2
Ro o Flux
[Wb]
-5
0
5
10
To que
[Nm]
1.3 1.4 1.5 1.6 1.7 1.8 1.9
2
Time [s]
80
100
120
Speed
[Rad·s-1]
Fi d
Fi q
(c) To al loss aul .
Fig. 1: Phase cu en , o o luxes on “dq” e e ence ame, and
ac ual speed in p esence o speed senso aul : (a) in e -
mi en aul , (b) o se aul , (c) o al loss aul . Wi h
Ω∗= 100 ad·s−1,Tl = 6.1Nm and φ∗
= 1 Wb. Each
aul is applied a = 1.5s.
d i e [32]. F om his s andpoin , he de ec ion could be
achie ed by compa ing only wo poin s om speed da a
be ween which he dis ance is p opo ional o he sam-
pling ime. In ou case, since T= 5 ·10−6s , i e s eps
dis ance is su icien ; τd= 5 ×T. The de ec ion sig-
nal is compu ed as illus a ed by he scheme in Fig. 2.
This p oposed speed senso aul s de ec ion scheme is
less un ime consuming compa ed o obse e based
app oaches o some simple signal p ocessing echniques
such as a e age s anda d de ia ion in [32].
Ω(𝑡 −𝜏𝑑)
Ω(𝑡)
− +
+ −
Th eshold
𝑖𝑓 𝜀1>0 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑚𝑝𝑢𝑙𝑠𝑒
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝜀1
𝜀2
∫
dsw
dw
|𝑥(𝑡)|
𝑖𝑓 𝜀2>0 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 = 0
Fig2
Fig. 2: De ec ion scheme o speed senso aul s. Wi h τd=
5×T.
Figu e 3 shows he simula ion esul s o he sug-
ges ed de ec ion me hod wi h h ee di e en aul s. I
is clea ha any ab up change in speed da a gene a es
impulses in “dω” cu e.
Hence, any impulses due o measu emen noise, load
o que o ansien s in speed a e kep unde a p ese
h eshold. A aul occu ence momen , “dω” exceeds
he h eshold gene a ing a de ec ion signal “dsω”. The
di e ence be ween “dω” and he h eshold is ep e-
sen ed by “1”. When i s alue is g ea e han ze o,
we ge an impulse which is hen in eg a ed o ge a
cons an signal “2”. Since his alue is e y small, i is
ans o med ia a elay o p oduce a meaning ul bina y
signal.
2.3. Cu en Senso Faul s E ec on
IFOC/Senso less IFOC
Th ee di e en aul s a e conside ed; o se aul , gain
aul , and o al loss o eedback in o ma ion. They a e
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 3
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
0
10
20
30
40
dw
0 0.5 1 1.5 2 2.5 3
Time [s]
-0.5
0
0.5
1
1.5
dsw
dw
Th eshold
Speed senso aul
(a) In e mi en aul .
0
5
10
15
20
dw
0 0.5 1 1.5 2 2.5 3
Time [s]
-0.5
0
0.5
1
1.5
dsw
dw
Th eshold
Speed senso aul
(b) O se aul .
0
50
100
150
dw
0 0.5 1 1.5 2 2.5 3
Time [s]
-0.5
0
0.5
1
1.5
dsw
Th eshold
Speed senso aul
dw
(c) To al loss aul .
Fig. 3: De ec ion esul s o speed senso aul s: (a) in e mi en
aul , (b) o se aul , (c) o al loss aul .
simula ed in Ma lab as ollows:





O se aul : Ic =Ic+ρ,
Gain aul : Ic =Ic×$,
To al loss: Ic =Ic×0,
(2)
whe e ρis he o se alue (ρ= 2A) and $is he gain
coe icien ($= 0.5).
The o se alue and he gain a e chosen ela i ely
small, so hey will no ha e a conside able impac on
elec ical and mechanical a iables, ye , hey should
be de ec ed by an algo i hm (so wa e) using he mea-
su emen s o o he non- aul y senso s. In he case o
IFOC wi h speed encode , cu en senso aul s cause
ei he luc ua ion o o o luxes (o se aul ) o de-
ia e hem om hei e e ences (gain and o al loss
aul ). Consequen ly, conside able o que oscilla ions
a e no iced wi h Temax −min ≈5Nm, which may lead
o long- e m o a mechanical de e io a ion o he sha .
