Article Tetrahexyldecyl ascorbate (THDC) degrades rapidly ...
Application of TLM and Cassie-Mayr Arc model on ... · 2.2 Arc Model When the insulation degrades...
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Application of TLM and Cassie-Mayr Arc model on Transformer Aging and Incipient Faults Simulation X. Wang, M. Sumner and D. W. P. Thomas * Abstract—The development of the transformer in- sulation failure undergoes three stages: insulation ag- ing, incipient faults and a short circuit. This paper presents a complete scheme to simulate single-phase transformers with insulation deterioration and arc- ing phenomena i.e. in the first two stages. The approach incorporates Transmission Line Methods (TLM), Jiles-Atherton Hysteretic Model, Composite Cassie-Mayr Arcing Model and Dielectric Model. A small 25kVA 11kV/220V power transformer with ag- ing and incipient faults is taken as example for simu- lation. Keywords: Deterioration, Incipient Fault, Insula- tion Aging, Transformer, Transmission Line Methods (TLM) 1 Introduction One of the most important electrical units in power sys- tem is transformer, the stability of which is significant for the reliability of the whole supply. Therefore vari- ous protection and monitoring schemes were developed in the last few decades. By now the differential relay that depends on the current difference to trigger the execu- tion units is widely applied in the transformer protection against internal faults[1]. With the aspect of transformer monitoring, lots of practical experience is accumulated during the periodical preventative experiments, while the state-based maintenance and hence online monitoring are developing rapidly. Although can not directly reflect the remaining life of the transformer, dissolved gas and par- tial discharge are still the most common monitored items under the major circumstance. In fact each scheme can be regarded as a recognition procedure, the key issue of which is how to effectively distinguish the major faults arising within transformers. A survey of the modern transformer breakdowns, which took place over a period of years, showed that 70%-80% of faults could be attributed to the failure of the internal * All authors are with George Green Institute for Electromagnet- ics Research, School of Electrical and Electronic Engineering, Uni- versity of Nottingham, Nottingham, United Kingdom NG7 2RD. Email: [email protected]. Manuscript was submitted on 05 September 2007 insulation between winding turns[2]. As a result, such in- ternal insulation faults inevitably become the main inves- tigated subjects. Actually the development from a per- fect condition to a complete breakdown undergoes several stages, which are insulation aging, incipient fault and a short circuit. After a transformer is installed on a site and because of some electrical, thermal or chemical effects, the internal insulation always weakens although it may develop very slowly. This deterioration is called aging, the main feature of which is the higher leakage current flowing through the insulation dielectric than the perfect condition. When the insulation degrades further, incip- ient faults appear in the form of some intermittent arcs within the insulation dielectric material. In such a case, if the transformer does not stop operating, the incipient faults will eventually turn into a permanent inter-turn short circuit that can cause serious damage and an out- age. Since most faults mentioned above are destructive, it’s desirable to undertake an accurate simulation to fa- cilitate analysis and distinguish the characteristics of dif- ferent stages in the deterioration of the insulation before the laboratory experiment. D.J.Wilcox introduced a time-domain modal analysis which described how a transformer model could be con- verted from the frequency domain into the time domain for ATP/EMTP implementation[3], but it did not con- sider the existence of internal faults. For the transformer with internal faults, Patrick presented the matrix model that can be easily obtained by the calculation on the in- ductance of the healthy transformer, so that it can be simulated by EMTP[4]. But some idealized assumptions on which Patrick’s model is based may affect its results. Hang Wang and Karen L. Butler proposed that the sim- ulation results be acquired from the standpoint of elec- tromagnetic fields with the assistance of finite element softwares e.g. ANSOFT’s Maxwell[5]. The effects of in- sulation aging and incipient faults were exhibited by the parallel connection of a constant voltage source with an increasing resistance. The validity of this method was confirmed by experiments. However on the other hand, the application of more sophisticated Composite Cassie- Mayr theory in modelling arc has proved to be more successful[6][7]. Engineering Letters, 16:1, EL_16_1_12 ______________________________________________________________________________________ (Advance online publication: 19 February 2008)
Transcript of Application of TLM and Cassie-Mayr Arc model on ... · 2.2 Arc Model When the insulation degrades...
