powe sys ems dis u bances. The e can be comple ely di e en de ini ions o powe
quali y, depending on he poin o iew o u ili ies, manu ac u e o load equipmen ,
o cus ome . Fo ins ance, u ili ies may de ine powe quali y as eliabili y and show
s a is ics demons a ing ha he sys em is almos 100 pe cen eliable. The
manu ac u e o load equipmen may de ine quali y powe as hose cha ac e is ics o
he powe supply ha enable he equipmen o wo k p ope ly. Howe e , powe
quali y is ul ima ely a cus ome -d i en issue and he cus ome ’s poin o e e ence
mus ake p ecedence. The e o e, a powe quali y p oblem can be de ined as any
powe p oblem mani es ed in ol age, cu en , o equency de ia ions ha esul s in
ailu e o mal unc ioning o cus ome equipmen .
The subjec o his pape is he analysis o he ol age quali y o sensing any
de ia ion o he ol age wa e o m ou o ce ain limi s. Al e na ing cu en powe
sys ems a e designed o ope a e a a sinusoidal ol age o a gi en equency ( ypically
50 o 60 Hz) and magni ude. Any signi ican de ia ion in he magni ude, equency,
o pu i y o wa e o m is a po en ial powe quali y p oblem. These de ia ions mus be
as de ec ed o u he ac ions o s o ing o classi ica ion and s a is ical s udies.
So wa e p ocedu es ha e been de eloped, applying he FFT o analyzing hese
dis u bances [1]; howe e , due o he g ea amoun o s o ed da a and he ime o
equi ed p ocessing, such p ocedu e is slow and no e y e icien . To minimize
s o age space, we need o ep esen signals by as ew bi s as possible. This is he da a
comp ession p oblem, and has been s udied o se e al decades especially o image
comp ession [2]. Likewise, he noise educ ion has been deal wi h om a s a is ical
poin o iew [3-5].
Con inuous and disc e e wa ele ans o m (DWT) ha e been used in analysis o
non-s a iona y signals and se e al pape s [6-8] ha e p oposed he use o wa ele s o
he analysis o powe sys ems. They a e able o emo e noise and achie e high
comp ession a ios because o he “concen a ing” abili y o he wa ele ans o m. I
a signal has i s ene gy concen a ed in a small numbe o wa ele coe icien s, his
signal will be ela i ely la ge compa ed o any o he signal o noise ha has i s ene gy
sp ead o e a la ge numbe o coe icien s. This means ha h esholding he wa ele
ans o m will emo e he low ampli ude and undesi ed coe icien s in he wa ele
domain and econs uc s he signal wi h li le loss o in o ma ion. Wa ele
h esholding has impo an applica ions in s a is ic. Donoho and Johns one [9]
p opose o s a wi h a wa ele decomposi ion o he da a se , h esholding la e he
coe icien s, and hen use he wa ele econs uc ion as an es ima e unc ion. This is
he model o he as and e icien algo i hm o da a-comp ession ha we conside in
his pape .
2. Powe Quali y Measu emen o Th ee-Phase Sys ems
The powe quali y measu emen sys em o powe quali y moni o (PQM) desc ibed in
his pape has been speci ically de eloped o he analysis o h ee-phase line
ol ages. I s o es da a by sampling he h ee phase- o-neu al ol ages
simul aneously. Then, an e icien measu emen algo i hm, based on he powe -
equency da a es ima ion ob ained om h ee equidis an samples o a sinusoidal
729Classi ica ion o Dis u bances in Elec ical Signals Using Neu al Ne wo ks
signal, calcula es he ins an aneous equency o he synch oniza ion o he ol age
and sampling pe iods. I allows he es ima ed powe equency o be de ined om he
ponde ed mean o he es ima ion pe o med in each phase R-S-T.
Thus, he de ec ed R-phase o he ol age signal can be p ocessed o cons uc a
pe ec h ee-phase sys em o being used as e e ence. The PQM de ec s indi idual
e en s, a he ime o occu ence, by compa ing he moni o ed signals o he e e ence
h ee-phase ol ages. When a h eshold pa ame e is exceeded, a dis u bance e en is
de ec ed. Th eshold pa ame e s a e adjus able o e a speci ied ange o accommoda e
di e en moni o ing ci cums ances.