In senso less ope a ion, MRAS speed es ima o loses
i s e iciency when cu en senso s p o ide inaccu a e
alues. Hence, his leads o a o al con olle ailu e.
Figu e 4 illus a es: “Ib” phase cu en , o o luxes
on “dq” e e ence ame, o que, and speed. We chose
o simula e he aul o only one cu en senso since
he occu ence p obabili y o wo o h ee aul s in a
sho ime pe iod is e y low. Bo h ope a ions a e
conside ed: wi h and wi hou a speed senso .
2.4. Faul y Cu en Senso
De ec ion and Isola ion
The simples way o de ec a cu en senso aul in
a balanced h ee-phase sys em is he sum o he h ee
cu en s. This sum is p ac ically null in no mal ope a-
ion o he d i e, ye i changes due o a cu en senso
aul . We adop ed he absolu e mean alue o h ee
cu en s sum “I ” as a aul indica o “dsi” when i ex-
ceeds ce ain h eshold “ζ” (Fig. 5). As o localiza ion,
a new algo i hm is p oposed based on RMS alues o
phase cu en s. The use o RMS alues pe mi s he
localiza ion o a cu en senso unde gain aul , un-
like a e age alues which a e null when cu en s s ill
al e na ing a e he aul . Hence, he e iciency o he
echnique p oposed in [7] is no e i ied wi h gain aul .
Mo eo e , he de eloped me hod in his pape is less
compu a ionally demanding han he one in [7].
The key idea o localiza ion is o look o he mini-
mum alue be ween wo RMS alues o phase cu en s.
Because his alue co esponds o he di e ence be-
ween he RMS cu en s measu ed by heal hy senso s,
hen he emaining phase cu en is measu ed by a
aul y one. F om Fig. 6, i he senso o phase “b” is
aul y, bwill be equal o “0” since i is he di e ence
be ween he alue chosen by he unc ion minimum and
he di e ence |Ia ms −Ib ms |. When b= 0, hen he
condi ional es is e i ied and he middle ou pu will
be equal o “1”. This la e is mul iplied by 2 which
is he index o phase “b”. Since aul y senso index is
no cons an be o e he aul occu ence we mul iply
i by “dsi” o a oid any alse localiza ion signal. The
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 4
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
-5
0
5
Ib [A]
-0.5
0
0.5
1
1.5
Ro o Flux
[Wb]
5
10
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
95
100
105
Speed
[ ad·s-1]
Fi d
Fi q
(a1)
To que
[Nm]
-20
0
20
Ib [A]
-0.5
0
0.5
1
1.5
Ro o
Flux [Wb]
-50
0
50
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
100
200
Speed
[ ad·s-1]
Fi dFi q
(a2)
To que
[Nm]
(a) O se aul .
-5
0
5
Ib [A]
-0.5
0
0.5
1
1.5
Ro o Flux
[Wb]
5
10
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
95
100
105
Speed
[ ad·s-1]
Fi d
Fi q
(a1)
To que
[Nm]
-20
0
20
Ib [A]
-0.5
0
0.5
1
1.5
Ro o
Flux [Wb]
-50
0
50
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
100
200
Speed
[ ad·s-1]
Fi dFi q
(a2)
To que
[Nm]
(b) O se aul wi h MRAS.
-5
0
5
Ib [A]
-0.5
0
0.5
1
1.5
Ro o Flux
[Wb]
5
10
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
95
100
105
Speed
[ ad·s-1]
Fi qFi d
(b1)
To que
[Nm]
-10
0
10
Ib [A]
-1
0
1
2
Ro o
Flux [Wb]
-50
0
50
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
50
100
150
Speed
[ ad·s-1]
Fi q
Fi d
(b2)
To que
[Nm]
(c) Gain aul .
-5
0
5
Ib [A]
-0.5
0
0.5
1
1.5
Ro o Flux
[Wb]
5
10
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
95
100
105
Speed
[ ad·s-1]
Fi qFi d
(b1)
To que
[Nm]
-10
0
10
Ib [A]
-1
0
1
2
Ro o
Flux [Wb]
-50
0
50
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
50
100
150
Speed
[ ad·s-1]
Fi q
Fi d
(b2)
To que
[Nm]
(d) Gain aul wi h MRAS.