Application of TLM and Cassie-Mayr Arc modelon Transformer Aging and Incipient Faults
Simulation
X. Wang, M. Sumner and D. W. P. Thomas ∗
Abstract—The development of the transformer in-sulation failure undergoes three stages: insulation ag-ing, incipient faults and a short circuit. This paperpresents a complete scheme to simulate single-phasetransformers with insulation deterioration and arc-ing phenomena i.e. in the first two stages. Theapproach incorporates Transmission Line Methods(TLM), Jiles-Atherton Hysteretic Model, CompositeCassie-Mayr Arcing Model and Dielectric Model. Asmall 25kVA 11kV/220V power transformer with ag-ing and incipient faults is taken as example for simu-lation.
Keywords: Deterioration, Incipient Fault, Insula-
tion Aging, Transformer, Transmission Line Methods
(TLM)
1 Introduction
One of the most important electrical units in power sys-tem is transformer, the stability of which is significantfor the reliability of the whole supply. Therefore vari-ous protection and monitoring schemes were developed inthe last few decades. By now the differential relay thatdepends on the current difference to trigger the execu-tion units is widely applied in the transformer protectionagainst internal faults[1]. With the aspect of transformermonitoring, lots of practical experience is accumulatedduring the periodical preventative experiments, while thestate-based maintenance and hence online monitoring aredeveloping rapidly. Although can not directly reflect theremaining life of the transformer, dissolved gas and par-tial discharge are still the most common monitored itemsunder the major circumstance. In fact each scheme canbe regarded as a recognition procedure, the key issue ofwhich is how to effectively distinguish the major faultsarising within transformers.
A survey of the modern transformer breakdowns, whichtook place over a period of years, showed that 70%-80%of faults could be attributed to the failure of the internal
∗All authors are with George Green Institute for Electromagnet-ics Research, School of Electrical and Electronic Engineering, Uni-versity of Nottingham, Nottingham, United Kingdom NG7 2RD.Email: [email protected]. Manuscript was submitted on 05September 2007
insulation between winding turns[2]. As a result, such in-ternal insulation faults inevitably become the main inves-tigated subjects. Actually the development from a per-fect condition to a complete breakdown undergoes severalstages, which are insulation aging, incipient fault and ashort circuit. After a transformer is installed on a site andbecause of some electrical, thermal or chemical effects,the internal insulation always weakens although it maydevelop very slowly. This deterioration is called aging,the main feature of which is the higher leakage currentflowing through the insulation dielectric than the perfectcondition. When the insulation degrades further, incip-ient faults appear in the form of some intermittent arcswithin the insulation dielectric material. In such a case,if the transformer does not stop operating, the incipientfaults will eventually turn into a permanent inter-turnshort circuit that can cause serious damage and an out-age. Since most faults mentioned above are destructive,it’s desirable to undertake an accurate simulation to fa-cilitate analysis and distinguish the characteristics of dif-ferent stages in the deterioration of the insulation beforethe laboratory experiment.
D.J.Wilcox introduced a time-domain modal analysiswhich described how a transformer model could be con-verted from the frequency domain into the time domainfor ATP/EMTP implementation[3], but it did not con-sider the existence of internal faults. For the transformerwith internal faults, Patrick presented the matrix modelthat can be easily obtained by the calculation on the in-ductance of the healthy transformer, so that it can besimulated by EMTP[4]. But some idealized assumptionson which Patrick’s model is based may affect its results.Hang Wang and Karen L. Butler proposed that the sim-ulation results be acquired from the standpoint of elec-tromagnetic fields with the assistance of finite elementsoftwares e.g. ANSOFT’s Maxwell[5]. The effects of in-sulation aging and incipient faults were exhibited by theparallel connection of a constant voltage source with anincreasing resistance. The validity of this method wasconfirmed by experiments. However on the other hand,the application of more sophisticated Composite Cassie-Mayr theory in modelling arc has proved to be moresuccessful[6][7].
