Effects of Hydrothermal Aging on the Breakdown Voltage of Polyesterimide

Nowadays, polymers are widely used in electrical devices such as electrical cables, motors, generators, etc., because of their excellent electrical and mechanical properties [1]. They perform a crucial function as solid insulating materials.

Insulating materials such as polyesterimide, polyamideimide, and polyimide are commonly used to insulate electrical machine windings. They are chosen because of many factors, including the working environment, applied voltage, rotation speed, and operating temperature.

Polyesterimide is a polymer that is widely utilized in electrical equipment. It has higher abrasion resistance, and excellent insulating characteristics [2].

However, these materials are subjected to various stresses (electrical, thermal, mechanical, and environmental), leading to the degradation in time of these polymers and thence to failures. The degradation of the polymer properties is named "aging phenomenon."

The principal stresses that can affect the performances of these insulators by an irreversible deterioration are temperature and humidity, which can act separately, leading to thermal aging by heat, hydrolytic aging by moisture, or in combination resulting in hydrothermal aging. These different types of aging are significant tests in the evaluation of electrical insulation systems.

Many authors have studied the thermal aging of polyesterimide. A decrease in the dielectric strength of polyesterimide with aging time has been mentioned by Brandes et al. [3] after exposing the material to different temperatures (155-220℃). A change in thickness and viscosity of polymer has been reported. The thermal index is 188℃. Araki and Taguchi [4] have explored the deterioration of twisted pair samples of polyesterimide aged at 230℃. The findings demonstrate no substantial change in dielectric strength during the early stages of aging. However, it increases and then decreases rapidly as aging progresses. This phenomenon is linked to material crosslinking due to thermal aging. The degradation is followed by a reduction in the dielectric layer thickness.

The thermal lifetime of polyesterimide has been studied by Nedjar [5]. The results show the evolution of breakdown versus thermal constraint. Its rise is related to polymer crosslinking, and its decline is attributed to the reduction of viscosity. The graph of thermal endurance is a straight line. The activation energy has been calculated, and the temperature index is 182℃.

Hydrolytic aging of polyesterimide is rarely studied, and the presence of moisture is accepted as hastening polymer degradation. It was reported that water could have three kinds of effects [6]. The first is physical: plasticization of the material showing a weakening of the molecular bonds. The second is chemical: hydrolysis of ester and amide bonds. The third is photochemical: generation of hydroxyl radicals. The hydrolytic degradation of polyester urethane elastomers is due to the acid-catalyzed hydrolysis of the ester group [7]. Samples of polyesterimide have been exposed to hydrolytic aging for 3000 hours under 90% relative humidity (RH) at 30℃ temperature [8]. The investigation reports that the breakdown voltage varies with hydrolytic exposure time. The difference between the breakdown voltage under AC and DC ramp and between the DC polarities has been reported. It was claimed that the water content of XLPE and TR-XLPE grows with aging time, and a drop of AC breakdown voltage with increasing water absorption was observed [9]. The penetration of water in the XLPE cable slices causes the generation of water trees [10].

Several authors have investigated hydrothermal aging of insulating solids. Researchers reported results on hydrothermal aging of polyesters and polyamides [11]. Other authors studied the degradation of polyvinyl chloride subjected to the combined action of temperature and humidity [12, 13]. Brun et al. [14] reported a decrease in modulus of elasticity and glass transition temperature of epoxy and silica composite material. The dielectric strength of wet materials can diminish by a factor of 5 to 10 compared to dried ones. Roggendorf et al. [15] measured dielectric loss factor, permittivity, and dielectric strength during hydrothermal aging. The water absorption in the polymer was evaluated.

Breakdown voltage is considered the most important dielectric property to define the insulating performance of the polyesterimide. The humidity and the temperature are the main stresses which can affect aggressively the material when they act together leading to hydrothermal aging of the polymer. This work aims to study the influence of hydrothermal aging on the breakdown voltage of polyesterimide. The results obtained show that the factor which affects the rise of breakdown voltage the most is the thermal effect, while its decrease is due to water absorption. The results demonstrate also that AC breakdown voltage is lower than DC one. It has also been noted that polarity affects the breakdown voltage under the DC ramp.

3.1 Statistical model of Weibull

The model largely used in statistical studies of dielectric strength of solid dielectrics is the Weibull model [17, 18]. This type of distribution will be used in the following study. The cumulative probability P (V), currently employed to analyze dielectric strength data, is the two-parameter Weibull distribution, provided by the following relation [18-20]:

$P(V)=1-\exp \left[-\left(\frac{V}{\alpha}\right)^{\beta}\right]$           (1)

where:

• $V$  is the breakdown voltage in kV.
• $\alpha$  is a scale parameter corresponding to the breakdown voltage for a probability of 63.2% in kV.
• $\beta$  is a shape parameter representing the slope of the straight line of the Weibull plot.

Eq. (1) may be transformed to the following form:

$\log \left(\ln \left(\frac{1}{1-P(V)}\right)\right)=\beta \log (V)-\beta \log (\alpha)$                 (2)

Eq. (2) is an equation of a straight line:

$Y=a X+b$            (3)

By identification between (2) and (3), we find:

$X=\log (V)$              (4)

$Y=\log \left(\ln \left(\frac{1}{1-P(V)}\right)\right)$                (5)

The experimental data plot must be a straight line of the coordinate system above, where P is the cumulative breakdown probability.