-10
0
10
Ib [A]
-1
0
1
2
3
Ro o Flux
[Wb]
-20
0
20
To que
[Nm]
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
90
100
110
Speed
[ ad·s-1]
Fi d
Fi q
(c1)
-10
0
10
Ib [A]
-1
0
1
2
3
-20
0
20
To que
[Nm]
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
50
100
150
Speed
[ ad·s-1]
Fi d
Fi q
(c2)
Ro o Flux
[Wb]
(e) To al loss aul .
-10
0
10
Ib [A]
-1
0
1
2
3
Ro o Flux
[Wb]
-20
0
20
To que
[Nm]
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
90
100
110
Speed
[ ad·s-1]
Fi d
Fi q
(c1)
-10
0
10
Ib [A]
-1
0
1
2
3
-20
0
20
To que
[Nm]
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
50
100
150
Speed
[ ad·s-1]
Fi d
Fi q
(c2)
Ro o Flux
[Wb]
( ) To al loss aul wi h MRAS.
Fig. 4: Phase cu en , o o luxes on “dq” e e ence ame, o que and ac ual speed in p esence o cu en senso aul o phase
“b” wi h speed senso and wi h MRAS. Ω∗= 100 ad·s−1,Tl = 6.1Nm and φ∗
= 1 Wb. Each aul is applied a = 1.5s.
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 5

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
+ −
+ −
+ −
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
Minimum
+ −
+ −
− +
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
𝑟𝑐
𝑟𝑏
𝑟𝑎
×3
×2
×1
+ + +
×
dsi
Faul y senso index
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
Minimum
+ −
− +
− +
𝑧𝑎
𝑧𝑏
𝑧𝑐
×3
×2
×1
+ + +
×
NAND
NOT dsi
𝑑Ω∗
𝑑𝑡
×𝜆𝒕𝒔
+ +
𝜆𝒔𝒔
− +
𝑦
×
Faul y in e e leg index
LPFLPFLPF
LPF LPF LPF
LPF LPF LPF
+ + +
Faul y
in e e leg
Localiza ion
RMS
dsi
NOT
𝐼𝑓
Ω∗
Faul y
cu en
senso
localiza ion
|𝑥(𝑡)|
mean
alue
𝐼𝑎𝑏𝑐
dsps
lsps
𝑑𝑠𝑖
𝑦0
Faul y senso
numbe
Faul y
in e e leg
numbe
𝑖𝑓 𝐼𝑓≥ 𝜁 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 = 1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡=0
𝑖𝑓 𝑟𝑗= 0 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝜌𝑚𝑖𝑛 <𝑧𝑗< 𝜌𝑚𝑎𝑥 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝑑Ω∗
𝑑𝑡 ≥1⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑖𝑓 𝑦>0⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
Fig5
Fig6
Fig8
Fig. 5: Global block scheme o cu en senso /in e e leg aul
de ec ion and isola ion.
p oposed algo i hms a e e i ied by simula ion and he
esul s a e shown in Fig. 7. Fo all h ee conside ed
aul s, he gap be ween he RMS alues co esponding
o heal hy senso s is he smalles . Faul y senso lo-
caliza ion block is in en ionally ac i a ed a e 0.035 s
om de ec ion momen , which is he ime equi ed o
ge a cons an localiza ion signal.
3. Faul y Powe Swi ch
De ec ion and Localiza ion
As an ex ension o senso aul diagnosis, we added a
block o iden i y he in e e leg wi h a aul y powe
swi ch. Sho ci cui aul s o powe swi ches canno
be localized as enough since he cu en o he DC
ol age sou ce inc eases in milliseconds o a high alue
which igge s he p o ec ion componen s ( use o e-
lay) o shu down he d i e. Only open ci cui aul s o
con olled powe swi ches a e conside ed because hey
a e mo e p one o aul s han an ipa allel diodes. One-
hal cycle o phase cu en passes due o he loss o an
in e e powe swi ch. Consequen ly, he RMS cu -
en in aul y in e e leg dec eases. Figu e 8 shows
he algo i hm o de ec and localize he aul y in e e
swi ch. Fo example, i op swi ch o he second leg is
open-ci cui ed, he RMS cu en o he second phase
"Ib ms " will ha e he lowes alue, and he wo o he
RMS cu en s "Ia ms " and "Ic ms " will ise o compen-
sa e he cu en d op. As illus a ed in Fig. 8, a e he
aul , zbs ays in he de ined in e al: ρmin < zb< ρmax
howe e : za,zc a y such as: ρmax < za,ρmax < zc.
