Dielectric Response and Space Charge in Epoxy Impregnated Paper Composite Laminates

Qingyu Wang and Zongren Peng

State Key Laboratory of Electrical Insulation and Power Equipment Xi’an Jiaotong University

Xi’an, Shaanxi, 710049, P.R.China

S. J. Dodd, L. A. Dissado and N. M. Chalashkanov Engineering Department, University of Leicester

University Road Leicester LE1 7RH, UK

ABSTRACT As the main material of the converter transformer dry-type bushing, the dielectric properties of epoxy/crepe paper at different temperatures and frequencies are related to the electric field and thermal field distribution of the bushing, which directly affects the safe and stable operation of the bushing. Here we report the dielectric response of samples of dry-type bushing insulation measured at a range of temperatures appropriate to operation and down to frequencies below those usually used. A significant loss peak observed below power frequency is interpreted as originating from the charging of internal epoxy resin interfaces by the transport of charge carriers on structured paths in the epoxy-impregnated crepe paper layers. A simulation model is proposed that allows estimation the space charge and field distribution at any given frequency.

Index Terms - converter transformer dry-type bushing, dielectric properties, epoxy/crepe paper, dielectric response process, space charge and field distribution

1 INTRODUCTION

IN order to meet the requirements of an oil-free valve hall, in China's UHV converter station the DC bushing generally adopts an epoxy-impregnated paper/SF6 gas composite insulation structure, with an epoxy-impregnated paper core as its main insulation. This paper core is cast with bisphenol A diglycidyl ether type epoxy resin E51, curing agent (methyltetrahydrophthalic anhydride) and accelerator (N, N-dimethylbenzylamine), and impregnated into crepe paper. The bisphenol A diglycidyl ether (Figure 1) type epoxy resin has a low degree of polymerization, and less than 10 % of the molecules have a value of n that is not zero, giving a degree of polymerization of less than 0.1 [1, 2].

Since epoxy-impregnated paper is a composite material of

epoxy and crepe paper, its dielectric response is complicated,

and at present there has been little in-depth research and analysis carried out on it, in contrast to oil-paper insulation (e.g. [3]). In [4] the dielectric spectrum of pure epoxy and epoxy /crepe paper composite was fitted to a parallel combination of a Havriliak- Negami (HN) dielectric relaxation and a DC conductivity. Thermally stimulated depolarization currents were used to determine the various trap activation energies. The detailed physical mechanisms of the various contributing processes were however not discussed. The effect of nano- Al2O3 filler on the dielectric properties of epoxy resin material was studied in [5], where a low-frequency dispersion phenomenon was clearly identified in the measuring frequency range. This was assigned to the movement of charge carriers between regions in the bulk material where opposite polarity carriers are bound together in the absence of an electric field, giving a frequency dependent bulk charge transport termed a quasi-DC (QDC) process [3, 6]. In contrast it was concluded in [7] that the increase in permittivity and loss tangent observed in epoxy/crepe paper composite material as compared to the pure epoxy was the result of interfacial polarization.

The differences in the physical interpretation of the dielectric response of epoxy /crepe paper composite materials presented in [4, 5, 7] has consequences for the diagnosis of

Figure 1. Diglycidyl ether of bisphenol-A (DGEBA).

Manuscript received on 2 March 2019, in final form xx Month 20yy, accepted xx Month 20yy. Corresponding author: L. Dissado.

changes due to ageing [7] and the accumulation of space charge at laminate interfaces [8] that results in enhanced local fields leading to breakdown [9] and hence require further work for their resolution. Here we investigate the dielectric response of laminated samples of epoxy-impregnated paper composite materials as a function of frequency and temperature. The results are first fitted to an equivalent circuit that represents each layer by a parallel combination of capacitance and QDC elements [6]. The physical interpretation of these circuit elements is then confirmed through the development of a simple simulation model for the ac-response based on local circuits. This model is then used to derive the accumulation of space charge at different frequencies. In this way we intend to determine the physical features governing the dielectric response of laminate epoxy/crepe paper composites and answer the question as to the relative roles of bulk processes and interface in developing space charge in the laminate at different ac frequencies.

