Operation at Reduced Atmospheric Pressure and Concept of Reliability Redundancy for Optimized Design of Insulation Systems

Abstract

Electrified transportation is calling for insulation design criteria that is adequate to provide elevated levels of power density, power dynamics and reliability. Increasing voltage levels are expected to cause accelerated intrinsic and extrinsic aging effects which will not be easily predictable at the design stage due to a lack of suitable modeling. Designing reliable insulation systems would require finding solutions able to control accelerated aging due to an unpredictable increase of intrinsic stresses and the onset of extrinsic stresses as partial discharges. This paper proposes the concept of reliability redundancy for the insulation design of aerospace electrical asset components, which is also validated at lower-than-standard atmospheric pressure. The principle is that extrinsic-aging-free design might be achieved upon determining the aging stress or abnormal service stresses distribution and being sure that aging will not generate conditions that can incept extrinsic aging (partial discharges) during operation life. However, such information is never, in practice, fully available to insulation system designers. Hence, especially in critical applications such as electrified aircraft, aerospace, and combat ships a further level of reliability should be added to a partial-discharge-free design, which can consist of the use of corona-resistant materials and/or of life models able to consider the accelerated aging effect of partial discharges (or any other type of extrinsic-accelerated aging factor). Innovative life modeling considering both extrinsic and intrinsic aging stresses, insulating material testing to estimate model parameters, and a metric for quantifying the extent of corona (or partial discharge) resistance can lead to establishing feasibility and limit conditions for optimized or fully reliability-redundant design. It is shown in the paper that if an extrinsic-aging-free design is not feasible, and it is therefore replaced by a redundant design, a further level of reliability redundancy can be provided by effective condition monitoring plans.

1. Introduction

Electrified transportation, including aircraft and aerospace vehicles (flying, mobile, or permanent installations) and ships, is moving toward higher voltage levels and the type and extent of stresses never experienced in the history of electrical assets [1,2,3,4,5,6,7,8,9,10,11,12]. Insulation system design must take into account the new types of electrical and thermal stress distributions, often largely divergent and of higher magnitude, which would require innovative methodologies to achieve feasibility and reliability with higher nominal voltage and specific power [13,14,15,16,17,18,19,20].

The three-leg approach, recently developed, can provide PD-free design, which is the first key point toward innovative, resilient, and reliable insulation system design [21]. The concept of reliability redundance is the second key. Reliability redundance means reaching a higher level of reliability, by not replicating or doubling circuits or apparatus, but by using new models and/or materials which provide the specified life and reliability, even with the occurrence of aging (or bad quality control) which are able to trigger extrinsic aging mechanisms (as partial discharges, PD) under operation. In other words, for example, motor insulation can be designed to be PD-free, and, in addition, PD-resistant insulation can be used [22].

Life models, PD measurements, and their applicability to low atmospheric pressure are dealt with in Section 2, where the permanent or discontinuous presence of PD is also considered. Examples of PD measurements where the type of source generating the PD is automatically identified are presented, since identifying the root cause of PD is fundamental to addressing remedial actions in design (and maintenance). Solutions using corona resistant and non-corona resistant materials (such as Kapton) are compared, at standard atmospheric pressure and reduced pressure (corresponding to cruising altitude for aircraft), and the effect on design reliability of low environmental pressure is discussed, based on surface discharge and surface erosion experiments performed on polyimide materials. The partial-discharge-free design approach (three-leg approach) and the concept of reliability redundancy are discussed in Section 3, with the main findings of the work summarized in Section 4.

2. Aging Modeling and Experimental Characterization

2.1. Dynamic Aging Modeling

The main aim of accelerated life tests is to estimate the voltage endurance coefficient, which is the inverse of the slope of the lifeline in an appropriate coordinate system (that linearizes the life model). For example, if the inverse power law is used for electrothermal stress, the life equation can be written as follows [23]:

$$L=t_R{\left({\displaystyle \frac{E}{E_R}}\right)}^{-n}$$

(1)

where $E_R$ the reference electric stress (generally close to the electric strength) and $t_R$ the relevant failure time at applied field $E=E_R$, while n is the voltage endurance coefficient (note that Equation (1) holds for AC and DC). Equation (1) provides a straight lifeline in a log–log coordinate system ($\log \left(E\right)\mathrm{v}\mathrm{s}.\log \left(L\right)$). Considering a probabilistic approach to insulation systems design, a life model associating design field, E_D, and life, L_DP, at probability P can be obtained as follows:

$$\log \left(L_{DP}\right)=\log \left(K_P\right)+\log \left(t_R\right)-n\log \left(E_D\right)+n\log \left(E_R\right)$$

(2)

where $K_P=-\left(\log {\left(1-P\right)}^{1/{\beta }_t}\right)$. P is expressed by the Weibull distribution of failure time, with shape parameter ${\beta }_t$. The electrical life model is valid at a certain temperature, thus, its parameters are temperature dependent.

