Partial Discharge Inception Modelling of Insulating Materials and Systems: Contribution of Electrodes to Electric Field Profile Calculation

Abstract

Partial discharge inception modeling is a powerful tool for material investigation and insulation system design in order to achieve the objective of PD-free operation of insulation systems. Model validation, however, requires accurate and repeatable testing conditions, and the aim of this paper is to look at the influence of electrodes and electric field simulation on partial discharge inception model prediction accuracy. Awareness of the geometric electrode configuration is important to forecast both the typology of discharge and the corresponding partial discharge inception voltage value. It is shown, in fact, that inaccurate evaluation of electrode shape (e.g., its flat part and contour) might impact significantly on electric field estimation, the typology of incepted discharges, and, thus, on model accuracy, i.e., on partial discharge inception voltage prediction, which is the basis for the partial discharge-free design of insulating materials and systems. In particular, small electrode curvature radius variations do not significantly affect the PDIV value or PD typology identification. However, worsening electrode/insulation specimen contact can significantly impact PD inception and typology evaluation.

1. Introduction

Partial discharge (PD) measurement is a fundamental tool for quality evaluation and diagnostic assessment of insulation systems [1,2]. Indeed, PD is, at the same time, one of the most harmful accelerated degradation causes for organic insulation and a fundamental diagnostic property for condition maintenance planning [3,4,5,6].

Since incoming electrical asset technologies are going to subject insulation systems to extreme stress conditions (particularly due to the progressive replacement of conventional energy transformation with power electronics with higher voltage [7] and specific power [8,9]), care shall be taken to keep under control the acceleration of both intrinsic and extrinsic aging mechanisms [10,11]. As partially discussed in [4] and generally defined in [10], intrinsic aging is related to the effect of maximum stress (e.g., peak electric field) on bulk degradation processes. It is modeled by resorting to typical laws such as the inverse power model for electrical and mechanical stress and the Arrhenius model for thermal stress [4,12,13]. Extrinsic aging has to do with local phenomena, such as hot spots and partial discharges. Even if local, this aging can be the prevailing cause of premature failure because, in general, an insulation system should be seen, from a reliability point of view, as a parallel of infinite microcomponents: failure of one of those causes the failure of the whole system (indeed, the extreme values of failure distributions, such as the Weibull one, stem from this reasoning [14]).

Based on the common consideration that PD is the prevailing cause of premature electrical failure of insulation systems, care should be taken in the design of insulation to ensure that PD is not incepted both at time zero (quality control and commissioning) and during the whole specified life. A fundamental tool should then be made available to insulation designers, that is, partial discharge inception models. A simple, deterministic, but experimentally proven approach to PD inception modeling was provided by Niemeyer [15], and a generalization of his work to cover heuristically both PD incepting in internal defects and surface discharges has been recently presented in [16]. Validation of these models is of utmost importance, whether their broad use at the design stage of an insulation system is foreseen.

This paper deals with a key potential issue, that is, the influence of electrode shape and the relevant electric field calculation on discharge model application and on PD phenomenology, i.e., PD source typology identification. The main purpose is to show, through field simulations, the PD inception model, and experimental tests, how inaccurate modeling of the electrode geometry could lead to wrong/misleading predictions in terms of the PD inception threshold and PD identification. In Section 2, PD inception model results and electric field simulations applied to the test object chosen for this assessment are presented. This section also recalls the “three-leg” approach, i.e., a methodology exploited in this paper, which has been recently proposed to achieve PD-free design of insulation systems. Section 3 shows how geometrical variations of electrode shape impact the inception field and partial discharge inception voltage (PDIV) estimation. This is made by considering two typologies of electrodes, namely electrode A and electrode B, triggering PD on the same dielectric specimens. Eventually, Section 4 validates the forecasts made in Section 3 by means of experimental tests using Electrodes A and B.

2. Background: Partial Discharge Inception Field Modeling and “Three-Leg” Approach

Recently, a new procedure, named the “three-leg” approach, has been proposed to achieve PD-free design of insulation systems. It holds for both AC and DC, and it is based on the following three steps (legs):

• electric field (and thermal stress) simulation,
• extrinsic aging threshold modeling (PD inception field and voltage in combination with leg 1),
• PD measurements for validation of the first two legs.

When the maximum field calculated under leg 1 matches the inception PD field estimated by the model from leg 2, then PD will be triggered in the insulation system under consideration. The voltage at which this occurs is the partial discharge inception voltage (PDIV), which can be validated by proper PD detection. An experimental validation is performed (leg 3) to support the PDIV estimation thus obtained. However, since PD is not just magnitude and repetition rate, PDIV measurements must be carried out with the support of proper hardware/software tools, allowing separation, recognition, and, eventually, identification of the different typologies of source-generating PD, i.e., internal, surface, and corona discharge (according to the descending order of harmfulness).

