基于油色谱数据的变压器可靠度评估方法
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第29卷第7期2013年7月
电力科学与工程
ElectricPowerScienceandEngineering
V01.29.No.7
Jul..2013
基于油色谱数据的变压器可靠度评估方法
张钰宁1,程养春1’2,田野1,陈凯1,宋安琪1,李成榕1’2,袁帅3,杨宁3(1.华北电力大学高电压与电磁兼容北京市重点实验室,北京102206;
2.华北电力大学新能源电力系统国家重点实验室,北京102206;
3.中国电力科学研究所,北京100192)
摘要:变压器是电力系统的枢纽设备,其运行的可靠性直接关系着电力系统的安全运行。为此,提出了一种基于色谱数据统计规律的变压器可靠度评估方法。首先对正常状态以及过热和放电异常状态时变压器的油色谱数据进行分布规律分析,采取曲线拟合的方式求取各状态下气体含量的概率密度函数以及累积分布函数。根据异常状态时数据的分布规律,利用变压器的可靠性与故障的累计概率之间的关系,得出各气体含量达到国标注意值时变压器的可靠度。最后按照国家安全预警体系将变压器异常状态划分为5个严重等级。
关键词:变压器;气相色谱分析;正常状态;故障;可靠度
中图分类号:TM855文献标识码:ADOI:10.3969/j.issn.1672—0792.2013.07.001
0Introduction
Atpresent,judgingwhetherthetransformerbreaksdownandthefaulttypemainlyusestheabso-lutevalueandtheratioofthedissolvedgasesinthefield㈨].Nationalstandard[3]andIEC-60599
4]pro-videtheattentionvalueofdissolvedgas,butreference[3]onlylistsouttheattentionvalueofH2,C2H2andtotalhydrocarbon,whichisnotverycomprehensive.Althoughreference[4]liststhetypesofdissolvedgascompletely,itsanalysisobjectisallDGAdataanditdoesn’tmakeadistinctionbetweenthenormalandab—normalofthesampleswithsimpleassumption90%dataintonormaldata.Besides,thestatisticaldataoftransformersinRef.[4]areglobal,SOitdoesn’tpro—videtheattentionvalueofthetransfotiBerinourcoun—try.Finally,neitherofthemgivesamethodfordeter—miningthereliabilityof
transformers.
Forthis,thisarticlecollectsatotalof18307setsofthedataofdissolvedgascontentinoilfrom12500kVnormallyoperationtransformersinNorthChina;altogether3001setsofdatafrom10220kVtrans—foFillersinNorthChinaand1959setsofdatainallfrom3110kVtransformersintheNorthChinaarea.
Inaddition,thistextalsocollects266groupsoftypi—caldissolvedgasdataof186overheatingfaulttrans—formersbeforeaccidentand233
groupsoftypicaldis—solvedgasdataof178dischargefaulttransformersbe—foreaccidentfromtherelevantliterature.Thispaperplanstoanalyzethestatisticaldistributionruleofdis—
solved
gas
inoilofnormal
transformeranddefectivetransformer,andthenprovidesthequantitativerelia—bilityassessmentrulesof
transformertomakethediag-nosisresultaccurate.
Asthereliabilityoftransformeriscloselyrelatedtothefaultcumulativeprobabilityoftransformer,andthecumulativeprobabilitycanbeobtainedfromtheprobabilitydensity,。5。thispapermakesdistributiontestonthenormalandfaultdissolvedgasdatasamples
收稿日期:2013—05—06。
基金项目:国家重点基础研究发展计划项目(973计划)(2009CB724508)。
作者简介:张钰宁(1988一),女,硕士研究生,从事高电压与绝缘技术等方面的研究,E—mail:zynlsc@163.con。
瓦西甬疆■西蕊磊耋NGtNEERING
2电力科学与工程2013焦
andcurvefitting【6jinthegaswhichdoesnotobey
any
knowndistribution.Throughthestatisticsandanaly—
sis,thispapercalculatesthereliabilityofthetrans—
former.Theresultnotonlyhasthe
advantagesofchar—
acteristicgasmethod,intuitiveandconvenient,but
alsohastheconceptofquantityandeasytoguideen—
gineeringpractice.