The presence of PD, permanent or sporadic, will take away an amount of life, which can be significant if partial discharges last a long time during apparatus operation. This can be modeled assuming that the electrothermal aging activation process is decreased by the additional degradation energy brought about by PD.

To model this aspect, we start from a thermodynamic approach resorting to the Eyring law, which has been used to describe global aging [24]. The reaction rate constant, r, which is inversely proportional to life can be written as follows:

$$r=\left({\displaystyle \frac{kT}{h}}\right)e^{-\left({\displaystyle \frac{∆G–f\left(E\right)}{kT}}\right)}$$

(3)

where k and h are Boltzmann and Planck constants, $∆G=G_a-G_1$ is the activation free energy, and f(E) is a function of electric field. The exponential term may account for the effect of an energy barrier lowering due to an electric field, which has often been explained by a linear relation, e.g., [25], as follows:

$$f(E)=e\Gamma E=h^{\prime }\left({\displaystyle \frac{E}{E_0}}\right)$$

(4)

where e and $\Gamma$ are electron charge and scattering distance or [24] as follows:

$$f\left(E\right)=n_{E}ln\left({\displaystyle \frac{E}{E_0}}\right)$$

(5)

where $E_0$ is a reference field below which electrical aging is negligible. This provides two types of electrical-like equations, that is, an exponential one (from Equation (4)), as follows:

$$L=A_T{e}^{-\left(h_{T}E\right)}$$

(6)

and one based on the inverse power law (from Equation (5)), as follows:

$$L=A_T{\left({\displaystyle \frac{E}{E_0}}\right)}^{-\left(n_T\right)}$$

(7)

where

$$A_T=C_0{\left(\left({\displaystyle \frac{kT}{h}}\right)e^{-\left({\displaystyle \frac{\mathsf{\Delta }G}{kT}}\right)}\right)}^{-1}$$

(8)

$$h_T={\left({\displaystyle \frac{h^{\prime }}{kT}}\right)}^{-1}$$

(9)

$$n_T={\left({\displaystyle \frac{n_F}{kT}}\right)}^{-1}$$

(10)

where $C_0$ is the proportionality constant between reaction rate and life. It is noteworthy that Equation (7) is a general form of Equation (1) where $n=n_T$ and $A_T$, the scale parameter, is exploited by a reference lifeline point.

This is a type of approach based on thermal degradation, where the effect of field is taken into account as a contribution to lowering the aging reaction barrier. The impact of PD can be modeled starting from the terms of Equation (3) and speculating that the exponential term, which accounts for the effect of an energy barrier lowering due to an electric field, may include the contribution of the extrinsic aging brought by PD. When PD is active, the effect on aging acceleration is to increase insulation damage rate. This could be accounted for in the model through a term that reduces the aging energy barrier, which increases the aging rate. Accordingly, in Equations (6) and (7), $h_T$ and $n_T$ can be replaced as follows:

$$h_{PD}=h_T-\mathsf{\Delta }{h}_{PD}$$

(11)

$$n_{PD}=n_T-\mathsf{\Delta }{n}_{PD}$$

(12)

so that Equation (1) will become, under PD, the following:

$$L_{PD}=t_{RPD}{\left({\displaystyle \frac{E}{E_{RPD}}}\right)}^{-n_{PD}}$$

(13)

As a general note, the effect of field in terms of variation (life decrease) from a low field on electrical life (coinciding, in practice, with thermal life) becomes stronger as n is larger ((6) and (7)). However, the design of an insulation system is based on accelerated life tests at a higher-than-design field, which mean that, having determined the starting point, E_R, t_R, Equation (1), generally through short-term tests, a lifeline is obtained through the other (at least) two life points and extrapolated to design life in order to determine the design field—Equation (2), see Figure 1. From this practical approach, the result shows that the larger the value of n, the longer life and the higher the design field. Also, it can be assumed that the starting point (E_R, t_R) would not be largely different with or without PD, since at high electric field, value breakdown is mostly determined by intrinsic degradation. Electrothermal life tends to thermal life when E tends to 0 (exponential) or E₀ (inverse power) according to models (6) and (7). This occurs faster if additional electrical aging occurs during life (as for PD appearance). It is noteworthy, from a modeling point of view, that E₀ is the limit for the validity of a linear model, hence slope will have to undergo a change between E₀ and 0 for the compatibility of thermal life brought about by the multi-stress model (3).

