Modeling Dynamic Propagation of Characteristic Gases in
Power Transformers Oil-Paper Insulation
A. Shahsiah, R.C. Degeneff and J.K. Nelson
Rensselaer Polytechnic Institute
110 8th Street
Troy, NY 12180, USA
ABSTRACT
This paper presents and verifies a new mathematical model to explain the dynamic
behavior of characteristic gases in the oil-cellulose insulation of high voltage devices like
power transformers. The model is based on the diffusion process. Parameters of the
model are already quantified from experiments and presented in previous publications.
The mathematical model and assumptions are presented here. The model solution is
obtained analytically and concentration change inside the paper insulation as a function
of time is simulated. The results are converted to the concentration change in the oil
using the principle of conservation of mass and validated with experimental
measurements. The model presented can be used to reduce the error of Dissolved Gas
Analysis due to the migration of characteristic gases inside a healthy power
transformer.
Index Terms — Transformers, diffusion, oil-paper system, Dissolved Gas Analysis.
1 INTRODUCTION
FAULTS in power transformers will cause decomposition
of the transformer liquid dielectric and generate gases. By
inspecting of the transformer liquid dielectric (oil), the type and
severity of faults can be detected using the type and amount of
the gases generated inside the transformer. The detection
method is called Dissolved Gas Analysis (DGA). The general
diagnostic methods using DGA are summarized in ANSI/IEEE
and IEC standards [1, 2]. Obviously, the detection method is
not able to measure the amount of the gases that are inside the
solid insulation. However, temperature variations can cause the
generated gases to migrate into the solid insulation or more
gases come out from the solid insulation into the liquid. This
could generate error in DGA measurements or trigger a false
alarm. A mathematical model can be used to convert the DGA
results to the real amount of gas present in the system based on
the current gas concentration in the oil and the system
temperature.
The results of previous research show that the migration
phenomenon in the oil-paper insulation of power transformers
can be explained by diffusion equations and the relevant
parameters have been obtained [3, 4, 5]. Findings of the
previous research include diffusion coefficients and steady-state
information on the characteristic gases in transformer insulation
Manuscript received on X Month 2006, in final form XX Month 2006.
systems. The mathematical model presented here is an attempt
to explain a portion of the dynamic behavior of characteristic
gases in oil-paper insulation systems that is due to the
temperature change. The proposed model is limited to the
migration of the gases that already exist in the insulation system.
Generation of new gases, either inside the paper insulation or in
the oil, is not considered. The migration phenomenon inside the
solid insulation is explained by the diffusion process.
Assumptions are made to limit the effects of the migration
phenomenon to the diffusion process inside a single oil duct of
power transformers. The mathematical model uses steady-state
information to predict the mass distribution in the paper
insulation during the transient conditions as a function of time
and distance inside the paper insulation. The boundary
conditions are found based on the physical facts. The
mathematical model is transformed into per-unit form to
simplify solving the equations. The model is then solved and the
results are compared with experiments. The model sensitivity to
the oil-paper boundary layer is investigated.
Experiments are designed to test the derived model. The
experimental setup and method are explained in this paper. The
experiments are based on measurements in the oil. The
mathematical model, however, solves for the amount of gas
inside the solid insulation. The principle of conservation of
mass is used to convert the amount of gas inside the paper
insulation to that inside the oil. Measurements inside the oil are
then used to compare the simulation results against experiments.
2 THEORY
2.1 THE DIFFUSION MODEL
Assuming a constant diffusion coefficient (at a certain
temperature), transfer of mass through a volume as a
function of time can be expressed by the following general
equation:
c
 D 2 c  v  c  ( Dc ln T ) (1)
t
in which c is the mass concentration in the oil, t is time, D is
the diffusion coefficient, v is the material velocity vector,
T is temperature, and  is the thermal diffusion factor. The
last term in Equation 1 is due to a thermal diffusion
phenomenon known as the Soret effect. This effect is
normally negligible compared to the diffusion caused by the
difference in partial pressures of the species. It is assumed
in this work that there is no generation of mass due to
chemical reactions.