2 EXPERIMENTAL DETAILS

2.1 MATERIALS

Dry transformer bushing insulation is made from rolled crepe paper impregnated under vacuum by the epoxy resin giving an epoxy-impregnated composite that is composed of a multilayer mesh structure with alternating pure epoxy and epoxy impregnated paper layers. Samples with a diameter of 80 mm were directly cut from a ±400 kV converter transformer dry-type bushing, all of which were cut perpendicular to the radial direction of the bushing core. After polishing by fine sandpaper, the sample thickness was about 1 mm, see Figure 2 which will contain on average two layers of impregnated crepe paper. The samples were cut from different positions in the bushing core, so the curing degree of each sample will be slightly different.

Because cured epoxy-impregnated paper is very hard its surface temperature becomes high during cutting leading to possible deformation and an uneven surface even after polishing. In order therefore to obtain a good electrode contact the sample was sputter coated on both sides with gold using a Quorum Q150T ion sputtering apparatus. Any moisture that may have entered the samples, whose concentration may vary because of differences in the degree of curing, was removed by drying each sample in an oven at 150 ±0.5 °C for two hours before measurement. Pure epoxy samples with the same thickness as the epoxy-impregnated ones were prepared in the laboratory following the same procedure so as to allow a comparison between them and the samples cut from the transformer bushing.

2.2 DIELECTRIC MEASUREMENT

The dielectric response was measured using a three-electrode system, see Figure 3, enclosed in a metal box in order to suppress electrical noise and signal interference. The Measurement call was placed in a temperature-controlled oven and connected to a Solartron 1296 dielectric interface, which in turn is connected to a Solartron 1255 frequency response analyzer. The dielectric interface probe ac voltage of 1.0 V

rms was applied to the samples and the resulting current amplitude and phase angle measured to determine the complex impedance of the sample and hence the complex capacitance as a function of frequency. The available frequency window was 10-5 to 106 Hz.

3 RESULTS

3.1 CAPACITANCE MEASUREMENTS

The real and imaginary parts of the complex capacitance were converted to complex relative permittivity by multiplying by d/S0, where S is the electrode area, d is the sample thickness, and 0 the permittivity of free space. Figure 4 shows the frequency dependence of the resulting real and imaginary relative permittivity of epoxy-impregnated paper and pure epoxy resin at 80, 100 and 120 °C, which are the typical temperatures in bushing cores at rated operating voltages and current.

The main feature of the response of the epoxy-impregnated paper laminate (Figure 4a) is a dielectric dispersion and its associated loss peak at around 10-3 Hz at T = 80 °C that moves to around 10-2 Hz at T = 120 °C. At frequencies below the dielectric dispersion the response is dominated by a loss process with a frequency dependence of r”(f) f-p. Since p < 1 this low frequency process cannot be regarded as contributed by a DC conductivity (r”(f) = dc/(2f0)), but must be regarded as QDC process [3, 6]. In contrast the response of the pure epoxy resin is almost featureless, except for the onset of a dielectric dispersion whose peak lies below the lowest frequency (10-4 Hz) measured. There is no indication of a QDC process in the frequency window at the

Figure 3. A photograph of the measurement cell. (The guard electrode sits concentrically over the current sense electrode (I).)

(a) (b)

Figure 2. (a) epoxy impregnated paper and (b) pure epoxy samples.

Guard Electrode

Current (I) Electrode

Voltage (E) Electrode

E from Dielectric Interface

I to Dielectric Interface

measurement temperatures. Figure 5 shows that a curve can be obtained for the epoxy-

impregnated paper laminate by translating the responses at different temperatures along the log(f) axis to bring them into coincidence (i.e. a time-temperature superposition). Since all responses can be brought together by the same translation they all have the same temperature dependence. This implies that the dispersion seen in the laminates is produced as a result of the same QDC charge transport process that can be observed at low frequencies. However in the case of the loss peak this charge transport is blocked at the interfaces between different layers of the laminate. The activation energy of the QDC charge transport process can be obtained from an Arrhenius plot of frequency shifts that are required to bring about coincidence in the master plot, which is shown in Figure 6. A value of about 1 eV is obtained for the temperature range 60 and 100 °C in the epoxy-paper laminate, but in the pure epoxy its amplitude is too small to allow a reasonable estimate to be made.