•
Ins an aneous ol age. Ins an aneous ol age ampli ude measu ed wi h espec o
he powe - equency sine wa e. Sho -du a ion ol age a ia ions such as impulsi e
and oscilla o y ansien s, wa e o m dis o ion and ol age luc ua ions can be
de ec ed. The measu emen in e al o sho -du a ion ol age a ia ion is om 500ns
o 50ms.
•
AC ms ol age. Wi h ms sensing, acco ding o he abo e s a egy o
synch oniza ion, he measu emen in e al is an in eg al numbe o cycles o he
undamen al powe equency. Ha monic con en , swell, long- e m in e up ions and
ol age unbalance e en s can be de ec ed. The measu emen in e al is om 1 cycle
o 1 min.
Ha ing de ec ed he dis u bance e en , he digi ized samples a e s o ed in memo y.
As subsequen p ocessing, measu emen , and epo ing o he dis u bance e en will
be based en i ely upon he s o ed samples, he PQM e ain wo-cycles da a om
be o e and a e he de ec ion poin o accu a ely econs uc he en i e dis u bance
e en .
Fu he mo e, he digi ized da a is o ma ed o p o ide a comp essed and de ailed
g aphic ep esen a ion o he dis u bance wa e o m. The e o e, he PQM includes wo
algo i hms: one o calcula ing he ha monic spec um o he incoming ol age da a,
using he disc e e ou ie ans o m (DFT), and o he algo i hm o il e ing and
comp essing he collec ed dis u bance da a using he disc e e wa ele ans o m
(DWT). The wo algo i hms a e applied concu en ly.
The con en ional DFT is applied o he o iginal digi ized samples, (n), ge ing he
se o ou ie coe icien s and he i s 50 ha monics in phaso o m. The second
algo i hm consis s o he ollowing s eps.
A. Wa ele decomposi ion. (n) samples a e ans o med in o de o gene a e a se
o signal coe icien s. The DWT used (Daubechies amily Db4) is applied o (n),
ge ing signals aj(n) and d1(n), whe e j is he index le el. Family Db4 is pa icula ly
app op ia e o de ec ing dis u bances o high equency ( ansien s), as i is mo e
localized in ime han o he membe s o he same amily a e.
B. Th eshold wa ele es ima o s and econs uc ed signal A p ocess o compa ison
be ween he inpu signal and he econs uc ed signal aj(n) begins. This p ocess s ops
when he di e ence be ween he wo signals is less han he se h eshold. One o he
goals o he p esen wo k is o each a high comp ession a io. This exp esses he
minimum amoun o da a necessa y o eco e ing he o iginal signal.
730 C. Leon e al.
In a i s phase, he algo i hm o coe icien il e ing pe o ms a compa ison o
signals aj wi h he o iginal signal (n) o ob ain he e o signal
ξ
j. In a second phase,
he absolu e maximum alue o
ξ
j is compa ed wi h a ixed h eshold
λ
. I he
magni ude o he e o signal is less han λ, hen he signal esul ing ( econs uc ed
signal) is he new econs uc ed signal (n)*. In bo h phases, he op imal ela i e e o
be ween he o iginal (n) and he econs uc ed (n)* signal is used o measu ing he
quali y o he es ima o .
These eco ding mechanisms make he PQM mos sui able o au oma ic
classi ying o dis u bance wa e o ms and analyzing complex powe -quali y p oblems
when p ope ly applied by he expe use .
2.1. Th ee-Phase A bi a y-Func ion Gene a o
We a e de eloping a h ee-phase a bi a y- unc ion gene a o (Fig. 1) ha simula es
all kinds o elec ical dis u bances in line ol ages such as oscilla o y ansien s,
wa e o m dis o ion, ol age luc ua ions, sag, swell, in e up ions and ol age
unbalance. Gene a ed signals simula e hose ob ained a low- ol age le el by line
ol age ansduce s.