Inside the oil-impregnated paper insulation there is no
transport of mass, therefore; movement of gases in this
medium is defined by diffusion only, ignoring the Soret
effect. Equation 1, therefore, reduces to Equation 2 inside
the paper insulation.
c p
t
 Dp
 2c p
(2)
x 2
in which cp is the gas concentration inside oil-impregnated
paper insulation, Dp is the diffusion coefficient of gas in this
medium, t is time and x is distance.
In the oil region it is assumed that the gases are quickly
mixed with the bulk of the oil, therefore; gas concentration
is evenly distributed in this region. Equation 2 defines the
dynamics of the oil-paper system in terms of the dissolved
characteristic gases. The dynamics of the system is a
function of temperature. In other words, the system is at
equilibrium at a certain temperature; when temperature is
changed, the system goes toward another steady-state
condition, the dynamics of which is defined by Equation 2.
Dependency of Equation 2 on temperature is reflected
through Dp which is a function of system temperature. In the
suggested diffusion model the average of the diffusion
coefficients at the two equilibrium temperatures are used in
Equation 2 to obtain the dynamic behavior of the system
during a step change from one temperature to another.
Oil
Boundary
layer
Oil
Paper
Cpi= Initial concentration at T1
Cos= Steady state concentration at T2
Cps= Steady state concentration at T2
Coi= Initial concentration at T1
Figure 1. Steady-state concentrations in an oil-paper system at two
temperatures.
Paper
cp
cw
co
x
d
d

Figure 2. Dynamic distribution of concentrations in oil-paper system in
transition between the steady-states at the two temperatures.
Figure 1 illustrates the oil-paper system in equilibrium at
two temperatures, T1 and T2. Figure 2 illustrates the same
system under dynamic conditions in transition between the
two temperatures.
Equation 2 is solved (along with the boundary conditions
that will be defined later) to find the concentration of gases
inside the oil-impregnated paper insulation as a function of
time and distance inside the insulation thickness. To verify
the model, however, gas concentration is measured inside
the oil (using the DGA method). The principle of
concentration of mass is used to correlate the measured gas
concentration inside the oil to that inside the paper
insulation. Equation 3 shows this correlation.
co 
1 
(c p  c ps )dx
 0
(3)
In Equation 3 co is the average concentration change in
the paper insulation,  is the paper insulation thickness, cp
is the apparent gas concentration in the paper insulation, cps
is the gas concentration in the paper insulation at the steady
state, t is time and x is distance.
2.2 BOUNDARY CONDITIONS
Boundary conditions for Equation 2 are defined for gases
inside the paper insulation in reference to Figure 2. The first
two boundary conditions are obtained based on the fact that
the initial and final steady-state concentrations inside the
paper insulation are equal to these values at the time zero
and time infinity (cpi and cps).
c p (t  0)  c pi
(4)
c p (t  )  c ps
(5)
The third boundary condition assumes that the paper
insulation is semi-infinite. In other words, gases inside the
paper insulation will not diffuse all the way to the other end.
This assumption is justifiable based on the diffusion timeconstant of gases inside the paper insulation. In the case of
carbon dioxide, for example, it takes about 550 hours for 90
percent of the total gas to diffuse all the way through a 1
mm piece of oil-impregnated pressboard (Hi-Val) at 23oC
based on the experimental data [3, 4]. Comparing this time
to the time that it takes for the oil and paper insulation at the
boundary to exchange gases when there is a temperature
change (almost immediate), the paper insulation can be
assumed semi-infinite. Equation 6 defines the third
boundary condition based on this assumption.
c p
x
|x    0
(6)
The fourth boundary condition is associated with the
diffusion of mass at the oil-paper boundary and is derived
based on the fact that there is no accumulation of mass at
the boundary. In other word, the rates of mass diffusion into
the paper insulation and out of the oil (or vise versa) are
equal at the boundary. This is shown in Equation 7.
 p Dp
c p
x
|x  0  o Do
co
c c
|x  0  o Do w o (7)
x
d
in which cp and co are concentrations inside the paper
insulation and the oil, respectively; cw is the concentration
of gas at the oil-paper surface (cw=cp|x=0) as illustrated in
Figure 2. Parameter δd is the thickness of the boundary
layer, Dp and Do are the diffusion coefficients in the paper
insulation and in the oil, ρp and ρo are mass densities of the
paper insulation and the oil, respectively, and x is distance
inside the paper insulation.