3.2 EQUIVALENT CIRCUIT FITTING

Because the epoxy-impregnated paper samples were cut along the radial direction of the core they can be simplified into 5 layers from top to bottom beginning with a pure epoxy layer, and alternating with epoxy/crepe paper layers. The equivalent circuit for these laminates therefore takes the form of five circuits in series, with each circuit corresponding to the dielectric response that is associated with a single layer.

The general form of such a circuit is given in Figure 7a, where the response of each layer is taken to be given by a parallel combination of a frequency-independent capacitance (C) and a QDC element. The epoxy layers are taken to give the same contributions (denoted 1), whereas layers labelled 2 and 4 are allowed to be different. In series circuits the system impedance is the sum of the impedances of all layers. Thus layers with the same dielectric response will appear in the mathematical representation of the system impedance as a single contribution with the frequency dependent response of a single layer but an amplitude that is that of a single layer multiplied by the number of layers. The construction given in Figure 7a will therefore allow for the possibility that differences in the state of impregnation between the layers

Figure 6. Arrhenius plot of the shift frequency for the epoxy impregnated paper samples.

Figure 5. Master curve of the frequency-dependent response of the epoxy. impregnated paper samples. The scales are correct at T=80 °C.

(a)

(b) Figure 4. Complex relative permittivity of (a) epoxy impregnated paper and(b) pure epoxy samples at temperature 80, 100 and 120 °C.

will result in differences in the response. It could however describe epoxy-impregnated layers with the same response together with epoxy to paper interfaces or electrode interface layers with a different response. A further consequence of the additive nature of the impedances is that the ordering of the different contributions has no relationship to the physical arrangement of the layers. The capacitance of each layer is taken to be frequency-independent over the measuring range both because it is the simplest approach and can be relaxed if necessary and also because it is what is observed in the response of the epoxy resin, see Figure 4. In this latter case the small dispersion below 10-3 Hz observable at 120 °C is attributed to the onset of a parallel QDC process.

The QDC form of response arises from charge transport on structured paths [3, 6] in the material such as the fractal paths of percolation structures below the percolation limit [10 - 12]. At high frequencies ( > c) the mobile charge carrier and its counter charge of opposite polarity remain bound together and the charges separate over a small region termed a cluster in [6], whereas at low frequencies ( < c) the mobile charge becomes separated from its counter charge and moves from cluster to cluster over long frequency-dependent distances (see [3, 6, 11] for greater detail). The structured paths on which the charge carriers move result in a smaller number of routes as the transport distance is increased with an increasing number of routes becoming blocked off leading to an increasing capacitance with lowering frequency and a reducing ac-conductivity (ac(f) = 2f0r”(f) f1-p, with r”(f) f-p being the imaginary component of the relative susceptibility contributed to r”(f) by the QDC process). The resulting QDC process gives a frequency dependent susceptibility of the form:

*( )( ) (0)

x

F

(1)

With the spectral shape function given by:

211 1

0 2 1( ) (1 ) (1 ,1 ; 2 ; (1 ) )

n

c c c

F F i F n p n i

(2)

where 2F1(-,-;-;(-)) is the hypergeometric function and the normalizing factor F0 is given by a ratio of Gamma () functions:

0

(1 ) (1 )

(1 )

n pF

p n

(3)

The asymptotic frequency dependencies of the QDC complex susceptibility are the following frequency fractional power laws [6, 10 -12],

1( ) ( ) when

( ) ( ) when

n

c

p

c

(4)

Here, 0.5 < n, p <1 for a QDC process. The limiting values of n = p = 0.5 correspond to a diffusion process, which relates to homogenous charge motion in space (not on structured paths) driven by a concentration gradient. The ac-conductivity corresponding to Equation (4) at < c gives zero conductivity in the limit of = 0 as the number of transport

paths becomes zero in the limit of infinite separation, as for example in a percolation system below the percolation limit. Only in the limit of p =1 does it correspond to a true DC conductivity [13].