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
(Advance online publication: 19 February 2008)
So following the authors’ previous work on simulation ofinternal short circuit faults[8], a method, which incorpo-rates Transmission Line Methods (TLM), Jiles-Athertonmodel for magnetic hysteresis and Composite Cassie-Mayr description of arc, is presented in this paper.
2 Transformer Model with Aging and In-cipient Fault
A single-phase two-winding transformer impedance isrepresented by two matrices [R] and [L] as follows, wheresuffixes p and s are for the primary and the secondaryrespectively; Ri and Lii are the resistance and the selfinductance of winding i; Mij is the mutual inductancebetween winding i and j.
[R] =[
Rp 00 Rs
][L] =
[Lpp Mps
Msp Lss
](1)
The terminal voltages and currents are then related by
[up
us
]= [R]
[ipis
]+ [L]
d
[ipis
]
dt(2)
where ui is the voltage and ii is the current of winding i.
Figure 1: Diagram of deteriorated insulation and possiblearcing path
After the transformer operates for a period, the insulationwithin the protection zone inevitably deteriorates. For ashell type transformer, the weakest insulation is usuallyat the locations between two adjacent layers of the wind-ing. So the effects of aging can be severe at these points.For example, the severest deterioration may take placein the primary as shown in Figure.1 (marked points).And from the fault location, the primary winding maybe divided to two (Figure.2(a)) or three sub-windings(Figure.2(b)).
Accordingly the matrices [R] and [L] in the expression (1)are converted to the matrices in the expression (3) for theconfiguration in Figure.2(a) and those in the expression(5) for the configuration in Figure.2(b)
(a) Deteriorationbetween leading-outterminal and adjacentlayer
(b) Deterioration be-tween two internaladjacent layers
Figure 2: Diagram of sub-windings in transformer withinsulation deterioration in the primary
[R] =
Ra 0 00 Rb 00 0 Rs
[L] =
Laa Mab Mas
Mba Lbb Mbs
Msa Msb Lss
(3)
ua
ub
us
= [R]
iaibis
+ [L]
d
iaibis
dt(4)
[R] =
Ra 0 0 00 Rb 0 00 0 Rc 00 0 0 Rs
[L] =
Laa Mab Mac Mas
Mba Lbb Mbc Mbs
Mca Mcb Lcc Mcs
Msa Msb Msc Lss
(5)
ua
ub
uc
us
= [R]
iaibicis
+ [L]
d
iaibicis
dt(6)
2.1 Aging Model
Traditionally the low frequency behavior of dielectric ma-terial can be represented in terms of an equivalent parallelcircuit as shown in Figure.3, where ud, id, Rd and Cd areapplied voltage, leakage current through dielectric, in-sulation resistance and parasite capacitance respectively.According to the literature[5] and experimental results,the equivalent capacitance Cd changes little during thedeterioration of insulation. Resistance Rd is large in thecase of perfect insulation, while it decreases significantlywith the effect of aging.
For considering the aging condition of the dielectric,the equivalent circuit in Figure.2 becomes as given inFigure.4. And the additional expression is generated(ud = ub).
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Figure 3: Equivalent circuit of insulation dielectric
(a) Deterioration between leading-out ter-minal and adjacent layer
(b) Deterioration between two internal ad-jacent layers
Figure 4: Diagram of transformer with aging model inthe primary
id = ia − ib =1
Rdub + Cd
dub
dt(7)
2.2 Arc Model
When the insulation degrades further, some intermittentarcs i.e. incipient faults begin to persist within the in-sulation. The process of arcing can be divided into ex-tinction stage and recovery stage. The former one lastsa few microseconds from the beginning of the arcing tothe moment when the arc current reaches zero, while thelatter one follows in time.