Based on Equations (11) and (12), it can be assumed that the PD degradation rate depends on the applied field and energy barrier lowering constant term, i.e., the higher the field, the shorter the life under PD, as ruled by a constant lifeline slope which depends on PD activity and the type of material. This may be true, however, only at a very first approximation. PD magnitude may or may not increase significantly with field, depending on the type of defect. Also, the PD activity can be intermittent during aging time. Internal cavities, for example, could have a magnitude varying only slightly with field, but their repetition rate would increase [26]). Surface discharges may work in the opposite way. Thus, since the lowering of activation energy consists of a contribution to the degradation of PD pulses (in turn, associated to their energy), an activation energy reducing term (given by the product of PD magnitude and repetition rate) could be properly considered. This may not fit the assumption of constant values for Equations (11) and (12), suggesting that it is likely that Δn_PD and Δh_PD will be functions of the test field. Hence, linear extrapolation would refer to the average values of two-such parameters, which would imply rough life estimates. Work can be conducted to exploit the field dependence, but this would introduce non-linearity and additional parameters into the life model. An alternative approach is to use the superposition effect as a function of field, as discussed in the following sections in the case of intermittent PD (thus, varying with time).

Taking into account the time variation of PD magnitude and repetition rate with time, at a constant field, which can be experienced commonly in insulation systems (especially in MV asset components), it could be feasible to resort to a cumulative aging model based on the superposition effect [16].

If, for example, $t_1$ is the part of the lifetime during which aging occurs under AC with no PD or a lower level of PD (lower associated degradation energy), $t_2$ is the part of the lifetime during which aging occurs under a level of PD, and $\delta =t_2/t_1$, aging can be described approximately by [16] as follows:

$${\displaystyle \frac{t_1}{L_{NPD}}}+\delta {\displaystyle \frac{t_1}{L_{PD}}}=1$$

(14)

where $L_{NPD}$ and $L_{PD}$ are life without and with PD, respectively, as provided by Equations (3) and (13), or with a lower and higher degradation energy PD activity.

Knowing the life models, (1) and (13), and $\delta$, the total insulation life can be estimated as follows:

$$L_t=t_1+t_2$$

(15)

Figure 2 shows an example of the application of Equations (14) and (15), reporting the extent of life reduction, compared with design life, as a function of $\delta$. The model parameters are: $E_R$ = 60 kV/mm, $E_{RPD}$ = 50 kV/mm, $t_R$ = 900 s, and $t_{RPD}$ = 180 s. The slopes of the lifelines are n₁ = 11 and n₂ = $n_{PD}$ varying from 7 to 9, to highlight the significant effect of the extent of the PD degradation that depends on the type of material.

The design life was considered to be 30 years at the design field of 17 kV/mm, failure probability 1%, without PD occurring during operation. As can be seen, when PD is active at increasing $\delta$, from 0 (no PD for all life) to 1 (50% of the life with PD), life decreases drastically the more that n_PD = n₂ is low. A summary of life values with respect to variation in n₂ are reported in

Table 1. Life at a design field of 17 kV/mm with variation in n₂, from model (13).

n2	Design Life When δ = 0.01 (PD Occurring for About 1% of the Total Design Life) (Days)	Design Life When δ = 0.11 (PD Occurring for About 10% of the Total Design Life) (Days)	Design Life When δ = 1 (PD Occurring for About 50% of the Total Design Life) (Days)
7	401 (1.1 years)	13.3	7.9
8	1060 (2.9 years)	51.5	23.2
9	2628 (7.2 years)	194.2	68.0

, for $\delta$ = 0.01 and 0.11 (PD occurring for only about 1% and 10% of design life, respectively), and $\delta$ = 1.

2.2. Experiments to Determine Life Model Parameters and Partial Discharge Endurance

Accelerated life tests performed on insulation tapes, plaques, and insulated wires with and without the introduction of inorganic fillers (with the latter able to delay the PD erosion mechanism), have shown significantly better endurance to those materials called “corona resistant” (a term to indicate increased endurance to PD). Both accelerated life tests and surface erosion tests indicate clearly that the corona resistant (CR) material can withstand PD much better than non-corona resistant (NCR) material [27]. Figure 3 shows a comparison of life test results under PD between a Kapton CR and an NCR material, based on accelerated life tests performed at high field, with a test cell featuring a rod–plane electrode configuration. Also, a lifeline without PD for an NCR material is reported (obtained using the aging cell immersed in oil). As can be seen, the voltage endurance coefficient (n, Equation (1)) for CR material is similar to that obtained for NCR material without PD, while it decreases (from 10.7 to 7.1) for NCR material with PD. To understand how much this can affect the design field and life, we consider a life of roughly 10⁵ h in Figure 3, which shows that the corresponding (design) field decreases from about 30 kV/mm for CR to 5 kV/mm for NCR material. Even if the scaling law for full-size insulation design [28] may reduce these values by at least 5 times, and extrapolation from very short test to long test times is almost meaningless, this result can provide a rough idea of the impact of a 30% reduction in voltage endurance coefficient on aging and life reduction.