The right-hand side of Equation 7 is derived based on the
assumption that the concentration change along the
boundary layer changes linearly. The reason is that the
equilibrium time constant of gases in the boundary layer is
much smaller than that in the paper insulation [3] and,
therefore, the system can be assumed at steady-state in this
region. Based on this assumption, the concentration
distribution in the boundary layer will be linear, since in
Equation 2 the term c / t will be equal to zero (steady
state). Hence, the term  c / x is also zero which means a
linear distribution of c with respect to x.
Rearranging Equation 7 results in Equation 8 which is the
last boundary condition of the problem.
2
2
  p  Dp  c p
c c
 

|x 0  w o
d
 o  Do  x
(8)
2.3 EQUATIONS IN PER-UNIT FORM
In order to make it easier to solve the proposed diffusion
model, the equations and boundary conditions can be
Table 1. Normalized variables
transformed into a per-unit form. Table 1 shows the
variables in per-unit which are underlined. The variable Ks
is the steady-state distribution coefficient which is the ratio
of the steady-state concentration of gases in the oil to the
steady-state concentration of gases in the oil-impregnated
paper insulation at a certain temperature (Ks=cos/cps).
Basically the mass concentrations are scaled between zero
and one based on their initial and steady-state values.
Therefore, the per-unit concentrations will define the
percentage of mass with respect to the final steady-state
value minus the initial value.
Substituting the normalized variables in Equations 2, 3, 4,
5, 6 and 8, results in the following set of equations. These
equations are to be solved for the concentration of gas
inside the paper as a function of normalized time and
normalized paper insulation thickness. It should be noted
that the two new variables, rv and rk, are defined to make the
equations more compact.
c p  2 c p

t
x 2
c p (t  0)  1
(9)
(10)
c p (t  )  0
(11)
c p
|x 1  0
x
c
rk p |x  0  (c w  co )
x
(12)
(13)
1
co  2rv  c p d x
(14)
0
rk 
1   p  Dp   d 
 
 
K s  o  Do   
rv 
1   p   
  
K s  o  d 
(15)
(16)
2.4 THE ANALYTICAL SOLUTION
The solution to the boundary value problem cannot be
found using conventional analytical methods because of the
last boundary condition stated in Equation 13. Guggenberg
and Melcher, however, solved the boundary value problem
of Equations 9 to 13, analytically, for the moisture diffusion
[6]. The general solution to this partial differential equation
can be found using the method of separation of variables in
the following form [7]:

c p ( x, t )   Bn cos  n (1  x)e n t
2
(17)
0
Variable description
Time
Paper thickness
Concentration in the paper
Concentration at the wall
Concentration in the oil
Normalized variable relation
t = t τp
x=xΔ
cp = cp (cpi – cps) + cps
cw = Ks cw (cpi – cps) + Ks cps
co = Ks co (cpi – cps) + Ks cps
the eigen values, γn, and constant coefficients, Bn, can be
found from the boundary conditions. Substituting Equation
17 (for a particular n) and Equation 14 into the boundary
condition of Equation 13 (using the fact that cw=cp at x=0)
yields:
rk
1
c p
 c p  2rv  c p dx  0
0
x
Gas type
integrating and rearranging Equation 18 results in the
following relation.
 n cot  n  rk n 2  2rv
Table 2. Average characteristic gas parameters
(18)
(19)
Solving Equation 19 gives the solution eigen values, γn,
that can be used in Eqution17 for the general solution.
Figure 3 illustrates the solutions of Equation 19.
CO2
CO
C2H2
C2H6
C2H4
Average Do
(cm2/s)
6.4×10-6
6.9×10-6
3.8×10-6
2.3×10-6
2.8×10-6
CO2
CO
C2H2
C2H6
C2H4
In order to find the constant coefficients, Bn, the first
boundary condition can be used. Using Equation 10 and the
general solution of Equation 17 the following relation can
be obtained:

1   Bn cos  n (1  x)
(20)
0
Multiplying both sides of Equation 20 by cos  m (1  x)
and integrating over the paper insulation thickness results in
Equation 21 (using the substitute variable u=1-x).
