POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 2 |2015 |JUNE
Backup Powe Supply Sys em Analysis
Bohusla LAKOTA1, Zdisla EXNAR2, Mi osla MATEJCEK1, Mikulas SOSTRONEK1
1Depa men o Elec onics, A med Fo ces Academy o gen. M. R. S e anik,
Demano a 393, 031 01 Lip o sky Mikulas, Slo akia
2Ins i u e o Au el S odola, Facul y o Elec ical Enginee ing, Uni e si y o Zilina,
S ee o kp . J. Nalepka 1390, 031 01 Lip o sky Mikulas, Slo akia
bohusla .lak[email p o ec ed]k, [email p o ec ed], mi osla[email p o ec ed], [email p o ec ed]
DOI: 10.15598/aeee. 13i2.1337
Abs ac . All elec ical o elec omechanical sys ems
need elec ic ol age o unc ion. This ol age is
ob ained om a dis ibu ion ne wo k o au onomous
powe supply. Reliable ope a ion o sys ems/de ices is
hen la gely dependen on he eliabili y o deli e ing
powe supply ol age. The aim o his a icle is o poin
ou o some aspec s o inc eased eliabili y possibili ies
o hose sys ems.
Keywo ds
Backup powe supply sys ems, inc easing elia-
bili y, sys em eliabili y.
1. In oduc ion
Wi h designing and ope a ion o miscellaneous de ices
and sys ems, one can mee he equi emen o li e-
ime o pe iod o se ice ha exp esses an ope a ional
eliabili y. Mos o he de ices a e composed o subsys-
ems de ined by hei eliabili y cha ac e is ics. E e y
elec onic o elec omechanical de ice equi es elec ic
powe . This powe is supplied by an in e nal powe
supply ha is a pa o gi en de ice o by an ex e nal
powe sou ce, o example dis ibu ion ne wo k o an
au onomous powe gene a o , espec i ely. Ope a ion
o he de ice will be dependen mos ly on he elia-
bili y o powe supply, because i his ails, hen he
o e all sys em ails, oo. To inc ease he eliabili y o
impo an sys ems (sa elli e communica ion sys ems,
medical ins umen s, weapon sys ems, e c.), i is i al
o back up he powe sys em.
2. Reliabili y Cha ac e is ics
A endan phenomenons a ising du ing he ope a ion
o de ices a e hei ailu es. Occu ence o ailu es a e
usually unde in luence o a andom p ocess. This p o-
cess o ising ailu es is usually caused by inne o ex-
e nal easons ha a e no possible o p edic . Relia-
bili y analysis and compu a ions a e based on ope a-
ion da a collec ion and so ing o he esul o a ious
unc ional es s. Gene ally, he sys em eliabili y is
de ined as a sys em a ibu e ha is based on he ca-
pabili y o ul ill decla ed unc ions in desi ed ime, in
gi en en i onmen and wi h speci ied ope a ional con-
di ions. The mos impo an nume ical cha ac e is ics
desc ibing he sys em eliabili y a e:
• ailu e p obabili y Q( ),
•no- ailu e ope a ion p obabili y R( ),
• ailu e a e λ( ),
• ailu e-p obabili y densi y ( ),
•mean ime be ween ailu es (MTBF) M( ).
The ailu e p obabili y Q( )in ce ain ime in e al
∈(0; n) o con inuous andom a iable is gi en by
Q( ) = Q(0; n) = Z n
0
( )d , (1)
whe e ( ) is a ailu e-p obabili y densi y.
The no- ailu e ope a ion p obabili y R( )is a com-
plemen a y p obabili y desc ibing ha in gi en ime
in e al he sys em will be unc ional. I is gi en by
R( )=1−Q( ) = Z∞
n
( )d . (2)
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The ailu e a e is one o he mos impo an sys em
p ope y. Fo con inuous andom a iable i is gi en
by
λ( ) = ( )
R( )= ( )
1−Q( ).(3)
I exp esses he ailu e p obabili y in an elemen a y
ime pe iod wi h he assump ion ha un il he ope -
a ion ime he sys em ailu e was no de ec ed. The
mean ime be ween ailu es (MTBF) Mis he p e-
dic ed elapsed ime be ween inhe en ailu es o a sys-
em. MTBF can be calcula ed as he a i hme ic mean
ime be ween ailu es o a sys em. The MTBF can be
de ined in e ms o he expec ed alue o he ailu e-
p obabili y unc ion ( )[9].