As two special cases of black box arc models, Cassie andMayr arc model have the general forms[9] given in theequations (8):
du
dt= Φ(u, i)
di
dt− uF (u, i)
Φ(u, i) =u
i
FM (u, i) =1θ
(ui
N0− 1
)forMayrModel
FC(u, i) =1θ
(u2
E0− 1
)forCassieModel (8)
where θ represents the arc time constant, u and i are thearc voltage and current respectively.
Then the composite Cassie-Mayr method models arcingphenomena by modifying the value of the arc resistancei.e. insulation resistance Rd in Figure.4. When the volt-age over the resistance Rd is larger than the constant arcvoltage E0 in case of steady state, the extinction stagebegins. During this stage, the resistance is dominated bythe Cassie’s equation with the initial value of Rd beingthe one in the aging model:
1Rd
dRd
dt=
1θ
(1− u2
d
E20
)(9)
After the current idR decreases to zero, the arc is com-pletely extinguished. Then the recovery stage beginswhich can be represented by the Mayr’s equation.
1Rd
dRd
dt=
1θ
(1− udiRd
N0
)(10)
Where N0 = E0Iωθ, I is the rms value of the interruptedcurrent in ampere. If the arc resistance Rd computedby Mayr’s equation starts to decrease, indicating reigni-tion, Cassie’s differential equation (9) is used with a newvalue E0 =
√N0Rm from the point the arc resistance has
reached the maximum value Rm. If the arc resistanceRd keeps increasing until it reaches the value before arcstarts, then the entire arcing process ends. And after thispoint, the aging model returns for use.
2.3 Hysteresis Model
For modelling nonlinear hysteretic cores the approach ap-plied here is to use the Jiles-Atherton model (J-A model)[10] to introduce hysteretic behavior. Based on the con-stitutive relationship for the flux density B = µ0(H+M),where µ0 is the permeability of free space, H is the mag-netic flux density and M is the magnetising intensity,each inductance in the matrices (3) and (5) are decom-posed.
Equations (4) and (6) including non-linear inductance aregiven in equations (11) and (12) respectively.
ua
ub
us
=
Ra 0 00 Rb 00 0 Rs
iaibis
+
L′aa M
′ab M
′as NaLm
M′ba L
′bb M
′bs NbLm
M′sa M
′sb L
′ss NsLm
d
iaibisim
dt
(11)
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
(Advance online publication: 19 February 2008)
ua
ub
uc
us
=
Ra 0 0 00 Rb 0 00 0 Rc 00 0 0 Rs
iaibicis
+
L′aa M
′ab M
′ac M
′as NaLm
M′ba L
′bb M
′bc M
′bs NbLm
M′ca M
′cb L
′cc M
′cs NcLm
M′sa M
′sb M
′sc L
′ss NsLm
d
iaibicisim
dt
(12)
where im is the normalized magnetization given by im =Ml and L
′ii/M
′ij are self/mutual inductance in the situa-
tion where the transformer core is removed and replacedby air. L
′ii/M
′ij and Lm can either be deduced from the
expressions for impedances given by Wilcox et. al [11][12]or approximated by
M′ij =
µ0NiNjA
l(13)
Lm =µ0A
l(14)
The classical J-A model [10][13] is described in the fol-lowing subsections:
2.3.1 Weighting coefficient
The magnetization is split into two parts, the anhystereticmagnetization and the irreversible magnetization. In nor-malized form, this is expressed by
im = βcian + (1− βc)iirr (15)
where βc is the weighting coefficient with 0 ≤ βc ≤ 1, ian
is the normalized anhysteretic magnetization and iirr isthe normalized irreversible magnetization.