This result holds for atmospheric pressure conditions. It is claimed in [29] that at low pressure the situation might reverse, that is, CR materials can have a smaller n than NCR materials. Tests were conducted on twisted pairs, with a very thin insulation coating, and somewhat simulated a PD phenomenon that can be associated with internal discharges. We must, however, understand how designs that make use of CR film, as in the ground insulation of rotating machines, behavior at low pressure (i.e., for aircraft and aerospace vehicles). This must be investigated by different accelerated aging tests at low pressure.

A leading criterion for the conception of accelerated life tests is that the most significant parameter to be estimated is the voltage endurance coefficient. The scale parameter of the lifeline will depend on the type of electrode (e.g., those with a large electric tangential field at the contour (triple point) or those with a Rogowski profile that makes the field at the contour uniform), but the slope is nevertheless given by the aging mechanism, e.g., with or without PD, according to Equations (1) and (13).

As an example, the type of electrodes shown in Figure 4, i.e., cylindrical with a smooth contour, can provide field profiles as in Figure 5 for both the normal (orthogonal) field that causes gas discharges near the triple point (Figure 4b), and the tangential field that promotes surface PD. As can be seen, the orthogonal field magnitude is prevailing on the tangential field, with both field profiles displaying significant divergence. However, as shown in the next section, because the PD inception mechanism on the insulation specimen surface is formally the same as that in gas (i.e., due to the orthogonal field component in Figure 5), but with different parameter values, the partial discharge inception voltage (PDIV) is lower for the insulation specimen surface than for gas discharges. Indeed, as seen in Figure 5, with Kapton CR material, the PDIV for the tangential field is 0.6 kV, while the PDIV for the orthogonal field is 2.7 kV.

Hence, with this type of electrode, most of the PD action will be driven by the surface field (surface discharges) at the PDIV, while increasing the overvoltage with respect to the PDIV (e.g., >4 PDIV) will also cause a significant contribution of gas discharge at the electrode contour. In general, the smaller the electrode contour radius, the larger the ratio between the surface tangential and the orthogonal field. This can allow the proper electrode shape to be chosen depending on the type of test. As an example, in the case of the accelerated erosion tests described below, when they are conducted at a large overvoltage compared with the PDIV, sharp contour electrodes should be chosen to avoid the overlap of two different extrinsic aging mechanisms due to gas and surface discharges.

The prevailing extrinsic aging mechanism consists of surface erosion, with a progressive transition during aging from surface damage to bulk degradation (through carbonized pits driving the field to become orthogonal), that causes the final bulk breakdown. As shown in [15], PD identification moves from mostly surface to prevailingly internal, constituting a metric for aging investigation itself. Such electrode configuration could be, therefore, a good compromise between the surface and bulk characterization of the capability of CR materials to withstand PD possibly generated by bulk or surface insulation defects.

Since the main purpose of accelerated aging testing is to estimate the voltage endurance coefficient under PD, which, as mentioned, is the main quantity for evaluating the endurance to PD of an insulating material (the scale of the lifeline comes from electrode shape, field calculation, and application of the size–effect algorithm), a dedicated accelerated test procedure was implemented, as described in [27]. This procedure allows for full control of the testing parameters and uses as short a test time as possible.

Accelerated erosion tests were carried out at three voltage levels (from 3.5 to 4.5 PDIV for NCR and from 4.5 to 5.5 PDIV for CR, at standard atmospheric pressure, SAP, where PDIV was estimated according to IEC 60270 [30]), with surface erosion measured at fixed times (e.g., every two hours). Mean erosion value (measured by a profilometer) was determined as a function of time for each test level. Having fixed an end point, e.g., time for a mean erosion depth increment of 50% with respect to unaged specimens, and having obtained at least three failure time points, the relevant lifeline, could be plotted according to Equations (1) and (13). Indeed, other end point criteria ranging from time to 20% to 120% erosion depth increments are discussed in [27], which describes in detail the test procedures and experimental results for Kapton specimens and shows that the voltage endurance coefficient does not change noticeably when the end point criterion is ≥50% erosion depth increment. Hence, to achieve a precise voltage endurance coefficient value in the shortest possible test time (the smaller the decrease of surface erosion, the better for reducing test costs), an erosion depth increment of 50% is considered an end point criterion.

To compare the above test results with conventional accelerated life tests prolonged until specimen failure, erosion tests were continued until specimen breakdown (tests were conducted on at least 5 specimens to obtain failure statistics), breakdown times were processed according to the Weibull distribution as follows:

$$F\left(d\right)=1-\exp \left[-{\left({\displaystyle \frac{t_F}{\alpha }}\right)}^{\beta }\right]$$

(16)

where t_F is failure time for each specimen, and α and β are scale and shape parameter, respectively. α corresponds to the failure time at a probability of 63.2% and β is the shape parameter (slope of Equation (16) properly linearized in the Weibull plot).