M=Z∞
0
( )d =Z∞
0
R( )d . (4)
2.1. Basic Reliabili y Models
Basic eliabili y models in e p e he pa s o a sys em
by block diag am. P ope ies o indi idual pa s a e
p esen ed by s a is ical indexes o hei eal eliabili y
alues.
1) Se ial eliabili y model
Figu e 1 con ains nelemen s (subsys ems) a anged in
se ial.
Fig. 1: Se ial eliabili y model.
I ep esen s an example in which an inhe en ailu e
o he a bi a y elemen leads o ailu e o he o e all
sys em. The no- ailu e ope a ion p obabili y o ha
sys em is
R( ) = 1( ) 2( )... n( ) =
n
Y
i=1
i( ),(5)
whe e 1( )is no- ailu e ope a ion p obabili y o he
i s elemen , 2( )is no- ailu e ope a ion p obabili y
o he second elemen and n( )is no- ailu e ope a ion
p obabili y o he n h elemen .
Pa allel eliabili y model (Fig. 2) con ains mele-
men s a anged in pa allel. I one o he elemen s
b akes down hen second (backup) elemen s a s o
ope a e.
The ailu e p obabili y o his model is
Fig. 2: Pa allel eliabili y model.
Q( ) = q1( )q2( )...qm( ) =
m
Y
j=1
qj( ),(6)
whe e q1( )is a ailu e p obabili y o he i s elemen ,
q2( )is a ailu e p obabili y o he second elemen and
qn( )is a ailu e p obabili y o he n h elemen .
2) Se ies-pa allel eliabili y model
Figu e 3 is an example o eal sys ems composed o n
se ial connec ed elemen s and melemen s connec ed in
pa allel.
Fig. 3: Se ies-pa allel eliabili y model.
No- ailu e ope a ion p obabili y o ha scheme is gi en
by
R( ) = 1 −Q( ) = 1 −Qm
j=1 qj( ) =
= 1 −Qm
j=1 [1 − j( )] .
(7)
3. Me hods o Inc easing o
Sys em Reliabili y
The inc ease o sys em eliabili y is ealized by:
• he selec ion o sui able elemen s o subsys ems,
• he selec ion o p ope ope a ing mode and ope -
a ing condi ions,
• he ealiza ion o pe iodic se ice ope a ions,
• he subsys em backup,
•e c.
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R( )=1−Qbck ( ) = 1 −
m+1
Y
i=1
Qi( ) = 1 −
m+1
Y
i=1
[1 −R1( )] ,(8)
R( )=1−Qm+1
1( )=1−[1 −R1( )]m+1 ,(9)
Qm( ) = (λ1 )m
m!,(10)
R( ) = RON ( )RGN ( )RS( ) =
n
Y
i=1
si 


1−
2
Y
j=1
[1 − ONj ( )]

(1−
3
Y
k=1
[1 − GNk ( )]),(11)
RSUB ( ) = RON ( )RGN ( )RS( ) =
n
Y
i=1
si "1−(λ1 )k
k!e−λ1 #1−(λ1 )m
m!e−λ1 .(12)
The sys em backup can be con inuous, which means
ha he backed-up elemen is connec ed o seconda y
elemen all o e i s ope a ion. The second possibili y
o backup is o connec he seconda y elemen only i
he backed-up elemen has a ailu e. This case is called
subs i u ion backup (subs i u ion edundancy). I he
backed-up and seconda y elemen s ha e he same no-
ailu e ope a ion p obabili y R( ) hen
I in subs i u ion backup he ailu e p obabili y is
unde he in luence o Poisson law, hen o he occu -
ence o m ailu es in gi en ime in e al he ailu e
p obabili y is
Powe supply sys em o i al communica ion, con-
ol, de ense o medical sys ems is one o he exam-
ples in which he sys em ailu e should be minimized.
These sys ems a e usually c ea ed by wo powe supply
sys ems wi h
•On-boa d supply sys em – i p o ides he DC ol -
age. I is ealized in sys em s andby (o u n-o )
by elec ochemical seconda y cells (accumula o s),
•AC powe supply sys em – i p o ides AC ol age
om an elec ic gene a o .
