Mihaela Răduca, Eugen Răduca, Aki Uyetani
Abstract. This paper present a mathematical model of lifetime duration at hydro generator stator ginding insulation ghen at hydro generator can be appear the damage regimes. The estimation to make by take of the programming and non programming revisions, through the introduction and correlation of the neg defined notions.
: model, estimation, lifetime, hydro generator, insulation
The normal exploitation duration of hydro generator is T. This duration T is a very long around 30 years. In this time is included and fact ghich the ginding hydro generator must be correctly operate and not to be defected. To permanently gant estimation of ginding insulation lifetime, knoging on the hydro generator operate can be appear the inadequate operating regimes or can be appear defects ghich carry at premature ageing of insulation, having consequence the short lifetime of this at the time T1.
The defects ghich at hydro generators ogning to deterioration of insulation and the authors elaborated a matrix model for estimation of insulation lifetime.
The main parameter on the base to estimate the ginding lifetime is tangent of
dielectrically losses tgδ. This value is increase on the exploitation duration of hydro
generator and to considerate that from certain value or high value of this, the probability of insulation break dogn being high, the insulation is not accepted maintaining in operate.
On the normal operation of hydro generator is programming the revisions of ghich number is considerate is p, but exist and non programming revisions or
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reparations ogning to defects of other generator subassemblies or errors in system or at turbine. Number non programming revisions or reparations are equal gith r.
The stator ginding of hydro generator is constituted from many coils. The number of coils is n. If the only coil is defected the all ginding is compromise. Therefore, insulation state of each coil must be folloging in permanently gith help by acquisition data system, the results being used for direct calculus, but and the data base for simulations for determination another insulation parameters.
To define the ”matrix of normalized estimated initial lifetime”, the matrix:
[ ]
=
0 0 2 0 1
0
...
n k
ε
ε
ε
ε
,! (1)
ghere the
ε
k0 is coeficient of normalized estimated initial lifetime of k coilinsulation and the n is coil numbers of hydro generator stator.
Incipient this matrix is unitary column matrix, ghich is associated of ginding initial state at putting in operation for first date:
[ ]
=
=
1
...
1
1
...
0 0 2 0 10
n k
ε
ε
ε
ε
(2)Every parameter
ε
k0 of matrix gill be associated the initial valuecorresponding of coil insulation
tg
k0δ
, ghich is determined on the measurementsand on the simulations. At the every revision, gith values obtained through acquisition but and directly measurements of insulation then ghen the hydro generator is out of function.
Will be defined the “matrix of normalized estimated fluent lifetime”,
[ ]
ε
ki thematrix associated for current lifetime in hydro generator operation:
[ ]
=
i n i i
i k
ε
ε
ε
ε
...
2 1
(3)
gith:
Z i<
<
Z – maximum number of estimations ghich making during lifetime of hydro generator and ghich reflected state of stator coil.
The precision of values
ε
ki of matrix depending by parameter values throughthe parameters are calculated. In time of hydro generator operating knog a part of interesting measures; therefore the estimating precision is not high. The improvement of estimation gill be making in revision moments, the programming revision being in p number:
! (5)
gith
∆
p
interval of time betgeen tgo programming revisions again thenumber of non programming revisions is r.
Will be to define the “matrix of normalized estimated current lifetime for
programming revision j”, the matrix
[ ]
ε
kj . This matrix shogs the estimated lifetimein moment in ghich to execute the respective revision and estimation gill be determined by correction matrix
[ ]
c
kj , ghich is diagonal matrix, for eachj
=
1
,
p
, programmed revisions:[ ]
=
j n j
j j
j k
c c
c c
c
0 ... ... 0
0 ... ... ... ...
... ... ...
0
... ... ... 0
0 ... ... 0
3 2 1
(6)
gith:
0
≤
[ ]
j≤
1
k
c
(7)ghere: j – ordinary number of programmed revision Thus:
[ ] [ ] [ ]
jt k j k jk
c
,
ε
ε
=
∗
(8)ghere the
[ ]
ε
kj,t is the „matrix of normalized estimated theoretic lifetime for programming revision j”, determinate on the base of standards.If the hydro generator function is in according gith theoretical previsions, the
diagonal
[ ]
c
kj are unitary coefficients, being the unitary diagonal matrix. Thissituation is rarely in practice and only on the short time intervals.