1

0

cos  mudu   Bn  cos  nu cos  mudu (21)
0
1
rk
rv
2×10-4
2×10-4
0.5×10-4
0.6×10-4
2×10-4
0.4
0.2
0.8
0.5
0.6
Table 3. Steady-state ratio (Ks) of characteristic gases in a system with the
paper-oil volumetric ratio of about 1:25
Gas type
Figure 3. Illustration of the solution eigen values.
Average Dp
(cm2/s)
1.5×10-8
3.8×10-8
1.9×10-8
1.6×10-8
8.2×10-8
Ks2
70oC
3.6
1.5
2.7
2.5
Ks1
23oC
1.6
1.1
1.5
1.0
Ks2
Average
2.6
5.2
1.3
2.1
1.8
thickness and time. The parameters to be used to solve the
equations are obtained from experiments for some of the
characteristic gases and documented in previous
publications [3, 4]. Some of these parameters are repeated
here in Tables 2 and 3 (averaged over the values at two
temperatures, 23oC and 70oC). In Table 2, D0 is the average
diffusion coefficient of gas in the oil and Dp is that in the
paper insulation.
It should be noted that the parameters rv and rk shown in
Table 2 are different from those shown in the reference [3].
In Table 2 the parameters rv and rk are not calculated from
Equations 15 and 16, rather they are the values obtained
from comparing the simulation and experimental results as
will be discussed later.
The simulation results inside the paper insulation show
the trends of the concentration change in normalized form.
In order to convert these values to parts per million (ppm),
the values of Ks shown in Table 3 and the knowledge of the
present gas concentrations in the oil are required. The
simulation result of concentration change inside the paper
insulation for carbon dioxide is calculated and plotted in
Figure 4.
0
Since the problem eigen values are not orthogonal (as
illustrated in Figure 3), none of the integration terms in
Equation 21 will be equal to zero. Therefore, the
coefficients, Bn, should be calculated for all n. Using the
first 50 eigen values calculated from Equation 19, the
integrations in Equation 21 are calculated (for n=050 and
m=050 ) and therefore, the first 50 coefficients are
obtained (B0, …, B50). Substituting these values into
Equation 17 provides the solution to the boundary value
problem (the infinite series approximated with the first 50
elements).
3 SIMULATION RESULTS
A MATLAB™ code has been written to solve the
boundary value problem shown in Equations 9 to 16 and to
obtain and plot the gas concentration inside the oilimpregnated paper insulation as a function of the insulation
Figure 4. The simulation results of carbon dioxide inside the paper
insulation thickness (all parameters are normalized to steady-state values).
4 EXPERIMENTS
Experiments have been conducted to test the validity of
the simulation results. Experiments are based on
measurements in the oil since measurements in the paper
insulation were not possible with the test equipment
available. Equation 14 is used to convert the simulation
results in the paper insulation to that in the oil. Oil samples
are taken from the experimental setup and gas
concentrations are measured using the DGA method.
compensates the oil samples withdrawn from the main
container for DGA measurements. The oil flow rate
between the main container and the relaxation chamber is
100 ml/min and the oil-paper volumetric ratio is about 25:1.
Figure 6 shows a schematic of the main container with
paper insulation (pressboard) and the counter-flow oil paths.
Pressboard
4.1 EXPERIMENTAL SETUP
Figure 5 shows the experimental setup designed to
validate the simulation results of the suggested diffusion
model. The setup utilizes the same basic design and method
used in the previous experiments to obtain the model
parameters [3, 4], while altered to meet the new objective.
Headspace
sampling port
1000
ml
Figure 6. The main container in the setup shown in Figure 5.
2000 ml
Oil sampling
port
Precision
pump
1000 ml
Main container
Reservoir
Relaxation
chamber
Inert gas
Oil flow
Heater tape
Main container
Figure 5. The experimental setup to validate the simulation results
The main container consists of one section, stacked with
layers of paper insulation (Hi-Val). The insulation inside the
main container is arranged in a way that ensures maximum
surface contact with the oil, as oil is circulated between the
container and the relaxation chamber. The main container is
wrapped with a heater tape the temperature of which is
precisely controlled by a PID controller. The edge of paper
insulation inside the main container is covered with silicone
encapsulating compound to prevent the gases from being
adsorbed or desorbed from the edge. This is because the
suggested model to be validated with these experiments is
one dimensional and considers gas migration only through
the surface of paper insulation. The relaxation chamber is
filled with the oil to eliminate the effect of gas partitioning
between the oil and the headspace. The reservoir
4.2 EXPERIMENTAL METHOD
The system is heated up to about 70oC and kept under
vacuum for about a week before the oil is introduced into
the system. In this way the gases and moisture already
trapped in the dry paper insulation is purged as much as
possible. Clean oil is then introduced into the system and
the pump is left running for another week to ensure the
equilibrium is reached between the oil and paper insulation.