In this way, n can be estimated from both erosion and failure tests (inverse power model, Equation (1) or (13)). It must be underlined that, as mentioned, n will not vary significantly with specimen thickness and area, but the scale parameter of lifelines can be deeply affected (depending on failure time/breakdown strength dispersion).

Detailed tests results are reported in

Table 2. Voltage endurance coefficients estimated from accelerated erosion and conventional accelerated life tests for CR material at different pressure levels.

Failure Criterion Considered for Estimating Lifelines	Voltage Endurance Coefficient (n) of Kapton CR
	SAP	0.5 bar	0.2 bar
Time to 50% erosion depth increment (tF50)	6.7	7.1	7.3
Breakdown time (tBD)	6.9	7.2	7.5

and

Table 3. Voltage endurance coefficients estimated from accelerated erosion and conventional accelerated life tests for NCR material at different pressure levels.

Failure Criterion Considered for Estimating Lifelines	Voltage Endurance Coefficient (n) of Kapton NCR
	SAP	0.5 bar	0.2 bar
Time to 50% erosion depth increment (tF50)	4.6	5.1	5.5
Breakdown time (tBD)	4.8	5.1	5.4

[27] and summarized in Figure 6, as regards to the end point of 50% in erosion tests and conventional accelerated life tests. Interestingly, the erosion tests provided the same voltage endurance coefficient as the accelerated life tests but in much shorter times (approximately one-tenth), which supports the use of the former rather than then latter for material PD endurance characterization.

The main output from the accelerated life tests was, however, that CR material has a voltage endurance coefficient of around 6.9, while NCR material shows n ≈ 4.8 at SAP, thus highlighting the significantly better performance of the former. As an example, based on the types of electrodes used in this study, am insulation thickness of 50 μm, a failure probability of 1%, the design field corresponding to a life of 30 years would be 12.2 kV/mm for CR and 4.9 kV/mm for NCR materials.

These results are confirmed by the same type of tests, but carried out at lower pressure, that is, 0.5 and 0.2 bar, which are equivalent approximately to 4000 and 10,000 m of altitude above sea level. Tests at 4, 4.5, and 5 PDIV for NCR, and 5.5, 6, and 6.5 PDIV for CR (estimated at the test pressure), were performed, measuring erosion depth distribution at the beginning of aging and every hour. Figure 7 reports the life points obtained by the criterion of time for a 50% increment in mean erosion depth (t_F50) compared with the results at atmospheric pressure, for CR and NCR materials.

The most significant outcome is that the voltage endurance coefficient, n, does not appear to change significantly while reducing pressure, so the n relevant to Kapton CR is still significantly larger than for NCR material.

From Figure 7 and Table 2 and Table 3, it may appear that the life of the insulating specimen increases as the pressure decreases, but this is due to the fact that tests were performed at multiples of PDIV at each pressure, not at the same PDIV multiple. To highlight that life, in fact, decreases as pressure decreases, accelerated life tests were performed on an NCR specimen at different pressure levels by maintaining the same applied voltage (3.5 PDIV SAP = 2.1 kV). As can be seen in

Table 4. Breakdown time of NCR specimen at 3.5 PDIV SAP, obtained from conventional accelerated life tests at different pressure levels.

Pressure [bar]	Applied Voltage [kV]	Breakdown Time of Kapton NCR [hours]
1 (SAP)	2.1 kV (3.5 PDIV SAP)	7.7
0.5	2.1 kV (3.5 PDIV SAP ≈ 4.66 PDIV at 0.5 bar)	3.0
0.2	2.1 kV (3.5 PDIV SAP ≈ 6.36 PDIV at 0.2 bar)	1.8

, the breakdown time of an NCR specimen is observed to reduce significantly with a reduction in pressure.

2.3. PD Measurements

Since accelerated life tests are based on multiples of the PDIV at the test pressure (to attempt to have approximately the same relative increments of electric field triggering PD at each pressure and to have directly comparable data in terms of lifelines), it is interesting to discuss how the mean PDIV varies with pressure and how PDIV can be measured. The results considered in this paper are relevant to measurements collected under an AC sinusoidal voltage, 60 Hz, but the expectation is that, fundamentally, the results will not change qualitatively by increasing frequency or using power electronics waveforms. This is because the PD inception model is not affected by voltage waveform (see Section 3), and the field distribution of a test object, as considered here, would not change with frequency. However, PD amplitude and repetition rate can be affected by the stochastic components of PD generation, from first electron availability to memory effect [26], so that voltage frequency and risetime variation can influence PDIV results.