Table 1. Fitting parameters of equivalent circuit.

(1)

A fit to the experimental data using the equivalent circuit of

Figure 7a, necessitated the parameters for layer 2 and 4 to be different. When this was allowed an excellent fit to the experimental data is obtained over the range 2x10-4 Hz to 103 Hz with the values of Table 1. A small deviation from frequency-dependence of the imaginary component below 2x10-4 Hz was found where electrode effects or layer arrangements that are slightly out of parallel come into play. In this low frequency region the model predicts a C”(f) f-p with a value of exponent p that is slightly bigger than that of the experiment. The loss peak around 0.1 Hz arises because the QDC circuit components of the series components corresponding to epoxy-impregnated paper layers and interface layers are greater than those in the epoxy layers.

(a) (b)

Figure 7. (a) Equivalent circuit with 1 indicating the components for theepoxy resin layers and, 2 and 4 those for epoxy-impregnated paper and other series layers; (b) equivalent circuit fit for the epoxy impregnated papersamples at 100 C.

PARAMETERS INDEX 1 INDEX 2 INDEX 4 p 0.55 0.91 0.63 n 0.99 0.97 0.8

c (rad/s) 7.5 1.16 21 QDC (o) (pF) 0.17 69 4.5

C (pF) 690 174 118

Since the QDC process is a charge transport process the difference in its amplitude in the epoxy and other layers results in an interface charge and the charging process yields a loss peak in the same way as a series resistance-capacitance circuit [14]. Because of the additive form of impedances in series it is not possible to determine whether the two layers (2 and 4) refer to the two epoxy impregnated layers, or to epoxy-impregnated paper and, boundary regions between it and epoxy or electrode interface regions. What is clear however is that there exists two types of layer with different frequency responses. The differences between the contributions of the these layers are small as regards the capacitance, which indicates that either the two layers are of similar thickness or there are more of one type than the other. The QDC component of each layer does differ in terms of amplitude, characteristic frequency ((0) and c of Equations (1) and (2)) and power law exponents. The large amplitude and low characteristic frequency of layer 2 together with p close to unity indicates a system in which a large concentration of charge carriers move in a nearly free manner, but for which it is more difficult to free them than in either the epoxy or the other type of layer. This may indicate an origin in the electrode interface but such an assignment cannot be definite. Because the responses cannot be assigned with any certainty to specific layers calculation of internal space charge build up requires a different kind of model, section 3.3.

3.3 MATLAB SIMULATION

In parallel with the equivalent circuit analysis, a 2-D time domain finite difference based charge transport model was developed in MATLAB in order to further elucidate the contribution of the crepe paper/epoxy to the overall dielectric response. The principle of the FDM method is to represent a set of partial differential equations (PDEs) by a set of algebraic equations. To achieve this, 2-Dimensional domain is discretized into a finite number of grid points. The number of grid points (nodes) used and the time step affect the stability and accuracy of the calculation. A 36 by 36 domain was defined as shown in Figure 8 to represent a 1mm by 1mm sample. The domain was split into 5 sub-domains to represent a sandwich of two crepe paper/epoxy layers separated by 3 pure epoxy layers. Each node was assigned a random relative permittivity and each bond between nodes was assigned a random electrical conductivity chosen from a top hat distribution (i.e. one that is uniform between upper and lower bounds) whose limits are given in Table 2. These values were chosen to get a good match with the measured dielectric properties of the sample at 100 °C. Dirichlet boundary conditions were applied to the top and bottom electrodes. A sinusoidal voltage of magnitude 1000 V was chosen to relate the calculations to a typical operating stress of 1 kV/mm under the assumption that the dielectric response has not changed with field (i.e. it is still in the linear regime). A frequency, , was applied at the top surface while the bottom surface of the domain was set to a constant voltage of 0 V. Neumann boundary conditions were set on the right and left edges of the sample. The governing equations for the simulation are as

follows [15]:

=- VE (5)

J = E (6)