Fig. 1. Th ee phase a bi a y- unc ion gene a o
A wide ange o pa ame e se ings and combina ion possibili ies make he
ins umen an app op ia e ool o aining a i icial neu al ne wo ks in he
classi ica ion p ocess o elec ical dis u bances. Local ope a ion ia PC-con ol, using
he LabView p og am unning unde Windows, makes he uni use - iendly du ing
es pa ame e se -up.
The ins umen enables es s o be pe o med in acco dance wi h EN-50160 and he
o he common s anda ds o he Eu opean Union (EU). Tes s can be p e-p og ammed
731Classi ica ion o Dis u bances in Elec ical Signals Using Neu al Ne wo ks
and s o ed o being ecalled a any a bi a y ime a he ouch o a bu on.
Con inuously a ying alues o h ee-phase ol ages and d opou ime can be de ined
o occu au onomously. These es s can also be p og ammed o un in an endless
loop.
A p esen , h ee a bi a y unc ions a e gene a ed a e comple ion o he
pa ame e se ings using he ini ial p og am. I supe imposes h ee sinusoidal signals
wi h combined ha monic con en (up o he 50 h ha monic). Powe equency
a ia ions, o al ha monic dis o ion and ol age imbalance o he h ee-phase ol age
signals can be ini ially selec ed oo. Fig. 2 shows he sc een o pa ame e se ings in
case o he ol age wa e o ms o Fig. 1.
Unlike a na u al en i onmen , howe e , whe e dis u bance e en s a e
unp edic able, he ins umen allows he use o de elop con olled, epea able
simula ions. Resul s om simula ion es ing can be used o alida e in eal ime a
comple e sys em o powe dis u bance analysis, including da a cap u e, eco ding,
classi ica ion, and epo ing he esul s. These wa e o ms can be used o ain an
ANN oo. The sys em can also gene a e h ee analogue sinusoidal signals o be
u ilized as AC h eshold o , o example, as e e ence in he dis u bance classi ica ion
aining p ocesses o he ANN.
Fig. 2. Pa ame e se ings showing he ha monic con en o he ol age wa e o m
3. PQ Dis u bances Classi ica ion Using Neu al Ne wo ks
In powe enginee ing, he analysis o PQ p oblems is no ocused only o he de ec ion
o elec ical dis u bances. Fa mo e impo an is he abili y o classi y a ious ypes o
dis u bances as well. As an al e na i e o classi y he PQ dis u bances, we conside
using an a i icial neu al ne wo k (ANN). This echnology has been widely used in
Powe Sys ems managemen [10-14]. A e o e alua e se e al al e na i es (ART2,
LVQ, Coun e p opaga ion, e c), au ho s selec ed a ully connec ed eed o wa d ANN
wi h a backp opaga ion lea ning me hod [15,16] based on Gene alized Del a Rule.
This ype o ne wo k can esol e he unc ion app oxima ion p oblem ( o ind he
732 C. Leon e al.

unknown unc ion ha ela es a se o aining pa e ns) [17,18]. To simula e ANNs
we used simul aneously a se o i e In el PIII 450Mhz compu e s.
Fig. 3. Feed o dwa d Neu al Ne wo k
The eed o wa d neu al ne wo k ype has an inpu laye , one o mo e hidden
laye s, and an ou pu laye , as shown in Fig. 3.
The neu ons in di e en laye s a e connec ed by means o weigh s. When a
aining pa e n p is p esen ed, he inpu o a neu on j is he sum o he weigh ed
inpu signal ipi :
(1)
whe e wji is he weigh o i h inpu a j h node. The ou pu
opj om he neu on is gi en by
(2)
when a sigmoid ac i a ion unc ion is used.