The main container is then sealed off and its oil content is
emptied into another container. The headspace area of the
new container is filled with a mixture of standard
characteristic gases with high concentrations and the
container is left in this condition over night with a magnetic
stirrer running inside the oil. Using this method, a high
concentration of characteristic gases is dissolved into the
oil. This inoculated oil is then returned back to the main
container of the experimental setup and circulated through
the system while the system is heated up to 70oC. Oil
sampling and DGA measurements are started at this point
and the time is marked at zero.
The system is left at 70oC with the pump running for
about two weeks. Then the system is cooled down to 23oC
and left running for another two weeks. This made sure that
gases inside the oil are in equilibrium with the paper
insulation inside the main container. After about 850 hours,
the temperature is stepped up back to 70oC and kept at this
temperature for about 300 hours. As soon as the system
temperature is increased a jump in the gas content of the oil
is observed through DGA measurements. Since there is no
source of gas generation (at this relatively low temperature),
the only conclusion is that these gases come from the paper
insulation as the oil and paper insulation solubility change
due to a temperature increase. The most obvious change is
in the concentrations of carbon dioxide and carbon
monoxide.
Concentration (ppm by vol.)
10000
CO
CO2
1000
100
Introducing gas
and temp. step
up (25-70C)
Temp. step
down (70C to
25C)
Temp. step up
(25C to 70C)
Temp. step
down (70C
to 25C)
Temp. step up
(25C to 70C)
10
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
Time (hours)
C2H4
Concentration (ppm by vol.)
10000
Introducing gas
and temp. step
up (25-70C)
C2H6
C2H2
Temp. step down
(70C to 25C)
Temp. step up
(25C to 70C)
Temp. step down Temp. step up
(70C - 25C)
(25C to 70C)
1000
100
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
Time (hours)
Figure 7. Experimental data of concentration change in the main container due to temperature changes.
The system is cooled down again for another 200 hours
and the experiment is repeated with more data points taken.
Figures 7 shows the data points obtained during the entire
time span of the experiments. The whole experiment took
about 1500 hours to obtain about 150 hours worth of data to
compare with the simulations.
4.3 EXPERIMENTAL RESULTS AND SIMULATIONS
Small jumps in gas concentrations can be seen at the time
of temperature increase from 25oC to 70oC in the case of
carbon dioxide and carbon monoxide. The discontinuous
happen between the hours of about 850 to 900 and the hours
of 1400 to 1500. The latter transition has more data points,
since it was clear while gathering the data between the hours
of 850 to 900 that more resolution was needed. This last
data set is plotted separately in normalized time and
concentrations. Simulation results in per-unit form are
compared with this data and shown in Figure 8.
5 THE EFFECT OF THE BOUNDARY LAYER
In the diffusion model introduced in Equations 9 to 16
the effect of the flow rate is considered only through the
boundary layer thickness.
Figure 8. Comparison of simulation and experiments for CO2.
The reason is that the concentration of the gases in the oil is
assumed uniform in that model. Sensitivity of the suggested
diffusion model to the boundary layer thickness is
introduced next.
Figure 9 shows the calculated square errors between the
simulation and experimental data as a function of
parameters rk and rv. The parameter rk, introduced in
Equation 15, represents the model dependency on the
diffusion coefficients (and therefore on temperature). It also
represents the dependency of the suggested model on the
flow rate since the boundary layer, δd, is a function of the
system flow rate. Substituting values of Table 2, for carbon
dioxide, for example, into Equation 15 and leaving the ratio
δd/∆ as a parameter results in Equation 22. It should be
noted that, in this equation, the ratio ρp/ρo is not taken into
account (since the concentrations in the model are measured
in ppm by volume and not by weight).
Figure 9. Sensitivity of the model to parameter constants rk and rv.
Comparisons are made between the simulations and experimental results
for carbon dioxide.