The test circuit is typical of PD lab testing, with the specimens and electrode system located in a pressure chamber (with pressure ranging from 1 bar to 10 mbar, voltage up to 50 kV, temperature −30 °C to 100°, variable humidity). PD was measured through a large-bandwidth high-frequency current transformer (from 10 kHz to 50 MHz) and an innovative PD detector providing automatic acquisition and analysis of PD (with identification of the type of defect generating PD as the output) [16,21]. Figure 8 shows PDIV variation with pressure: the lower the pressure, the smaller the PDIV (as known already from the literature [31,32,33]).

2.4. Damage Quantification

In order to quantify the damage rate produced by PD as a function of pressure and the type of insulating material, and thus the impact on the activation energy of the electrothermal aging process, reference could be made to the definitions reported in [34]. Damage can be considered as the disruption of polymer bonds (e.g., C–H bonds) and the growth of local degradation in the form of a semiconductive pit [35]. The damage density per unit time due to partial discharges has been estimated roughly in [34,36] by $D_d$, a dimensionless quantity related to the number of effective hot electrons produced by PD per unit time (e.g., one period of the supply voltage) which contributes to dissociative electron attachment (DEA) as follows:

$$D_d=R·{\displaystyle \frac{\overline{q_{\mathrm{N}}}}{q_{\mathrm{s}}}}·F_{\mathrm{e}\mathrm{f}\mathrm{f}}·F_{\mathrm{h}\mathrm{o}\mathrm{t}}$$

(17)

where $F_{\mathrm{h}\mathrm{o}\mathrm{t}}$ is a coefficient accounting for the probability that an electron involved in a PD with a certain amplitude is exceeding an energy level, e.g., 8 eV (structural defects may reduce this value to 4 or less eV [37]), able to cause permanent and irreversible degradation. Based on [36], it can be assumed that $F_{\mathrm{h}\mathrm{o}\mathrm{t}}\approx 0.23$, varying with the size of the volume where PD is active. $F_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the fraction of effective hot electrons contributing to damage, which is taken here = 0.1, according to [35]. $\overline{q_{\mathrm{N}}}$ is the average measured charge amplitude (in V) at nominal voltage and $R$ is mean PD repetition rate. $q_{\mathrm{s}}$ is a measurement sensitivity factor which is considered here as 5 mV. $D_d$ is expected to vary as a function of time (e.g., $\overline{q_{\mathrm{N}}}$ and/or R may increase with time), material, pressure, and the total damage, $D_T$, over a given time (under operation or lab testing) will be the integral of Equation (17).

Equation (17) can be rewritten in relative value dividing its quantities at reference pressure to those measured or derived at atmospheric pressure, at constant applied voltage, obtaining the following:

$$D_r=R_r·q_r·k_{\mathrm{r}}{F}_{\mathrm{r}}$$

(18)

where

$$F_{\mathrm{r}}={{(F}_{\mathrm{e}\mathrm{f}\mathrm{f}})}_a/{{(F}_{\mathrm{e}\mathrm{f}\mathrm{f}})}_p$$

(19)

$$k_{\mathrm{r}}={\left(F_{\mathrm{h}\mathrm{o}\mathrm{t}}\right)}_p/{\left(F_{\mathrm{h}\mathrm{o}\mathrm{t}}\right)}_p$$

(20)

with subscript a and p indicating tests at atmospheric and reduced pressure, respectively.

It can be speculated that both $F_{\mathrm{h}\mathrm{o}\mathrm{t}}$ and $F_{\mathrm{e}\mathrm{f}\mathrm{f}}$ will be influenced by the type of material and pressure. Specifically, it can be assumed that $F_{\mathrm{e}\mathrm{f}\mathrm{f}}$ could decrease when introducing inorganic particles, i.e., in CR materials, thus, damage would occur at a slower rate compared to NCR materials. $F_{\mathrm{h}\mathrm{o}\mathrm{t}}$ would increase when pressure decreases, for both CR and NCR materials. However, significant variations can likely occur, based on the above results, mostly at very low pressures (e.g., 0.01 bar). Hence, $k_{\mathrm{r}}$, which is a coefficient taking into account the increased fraction of effective electrons able to dissociate material molecules due to the higher energy involved in PD discharge at low pressure, can be kept approximately constant with pressure and material, that is, $k_{\mathrm{r}}$ = 1. This implies that we associate the variation in $F_{\mathrm{r}}$ to $F_{\mathrm{e}\mathrm{f}\mathrm{f}}$., i.e., to material property, and the increased damage at lower pressure to the product $n_r·q_r$. As regards $F_{\mathrm{r}}$, its value could be around 1.4, based on the voltage endurance coefficient values of Figure 6 and Figure 7. Since, at atmospheric and reduced pressure, the terms $n_r$ and $q_r$ are higher for NCR than CR materials, the smaller degradation rate for CR can be attributed to the product $n_r·q_r$.