T aining p ocess is ca ied ou using he backp opaga ion algo i hm. This lea ning
me hod upda es he in e connec ion weigh s using he Gene alized Del a Rule. In his
me hod, he e o a a gi en ou pu node opj, when a aining pa e n p is p esen ed, is:
(3)
whe e pj = a ge alue o j h ou pu node p oduced by inpu pa e n p; and ´’=
i s de i a i e o ac i a ion unc ion used by node j. The e o a a gi en non-ou pu
node j, when aining pa e n p is p esen ed, is:
(4)
ne w i
pj ij pi
i
=
∑
o ne e
pj j pj ne pj
=× =
+
−
1
1
δ
pj pj pj j pj
o ne
=−
()'
δδ
pj pj pk kj
k
ne w
=
∑
'()
∑∑
∑∑
∑∑
∑∑
∑∑
∑∑
X1
X2
Xn
Y1
Y2
Yn
733Classi ica ion o Dis u bances in Elec ical Signals Using Neu al Ne wo ks
in which k = numbe o neu ons in nex laye ; and
δ
pk = al eady compu ed o he
k h neu on in he nex laye . Weigh s may be modi ied a e each aining pa e n is
p esen ed. So, he weigh change applied o weigh wji , a e pa e n p has been
p esen ed, is:
(5)
whe e η = lea ning a e; and α = momen um ac o . E ec i eness and con e gence
o he lea ning algo i hm depend on he alue o and . I he selec ed lea ning a e is
oo high, he ne wo k ends o oscilla e a oiding he lea ning p ocess o he co ec
mapping om he inpu o he a ge . I he alue o is e y small, he ne wo k can
ake a e y long ime o lea n. Momen um ac o is used o speed ne wo k aining.
P ope selec ion o a momen um ac o can p e en ne wo k om oscilla ing.
Mean Squa e E o (MSE) is he measu e o how well he ne wo k ou pu ma ches
a ge ou pu . MSE is calcula ed a he end o each aining cycle. MSE is summed
o e each ou pu node o each pa e n. The MSE a he end o a gi en cycle is:
(6)
in which N = numbe o pa e ns; and T = numbe o ou pu s nodes.
The e a e no speci ic ules o selec an op imal ANN a chi ec u e [19]. In he PQ
p oblem he numbe o inpu neu ons is 113, clus e ing in h ee g oups:
- 48 ime inpu s, sampling an elec ical signal pe iod o 20 ms, in o de o de ec
impulsi e o oscilla o y ol age- ansien s.
- 50 RMS inpu s, one o each elec ical signal cycle du ing 2 second, in o de
o de ec long-du a ion dis u bances like o e ol ages o unde ol ages.
- 15 main ha monics o he signal inpu s, o de ec wa e o m dis o ions.
The numbe o ou pu neu ons is 8: one o a global e alua ion o he ol age
quali y (PQ) and 7 o each dis u bance: powe equency a ia ions, ansien s, sags,
sho du a ion in e up ions, swells, long du a ion in e up ions and wa e o m
dis o ions.
To selec he o he a iables ela ed wi h he ANN design and aining is usually
e y complex. Fo example, he numbe o hidden neu ons and he numbe o hidden
laye s o use a e di icul o be de e mined. I he a chi ec u e is oo small, he
ne wo k may no ha e enough deg ees o eedom o lea n he p ocess co ec ly. On
he o he hand, i he ne wo k is oo la ge, he solu ion may no con e ge du ing
aining o he ne wo k may o e lea n he da a.
In o de o selec he bes al e na i e, we ha e de eloped a h ee phase heu is ic
me hod. The i s phase began es ing he ans e unc ions o each neu on laye
MSE NT o
pj pj
j
T
p
N
=−
==
∑∑
12
11
()
∆∆
pji pjpi p ji
wo w
=+
−
ηδ α
() 1
734 C. Leon e al.
(linea , sigmoid o anh), weigh ini ializa ion ( andomly o used speci ied alues),
lea ning ule (Gene alized o Cumula i e Del a Rule), and he o de o aining
pa e ns p esen a ion. A second phase se s he numbe o hidden neu ons (10 o 140),
he numbe o hidden laye s (3 o 5), he lea ning a e (0.1 o 0.5) and momen um
ac o (0.1 o 0.5). O he objec i e o his design phase is o es ablish he u ili y o
using pa ially connec ed ne wo ks (each ANN ou pu only depends on a pa o he
inpu s). In his second phase 200 ne wo k a chi ec u es we e es ed. The hi d phase
objec i e is o es he addi ion o Gaussian noise o inpu aining pa e n and li le
a ia ions on hidden neu ons numbe .