1Analysisofthedistributionofdissolvedgas
inoilofnormaltransformer
Thissectionanalyzesallnormaldissolved
gases
(H2,CH4,C2H6,C2H4,C2H2,COandtotalhydro—
carbon)datasamplesofthetransformersofthreevolt—
ageclasses.
Thehistogramisusedto
represent
thefrequency
distributionofthecontinuousdataforcheckingthe
shapeanddistributionofsampledata.Therectangular
areaofhistogramindicatesthefrequency,andthesum
oftherectangularareaisequivalenttothesumofeach
frequency….Therefore,throughthehistogramwecan
haveanintuitiveunderstandingoftheprobabilitydis—
tributionofsampledata.Typicalhistogramsofthedis—
solvedgasesareshowninfigure1.Thecurveinthe
figureisthenormaldistributioncurve.
墨厂—————一
一
×2
0
04080
gascontent/(I.tL?L1)
(a)H:o
o
o
__
×
lO
O
02040
gascontent/(1aL?L-1)
(b)C:H。
Fig.1I-mtogrmofso眦dissolvedgases
FromFigure1wecanseeexactlythatthedistri—butionofH2andC2H6dissolvedintransformeroildoesnotobeythe
normaldistribution.ThediagramsalsoshowthattheH2distributionissimilartotheWeibull
distributionandthesamplesofC2H6contain
alargenumberofzeros.Likewise,otherdissolvedgasesalsodonotobeynormaldistribution,andC2H4andC2H2
alsohavelotsofzeros.ThezeroproportionofeachgasisshowninTable1.
Tab.1Zeroproportionofnormaldata(%)
Fromtable1,wecan
seethatthezeroproportionofC2H6,C2H4andC2H2isverylarge,sowecan’tig—notetheeffectofzero.BecauseSPSS(StatisticalProductandServiceSolutions)softwaremakesWeibulldistributiontestonthesampleexcludingze—ro,theabovethreekindsofgasesarenotsuitableforusingSPSSfor
Weibulldistributiontest.Thisarticle
willcarry
onthecurvefittingforthem.Thezeropro—portion
oftheremaining
gasesissmaller,soitcanbeignoredfortaking
Weibulldistributiontest.
Todeterminewhetheravariableissubjecttosomeprobabilitydistributionneedstousedistribution
test.SPSSmainlyprovidestwo
waystocarrydistribu—
tiontestonsample:oneisKolmogorov—Smirnov
test,andtheotherisP—Pplot(probability—probabilityplot)orQ—Qplot(quantile—quantileplot).Assume
thatsingle-?sampleK——S
inspection
confidenceintervalis1一a.Ifthetestofsignificanceisgreaterthana,thesampleobeystheassumeddistribution,otherwiseitdoesn’tobeythedistributionrule.Asingle—sample
K—_Stestonthesamplecannot
processsampledataatthesametime,whiletheP—Pdiagramcananalyzethedistributionandcarrycorrelationprocessingonda—taatthesametinle[8。.
ThissectionwilluseP—Pplotfortest.P—Pplotisdrawnaccordingtotherelationshipbetweenthecu—
mulative
proportionofvariable
andthecumulative
pro—portionofthegiven
distribution.Thetwostandardsfortestingwhetherthedatafitwelltothegivendistribu—tionare:(1)thecontactratioofdatapointsandlineontheP—Pplot;(2)whetherthepointsontheP—PtrendplotfluctuateinsmallrangeaboutlineY=0.
Fromthehistogram,somedissolved
gasesmayo—bey
Weibulldistribution,soweuseP—P
plotforthesampledatatotest
Weibulldistribution.The
probabil—
第7期
ELECTRICPOWERENGtNEERING张钰宁,等基于油色谱数据的变压器可靠度评估方法3
itydensityfunctionofWeibull‘distribution八戈)is¨?showninformula(1),andthetestresultsofH,are()E¨nshowninfigure2.嚣;
FromtheP—Pplotinthefigure2,wecansee…
¨1thatthedatacanbewellcontactwithline.andinthe
P—Ptrend
plot,thefluctuationofdatapointissmall.
sowecanthinkthatH,obeyWeibulldistribution[9。.
Similarly,itisknownthatCH4,COandtotalhydro—
carbonalsoobeyWeibulldistribution,andthe
gas
probabilitydensityanddistributionparametersarelis—
tedintable2.
八戈)x/A'),zI>0
(1)
Wherekisthe
shapeparameterandAisthescaleparameter.