The di e ence be ween he ou pu o he unc ion min-
imum and Ij ms is no ed as zj. Wi h jis he phase
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
+ −
+ −
+ −
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
Minimum
+ −
+ −
− +
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
𝑟𝑐
𝑟𝑏
𝑟𝑎
×3
×2
×1
+ + +
×
dsi
Faul y senso index
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
Minimum
+ −
− +
− +
𝑧𝑎
𝑧𝑏
𝑧𝑐
×3
×2
×1
+ + +
×
NAND
NOT dsi
𝑑Ω∗
𝑑𝑡
×𝜆𝒕𝒔
+ +
𝜆𝒔𝒔
− +
𝑦
×
Faul y in e e leg index
LPFLPFLPF
LPF LPF LPF
LPF LPF LPF
+ + +
Faul y
in e e leg
Localiza ion
RMS
dsi
NOT
𝐼𝑓
Ω∗
Faul y
cu en
senso
localiza ion
|𝑥(𝑡)|
mean
alue
𝐼𝑎𝑏𝑐
dsps
lsps
𝑑𝑠𝑖
𝑦0
Faul y senso
numbe
Faul y
in e e leg
numbe
𝑖𝑓 𝐼𝑓≥𝜁 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡=0
𝑖𝑓 𝑟𝑗= 0 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 = 1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝜌𝑚𝑖𝑛 <𝑧𝑗< 𝜌𝑚𝑎𝑥 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝑑Ω∗
𝑑𝑡 ≥1⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑖𝑓 𝑦>0⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
Fig5
Fig6
Fig8
Fig. 6: Isola ion scheme o aul y cu en senso .
index and j=ao bo c. The in e al limi s: ρmin,
ρmax a e chosen close o ze o, whe e ρmin =−0.04 and
ρmax = 0.04. The condi ional es ou pu equals one
i zjis included in he in e al [ρmin,ρmax] o he wise
i equals ze o. In he conside ed case, he ou pu o
he condi ional es block is [1 1 1] be o e he aul
and [0 1 0] a e he aul occu ence. When hese
bina y alues pass by he NAND unc ion, hey gene -
a e a de ec ion signal “dsps” which is null be o e he
aul -in s eady s a e- and equal o 1 a e i . Since
he an ipa allel diode allows he con inui y o cu en ,
an open swi ch aul a ec s sligh ly he sum o h ee
cu en s. This is used o di e en ia e be ween senso
and powe swi ches aul s. We mul iply by he in e se
o he senso aul de ec ion signal “(dsi)” o u n o
he localiza ion block o powe swi ches aul s when a
cu en senso aul occu s. Also, o elimina e any alse
ala m due o di e en changes in speed e e ence, we
se an adap i e h eshold in unc ion o speed e e ence,
whe e he λss and λ s a e he s eady and ansien s a e
h esholds espec i ely. λ s is ac i a ed only i he e -
e ence speed changes and i s de i a i e is supe io o
one. The localiza ion o he uppe swi ch aul in he
second in e e leg is simula ed in Ma lab and he e-
sul is illus a ed in Fig. 9. No ice ha in a ansien
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 6
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
2
3
4
IabcRMS
[A]
IaRMS IbRMS IcRMS
-10
0
10
Cu en s
Sum
0
1
2
absolu e
mean o
he sum
0
0.5
1
De ec ion
Signal
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
0
1
2
Faul y
Senso
Numbe
I
ζ
(a) O se aul .
1
2
3
4
IabcRMS
[A]
IaRMS IbRMS IcRMS
-10
0
10
Cu en s
Sum
0.5
1
1.5
Absolu e
mean o
he sum
0
0.5
1
De ec ion
Signal
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
0
1
2
Faul y
Senso
Numbe
I
ζ
(b) Gain aul .
0
2
4
6
8
IabcRMS
[A]
IaRMS IbRMS IcRMS
-20
0
20
Cu en s
Sum
0
5
Absolu e
mean o
he sum
0
0.5
1
De ec ion
Signal
1.2 1.3 1.4 1.5 1.6 1.7 1.8
Time [s]
0
1
2
Faul y
Senso
Numbe
I
ζ
(c) To al loss aul .