Also in derivation of Equation 22 the right hand side of
Equation 15 is multiplied by a factor of 25 which is the oilpaper volumetric ratio of the experimental system from
which the values of Ks are calculated and shown in Table 3.
 
rk  0.025 d 

(22)
In the experiments conducted to validate the model, the
thickness of the paper insulation was 1 mm. The boundary
layer is usually much smaller than the paper insulation
thickness and is in the range of μm. The thickness of this
layer is considered 7 μm from reference [6]. From Equation
22 the value of rk is estimated as about 2×10-4 for this
particular example. From Figure 9 it can be seen that for
small values of rk (about 0.01 or less) the error does not
change appreciably. In other words, if the ratio of δd/∆ in
Equation 22 is bigger by a factor of 100, for example, the
value of rk will change to 2×10-2, and, as it can be seen in
Figure 9, this will not cause a significant change in the
simulation error. This shows that the model is not very
sensitive to the boundary value thickness and therefore to
the system flow rate. It can be concluded then, as long as
the flow rate is high enough to mix the gas present in the
bulk of the oil (so that the assumption of uniform
concentration in the oil stands), the boundary layer
thickness is not a big factor in the system diffusion process.
6 SUMMARY AND CONCLUSIONS
The proposed mathematical model shown in this paper is
an attempt to explain the dynamic behavior of characteristic
gases in the oil-paper insulation systems. This study is
limited to the migration of gases that already exist in the
insulation system. This paper suggests and verifies a model
to explain the propagation of gases between the oil and the
paper insulation due to temperature variations in a structure
consisting of a single oil duct with limited length.
Assumptions are made to limit the model to the process of
diffusion, considering a sudden temperature change in the
whole system. The model is solved analytically, and the
results are tested against experiments.
A diffusion boundary layer is assumed at the oil-paper
interface and the diffusion equation is used to model the
migration of gases inside the paper insulation. The principle
of conservation of mass is used to calculate the total mass
exchange in the oil due to diffusion from and into the paper
insulation. Sensitivity of the system to the variations of the
diffusion boundary layer is studied and presented in this
paper using the suggested model.
The DGA method is based on gas chromatography which
by itself is not a very accurate method [11]. Any model
verified by DGA, therefore, cannot be more accurate than
this measurement method. The DGA method, however, is
the best available tool to date to assess the reliability of
power transformers. The mathematical model presented in
this paper should be perfected to give an accurate prediction
of the DGA results. However, the following comments can
be made on the impact of the temperature profile on the
DGA results according to the developed model, obtained
experimental data, and engineering judgment.
- Carbon dioxide and carbon monoxide are affected by
temperature variations in power transformers more than
hydrocarbons [3, 10].
- In an oil-paper system with volumetric ratio of 25:1, the
absolute values of the DGA result could have an error as
high as 40% and 30% for carbon dioxide and carbon
monoxide, respectively [4].
- The standard ratio method (reference [12]) eliminates this
error to some degree; however, one should be careful in
relying on the standard method if the ratio of the gases is
close to the critical limits [4].
- The DGA error is likely to be more significant when a
transformer is brought back to service after a relatively
long period of outage (more than about 48 hours) rather
than during the normal operating time. The reason is that
when the temperature is cooled down to the ambient, a
bigger temperature step change will be imposed on the
system when the transformer heats up to about 80oC. The
DGA error of carbon dioxide and carbon monoxide
above 80oC will not be significant [3, 10].
Future work should include considering the solution of
mass, heat and flow equations simultaneously in the whole
insulation structure of a typical power transformer. The
insulation structure should also be considered more
complex. The results of the research presented in this paper
pave the way to a more accurate model in the future. A
complete mathematical model can explain the behavior of
characteristic gases in oil-paper insulation systems and
reduce the DGA errors.
ACKNOWLEDGMENT
The authors would like to thank the DEIS Liquids
Technical Committee and the DEIS Education Committee
for supporting this work.
REFERENCES
[1]
ANSI/IEEE C57.104-1991, IEEE guide for the Interpretation of
Gases Generated in Oil-Immersed Transformers, IEEE/ANSI
standard, 1992.
[2] IEC 60599, Mineral oil-impregnated electrical equipment in
service-- Guide to the interpretation of dissolved and free gases
analysis, IEC publication, March 1999.