( ) E = (7)

t

J (8)

where E is the electric field strength, J is the current density, V is the node voltage, is the conductivity, is the charge density, is the dielectric constant, and t is the time. Substituting Equation (6) and Equation (8) into Equation (7) gives the transient equation of local (body) charge density:

( )t

J (9)

The initial conditions imposed were that the voltage was at the peak voltage and that the current density and the charge density were zero at time t = 0. For each frequency, , of the applied voltage, time steps corresponding to 65000 steps per cycle of the applied voltage were used. At each time step, the electric potential distribution was determined by solving the finite difference representation of Equation 7 of the 2-D domain. The electric field distribution was then determined from Equation 5 and current densities calculated from Equation 6. The space charge accumulating at each node was then calculated using Equation 9. At each time step the total current density through the sample was calculated. By comparing the magnitude and phase of the current density with the applied voltage, the complex impedance at frequency was obtained. Repeating the simulation at different frequencies, , enables the frequency dependent dielectric properties to be obtained. The complex impedance was then converted to complex permittivity to obtain the dielectric spectra shown in Figure 9.

It can be seen from the figure that the MATLAB simulation result is basically consistent with the equivalent circuit fitting result over the frequency range below 10 Hz where the long range transport (”(f) f-p) part of the QDC process (Equation (4); < c) in the epoxy-impregnated paper dominates the response. The mathematically based QDC process at frequencies < c is therefore well described by the simulation concepts of a distributed local conductivity that is both in series and in parallel with a distributed local permittivity [10, 11]. The random selection of local bond and node values results in a structure with the form of a percolation system for which the low frequency susceptibility exponent p will be governed by the fractal dimension of the transport system [10].

Since the conductivity and dielectric constant at each node in the sample cannot be accurately known, the range of parameters adopted for the simulation are based on assumed values from the measured data of pure epoxy resin and epoxy impregnated paper composite parameters. The structure of the experimental epoxy-impregnated paper sample may also be

slightly different from the simulation model. Therefore, the simulation result deviates from the experimental result at high and low frequencies. The simulation result in the low and middle frequency region has the same behavioral trend as the experimental result and the relaxation peak appears in the middle frequency region, due to charging of the interfaces between the layers caused by the discrete difference in conductivity ranges of the epoxy layer (low conductivity range) and the epoxy impregnated paper (high conductivity range), see Table 2.

In the low frequency region, the real and imaginary parts of the dielectric constant in the simulation are slightly larger than

the experimental results, which may be due to the difference between the conductivity parameters in the epoxy/crepe paper layer set in the simulation and the sample parameters used in the experiment, and the difference between the simulation model and the actual sample structure. This is the same as found from the equivalent circuit fitting and implies that the deviation is not due to the choice of sample parameters but from factors that do not feature in either approach, such as deviation from an exact layer arrangement. In the high frequency region, the simulation deviates from the experimental data. When allowance is made for the noise level of the measuring system on the imaginary permittivity the deviation is substantially removed, as shown in Figure 9. Alternatively, the excess loss of the epoxy at high frequency (above that expected for pure DC conductivity) as shown in Figure 4 may contribute to the deviation between the simulation and experimental data at frequencies above 10 Hz. However, the equivalent circuit description gives an alternative explanation in which the frequency response of this region is given by the relative displacement of bound charge carriers of opposite polarity, with c being the frequency at which they become independent. The size scale of the simulation model excludes this feature and it is noticeable that its deviation from experiment starts to occur roughly where c (10 Hz). Since this contribution to the QDC response has been measured in frequency and amplitude ranges for which instrumental noise is not large, it is reasonable to conclude that the intra-cluster displacements is its most likely origin [6, 10, 13].