Fig. 7: De ec ion and isola ion esul s o cu en senso aul s:
(a) o se aul , (b) gain aul , (c) o al loss aul .
s a e (0< < 0.25) “dsps” is no null, which could
p oduce a alse ala m i we did no use an adap i e
h eshold. The p e-localiza ion signal “lsps” is ac i-
a ed by “dsps” because i has no meaning un il he
aul occu ence, whe e i s alue indica es he aul y
leg.
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
+ −
+ −
+ −
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
Minimum
+ −
+ −
− +
|𝑥(𝑡)|
|𝑥(𝑡)|
|𝑥(𝑡)|
𝑟𝑐
𝑟𝑏
𝑟𝑎
×3
×2
×1
+ + +
×
dsi
Faul y senso index
𝐼𝑏𝑟𝑚𝑠
𝐼𝑎𝑟𝑚𝑠
𝐼𝑐𝑟𝑚𝑠
Minimum
+ −
− +
− +
𝑧𝑎
𝑧𝑏
𝑧𝑐
×3
×2
×1
+ + +
×
NAND
NOT dsi
𝑑Ω∗
𝑑𝑡
×𝜆𝒕𝒔
+ +
𝜆𝒔𝒔
− +
𝑦
×
Faul y in e e leg index
LPFLPFLPF
LPF LPF LPF
LPF LPF LPF
+ + +
Faul y
in e e leg
Localiza ion
RMS
dsi
NOT
𝐼𝑓
Ω∗
Faul y
cu en
senso
localiza ion
|𝑥(𝑡)|
mean
alue
𝐼𝑎𝑏𝑐
dsps
lsps
𝑑𝑠𝑖
𝑦0
Faul y senso
numbe
Faul y
in e e leg
numbe
𝑖𝑓 𝐼𝑓≥ 𝜁 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 = 1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡=0
𝑖𝑓 𝑟𝑗= 0 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 = 1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝜌𝑚𝑖𝑛 <𝑧𝑗< 𝜌𝑚𝑎𝑥 ⇒𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑤𝑖𝑡ℎ 𝑗=𝑎 𝑜𝑟 𝑏 𝑜𝑟 𝑐
𝑖𝑓 𝑑Ω∗
𝑑𝑡 ≥1⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
𝑖𝑓 𝑦>0⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =1
𝑒𝑙𝑠𝑒 ⇒ 𝑜𝑢𝑡𝑝𝑢𝑡 =0
Fig5
Fig6
Fig8
Fig. 8: Faul y leg isola ion algo i hm.
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8
2
4
6
IabcRMS
[A]
IaRMS IbRMS IcRMS
1.45 1.5 1.55 1.6 1.65 1.7
0
0.2
0.4
z1,z2,z3
& h esholds
z1 z2 z3 ho1 ho2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
5
10
lsps,
dsps,
NOT(dsi)
lsps dsps NOT(dsi)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
2
4
6
y0
y0 Adap ed h eshold
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time [s]
0
1
2
Faul y leg
Index
Fig. 9: Faul y leg isola ion esul s.
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 7
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
Since no cu en senso aul occu ed, “(dsi)” is con-
s an ly equal o “1”. The de ec ion and localiza ion de-
lay is due o he low pass il e s used o educe signals
luc ua ions.
4. Imp o ed AFTC
4.1. O e iew o he AFTC Scheme
Figu e 10 shows he o e all scheme o he IM d i e wi h
an AFTC and a de ec ion mechanism. A speed encode
and h ee cu en senso s a e used o measu emen .
All senso s da a pass by a de ec ion block o de ec any
senso mal unc ion. Re e ence ol ages a e gene a ed
by he ac i e aul ole an con olle .
The AFTC block inco po a es ou di e en con ol
echniques, each one o hem equi es a ce ain mini-
mum o senso s o unc ion p ope ly. The selec ion o
he con ol s a egy is achie ed au oma ically depend-
ing on he ou pu s o he senso s aul s de ec o . In
Tab. 1, we summa ize he possible de ec o ou pu s,
emaining heal hy senso s, and he chosen con olle .