[3] A. Shahsiah, Modeling dynamic propagation of characteristic gases
in transformer oil/paper insulation and transformer fault
diagnostics, Ph.D. thesis, Rensselaer Polytechnic Institute, May
2006.
[4] A. Shahsiah, R.C. Degeneff, and J. Keith Nelson, "A study of the
temperature based dynamic nature of characteristic gases in oilcellulose insulation systems," IEEE Transactions on Dielectric and
Electrical Insulations, submitted May 2006.
[5] A. Shahsiah, R.C. Degeneff, and J. Keith Nelson, "A new dynamic
model for propagation of characteristic gases in transformer oilcellulose structure due to temperature variations," in Proc. IEEE CEIDP, October 2005, pp. 269-272.
[6] P. A. von Guggenberg, J. R. Melcher, "Moisture dynamics in
paper/oil systems subject to thermal transients," EPRI, report No.
EL-6918, 1990.
[7] G. Cain, G.H. Meyer, Separation of variables for partial differential
equation: an eigen function approach, Chapman & Hall/CRC, 2006.
[8] ASTM D 2779, Standard test method for estimation of solubility of
gases in petroleum liquids, American Society for Testing and
Materials, 1992.
[9] Detroit Edison Company, Development of an oil deterioration test
method to monitor the condition of high pressure fluid filled cables,
EPRI, Tech. Rep. EL-7895-1, 1991.
[10] H. Kan, T. Miyamoto," Proposals for an improvement in transformer
diagnosis using Dissolved Gas Analysis (DGA)." IEEE Electr. Insul.
Mag., Vol. 11, No. 6, November/December 1995.
[11] M. Duval, J. Dukarm, "Improving the reliability of transformer gasin-oil diognosis." IEEE Electr. Insul. Mag, Vol. 21, No. 4,
November/December 2005.
[12] IEC 60599, Mineral oil-impregnated electrical equipment in
service-- Guide to the interpretation of dissolved and free gases
analysis, IEC publication, March 1999.
Ahmad Shahsiah (M’01) was born in Tehran,
Iran in 1972. He received the B.Sc. degree in
electrical
engineering
from
Tehran
Polytechnic, Tehran, Iran in 1996, the M.Sc.
and Ph.D. degrees in electric power
engineering from the Rensselaer Polytechnic
Institute, Troy, NY, USA in 2001 and 2006,
respectively. He is currently working as a
consultant engineer at Exponent, Inc. Ahmad
Shahsiah is the recipient of the DEIS student
fellowship award in 2005.
Dr. Robert Degeneff is Professor of Electric
Power Engineering at Rensselaer Polytechnic
Institute in Troy, New York and been with the
school for 17 years.
The department is
involved in research in to the design and
performance of utility and industrial power
apparatus. Additionally, Dr. Degeneff is
president of Utility Systems Technologies, Inc.
which builds electronic voltage regulators and
power quality mitigation equipment and
provides consulting to the utility industry. Before joining RPI , Dr.
Degeneff was with General Electric for 16 years. Initially as a Senior
Development Engineer with GE's Large Power Transformer Department
and later, as a manager in various positions of increasing responsibility in
the power transformer business, HVDC systems, and utility planning.
Dr. Degeneff received his B.Eng degree from Kettering Institute and his
masters and D.Eng from RPI. He is a member of Tau Beta Pi, Eta Kappa
Nu and Sigma Xi. He is a PE in New York and a Fellow in the IEEE. He
has published over six dozen papers (two IEEE prize papers) and holds
eight patents.
J. Keith Nelson: Fellow ‘90, was born in
Oldham, UK and received his B.Sc(Eng)
and Ph.D degrees from the University of
London, UK. He is currently Philip Sporn
Chair of Electric Power Engineering at the
Rensselaer Polytechnic Institute. Prior to his
appointment at Rensselaer, he was manager
of Electric Field Technology Programs at
the General Electric R &D Center in
Schenectady, NY. He has held numerous
IEEE appointments including that of the Presidency of the Dielectrics &
Electrical Insulation Society, 1995-6. He is a chartered electrical engineer,
a Fellow of both the IEEE and IEE and the recipient of the IEEE
Millennium Medal.