4 DISCUSSION

4.1 NATURE OF DIELECTRIC RESPONSE

The loss peak identified in [4] at 2x103 Hz (T = 160 C) is outside the effective frequency window of this work, while the weak loss peak at 1- 10 Hz is not resolved. Its presence may be the cause of a tiny deviation of the equivalent circuit and simulation in this frequency region. The lowest frequency measured in [4] was 0.1 Hz and the response between 0.1 Hz and 1 Hz was interpreted as an ideal DC conductivity. By extending the frequency range down to 10-4 Hz and fitting the resulting data using equivalent circuits and a simulation model we have shown that this response is actually a frequency-dependent quasi-DC transport taking place on structured paths within the dielectric. The charging of the internal interfaces between the laminate layers by this transport process gives rise to the strong loss peak process observed at ( 10-2 Hz at T =120 C). At frequencies below 10-3 Hz (at T =120 C) the response is governed by the high impedance charge transport of the epoxy layers.

A dominating QDC charge transport has been observed in epoxy resins and their composites previously, e.g. [5, 16-19], where the charge carrier has been taken to be ions, either in a water component, supplied by the paper component [3 - 5], or in printed wiring boards supplied by the conductor [20]. In the case of epoxy-impregnated crepe paper it is difficult to remove absorbed moisture completely even with heat treatment so it is possible that hydrogen ions from residual absorbed water may act as charge carriers, however paper

Figure 9. Comparison curves for the experimental results, fitting results andthe simulation results of the relative permittivity of the epoxy impregnatedpaper sample at 100 C.

Table 2. Parameters of simulation.

Parameters Pure epoxy

layer Impregnated Paper Layer

Conductivity (S/m) 5e-14 - 1e-13 1e-13 - 1e-11

Relative permittivity 3.3 - 3.4 3.4 - 5

Figure 8. Simulation model for the epoxy impregnated paper sample.

contaminants (ash, iron, and copper) may also contribute charge carriers [4]. Ionic transport takes place by the transfer of ions between local cages with the displacement of the surrounding polymer material required for the transfer to take place defining the activation energy. The work on epoxy-impregnated glass fibre [17, 18] indicated that the ion cages were formed along interface between the epoxy and the fibres with the epoxy displacing to allow transport with an activation energy of 1.1 eV. Transport between binding sites on the fibre surfaces was ruled out because the activation energy for transport on the fibre mats without epoxy impregnation was found to be much lower at 0.67 eV. The epoxy-impregnated crepe paper can be expected to behave in a similar way with ion cages formed along the interface between the epoxy and the crepe paper with ion transport taking place along the structured paths formed by these interfaces [6] and requiring an activated displacement of the epoxy chains with a similar activation energy such as found here ( 1 eV). The QDC process in the epoxy layers would require a similar activation energy consistent with ion transfer between epoxy cages, but its amplitude is much smaller than that in the epoxy-impregnated layers, Figure 4b. The ac-conductivity of the low frequency branch of the QDC process is given by:

ac = (0)(c)p01-p (10)

Taking c/2 as the jump frequency for hopping conduction, together with the corresponding expression for the low field mobility [21];

= (a2e/2kT)c (11)

where k is Boltzmann’s constant, T is the temperature in Kelvin, e is the electron charge and a is the jump distance, we find that (0) has the following approximate form:

(0) nione (a2/2kT0) (12)

Here nion is the ion concentration. Thus the small amplitude for (0) in the epoxy layers could be the result of a low concentration of mobile ions, which is the most likely explanation, or a smaller jump distance than in the epoxy-impregnated paper where the distance between neighboring cages would be determined by the topology of the epoxy-paper interface.

4.2 SPACE CHARGE AND FIELD DISTRIBUTION

Charge transport within layers with a discontinuity at the boundaries will inevitably lead to space charge accumulation there. The equivalent circuit model shows that charge will start to build up in AC fields but only at frequencies below a few Hertz where < c (i.e. f < fc 1 Hz) for which long range transport sets in. This model can be used to estimate the build-up of space charge at these interfaces at a given frequency, but without detailed knowledge of the geometry of

the structured transport paths it is not possible to determine its internal distribution within the layers. Such a calculation however is an essential part of the simulation model.

Epoxy resin impregnated bushings have applications as transformer bushings on a conventional 50 Hz ac power grid as well as converter transformers used in HVDC converters. In the case of line commutated converters the converter bushings are subject to a combined ac and dc voltage. Due to the 12 point per cycle commutation of the thyristor valves, the ac voltage has substantial harmonic frequency components at the fundamental 50 Hz frequency as well as substantial harmonics of the switching frequency of 600 Hz.