Tab.2ParametersofWeibullofdissolvedgases
GasH2CH4Total
HydrocarbonCOShapeparameterk0.05320.12360.13260.0042ScaleparameterA1.0041.15881.0270.9848
Thissectionwilltakecurvefitting
waytocalcu—
latethedistributionfunctionfor
C2H6,C2H4andC2H2
duetothelargenumberofzeros.Their
probabilitydensityfunction(PDF)f(戈)issimulatedwithfor—mula(2)andcumulativedistributionfunction(CDF)F(z)issimulatedwithformula(3).Typicalfittingresultsareshowninfigure3.
八戈)=Y0+ate一下+02e一下(2)F(戈)=儿+a1(1一e一∥“)+u2(1一e一加2)(3)
WhereY0,al,u2,tlandt2arethevaluesthatare
tobeset
00
004
OOO
O-8
eprobabiIit)
Fig.2ResultsofWeibulldistributiontestofH
。矧r
铡/
’1’1’’’’—’T’。’’’‘r。。’‘‘‘r’’’‘’’‘’+●’+1一
Fig?3FittingresultsofPDF&CDFofC2H6
2Statisticalrule
analysisofdissolvedgasinoil
ofdischargedefectsandoverheatingfault
Thisarticlealtogethercollects232
groupsofdis—
chargefaultdata,including20groupsofpartialdis.
chargedata,65groupsoflowenergydischargedata
and99
groupsofhighenergydischargedata.Because
partialdischargesampledataaretoosmallandtheer—
rorofstatisticalruleisbig,soseparatestatisticala—
nalysisisnotcarriedout.Accordingtothedivision
standardinRef.[10],overheatisdividedinto
an-
der700oCoverheatandabove700oCoverheat.
Firstofall,takingnormaldistributionK—Stest
for
everysample(dischargetotalsample,lowenergy
andhigh
energydischargesample,overheatingsam—
pie)respectively.Seta=0.05,thecalculationre—
suitsshowthatthedoublesideprogressive
significance
arelessthan0.05,soallthe
samplesdonotobevthe
normaldistribution.Whendatado
notobevthenor—
maldistribution
ornormaldistributionfittinglevelis
relativelypoor,afeasiblemethodofdataprocessingis
dataconversion.Inthispaper,the
samplestakethe
logarithmbeforethedistributionruleanalysis.Be—
causethezerovalueofthesamplecannotbetaken
logarithm,wecansetitasalackofsystem.Thezero
proportionofeachgasisshownintable3.
Tab.3ZeroProportionoffaultdata(%)
H2CH4C2H6C2H4C2H2
M
hydrocarbon
Overheat2.630.001.130.3836.090.00
Discharge0.000.433.020.8616.380.00
Throughtable3,itisknownthatthezeropropor一分
如
“
菇
后P叽
=
一4
m
|o出
一
w
一
”
~
曲
括m
0
O
呲
瞄唧山
一
廿
U
P
¨~
却
州
。
帅咖
‰
暖i:丫聂l百—≯石西萎R
ENGiNEERiNG
4
电力科学与工程
2013焦
tionofthefivekindsofgasesis
small,which
can
betreated
asa
lackofsystembeforelogarithmictreat—
ment.When
overheatinganddischarge,the
zero
pro—
portionofC2H2isbiggerandnotsuitableforlogarith—
micnormaldistributiontest.Thispaperuses
theCHIVe
fitting
method(formula(2)andformula(3))to
ob—
tainthedistilbutionrule.
TakingK—Stest
forH2and
so
on,allprogres—
sivesignificanceofdischargedefectsampleisgreater
than0.05,indicatingthattheyobeythe
lognormal
distribution.So
at
the
differentdegrees
ofdischarge,
allthegasesobeythelognormaldistributionexcept
C2H2.Foroverheatingfaultsample,onlytheprogres—
sivesignificanceofCH4intheoverheatingtotalsample
is
lowerthan0.05anddoes
not
obeythe
lognormal
distribution.Thus,intheoverheatingtotal
sample,
allthe
gasesobey
thelognormaldistributionexcept
CH4andC2H2,thedistributionparameters
are
shown
intable4.Tothegaswhichdoesnotfollow
lognormal
distribution,thispaper
uses
formula(2)andformula
(3)for
curve
fitting.Theprobabilitydensityfunction
f(戈)oflognormal
distributionis:
八戈)=ilxor贯一掣
。己+n
(4)
Where/.t
istheaverageofthelogarithmofthe
variableand
or
is
thestandard
deviationofthelog—
arithmofthevariable.