The most recent innovative approach (described, e.g., in [17]) possesses software for PD acquisition and analysis that is fully automatic and outputs the identification of the type of source-generating PD [18].

2.1. A Model for PD Inception

A simple (even if approximate, being deterministic) general model for PD inception, taken from [15], which is valid for both discharges in gas (due to the orthogonal field component) and discharges on insulation surface/interfaces (due to the tangential field component) is [16]:

$$E_i={\left(E/p\right)}_{cr} p\left(1+\frac{B}{{\left(p{k}_{s}d\right)}^{1/\mathsf{\beta }}}\right)$$

(1)

where E_i is the inception field, d is the distance from HV to ground (creepage) or defect height (for surface and gas discharges, respectively), and $p$ is the pressure of the surrounding gas. (E/p)_cr, B, and $\beta$ are empirical parameters whose values change from internal to surface discharges, as shown in

Table 1. Parameter values of the generalized partial discharge inception model (1), function of the type of discharge.

Discharge Type	${\left(\mathit{E}/\mathit{p}\right)}_{\mathit{c}\mathit{r}}$	$\mathit{B}$	$\mathit{\beta }$	ks
Gas discharge	25.2	8.6	2	1
Surface discharge	8.0	4.3	2	≤1

. $k_s$ is a scale parameter, taking into account the effective streamer length, that becomes = 1 for a uniform field but <1 in the presence of a field gradient. It sets a sort of uniform field volume around the triple point in which partial discharges can occur at an almost uniform field, near to the peak field value. In the case of internal discharges, $k_s$ = 1. If $k_s$ = 1 also for surface discharges, then the classic, standardized concept of creepage keeps working, but for $k_s$ < 1 (which is the most likely case in power modules and high-energy density assets), PD-free insulation system design must resort to (1) since localized PD (at triple points) is a fundamental cause of premature failure.

An expression for $k_s$, based on the extent of field gradient [16], could be given by:

$$k_s=\frac{l{\left(0.9E_{max}\right)}^{+}-l{\left(0.9E_{max}\right)}^{-}}{d}$$

(2)

being $E_{max}$ the maximum value of tangential surface field obtained from the electric field profile calculation (if it is not monotone), l (0.9E_max)⁺ and l (0.9E_max)⁻ are the horizontal distances on the test object surface, where the tangential fields are 90% of $E_{max}$, considering the negative and positive slopes of the field profile.

To estimate approximately the partial discharge inception voltage, PDIV_m, based on the inception field E_i value computed with (1), the linearity of the Laplace equation can be exploited, starting from the relationship between the applied voltage (V_sim) and the resulting peak field, E_p,sim (computed by a FEM software, 1st leg, where, e.g., V_sim = 1 kV) [15]:

$$\frac{V_{sim}}{E_{p,sim}}=\frac{PDI{V}_m}{E_i}.$$

(3)

2.2. Electrode Design and Field Calculation

To validate the PD inception model and, thus, be able to carry out PD-free insulation design, the test object must be able to trigger exactly the type of PD (i.e., internal or surface), which is the potential issue in the designed insulation system. Focusing on electrodes and, e.g., surface discharges, the chosen electrode shape must be able to trigger PD on the surface, driven mostly by the tangential field rather than the orthogonal one, at the triple point (i.e., the point involving electrode contour, insulation surface, and surrounding gas). The focus here is on the test cell, represented in Figure 1, which is able to trigger surface discharges in order to characterize the PD surface resistance of insulating materials, which is of paramount importance to the design of insulation systems based on the redundancy concept. The purpose would be to allow an insulation system to withstand PD for all or part of its operation, still providing the specified life at a selected failure probability.

The electrode system and test sample adopted in this study are sketched in Figure 2a. The contact between the electrode and insulation specimen is flat (i.e., perfectly adhering to the surface of the sample), and the curvature radius of the electrode is 750 μm. A zoom of the electrode contour is highlighted in Figure 2b, being l the distance along the horizontal direction from the triple point and h the corresponding orthogonal distance from the sample to the electrode surface, so that in (1) d ≡ l or d ≡ h for surface and internal discharges, respectively.

Electric field calculations can be carried out, e.g., by the commercial FEM software COMSOL Multiphysics©, for an AC sinusoidal (60 Hz) excitation voltage, V_sim, of 1 kV. Let us note that field profiles do not change (for this test object) with increasing frequency (thus they would also hold for the PWM modulation waveform, referring to peak voltage).