We note that for $\mathrm{Y}=0, \mathrm{~V}=\alpha=\mathrm{V}_{\mathrm{b}}$.

$P\left(V_{b}\right)=1-e^{-1}=63.2 \%$             (6)

$\mathrm{V}_{\mathrm{b}}$  is the nominal breakdown voltage.

In this study, the two-parameter Weibull distribution was used to plot the measured values of breakdown voltage. The data were arranged in ascending order, starting with the smallest and working up to the greatest. For any value Vi, the cumulative breakdown probability is determined using the following relationship [17, 21, 22]:

$P_{i}=\frac{i}{N+1} 100 \%$             (7)

where:

• $P_{i}$  is the cumulative failure probability in %.
• N is the total number of tested samples.
• $i$  is the value rank of breakdown voltage $V_{i}$.

In this work, N was fixed equal to 50.

3.2 Maximum likelihood method

The maximum likelihood method estimation is a well-known method to treat data of dielectric breakdown.

The two parameters of a Weibull distribution were found by using a likelihood function L [23]:

$L(\alpha, \beta)=\prod_{i=1}^{N} \frac{\beta}{\alpha}\left(\frac{V_{i}}{\alpha}\right)^{\beta-1} \exp \left[-\left(\frac{V_{i}}{\alpha}\right)^{\beta}\right]$           (8)

To find the maximum likelihood estimation for the parameters $\alpha$ and $\beta$ in Eq. (8), we must solve the system of equations as follows:

$\frac{\partial \log (L(\alpha, \beta))}{\partial \alpha}=0$,                  (9)

$\frac{\partial \log (L(\alpha, \beta))}{\partial \beta}=0$             (10)

The unknowns of the equation system are $\alpha$ and $\beta$ .

The results show the Weibull diagrams of the breakdown voltage, the variation of the breakdown voltage, and the shape parameter of polyesterimide versus the hydrothermal aging time under AC and DC electric fields, at two different temperatures of 90℃ and 100℃. These results are interpreted as follows:

1. The Weibull graphs of voltage breakdown lead to a large dispersion of experimental points in the low probabilities. These results are in line with what is found in the literature.

2. The breakdown voltage changes with aging time. Its rise is linked to the polymer rearrangement and crosslinking by the thermal action, causing a reduction of the mean-free path of charge carriers and decreasing their mobility. A decrease in breakdown voltage is due to the material plasticization by the water absorption, reducing the molecular bonds and increasing the free volume.

3. The magnitude of breakdown voltage under the AC ramp is less under the DC ramp. The phenomenon is partly due to the difference in dissipated energy between the two types of electric field and in part due to the fatigue caused by AC constraint. This phenomenon has been reported by Crine [25]. Gockenbach and Schillet [26] claimed that the DC breakdown voltage of XLPE cable is greater than that observed in an AC electric field.

4. Obviously, the breakdown voltage under the DC ramp depends on the polarity [27, 28]. This phenomenon is explained by the amplitude and space charge distribution among the electrodes varying with the polarity of the applied voltage [29].

5. Under AC and DC rump conditions, the breakdown voltage at 100℃ oscillates from the beginning until 5000 h. Beyond this time, it decreases to less than 50% of its original value. This irreversible diminution is related to the rise of water amount within the polymer, which can partly facilitate the initiation of water trees, leading to reduced breakdown voltage, and partly the hydrolysis reaction of polyesterimide because of the presence of the hydrolyzable ester and imide groups. Abderrazzaq [30] reported that water trees could be initiated and developed within polyester resin by simultaneous action of moisture and alternating electric field. Douar et al. [31] have explained that moisture absorption is the main reason for the breakdown voltage decreasing for polyamides, and their hydrolysis is caused by excessive moisture absorption because of the presence of amide groups which attracts water molecules.

6. The reduction of breakdown voltage at 90°C under 50% is earlier compared to 100℃. It is around 2000 h, and 7000 h for 90℃, and 100℃, respectively. The structure of the absorbed water at 90℃ stays in its original state and accelerates the material conductivity. In contrast, at 100℃, the absorbed water is divided into small entities because of the scission of hydrogenous links.

7. The curves giving the shape parameter as a function of aging time have an irregular evolution with the presence of several peaks. These variations reflect the random distribution of defects within the dielectric during aging. The rearrangements in the molecular structure of material explain the increase in the shape parameter. In contrast, its decrease is allotted to the rise in the defect size and the kind of defect. Coppard et al. [32] established that the shape parameter is linked to the size diffusion of the defects in polyethylene. Also, Katsuta et al. [33] revealed that the shape parameter depends on the kind and size of defects in XLPE cable.

8. The shape parameter at 100℃ presents several minimum values compared to 90℃. This phenomenon can be explained by the size augmentation of the defects caused by the thermal action. Fabiani and Simoni [34] reported that thermal aging could significantly produce the size enlargement of micro-cracks and voids in the material.

9. The shape parameter at 90℃ varies until 5500 h. After this time, it decreases irreversibly, which can be attributed to the diminution of defects caused by the rearrangement and crystallization of the polymer structure.

10. The polymer degradation is characterized by a change in color of the material from yellow to brown and then to black. In advanced aging times, we even noticed the crumbling of test specimens.