2.3.2 Modified langevin function
The anhysteretic magnetization dependence is given by amodified Langevin function, i.e.
ian = isat
[coth
(iL + αim
iaht
)− iaht
iL + αim
]= isatL(γ)
(16)where iL is the ampere-turn sum of all exciting currents,isat is the normalized saturation magnetization, α is theinterdomain coupling coefficient and iaht is the normal-ized anhysteretic magnetization form factor. The co-efficients isat, α, iaht are positive constants. Also L(γ)
denotes the modified Langevin function with argumentγ = iL+αim
iaht. To avoid difficulties with the modified
Langevin function for small arguments, a linear approxi-mation is used where for |γ| < 0.001 we put L(γ) ≈ γ
3 .
2.3.3 Differential equation for the irreversiblemagnetization
In the Jiles-Atherton model, the derivative of the normal-ized irreversible magnetization with respect to the induc-tor current is
diirr
diL=
[δm(ian − iirr)
δicoe − α(ian − iirr)
](17)
where the migration flag δm is given by:
δm =
1 : if diL
dt > 0 and ian > iirr
1 : if diL
dt < 0 and ian < iirr
0 : otherwise(18)
3 TLM Modelling
The transformer equations are solved using the timedomain TLM method as described in [14]. In TLMan inductor element is represented by a short circuitedtransmission line stub as given in Figure. 5, which isreduced to a serial voltage source and surge impedanceas shown. At each time step n the following equationsare solved.
un = ZLin + 2uin (19)
un = uin + ur
n (20)
uin+1 = −ur
n (21)
where ZL = 2L∆t ; ∆t is the time length of each step; the
suffix n stands for the nth time step; uin is the incident
voltage in nth time step; urn is the reflected voltage in
nth time step.
Figure 5: Representation of Inductor in TLM
Similarly a capacitor element can be described by an opencircuited transmission line stub as given in Figure.6 andthe iterative equations are
un = ZCin + 2uin (22)
un = uin + ur
n (23)
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
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Figure 6: Representation of Capacitor in TLM
uin+1 = ur
n (24)
where ZC = ∆t2C
Therefore for the simulation of an aging or arcingtransformer with a nonlinear hysteretic core and withthe terminal relationships as turn to earth fault as givenby equation (11) and Figure.4(a): the self impedances(inductances) can be modelled as given by equations(25), the controlled sources representing mutual termsof the type M
′ij
dij
dt are given by equation (26) and thecapacitor Cd is represented by equation (27) as follows:
uii = Ziiii + 2uiii (25)
uij = Zijij + 2uiij (26)
ud = Zdidc + 2uid (27)
where Zii = 2L′ii
∆t ; Zij = 2M′ij
∆t ; Zd = ∆t2Cd
and thereis a term representing the magnetization Lm
dim
dt given by
um = Zmim + 2uim (28)
where Zm = 2Lm
∆t
The magnetization im is non-linear so that an iterativesolution for the following simultaneous equations has tobe found.