Typically, the orthogonal field is predominant over the tangential one at the same excitation voltage V_sim. However, this does not mean that gas discharges are preferred over surface discharges, because the models for the inception of surface and gas PD have the same expression but different parameter values (see Table 1), leading to different inception field thresholds for gas and surface discharges.

In order to estimate the PD inception field and voltage, field simulations (1st leg) are correlated to the inception field models (2nd leg). Indeed, the correspondence of the maximum field value (or close to it, see (2)) and relevant voltage with the inception field will provide the inception voltage, which can be calculated approximately by (3). To clarify this, Figure 3 shows an example of PDIV computation (exploiting the 1st and 2nd legs): PDIV is the voltage value at which the resulting field intercepts the PD inception field, obtained by (1). This holds for both surface (along the l direction) and gas discharge (along the h direction); see Figure 3a and Figure 3b, respectively. Referring to Figure 3, intercepts occur at 9.1 kV/mm and 1.6 kV/mm for orthogonal and tangential fields, respectively, that correspond to PDIV = 3.3 kV for gas discharge and PDIV = 1.7 kV for surface discharge. Hence, surface PD is present at a lower voltage, which indicates that the considered electrode system is appropriate to test surface discharge phenomenology and to carry out PD-free design of the insulation system surface/interfaces.

3. Impact of the Electrode Shape on the Electric Field Computation and PD Inception Field Estimation

3.1. Influence of Electrode Curvature Radius

Inaccurate evaluations of electrode shape (i.e., their curvature radius and contour shape) can have a significant impact on the computation of electric field in the space surrounding electrode contours, which could affect the estimation of the PD inception field, the typology of incepted PD, and, due to their influence on k_s and d, the accuracy of model (1).

In this section, parametric simulations quantify the effect of small geometrical variations of the HV electrode contour of Figure 2b on the estimation of electric field profiles (both orthogonal and tangential to the insulation surfaces) and on surface and gas PD inception field and voltage. Practically, such variations (shape and curvature radius of the HV electrode) could be due to manufacturing defects, usage deterioration, or electrode surface machining to remove tracks from previous discharges.

A 0.6 mm single-layer XLPE specimen is used in the simulation (and validation experiments described in the next section). The reference curvature radius, R, of the high voltage electrode (zoomed in Figure 2b), i.e., 750 μm, is varied by steps of 25 µm, from a minimum of 600 µm to a maximum of 900 µm. For each curvature radius, both the surface and gas inception fields (see (1)) and the relevant inception voltages (see (3)), are computed. The results are summarized in

Table 2. Variation in surface, gas inception fields, and PDIV with the curvature radius R of the HV electrode. The insulation test object is a single-layer XLPE specimen with a mean thickness of 0.6 mm (refer to Figure 2 for the geometrical model).

Radius R (mm)	Surface Inception Field (kV/mm)	Surface PDIV (kV)	Gas Inception Field (kV/mm)	Gas PDIV (kV)
0.600	1.64	1.54	9.1	3.3
0.625	1.64	1.56	10.1	3.4
0.650	1.64	1.58	9.5	3.3
0.675	1.62	1.60	9.4	3.3
0.700	1.61	1.61	9.9	3.3
0.725	1.60	1.63	9.8	3.1
0.750	1.60	1.66	9.1	3.3
0.775	1.60	1.67	9.5	3.4
0.800	1.59	1.71	9.2	3.3
0.825	1.58	1.70	10.2	3.3
0.850	1.57	1.72	10.5	3.3
0.875	1.57	1.74	9.6	3.3
0.900	1.57	1.75	9.4	3.3

and graphically represented in Figure 4.

Regarding surface discharges, Table 2 shows a slight decrease in the value of the inception field with the increment of the curvature radius, R. This is due to the increase in the scale parameter k_s (see (2)) which in turn depends on the tangent field profile shape (see Figure 4a). On the contrary, surface PDIV increases with the curvature radius (R), since the peak of the field profile decreases slightly with the increment of R (see Figure 4a). Hence, Table 2 shows that a variation of 300 µm in the HV curvature radius causes a difference of 0.07 kV/mm for the inception field of the tangential component and a difference of 0.2 kV in the surface PDIV estimation.

Referring to gas discharges, Figure 4b highlights that changes in the electrode curvature radius shift the orthogonal field curves, thus varying the intersection point between the computed and PD inception fields. However, Table 2 indicates that gas PDIV values are always very close to 3.3 kV, thus being reasonably stable with electrode curvature radius.