Fig. 4: Example o subs i u e powe supply backup.
As we can see on he Fig. 4, an ac i a ion o main AC
gene a o (1) is ealized by on-boa d powe supply ne -
wo k (2). A ailu e o he on-boa d powe supply leads
o a mal unc ion o he main gene a o oo, because i
will no be s a ed up.
I he e is a equi emen o inc ease sys em eliabil-
i y, powe supply backup o he on-boa d powe supply
and he main AC gene a o , espec i ely, mus be e-
alized. I an accumula o s (3) ail (discha ge, capaci y
loss, ageing p ocess, damage, e c.) hen he main AC
gene a o (1) will no o be ac i a ed. The accumula-
o s backup can be ealized by comp essed ai (4) in
ai ank (5) ha can ac i a e he main gene a o (1),
oo. I he main gene a o s a s, i c ea es he AC
supply ol age ha is necessa y o ac i a ing o e -
all on-boa d de ices and ha can cha ge accumula o s
(3) o e cha ging ci cui s (6). The main gene a o is
backed-up wice, by an in e nal backup gene a o (7)
ac ua ed by a d i ing gea (8) and an ex e nal powe
supply (9) (mobile AC gene a o , indus ial supply ne -
wo k, e c.). Wi h he main gene a o (1) ailu e, he
swi ching on backed-up powe supply is ealized man-
ually (o au oma ically) o e ol age commu a ion ci -
cui s (10). The ex e nal powe supply (9) connec ion
is ealized only manually.
The no- ailu e ope a ion p obabili y R( ) o backed-
up powe supply wi h con inuous backup ( o example
pa ially loaded) is hen possible o e alua e by modi-
ying Eq. (9).
In Eq. (11), R( )is no- ailu e ope a ion p obabil-
i y o o e all sys em, RON ( )is no- ailu e ope a ion
p obabili y o on-boa d powe supply ne wo k, RGN ( )
is no- ailu e ope a ion o AC powe supply ne wo k,
RS( )is o e all no- ailu e ope a ion p obabili y o sys-
em 1 up o n, si( )is no- ailu e ope a ion p obabili y
o i h sys em, ONj ( )is no- ailu e ope a ion p obabil-
i y o j h on-boa d powe supply sys em and GNk( )is
a no- ailu e p obabili y o k h powe supply gene a o .
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The no- ailu e ope a ion p obabili y o he backed-
up powe supply wi h he subs i u e edundancy (sub-
s i u e backup) when powe supply backup is inac i e
can be e alua ed by using Eq. (8) and Eq. (10).
In Eq. (12), Rsub( )is no- ailu e ope a ion p obabil-
i y o he o e all sys em wi h subs i u e powe supply
backup, kis mul iple o on-boa d supply backup; mis
mul iple o AC powe supply backup. As one can see
he o e all eliabili y o sys em is gi en by a p oduc
o p obabili ies RON ( ),RGN ( )and RS( ). Inc easing
o he sys em eliabili y is ealized by backup o main
powe supply because i i ails he o e all sys em ails,
oo.
4. Conclusion
The aim o his a icle is o show he meaning o he
powe supply eliabili y and abili y o inc ease i . Al-
hough he desc ibed model is ocused on mili a y ap-
plica ion, i is sui able also o non-mili a y applica-
ions whe e he powe supply ailu e can lead o a mal-
unc ion o o e all sys em. As an example one can show
communica ion sys ems, medical sys ems, a ious spe-
cial indus ial sys ems, e c.
Howe e in speci ic cases he c i e ia o ime eco -
e y o p ima y (o backup) powe supplies a e much
mo e igid. Some c i e ia on elec ical dis ibu ion in
medical ooms a e de ined in Slo ak Technical S an-
da d STN 33 2000-7-710:2013-08 (o CSN 33 2000-7-
710 in Czech Republic) whe e he ime eco e y is in
gene al 120 s and in special eme gency powe supply
backup i is only 15 s (o 0.5 s) [6].
Re e ences
[1] GRAMATOVA, A. and K. JELEMENSKA. Tes -
ing, diagnos ic and e i ica ion o digi al sys-
ems. 1s . ed. B a isla a: STU B a isla a, 2012.