Figure 10 shows the charge and y-direction electric field distribution curves along the middle of the simulation grid estimated from the simulation model for an applied voltage of 1000 V and at frequencies of 0.001 and 50 Hz, and T = 100 C. As shown in Figure 10a, when the voltage frequency is 0.001 Hz, the amount of charge is larger in the pure epoxy layers, because they have a larger resistance than the epoxy-crepe paper layers. At low frequencies (f << fc in the equivalent circuit representation), the electric field distribution, Fig. 10 (b), is similar to that expected for a DC field, mainly depending on the conductivity of each node. The field in the lower conductivity pure epoxy layer reaches 5000 V/mm, which is more than five times the average field strength of the sample, 1000 V/mm. In contrast the field in the epoxy-impregnated paper layer is almost zero. Thus in this case the epoxy layers are highly polarized, while the epoxy-impregnated paper layers are essentially unpolarized.

When the voltage is at the power frequency of 50 Hz

(corresponding to f > fc in the equivalent circuit representation), the charge amount is reduced by about three orders of magnitude compared to that at 0.001 Hz. In this case the charge is concentrated in the epoxy-crepe paper layer. The electric field distribution of the sample at power frequency 50 Hz voltage mainly depends on the dielectric constant of each node, and thus the layers are capacitively coupled rather than

(a) (b)

(c) (d)

Figure 10. Simulation results at T = 100 C of charge distribution and electric field distribution along the y direction of the sample: (a) and (b) at 0.001 Hz: (c) and (d) at 50 Hz. The simulation grid is that of Figure 8.

resistively coupled as at the low frequency). Therefore, the electric field distribution in the pure epoxy layer with lower dielectric constant is significantly higher at a maximum of 1150 V/mm than that in the epoxy-crepe paper layer with higher dielectric constant, where local variations yield an uneven distribution around an average of about 900 V/mm, as shown in Figure 10d. In this case the difference in electric field within the two types of layer is considerably less than the one obtaining at low frequencies or at DC.

The high fields in the epoxy layers eventuating either at dc or at low frequency poses a risk to the survival of the bushing insulation at these frequencies [22]. In the present case the frequency at which it occurs is below the power frequency at which the insulator is used. However it is known that several factors, such as moisture, temperature, and ageing, [3, 5, 16-19] can increase the value of c and move the onset of the high field generation to higher frequencies. The dielectric response, through an analysis to determine c, can therefore act as diagnostic factor for the state of the insulation and the breakdown risk it poses during operation, and particularly one that can be used during operation. When used in conjunction with the corresponding simulation model it is even possible to estimate the internal local fields at the operating frequency and hence improve the detail of the risk assessment.

5 CONCLUSIONS It has been found here that epoxy-impregnated paper

laminate samples cut from dry transformer bushing insulation exhibits a substantial dielectric loss peak at lower frequencies than previously measured. It has shown that the peak is produced by the charging of the epoxy layers by a charge transport process in the epoxy-paper layers. The charge transport is however not an ideal DC conductance, but instead is a QDC process in which the displacement of charge carriers along structured paths related to the crepe paper-epoxy interfaces, which gives an ac conductivity that reduces towards zero with decreasing frequency as the transport distance increases. Above a characteristic frequency the carriers are bound together as ion-pairs and no longer contribute to charge transport. An equivalent simulation model has been proposed that allows the dielectric response to be correlated with the space charge and internal field distribution at any chosen frequency. The combination of dielectric response and proposed simulation model point the way towards a detailed non-destructive diagnostic methodology for the state and life risk of dry transformer insulation.

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Qingyu Wang was born in Henan province, China, in 1991. She received the Bachelor degree in electrical Engineering from Xi’an Jiaotong University, Xi’an, China, in 2013. Currently she is working for the Ph.D degree in High-voltage and Insulation technology at Xi’an Jiaotong University. Her area of interest lies on structure design and optimization of extra-high voltage and ultra-high voltage insulation system.