This quantitative discussion holds as simulations and inception field models are considered (first and second legs, see Section 2), showing that only slight variations of PDIV values come from a variation of the curvature radius <300 μm. Regarding PD detection, it can therefore be argued that such curvature radius variations do not noticeably affect measurement accuracy.

3.2. Influence of Electrode-Specimen Contact Area

The electrode configuration used to trigger surface PD, Figure 1 and Figure 2, is geometrically modeled by considering its zoomed image taken by a microscope (see Figure 5a); this allows the accurate geometrical profile sketched in Figure 5b to be achieved. In particular, it is noteworthy that the contour of the base touching the tested specimen would present a curved shape (which can be modeled by a quadratic law) rather than straight. The cause of this curvature could be a design purposely developed to reduce electric field concentration along its contour (as for pseudo-Rogowski electrodes) or, practically, a manufacturing defect or usage deterioration. Ideally, in fact, such electrodes should be thought to have a straight, flat base, as in the example represented in Figure 6, where both a particular HV electrode (Figure 6a) and the derived accurate geometrical profile (Figure 6b) are shown.

From now on, let us define the electrode with the curve-shaped contact surface as electrode A and the electrode with the perfect flat-shaped contact surface as electrode B.

Calculations shall then be made to evaluate whether electrode A provides significantly different values of the PD inception field compared to electrode B. This, indeed, could affect the discharge model validation and, thus, the application of the three-leg approach for the insulation system’s PD-free design. Eventually (see Section 4), an experimental validation will be performed to verify the validity of the computations made with electrodes A and B.

As regards simulations relevant to electrodes A and B, the electric field computations start at the intersection of the electrode profile with the horizontal line at 40 µm (at 2.1 mm from the symmetry axis for electrode A and 0.24 mm for electrode B, Figure 7). This choice comes to avoid unrealistic electric field values at the triple points, and it is supported by PD physics: it has been shown, indeed, that distances between the surface electrodes and specimens lower than 30–40 μm are unlikely to generate significant PD even at relatively high fields.

Table 3. Surface and gas inception fields and voltage for Electrode A and B configurations.

	Surface Inception Field (kV/mm)	Gas Inception Field (kV/mm)	Surface PDIV (kV)	Gas PDIV (kV)
Electrode A	1.3	2.9	1.9	1.3
Electrode B	1.6	9.1	1.7	3.3

summarizes the estimates of PD inception field and voltage for gas and tangential discharges, referring to electrodes A and B. Computations made by means of (1)–(3) show there is a significant incremental factor of 2.5 between the gas PDIV values for electrodes A and B, while the surface PDIV is not affected as much by the slight rounding of the contact surface (A vs. B). In practice, this means that for electrode A, gas discharges have a lower PDIV value compared to surface ones; thus, the cell designed to generate surface discharges (Figure 1 and Figure 2), with the purpose of establishing criteria for a PD-free design of the insulation surface, might not work properly if electrode B is replaced by electrode A.

To go more in detail, Figure 8 and Figure 9 display the orthogonal electric fields computed at V_sim =1 kV AC and at the PDIV values, together with the gas PD inception field from (1), for electrodes A and B. It can be seen (from curve intersections) that the gas discharge PDIV is 1.3 kV for electrode A (Figure 8b), but 3.3 kV for B (Figure 9b), which supports the estimates in Table 3. Noticeably, the intersection of the electric field profile and gas discharge model for electrodes A and B is at 2.45 and 0.38 mm from the axial symmetry axis, respectively.

4. Experimental Validation

4.1. Test Set-Up

The experimental set-up is sketched in Figure 10. This arrangement is designed to trigger surface PD on a single-layer specimen (see sample in Figure 10) placed between two electrodes (high voltage, HV, and ground, GRD, both made of brass). In this study, 0.6 mm single-layer XLPE specimens are considered.

The AC power supply is connected to an HV transformer, controlled by a variac. The low-voltage electrode is connected to the ground by means of a wire passing through a high-frequency current transformer (HFCT, bandwidth 100 kHz–50 MHz), which serves as the sensor for PD measurement. The HFCT is then connected to the above-described PD detector (PDA) interfaced to a PC running the innovative SRI (Separation, Recognition, Identification) software [5,18,19].

Experiments were conducted in a climatized room (average temperature of 20 °C) under constant atmospheric pressure and humidity.

4.2. PDIV Measurements and Discussion

Repeated PDIV_AC measurements were performed on XLPE specimens using electrodes A (Figure 5) and B (Figure 6). The purpose was to validate the PDIV estimations summarized in Table 3.