f1 = (Zaa + Ra)ia + Zabib + Zasis
+(Zd ‖ Rd)(ia − ib) + NaZmim − usrc
+2(uiaa + ui
ab + uias +
uidRd
Rd + Zd+ Naui
m) = 0
(29)
f2 = Zbaia + Zbbib + Zbsis
−(Zd ‖ Rd)(ia − ib) + NbZmim
+2(uiba + ui
bb + uibs −
uidRd
Rd + Zd+ Nbu
im) = 0
(30)
f3 = Zsaia + Zsbib + (Zss + Rs + Zload + Rload)is+NsZmim + 2(ui
sa + uisb + ui
ss + uiload + Nsu
im) = 0
(31)
We have chosen the Newton-Raphson technique for itsefficiency and stability so the solution is found through
the following iterative procedure
iaibis
p+1
=
iaibis
p
−
∂f1∂Ia
∂f1∂Ib
∂f1∂Is
∂f2∂Ia
∂f2∂Ib
∂f2∂Is
∂f3∂Ia
∂f3∂Ib
∂f3∂Is
−1
p
f1
f2
f3
p
(32)where p is the iteration number and
The iteration is started with initial values taken fromthe TLM previous time step and continued until suitableconvergence criteria are met. In this work this is set as∣∣∣(ia)p+1 − (ia)p
∣∣∣ < τ and∣∣∣(ib)p+1 − (ib)p
∣∣∣ < τ
and∣∣∣(is)p+1 − (is)p
∣∣∣ < τ
Similarly for the simulation of transformer with turn toturn fault governed by equation (12) and Figure.4(b)
f1 = (Zaa + Zac + Ra + Zca + Zcc + Rc)ia+(Zab + Zcb)ib + (Zas + Zcs)is+(Zd ‖ Rd)(ia − ib) + (Na + Nc)Zmim
−usrc + 2(uiaa + ui
ab + uiac + ui
as + uica + ui
cb
+uicc + ui
cs +ui
dRd
Rd + Zd+ (Na + Nc)ui
m) = 0
(33)
f2 = (Zba + Zbc)ia + Zbbib + Zbsis
−(Zd ‖ Rd)(ia − ib) + NbZmim
+2(uiba + ui
bb + uibc + ui
bs −ui
dRd
Rd + Zd+ Nbu
im) = 0
(34)
f3 = (Zsa + Zsc)ia + Zsbib
+(Zss + Rs + Zload + Rload)is + NsZmim
+2(uisa + ui
sb + uisc + ui
ss + uiload + Nsu
im) = 0
(35)
Note that ia = ic and hence only ia is required to besolved
4 Simulation Results
A small 25kVA, 11kV/220V power transformer with thegeometry given in Fig. 7 is modelled so as to demonstratethe modelling procedure. The Jiles-Atherton parametersare typical of a core made of FeSi sheets [15].
Figure.8 and Figure.9 show some simulation results of thetransformer with deterioration insulation in the primarywinding. Parameters of the aging model and Cassie-Mayrarc model are as follows: Rd = 1400Ω;Cd = 6.06pF ;E0 =397.22V ;θ = 0.1ms. During the time section from 0.5sto 0.55s, three arcs take place and some characteristics ofarcs can be observed e.g. the arc voltage is almost a flat-top waveform as shown in Figure.8(d) and Figure.9(c).
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
(Advance online publication: 19 February 2008)
Figure 7: 25kVA 11kV/220V power transformer geom-etry. Unit a = 0.0587375m and magnetic path lengthl = 12a. Number of turns in primary Np = 2509; Numberof turns in secondary Ns = 51. Jiles-Atherton parame-ters: Saturation magnetization Ms = 1.47×106A/m; An-hysteretic form factor Ha = 40.0A/m; Interdomain cou-pling coefficient α = 0.00008; Coercive field magnitudeHc = 60.0A/m; Magnetization weighting factor βc=0.55;Supply voltage source: resistance Rsrc = 1.565Ω, induc-tance Lsrc = 2.4132µH
5 Conclusion and Future Work
By incorporating Transmission Line Methods (TLM),Jiles-Atherton Hysteretic Model, Composite Cassie-MayrArcing Model and Dielectric Model, the simulation re-sults of transformer with aging insulation and incipientfaults can be acquired. Although the results seem rea-sonable, they need to be validated by the experiments.
References
[1] A. C. Franklin and D. P. Franklin, The J&P Trans-former Book 11th Edition, England: Butterworth &Co. (Publishers) Ltd., 1983.
[2] K. L. Butler and M. Bagriyanik, ”Identifying trans-former incipient events for maintaining distributionsystem reliability,” in Proceedings of the 36th HawaiiInternational Conference on System Sciences, 2003.
[3] D. J. Wilcox, M. Conlon, D. J. Leonard andT. P. McHale, ”Time-domain modelling of powertransformers using modal analysis,” IEE Proceeding:Electric Power Application, vol. 144, no. 2, pp. 77-83, March 1997.