These speculations are confirmed by Figure 9, which displays the behavior of damage density, and Equations (17) and (18), for CR and NCR materials, as a function of pressure, having estimated the model parameters from measurement results and based on the above considerations. As can be seen, the behavior of damage density shown in Equations (17) and (18) follows the same trend indicating that the degradation rate increases with reducing pressure. Even at 4.5 PDIV, the damage density of NCR material is noticeably higher than that of CR material at 5.5 PDIV at SAP, and as the pressure reduces, the damage density is significantly higher in the case of NCR material when compared to CR material.

3. Extrinsic-Aging-Free Design and Reliability Redundancy

3.1. Three-Leg Approach for a PD-Free Design

An approach developed to reach a PD-free design was presented in [21]. Referring to electrothermal stress and relevant insulation reliability, it is based on three steps, or legs:

• Electric field calculation;
• Matching with PD inception field models;
• Validation by PDIV measurements.

It is applicable to AC sinusoidal, modulated, and DC supplies, including voltage and load transients, but the focus here is on AC sinusoidal or modulated supplies.

Since electrical aging is driven by electrothermal stress, the first leg is calculating the electric field distribution at operating temperatures in the insulation system to be designed, involving both bulk and surface sub-components. Field depends mostly on the shape of the conductive part and the properties and shape of the insulating material. Under DC, electric field also displays a large dependence on temperature and the field itself, being driven by conductivity [37].

In order to determine, at the design stage, the relation between maximum (or mean, as in cables) field and life/reliability, models that incorporate both intrinsic and extrinsic aging are needed. The former is relevant to “geometric” stresses, that is, to bulk degradation (these stresses are calculated under the first leg). The latter is brought about by accelerated aging processes caused by the design, material, or assembly defects, such as PD, or by material properties, such as space charge.

To deal with intrinsic aging design, we utilize Equations (6) and (7) to determine electrothermal life. Fixing design life at a selected failure probability, the maximum (for thin insulation) or mean (for thick insulation) design field can be estimated, based on the lifelines provided by accelerated life tests and sufficient extrapolation. Then, we have two possible directions. One is PD-free design. The other follows the assumption that PD can occur because the design is unfeasible without PD or the designer does not trust that for the whole operating life the insulation system will remain PD free. Consequently, an estimation of the time extent of PD occurrence (at least a worst case estimate) can be formulated (e.g., the time an aircraft is schedules to fly at cruising altitude in relation to the total specified aircraft life). The former approach must resort to models for PD inception in bulk and surface insulation, to minimize the risk of PD inception. The latter must also consider the use of a dynamic life model, as provided by Equations (14) and (15), where the presence of PD can be quantified after insulation and life under PD has been assessed by accelerated life testing (Section 2.2). The synthesis of the two procedures is the reliability redundancy concept presented in Section 3.2.

The derivation of a new, general model valid to estimate the inception field for bulk-defect and surface discharges is described in Equation (21). The model, approximate and deterministic (while, we must remember, PD is a process with a stochastic component [26,36]), is derived from previous work [38], and has the expression as follows:

$$E_i={\left({\displaystyle \frac{E}{p}}\right)}_{cr}·p\left(1+{\displaystyle \frac{B}{{\left(p{k}_{s}l\right)}^{\frac{1}{\beta }}}}\right)$$

(21)

with

$$B={\displaystyle \frac{{\left(\frac{K_{cr}}{C}\right)}^{\frac{1}{\beta }}}{{\left(\frac{E}{p}\right)}_{cr}}}$$

(22)

where E_i is the surface PD inception electric field, l is distance between positive and negative electrodes or internal defect height, (E/p)_cr, K_cr, C, β are parameters related to the physics of the ionization process, and k_s is the factor taking into account the field gradient, i.e., the shape of field profile. The origin of k_s stems from the assumption that discharge models in insulation bulk cavities/delamination hold for uniform field along defect height l [38], thus, in the presence of field gradient, an equivalent distance must be defined where most of the field variation is involved in electron avalanche generation. While reasonable values for B and ${\left(E/p\right)}_{cr}$ at a polymer/air interface are proposed in [38] for gas discharge in internal cavities, i.e., $\beta$ = 2, $C$ = 4.15 × 10⁻⁴ Pa.m.V², and ${\left(E/p\right)}_{\mathrm{c}\mathrm{r}}$ = 25.2 V.Pa⁻¹.m⁻¹, $K_{cr}$ ≈ 20 (thus $B$ = 8.6 Pa^1/2.m^1/2), values more appropriate for surface discharges, which take into account the contribution of the interface between insulating material and gas, are ${\left(E/p\right)}_{cr}$ = 8 V.Pa⁻¹.m⁻¹, C = 7.6 × 10⁻³ Pa.m.V⁻², and $K_{cr}$ ≈ 9, keeping the same value of β as for internal defects, so that B = 4.3 Pa^1/2.m^1/2 [21]. The value of k_s depends on electric field profile, ranging from 1 when the field is uniform (thus providing the model for internal defects in [38]) to very low values when the field is strongly divergent, as in printed circuit boards [21].

