**5. Dependencies of the diagnostic parameters**

The structural dependencies of the tan, the relative permittivity *<sup>r</sup>* and the conductivity are shown in Figure 6. A temperature increase results in an increase of the mobility of the (polarized) molecules, the charge carriers and the number of electrons having at least the necessary energy to overcome the potential barrier or in other words the activation energy *<sup>a</sup> E* , (Küchler, 2009). Therefore, there is a constant rise of conductivity, (Bayer, Boeck, Möller, & Zaengl, 1986):

$$\tan \delta\_{\rm con} = \mathbf{A} \mathbf{e}^{-E\_s/\mathbf{k}T} \tag{9}$$

Empiric Approach for Criteria Determination of Remaining Lifetime Estimation of MV PILC Cables 263

)

increases with rising test voltages, and

on voltage.

PILC cables (viscosity of 50 mm2/s by 100°C) reaches its maximum in the vicinity of -8°C and the minimum in the region of 30°C. It was shown and discussed in (Mladenovic & Weindl, Influence of the thermal stress on the diagnostic parameters of PILC cables, 2010) that temperatures around 30°C are also not optimal for diagnostic measurements of MV PILC

Unlike to the temperature, the test voltage can be adjusted and is therefore used as a parameter for some diagnostic methods. According to equation (1), the differential tan(

Theoretically, it is to be expected that the dissipation factor raises with an increase of the voltage since these means an injection of more energy, enhancing the energy of the charge carriers and a multiplication of the ions. Therefore, the conductivity and in this way the tan

is principally rising with increasing test voltages. It was shown in (Bayer, Boeck, Möller, &

The dominating ageing process in paper-mass insulation systems is a degradation of the cellulose which results in a higher moisture content. Since the conductivity and permanent resistivity of the water is much higher than of cellulose-mass it can be expected that cables

The behavior of PD activity with varied test-voltage is already well known and widely used as a diagnostic criterion for the detection of numerous failures that can occur in cables and

Moreover, a stepwise increase of the dissipation factor with the test-voltage is often interpreted as a result of increased PD activities within the insulation. Anyway, the rate of the losses caused by PD activity in the total dissipation losses is very indistinct, since it is defined by the cable length, the number of weaknesses, the PD intensity, etc., (Mladenovic & Weindl, Comparison of the parametric Partial Discharges and Dissipation factor

For a successful development of reliable ageing models, it is of prime importance to have different but constant ageing conditions and access to the regularly measured and monitored parameters up to the failure events. Therefore the characteristic key-values of the

artificial ageing period of two years. Beside the main field of thermo-electrically aged cable samples, selected cables were set under thermal stress only, while another group cables was electrically aged. In this way it should be possible to determine the parameters in the ageing models and the influence of each stress type on the ageing rapidity. The thermal ageing can principally be modeled by Arrhenius law, the electrical ageing by e.g. the inverse power law. When concurrent stress conditions are applied combined and complex ageing models

were acquired selectively for each cable at least daily over the complete

measured at two times the nominal voltage *U*2 and the nominal voltage *U*1 are

cables based on the dissipation factor.

Zaengl, 1986) on the example of epoxy resin, that *<sup>r</sup>*

that the gradient is steeper for higher temperatures.

Characteristics of MV PILC Cables, 2012).

**6. Artificial ageing experiment** 

with higher moisture content show stronger dependency of the tan

values-tan

cable garnitures.

PD and tan

partially used for this purpose.

where are: A - the pre-exponential factor, *T* is the absolute temperature and k Boltzmann constant.

**Figure 6.** Structural dependencies of the dissipation factor tan, relative permittivity *<sup>r</sup>* , and conductivity on temperature with three different polarization mechanisms (dashed blue line)

On the other hand, the polarization processes show different resonant phenomena over a wider temperature range. Appropriate temperatures drive different polarization processes. Even one polarization process like the orientational polarization can have e.g. two resonant temperatures due to the presence of different molecular structures, like e.g. moisture in the paper-mass insulation system. Therefore, with an increasing temperature the relative permittivity rises stepwise at discrete temperatures as a consequence of increased dipole mobility. Finally, with higher temperatures *<sup>r</sup>* decreases again due to the thermal agitation which results in a partial disorganization of the dipole arrangements caused by the field. The activity of PD, if any, will change according to ideal gas and Paschen's law, (Mladenovic, Determination of the Remaining Lifetime of PILC cables based on PD and tan(δ) diagnostics, 2012, to be published). Also, conductive channels within insulation, if present, will develop faster leading to the complete breakdown of the insulation.

Since the temperature cannot be adjusted in field measurements, the temperature dependency of tanδ is inappropriate to be used as a diagnostic criteria directly. Although, it is very important to know its characteristic behavior for different ageing situations and to have reference tan-temperature-condition profiles, so that the measured parameters can be evaluated correctly. According to (Bayer, Boeck, Möller, & Zaengl, 1986) the tanof MV PILC cables (viscosity of 50 mm2/s by 100°C) reaches its maximum in the vicinity of -8°C and the minimum in the region of 30°C. It was shown and discussed in (Mladenovic & Weindl, Influence of the thermal stress on the diagnostic parameters of PILC cables, 2010) that temperatures around 30°C are also not optimal for diagnostic measurements of MV PILC cables based on the dissipation factor.

Unlike to the temperature, the test voltage can be adjusted and is therefore used as a parameter for some diagnostic methods. According to equation (1), the differential tan() values-tan measured at two times the nominal voltage *U*2 and the nominal voltage *U*1 are partially used for this purpose.

Theoretically, it is to be expected that the dissipation factor raises with an increase of the voltage since these means an injection of more energy, enhancing the energy of the charge carriers and a multiplication of the ions. Therefore, the conductivity and in this way the tan is principally rising with increasing test voltages. It was shown in (Bayer, Boeck, Möller, & Zaengl, 1986) on the example of epoxy resin, that *<sup>r</sup>* increases with rising test voltages, and that the gradient is steeper for higher temperatures.

The dominating ageing process in paper-mass insulation systems is a degradation of the cellulose which results in a higher moisture content. Since the conductivity and permanent resistivity of the water is much higher than of cellulose-mass it can be expected that cables with higher moisture content show stronger dependency of the tanon voltage.

The behavior of PD activity with varied test-voltage is already well known and widely used as a diagnostic criterion for the detection of numerous failures that can occur in cables and cable garnitures.

Moreover, a stepwise increase of the dissipation factor with the test-voltage is often interpreted as a result of increased PD activities within the insulation. Anyway, the rate of the losses caused by PD activity in the total dissipation losses is very indistinct, since it is defined by the cable length, the number of weaknesses, the PD intensity, etc., (Mladenovic & Weindl, Comparison of the parametric Partial Discharges and Dissipation factor Characteristics of MV PILC Cables, 2012).