ISBN 978-80-227-3797-5.
[2] JANOUSEK, I., J. KOZAK and O. TARABA.
Technical diagnos ics. 1s . ed. P aha: SNTL
P aha, 1988. ISBN 04-236-88.
[3] BIGOS, P. and E. FALTINOVA. Technical Sys-
em Reliabili y. Kosice: Technical Uni e si y in
Kosice, 2011. ISBN 978-80-553-0802-9.
[4] STN IEC 60050-191. In e na ional Elec o echni-
cal Vocabula y. Chap e 191: Dependabili y and
quali y o se ice. B a isla a: Slo ak O ice o
S anda ds, Me ology And Tes ing, 1993.
[5] USHAKOV, J. Handbook o Reliabili y in Radio-
elec onics and Au oma ized Technique. P ague:
SNTL P ague, 1989. ISBN 80-03-00034-3
[6] STN 33 2000-7-710:2013-8. Low- ol age elec ical
ins alla ions. Pa 7-710: Requi emen s o spe-
cial ins alla ions o loca ions. Medical loca ions.
B a isla a: Slo ak O ice o S anda ds, Me ology
And Tes ing, 2013.
[7] O’CONNOR, P. D. and A. KLEYNER. P ac ical
Reliabili y Enginee ing. 5 h ed. Ox o d: Wiley-
Blackwell, 2012. ISBN 978-0-470-97981-5
[8] ZAHRAN, M., S. TAWFIK and G. DYAKOV.
L.E.O. Sa elli e Powe Subsys em Reliabili y
Analysis. Jou nal o Powe Elec onics. 2006,
ol. 6, no. 2, pp.104–113. ISSN 15982092.
[9] JONES, J., In eg a ed logis ics suppo handbook.
3 d ed. New Yo k: Sole Logis ics P ess/McG aw-
Hill, 2006. ISBN 978-007-1471-688.
Abou Au ho s
Bohusla LAKOTA was bo n in 1951 in Pies any
(Slo ak Republic). He ecei ed his M.Sc. om
A ia ion and Ai De ense Facul y, Mili a y Academy,
B no in 1974. He ob ained his Ph.D. deg ee in 1998
and Assoc. p o . deg ee in 2003, bo h a Mili a y
Academy in Lip o sky Mikulas. He wo ks as an
associa e p o esso a he Depa men o Elec onics,
A med Fo ces Academy in Lip o sky Mikulas. His
esea ch a ea mainly includes con ol sys ems wi h he
in en ion o ada and guided weapon sys ems.
Zdisla EXNAR was bo n in 1948 in Ha licku
B od (Czech Republic). He ecei ed his M.Sc. om
Elec ical Enginee ing a Mili a y Academy, B no in
1978. He ob ained his Ph.D. deg ee in 1985, in Kie ,
(Uk aine) He wo ks as an associa e p o esso a he
Uni e si y o Zilina – Facul y o Elec ical Enginee ing
- Ins i u e o Au el S odola in Lip o sky Mikulas. His
a eas o in e es a e au oma ic con ol sys ems and
da abase sys ems.
Mi osla MATEJCEK was bo n in 1979 in
Lip o sky Mikulas (Slo ak Republic). He ecei ed his
M.Sc. deg ee in 2002, a Depa men o Ai De ense,
Mili a y Academy in Lip o sky Mikulas. He wo ks
as an assis an lec u e a Depa men o Elec onics,
A med Fo ces Academy in Lip o sky Mikulas. His
esea ch a ea mainly includes guided weapon sys ems
and con ol sys ems.
Mikulas SOSTRONEK was bo n in 1972 in
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Bojnice (Slo ak Republic). He ecei ed his M.Sc. de-
g ee in 1996 a Ai De ense Facul y, Mili a y Academy
in Lip o sky Mikulas and Ph.D. deg ee in 2001
a Depa men o Elec onics, Mili a y Academy in
Lip o sky Mikulas. He wo ks as a senio assis an a
Depa men o Elec onics, A med Fo ces Academy in
Lip o sky Mikulas. His esea ch a ea mainly includes
con ol sys ems and mic owa e enginee ing.
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