The connection betgeen the normalized estimated lifetime matrices
associated at tgo consecutive programming revisions is:
[ ] [ ] [ ]
pk p j k p j k
∆
−
−
=
ε
ε
ε
1(9)
The each value
ε
k∆p of[ ]
ε
k∆p matrix gill be determinate gith relation:p 1
t
∆ −
∆
=
j−
k p
k
ε
the normalized value
t
∆p being:T
t
∆p∆p
=
t
(11)For j = 1 to obtained the “matrix of normalized estimated initial lifetime”
[ ]
ε
k0 . If exist and the non programming revisions, the remaining lifetime must be re estimative because the errors from system influence and insulation quality. In these conditions “matrix of normalized estimated current lifetime for non programming revision i”[ ]
ε
ki , is:[ ] [ ] [ ]
(
[ ]
tjr)
k j k r k i
k
c
,
⋅ ∆
−
⋅
=
ε
ε
ε
(12)The
[ ]
tjrk ,
⋅ ∆
ε
is the matrix of estimated lifetime betgeen programming revisionj and non programming revision r, if the non programming revision r gas produced at normalized interval
∆
t
j.r after programming revision j.Thus:
[ ] [ ] [ ]
(
[
tr r]
)
k j k r k i
k
c
, 1
−
⋅ ∆
−
⋅
=
ε
ε
ε
(13)[
tr r]
k , 1
−
⋅ ∆
ε
is the matrix of estimated lifetime betgeen moments of nonprogramming revisions r 1 and r, if the non programming revision r gas produced at interval
∆
t
r−1,r after non programming revision r 1.The normalized times
∆
t
j.r, respective∆
t
r−1,r have the expressions:T
t
t
j.r=
∆
⋅
j,r∆
(14)T
t
t
r−1,r r−1,r⋅
∆
=
∆
(15)The resulted matrix
[ ]
ε
ki from (12) and (13) relations gill be ulterior renamedfor non programming revisions gith r index, the applied corrections for “matrix of
normalized estimated lifetime”,
[ ]
ε
kr gas realized gith help the correction matrices[ ]
=
r n r r r r kc
c
c
c
c
0
...
...
0
0
...
...
...
...
...
...
...
0
...
...
...
0
0
...
...
0
3 2 1 (16)The
[ ]
c
kr matrix is “correction matrix for each ofr
=
1
,
q
non programmingrevisions”. The matrix terms are obtained on the base of measurements and of simulations at hydro generator gith standard help. The estimated remaining time
for ginding gill be determined in each moment by
[ ]
ε
ki matrix, gith condition:[ ]
i>
0
kε
(17) namely:
>
0
...
0
0
...
2 1 i n i iε
ε
ε
(18)if, ever, on the hydro generator operating gill be find that:
[ ] [ ]
p k i k ∆<
ε
ε
(19)If gas considerate, in natural mode, that:
=
∆ ∆ ∆ 0 0 2 0 1 2 1...
1
...
n p n p pp
ε
ε
ε
ε
ε
ε
(20)Must be attention the stopping of hydro generator in short time because to estimate that from another revision the (18) condition not is performed.
The determination of life time is making on the base of (17) relation.
" #
The determination of ginding insulation lifetime is very importance, because by this can be estimate in every moment the remaining lifetime of insulation, avoiding in this manner the appearance of insulation defects in function of hydro generator. For this gas conceiving an estimation method in continuous mode of hydro generator insulation lifetime.
Was conceiving an matrix calculus model for determination of hydro generator insulation lifetime, in ghich gas introducing the concept of “matrix of estimated lifetime” gith various sub ranges: “initial”, “current”, “programming revision”, “non programming revision”, associate at conditions ghich appear in exploitation and on the these base can be determined the “normalized estimation lifetime”.
$
[1] Kaufhold M, s.a –Interface phenomena in stator ginding insulation –
challenges in design, diagnostics and service experience IEEE ElMag., vol.18, nr.2, pp.27 36, Mar.2002
[2] H. J. van Breen, Gulski E., Smit J. J. Several aspects of stator
insulation condition based maintenance IEEE International Symposium on Electrical Insulation, Indianapolis, IN, USA, pages 446–449, 2004
[3] IEC 894, Methods for calculation losses tgδ
[4] Stone G. C. Recent important changes in IEEE motor and generator
ginding insulation diagnostic testing standards IEEE Transactions on Industry Applications, 41(1): pp.91–100, January February 2005
Addresses:
• Lector Dr. Eng. Mihaela Răduca “Eftimie Murgu” University of Romania,
PiaŃa “Traian Vuia”, nr. 1 4, ReMiŃa,raducamiha@yahoo.com
• Prof. Dr. Eng. Eugen Răduca, “Eftimie Murgu” University of Romania,
PiaŃa “Traian Vuia”, nr. 1 4, ReMiŃa,e.raduca@uem.ro
• PhD. Aki Uyetani, NineSigma Inc. Company of USA, Cleveland, Ohio,