1
Ω∗
DC powe supply
Ac i e Faul
Tole an
Con olle
𝑉
𝑎
∗
𝑉
𝑏
∗
𝑉
𝑐
∗
dsw
dsi
Speed and Cu en
Senso Faul s
De ec o
𝑖𝑎
𝑖𝑏
𝑖𝑐
Ω
Faul
Faul
Fig. 10: O e all scheme o he IM d i e wi h AFTC.
Tab. 1: De ec ion signals and he selec ed con ol echnique.
dsi dsw
Remaining
heal hy
senso s
Con olle numbe 1:
IFOC 0 0
Speed senso ,
h ee cu en
senso s
Con olle numbe 2:
IFOC senso less 0 1
Th ee cu en
senso s, DC
ol age
measu emen
Con olle numbe 3:
V/ CL 1 0 Speed senso
Con olle numbe 4:
V/ OL 1 1 No senso s
a ailable
4.2. Smoo hening he T ansi ion o
V/ CL Con ol
In AFTC, a e de ec ing a senso aul , a econ igu a-
ion o he con ol scheme is necessa y, bu his s ep is
no always s aigh o wa d. As shown in Fig. 11, he e
is a phase shi be ween he e e ence ol age o IFOC
and V/ CL. Thus, he ansi ion be ween hese wo
con ol echniques p oduces signi ican o que dis o -
ion and conside able speed luc ua ion due o a decel-
e a ion o he o a ing magne ic ield.
Fig. 11. Re e ence ol age o IFOC and V/
CL on “𝛼𝛽” e e ence ame
𝑉
𝑠𝛽
𝑉
𝑠
∗
ሬ
ሬ
ሬ
ሬ
Ԧ
𝐼𝐹𝑂𝐶
𝑉
𝑠
∗
ሬ
ሬ
ሬ
ሬ
Ԧ
𝑉
𝑓 𝐶𝐿
Di ec ion o
Ro a ion
𝜑
𝑉
𝑠𝛼
𝜃
𝑉
𝑓𝐶𝐿
𝜃
𝐼𝐹𝑂𝐶
Fig. 11: Re e ence ol age o IFOC and V/ CL on “αβ” e e -
ence ame.
Se e al esea che s sugges ed some ideas o educe
he e ec o he ansi ion, o example, Diallo e
al. ecommend ha he swi ching mus be pe o med
when he phase shi be ween he e e ence ol ages o
ec o con ol and scala con ol is almos ze o [33].
Howe e , in hei pape , he selec ion o he sui able
swi ching momen is no done au oma ically by he
con olle bu p og ammed by he au ho s. In [34],
he au ho s educed he phase shi be ween he con-
olle s by eadjus ing he PI pa ame e s o V/ CL.
In hese pape s, he p ocess om de ec ion o ansi-
ion is no well cla i ied. In his sec ion, we p esen a
new app oach o smoo hen he ansi ion in he AFTC
by linking e e ence ol ages o wo con olle s whe e
one is ac i e and he o he is on s andby be o e he
ansi ion momen . Then, he con olle in s andby is
libe a ed g adually o ake o e when i is selec ed. Be-
sides, an adap a ion o he e e ence speed is necessa y
o achie e a be e pe o mance.
The new scheme o V/ CL con ol is shown in
Fig. 12. Basically, wo main modi ica ions on V/ CL
con ol a e done o smoo hen he ansi ion o i om
IFOC due o a cu en senso aul :
•The i s modi ica ion consis s o p epa ing he
con olle V/ CL o ake o e by ixing i s e e -
ence ol age on IFOC’s, i.e. he elec ic equen-
cies o he wo con olle s a e equalized. This is
pe o med by he ollowing equa ion:
ω0
sV
CL =ωsV
CL −ωsV
CL −ωsIF OC ·RcCL,
(3)
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 8
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 16 |NUMBER: 1 |2018 |MARCH
PI
Vboos
+ -
+ +
V/
𝑽𝒂𝒃𝒄
∗
𝑽𝒎
𝜽𝒔
PWM
In e e
+ +
𝑽𝒂𝒃𝒄
𝜔𝑠𝑉𝑓
+ -