擒爹一
40
20
O
Logarithmofthegas
conten
(b)CH。
Fig.4
Histogramofsomedissolvedgasesinlogs
Typicalhistogramsaftersamplestakinglogarithm
are
showninfigure4.Figure4denotesobviouslythat
thesamplesobeynormal
distributionaftertakinglog—
arithm.
Tab.4
Parametersofiognormalofdissolvedgases
3
Reliabilityanalysis
Reliability
istheabilityoftheproductperforming
a
required
functionunder
specifiedconditions
and
withintherequiredperiod,sothedegreeof
reliability
referstothe
probability
oftheproductcompletingpre—
scribedfunctionwithintheprescribedtimeandcondi—tions,whichisusuallyrecorded
as
R(£).
R(t)=P(T>t)
(5)
Reliability
is
closelyrelated
to
cumulativefaultprobabilitywhichsaysthe
probability
oftheequipment
that
can’t
completerequiredfunctionunderspecified
conditionsandwithintheprescribedperiodoftime,
recorded
as
F(t).
According
to
the
probabilitycomplementarytheo—
rem,we
can
get:
R(t)+F(£)=1
(6)
Ifthefaultdatadistributionis
known,F(£)can
beobtainedand
socan
R(t).
According
to
theaboveanalysis,we
canobtain
theCDFdiagramsofthedissolvedgases
at
different
stateswhich
are
shownin
figure5.Wherein,A
repre—
sents
normal,BrepresentsoverheatingfaultandC
re—
presentsdischarge
fault.The
Xcoordinateis
sample
aftertaking
logarithm.Formthefigure5,itisknown
thatthe
normaldata,overheatingfaultdata
anddis—
chargefaultdataofthedissolvedgasoverlapeachoth—er;theoverheatingdataofothergases
are
more
con—
centratedthan
dischargedata
inadditiontothetotal
hydrocarbon.Nationalstandardsprovidetheattention
L
p
0
m
1e
n
∞
S
,‘
6弘H
m
a
第7期
张钰宁,等基于油色谱数据的变压器可靠度评估方法
ELEC下R:0P0诲拦R垂KGl魏薹基建}NG
valueofH2is
150
cL舻L
anCPtotalhydrocarbonisalso
150斗L/L.Theattention
valueofC2H2ofabove330
kVrunningtransformeris1灿L/L,andbelow330kv
is5斗I/L.The
reliabilitycorresponds
toattention
valueiSshownintable5.
0?8
言0.6
u04
0.20
O
2
4
6
8
lO
ln(x)
(a)H
1
0.8t臣O.6?o0.4.
O.2O一
—丛习1
0
5
10
ln(x)c)C!H
1_7
O.8l7
kO6
o
U04
0.20
)
0510
ln(x)fe)C,H,
e
0.4O.20
0.8kO.6o
U0.4
O
O
5
lO
ln(x)(b)C:H;
O
5
10
ln(x1(d)CH。
1厂1∥1
{
j,\
剧1
6
8
10
nCx
Fig.5CDFofdissolvedgasesTab.5
ReliabilityofMannvalue
Fromtable5,we
can
see
thatthereliability
cor—
iesponds
to
theattentionvalueofeachdissolvedgasisalmostmorethan0.5
securitywhichisshownintable6.
Tab.6
Faultseverity
肛L/L
According
to
theaboveanalysis,weconclude:
(1)Thedataof
characteristic
dissolvedgases
H2,CH4,COandtotalhydrocarbonofnormalopera—
transformerobey
Weibull
distributionwhileC2H6,
C2H4andC2H2disobeyanyknowndistributiondueto
lots
of
zero
values.Thecharacteristic
gasesH2,
C2H6,C2H4andtotalhydrocarbonofdischargeandO—
verheatingfaultobey
thelognormaldistribution,and
CH4ofdischargeobeysthelognormaldistribution,but
CH4ofoverheatingdoes
not
obeythelognormaldistil—
bution,C2H2disobeysanyknowndistributiondue
to
a
largenumberof
zero
values.