The PDIV_AC measurement procedure was the same for both electrodes. The AC voltage at the HV electrode was slowly increased by steps lasting 30 s to record and analyze PD at each voltage step by means of the SRI software. The procedure was continued till the PDIV_AC value was reached, which is the voltage level at which the PD activity starts persistently [20]. Five measurements were conducted for the same test arrangement after de-energizing the sample and waiting for enough time (approximately 5 min) to make sure that PD-generated space charge was not able to affect successive PD measurements.

Table 4. Repeated PDIV measurements performed by electrodes A and B: each measurement is associated with its PD identification likelihood (ID) obtained by the SRI software. The final results are given in terms of the mean PDIV within its 95% confidence intervals.

	Electrode A		Electrode B
N. of Acquisition	PDIV (kV)	ID	PDIV (kV)	ID
1	1.3	Internal 1	1.6	Surface 1
2	1.1	Internal 1	1.7	Surface 1
3	1.2	Internal 1	1.6	Surface 0.8
4	1.1	Internal 1	1.8	Surface 0.9
5	1.3	Internal 0.9	1.8	Surface 1
	PDIVAC = (1.2 ± 0.3) kV Predominantly internal		PDIVAC = (1.7 ± 0.3) kV Predominantly surface

reports the PDIV_AC measurement values for each acquisition with electrodes A and B. Besides the PDIV_AC values obtained from each measurement, the mean values within the 95% confidence intervals, considering a Gaussian distribution for the measurement data, are reported [21]. For electrode A, PDIV_AC is 1.2 ± 0.3 kV (PD identified as internal), whereas for electrode B, it is 1.7 ± 0.3 kV (PD identified as surface). It is noteworthy that PD are identified as internal with a likelihood of 0.9 to 1 for electrode A, and surface with a likelihood of 0.8 to 1 for electrode B. The likelihood level is a number between 0 and 1, and it comes as an output of the fuzzy engine used for automatic identification [18]. For example, a likelihood 1 of surface PD means that the collected PD signals certainly come from surface discharges, whereas a likelihood 0.5 internal and 0.5 surface means that most likely both gas and surface sources contribute to generating the detected PD signals.

This result is consistent with the observation made in Section 3 (see Table 3), referring to the simulations and the inception models. The PDIV values of Table 3 to be considered are 1.2 ± 0.3 kV for electrode A, for which gas PD are triggered for a voltage threshold lower than the one for surface discharges, and 1.7 ± 0.3 kV for electrode B, for which surface PD are triggered for a voltage threshold lower than that for gas discharges. Indeed, comparing the measured PDIV of Table 4 with those in Table 3, a good fit between the experimental results and the predicted values is observed since the estimated PDIV values are placed inside the uncertainty interval of the measured quantities. Therefore, the three-leg approach is validated in the experiments involving both electrodes. Notably, correct surface discharge testing is achieved only by electrode B, since A triggers more likely gas discharges (identified as internal) than surface discharges.

Figure 11 and Figure 12 show two examples of graphical outcomes produced by the SRI software by using electrode A (Figure 12) and electrode B (Figure 12). They refer to the first acquisitions of Table 4 of electrode A (applied voltage of 1.3 kV, ID_internal = 1) and electrode B (applied voltage of 1.6 kV, ID_surface = 1).

5. Conclusions

It is known that characterizing the PD inception and endurance of insulating materials and systems must take real electrode geometrical characteristics carefully into account. To quantify this speculation, a specific electrode configuration meant to trigger surface PD on polymeric specimens was considered. Electrode geometrical characteristics (contour curvature radius and electrode contact shape/dimensions) were varied to assess their impact on the computation of the electric field profile and PD inception field estimates, the latter based on the three-leg approach (methodology that gathers coherent field computations, inception modeling, and experimental activity supported by SRI software).

Simulation and parametric analysis results, validated by experimental testing, show that small electrode curvature radius variations (lower than 300 μm) do not impact significantly on the estimated and measured PDIV, as well as on PD typology identification. However, small deviations in the shape of the electrode contact area that lies on the specimen from the theoretically flat one can impact drastically on PD inception evaluation. This affects insulation system design, which must be based on criteria that allow PD-free insulation system operation as well as the type of defect generating PD and, thus, its harmfulness (thus diagnosis). As an example, if the purpose of testing is to characterize surface discharge inception and surface PD resistance, a lack of accuracy in electrode profile can trigger gas discharges rather than surface ones, which will provide misleading results for both design and diagnostic purposes.