𝜔𝑠𝐼𝐹𝑂𝐶
×
Con olle
Numbe
1s
O de
LPF
2nd
O de
LPF
+ -
∫
𝒑
𝛀∗
+ -
×
𝛀
+ + +
Vboos
+ +
V/
𝑽𝒂𝒃𝒄
∗
𝑽𝒎
𝜽𝒔
PWM
In e e
𝑽𝒂𝒃𝒄
𝜔𝑠𝑉𝑓
𝑂𝐿
+ -
×
1s
O de
LPF
+ +
∫
𝑘𝑑2(𝑡−𝜏𝑑2)
𝛀∗
+ +
𝜔𝑠𝑉𝑓
𝐶𝐿
𝒑
𝛀∗
1s
O de LPF wi h
adap i e ime cons an
𝝉
Adap i e
gain
Ω∗ ′𝑉
𝑓𝐶𝐿
𝜔𝑠𝑉
𝑓𝐶𝐿
′
ℛ𝑐𝐶𝐿
ℛ𝑐𝐶𝐿
ℛ𝑐𝑂𝐿
𝐴ℛ𝑐𝑂𝐿
𝜔𝑠𝑉
𝑓𝑂𝐿
′
Ω∗ ′𝑉
𝑓𝑂𝐿
𝑘𝑑1(𝑡−𝜏𝑑1)
𝑖𝑓 𝑐𝑛≠3 ⇒𝑜𝑢𝑡𝑝𝑢𝑡=1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡= 0
Con olle
Numbe
𝑖𝑓 𝑐𝑛≠4 ⇒𝑜𝑢𝑡𝑝𝑢𝑡= 1
𝑒𝑙𝑠𝑒 ⇒𝑜𝑢𝑡𝑝𝑢𝑡=0
Fig13
Fig. 12: Modi ied V/ CL con ol o so ansi ion. “Dashed line” s ands o all he modi ica ions on he basic scheme.
whe e ω0
sV
CL is he new elec ic equency o V/
CL con ol. RcCL is he eleasing coe icien . I
equals o “1” as long as V/ CL con olle is no
selec ed. A he ansi ion A he ansi ion mo-
men RcCL goes o “0” g adually h ough a low
pass il e . This means ha he V/ CL con ol
becomes independen a e ansi ion.
•The second modi ica ion consis s in adap ing Ω∗
by Eq. (4), assumed as an an icipa ion ac ion, o
educe all so s o speed de ia ions om he e e -
ence, including speed a ia ion due o ansi ion.
Ω∗0
V
CL = (Adap i e gain)·2nd O de LPF·
Ω∗−Ω) + RcCL ·kd1( −τd1),
(4)
whe e:
–Ω∗0
V
CL is he adap ed speed e e ence o V/
CL con ol.
–kd1( −τd1)pe mi s an ins an aneous ampli-
ica ion o speed e e ence a e he swi ching
momen . I is delayed by τd1 o keep a maxi-
mum alue o a sho ime s a ing om he
swi ching ins an .
–The 2nd o de LPF is conside ed as a e e -
ence sys em. The di e ence be ween i s ou -
pu and Ωis added o he e e ence speed
h ough he adap i e gain. So, he esponses
o he IM d i e and e e ence sys em a e in-
ended o be simila . This simple modi ica-
ion b ings many ad an ages, i does no only
so en he ansi ion bu also imp o es he
dynamic beha io by educing he o e shoo
and he e ec o he load o que.
–The adap i e gain is compu ed in unc ion o
Ω∗using a designed lookup able. This la -
e is o med o ele en-speed e e ence poin s
and he co esponding gain alues allowing
he smoo hes ansi ion om IFOC o V/
CL con ol.
4.3. Smoo hening he T ansi ion o
V/ OL Con ol
The new scheme o V/ OL con ol is shown in Fig. 13.
Same imp o emen s a e made o V/ OL con ol o
smoo hen he ansi ion o i om senso less IFOC o
V/ CL.
•~
V∗
sV
OL is linked o ~
V∗
sV
CL by Eq. (5):
ω0
sV
OL =ωsV
OL +ω0
sV
CL −ωsV
OL ·ARcOL,
(5)
whe e:
–ω0
sV
OL is he new s a o elec ic speed o V/
OL con ol.
–ARcOL is an adap i e eleasing coe icien .
I s alue is always equal o “1” ill he V/
OL con ol is selec ed, hen, i ansi s o “0”
g adually h ough a 1s o de LPF wi h an
adap i e ime cons an “τ”. A lookup able
is composed o ele en speed e e ence poin s
and he co esponding “τ” alues chosen o
allow he smoo hes elease o ~
V∗
sV
OL .
c
2018 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 9