(2)According
to
the
earlywarningsystem
of
national
security,transformerabnormal
state
can
be
If
a
group
ofDGAdataisobtainedinthefield.dividedintofiveseriouslevels
or
bedividedintodif-
thecumulativeprobabilityofthefaultcan
befoundin
ferentlevelsoffailure‘severityifrequiredon
thebasis
figure5.Thenaccordingto
formula(6),the
reliabil—
ofthe
abnormaldatadistribution.
ityofthisvaluecanbeobtained.Accordingtothe
re—
liabilitywe
can
judge
whether
transformer
breaksdownReferences
andtheseverityofthefault.Thispaperdividesrelia—bilityaccording
to
theearlywarningsystemofnational
[1]徐志钮,律方成,赵丽娟.基于RPROP算法的变压器
碉川
彩历
幽
EkE0亨曩iSP0嚣薹塞耋鬻0iNE基疑;裴0
6电力科学与工程2013年
油中溶解气体分析故障诊断[J].电力科学与工程,2005,(2):70—72.XuZhiniu,LuFangcheng,ZhaoLijuan.TransformerDGAfaultdiagnosisbasedonrpropalgorithm[J].ElectricPowerScienceandEngineering,2005,(2):70—72.[2]胡资斌,朱永利,董卓.基于遗传程序设计的变压器油中溶解气体含量预测[J].电力科学与工程,2011,27(7):7—11.HuZibin,ZhuYongli,DongZhuo.Predictionofgasescon—tentdissolvedinpowertransformeroilbasedongeneticpro?gramming[J].ElectricPowerScienceandEngineering,2011,27(7):7—11.[3]GB/T7252--2001.变压器油中溶解气体分析和判断导则[s].[4]IEC60599--2007.Mineraloil—impregnatedelectricale-quipmentinservice—guidetotheinterpretationofdissolvedandfreegasesanalysis[S].[5]王有元.基于可靠性和风险评估的电力变压器状态维修决策方法研究[D].重庆:重庆大学,2008.[6]陈光,任志良,孙海柱.最小二乘曲线拟合及Matlab实现[J].兵工自动化,2005,24(3):107—108.ChenGuang,RenZhiliang,SunHaizhu.CurvefittinginLeast-SquaremethodanditsrealizationwithMatlab[J].OrdnanceIndustryAutomation,2005,24(3):107—108.[7]包红,徐娜,李新,等.利用SPSS统计软件分别绘制以频数和频率为纵坐标的直方图[J].数理医药学杂志,2010,23(6):717—719.
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[10]IEEEStdC57104—2008.IEEEGuidefortheinterpreta—tionofgasesgeneratedinoil??immersedtransformers?-redline
『S].
AReliabilityEvaluationMethodforTransformer
BasedonDataofDissolvedGasAnalysis
ZhangYunin91,ChengYangchunl一,TianYel,ChenKail,SongAnqil,
LiChengron91”,YuanShuai3,YangNin93
(1.BeijingKeyLaboratoryofHighVoltageandEMC;
2.StateKeyLaboratoryofAlternateElectricalPowerSystemwithRenewableEnergy,
NorthChinaElectricPowerUniversity,Beijing102206,China;
3.ChinaElectricPowerResearchInstitute,Beijing100192,China)
Abstract:Thetransformeristhekeyapparatusinelectricpowersystem.Itsreliabilitydirectlyaffectsthesafeop-erationofpowersystem.Therefore,areliabilityevaluationmethodfortransformerbasedonthestatisticalregulari.tiesofthegaschromatographydataoftransformersisproposed.Firstly,byanalyzingthedistributionruleofthegaschromatographydataoftransformersundernormalconditionandthegaschromatographydataofdischargeandover—heatfaults.theprobabilitydensityfunctionandthecumulativedistributionfunctionofthegascontentindifferentconditionswereobtainedbycurve-fittingmethod.Secondly,accordingtothedistributionruleofthegaschromatog-raphydataofdischargeandoverheatfaults,thetransformerreliabilitywheneachgascontentreachedtheattentionvalueofGBwasobtainedusingtherelationshipbetweenthereliabilityandthecumulativeprobabilityofthefailureofthetransformer.Finally,accordingtothenationalsecuritywarningsystem,faultconditionoftransformerscanbedividedintofivegrades.
Keywords:transformer;dissolvedgasanalysis;normalcondition;fault
condition;reliability
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