Fig. 4. Va ia ion o MSE du ing he aining p ocess (1800 epochs)
Ano he p oblem is o selec he aining pa e ns. In he PQ p oblem we gene a e
1100 pa e ns by using he h ee-phase gene a o o elec ical dis u bances desc ibed
abo e. Au ho s selec ed 900 pa e ns o use du ing aining, 110 alida ion pa e ns o
a oid ha he ANN o e lea ns he aining pa e ns, and 90 es ing pa e ns used o
e alua e he pe o mances o he ne wo k. The aining, alida ion and es ing pa e ns
ange alues a e be ween -1 and 1 (inpu s a e scaled by he maximum alue o he
pa e ns). Au ho s employed a o al o 5,000 aining cycles. Fig. 4 shows he
educ ion o MSE du ing he aining p ocess o one a chi ec u e. The esul s
ob ained a e aining he ANN o each possibili y wi h di e en a chi ec u es a e
shown in Table 1. The bes es esul is a MSE o 0.0554 (94.5% o co ec PQ
dis u bances classi ica ion).
0200 400 600 800 1000 1200 1400 1600 1800
10-3
10-2
10-1
100
735Classi ica ion o Dis u bances in Elec ical Signals Using Neu al Ne wo ks
Table 1. Resul s o he ANN selec ion heu is ic p ocess
Phase Pa ame e Bes esul s
Ph.1 T ans e unc ion pe laye Linea ( i s laye ), Sigmoid (o he laye s)
Weigh ini ializa ion Randomly be ween -1 and 1
Lea ning ule Gene alized Del a Rule
T aining pa e ns p esen a ion Randomly
Ph.2 A chi ec u e 113 - 100 - 100 - 9 pa ially connec ed
Lea ning a e 0.5
Momen um ac o 0.5
Ph.3 Gaussian inpu noise I ele an
Va ia ion on hidden neu ons 113 - 100 - 100 - 9 pa ially connec ed
I we analyze he e o ob ained o each ou pu (Table 2) we can see ha he wo s
igu e is he ou pu numbe 8 (wa e o ms dis o ions p oblems), bu e en in his case,
he es MSE is mino han 8%. The only o he ou pu MSE uppe 5% is he MSE o
ou pu 1 ( ha o e s a global e alua ion o he signal PQ). As conclusion, he e o s
ob ained a e sa is ac o y o de ec and classi y PQ dis u bances. The nex phase in ou
p ojec is o in eg a e he ANN in o he powe dis u bance moni o o h ee phase
sys ems desc ibes abo e.
Table 2. MSE o each ANN ou pu .
ANN Ou pu MSE alue
Uni 1: Global ol age quali y (PQ) 0.051
Uni 2: Powe equency a ia ions 0.009
Uni 3: T ansien s 0.026
Uni 4: Sags 0.005
Uni 5: Sho du a ion in e up ion 0.001
Uni 6: Swells 0.032
Uni 7: Long du a ion in e up ion 0.001
Uni 8: Wa e o m dis o ion 0.075
4. Conclusions
This pape desc ibes he de eloping o a powe dis u bance moni o o h ee-phase
sys ems. This sys em classi ies and s o es sho - e m and long e m dis u bances, and
wa e o m dis o ions in elec ical h ee-phase AC signals, using a ully connec ed
eed o wa d neu al ne wo k wi h a backp opaga ion lea ning me hod. Wa ele
ans o m is used o comp ess da a. An a bi a y unc ion gene a o has been
de eloped o aining he ANN. P elimina y es s show ha he sys em ob ains good
esul s in he classi ica ion o elec ical PQ incidences. The nex p ojec phase is o
in eg a e he ANN in o he powe dis u bance moni o .
736 C. Leon e al.