[4] P. Bastard, P. Bertrand and M. Mevnier, ”A Trans-former model for winding fault studies,” IEEETrans. on Power Delivery, vol. 9, no. 2, April 1994.
[5] H. Wang and K. L. Butler, ”Modeling transform-ers with internal incipient faults,” IEEE Trans. onPower Delivery, vol. 17, pp. 500-509, April 2002.
[6] D. W. P. Thomas, E. T. Pereira, C. Christopoulosand A. F. Howe, ”The simulation of circuit breakerswitching using a composite cassie-modified mayrmodel,” IEEE Trans. on Power Delivery, vol. 10,no. 4, pp. 1829-1835, October 1995.
[7] S. Porkar, G. B. Gharehpetian, K. Feser, ”A disk-to-disk breakdown and arc modeling method forfault diagnosis of power transformers during impulsetesting,” Springer: Electrical Engineering, vol. 86,pp. 261-265, 2004.
[8] X. Wang, M. Sumner and D. W. P. Thomas, ”Simu-lation of single-phase nonlinear and hysteretic trans-former with internal faults,” in Proceedings of PowerSystems Conference and Exposition, PSCE’06. 2006IEEE PES, pp. 1075-1080, Atlanta, USA, October2006.
[9] J. L. Guardado, S. G. Maximov, E. Melgoza,J. L. Naredo and P. Moreno, ”An improved arcmodel before current zero based on the combinedMayr and Cassie arc models,” IEEE Trans. onPower Delivery, vol. 20, no. 1, pp. 138-142, January2005.
[10] D. C. Jiles, J. B. Thoelke and M. K. Devine, ”Nu-merical Determination of Hysteresis Parameters forthe Modeling of Magnetic Properties Using the The-ory of Ferromagnetic Hysteresis,” IEEE Trans. onMagnetics, vol. 28, no. 1, pp. 27-35, January 1992.
[11] D. J. Wilcox, M. Conlon and W. G. Hurley, ”Cal-culation of self and mutual impedances for coilson ferromagnetic cores,” IEE Proceedings, Part A:Physical Science, Measurement and Instrumenta-tion, Management and Education, Reviews, vol. 135-A, no. 7, pp. 470-476, September 1988.
[12] D. J. Wilcox, W. G. Hurley and M. Conlon, ”Calcu-lation of self and mutual impedances between sec-tions of transformer windings,” IEE Proceedings,Part C: Generation, Transmission and Distribution,vol. 136, no. 5, pp. 308-314, September 1989.
[13] J. Paul, C. Christopoulos and D. W. P. Thomas,”Time-domain simulation of nonlinear inductors dis-playing hysteresis,” COMPUMAG 2003, pp. 182-183, Saratoga Springs, New York, July 2003.
[14] C. Christopoulos, The transmission-line modelingmethod : TLM, New Jersey, USA: IEEE Press, 1995.
[15] A. Benabou, S. Clenet and F. Piriou, ”Comparisonof Preisach and Jiles-Atherton models to take intoaccount of hysteresis phenomenon for finite elementanalysis,” Journal of magnetism and magnetic ma-terials, vol. 261, no. 1, pp. 139-160, 2003.
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
(Advance online publication: 19 February 2008)
(a)
(b)
(c)
(d)
Figure 8: Terminal currents and arc voltage/current forthe transformer with deterioration/aging insulation andsome incipient faults between 125th and 375th turns onthe primary winding. (a) Primary Current. (b) Sec-ondary Current. (c) Arc Current. (d) Arc Voltage.
(a)
(b)
(c)
Figure 9: Zoomed in details of Figure.8 in dot circle (a)Primary Current. (b) Arc Current. (c) Arc Voltage.
Engineering Letters, 16:1, EL_16_1_12______________________________________________________________________________________
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