Comparing the value of E_i for a specific defect or surface configuration with that of the maximum field (precisely 95% of it) in correspondence with bulk and interface defects or surface triple points, and using different levels of voltage, an estimate of the PDIV can be obtained. The design is PD-free if the operating voltage and transient over voltages lie below PDIV.

The third leg is the experimental validation of the PDIV thus calculated. PD measurements must be performed by techniques able to identify the type of defect generating the PD, i.e., internal, surface, or corona [16,21]. Detecting solely PD does not aid in optimizing design or, possibly, setting remedial actions in the case of PD occurring in insulation bulk or on surfaces. Indeed, such actions will be radically different in the former or latter case.

Feasibility of a PD-free design can be achieved by this approach as shown, for MV power electronic boards, as in [21]. If a design does not appear to be feasible according to the specifications, different materials can be chosen, improvement of manufacturing technology can be managed, or different profiles for metallic parts determined. The main purpose would be to minimize the size of bulk defects (e.g., below 10 μm it is unlikely that PD can be generated [26]), increase insulation thickness and/or modify permittivity (conductivity, temperature gradients in DC) to reduce the electric field inside defects, change the distance and shape of metallic parts (wires, connectors, electrodes) for the same purpose of field reduction, especially on insulation surfaces.

However aging effects and abnormal unexpected stress might not have been accounted for at the design stage, which brings this study to the idea of reliability redundancy considered in the next section.

3.2. Reliability Redundancy

The concept of reliability redundancy is quite simple. We have to consider that, in spite of even good design, real stresses during use could be larger than those considered during design, e.g., aging can increase the size and density of defects, pressure or environmental changes can occur during operation, and there is also the risk that stress levels will evolve with time due to the modification of electrical assets (amelioration, refurbishing, extension). All of this can cause unexpected or uncontrollable extrinsic accelerated aging, as provided by PD inception. Hence, a design may not be able to reach the target specifications in terms of life and reliability. Here, new materials can help: if we can use insulating materials for a design that has good endurance to extrinsic aging, such as that caused by PD, or has a large value of n even if PD is permanently or sporadically active (n_PD, Equation (13)), then designs can be made by referring to such materials. An advantage is that if PD is not active during service life, the life estimated in the specifications will be conservative and life will be even longer than expected. If PD occurs for most or part of service life, the design will anyway meet the specifications for PD-resistant materials and their life parameters, Equation (13). This can be seen as a sort of reliability redundancy.

Fundamentally, we can think of two design approaches: optimized design with partial reliability redundancy, or full redundancy. The former requires knowledge of $\delta$ (see Equation (14)), so that t₂ can be derived having fixed $L_t$, with $t_2$ = $\delta t_1$ (see Equation (15)). In this way, the maximum time at which PD can be active is established by the insulating material utilized, and the design field can be as large as possible with such constraints (Figure 2).

This principle should apply at atmospheric pressure but there are doubts, in some studies, that the full redundancy concept can also apply at reduced pressure [29]. Based on the results reported in Figure 7, it can be speculated that, at least regarding the surface discharges of the tested materials, it will be fully valid even at low pressures, e.g., for the design of insulation systems in aircraft, vehicles on planets, such as Mars, and satellites. Such consideration might not apply in some cases, e.g., twisted pairs discussed in [29], perhaps due to very thin insulation and, most likely, issues in nano structuration (dispersion, type of nanofiller, etc.).

In any case, the concept of partial reliability redundancy will nevertheless also be valid for low-pressure insulation systems. In fact, Equations (13) and (14) apply for any reference material: the only risk is that feasibility is not achievable for the desired specifications because of the design field resulting from the model being too low. As an example, considering the same material characteristics of Figure 2, but considering n_PD = 4 (independently of being a corona-resistant or not corona-resistant material), if PD is active for 50% of the operation time, the design field to achieve a life of 30 years at a failure probability of 1% becomes 1.2 kV/mm (while with just 10% of PD occurrence time, the design field becomes 1.9 kV/mm).

If CR material, such as that tested in Section 2.2 (with n = 7.5 from Table 2 and Table 3) is used, and assuming that, under AC sinusoidal voltage, PD is active during 50% of the lifetime (e.g., due to the effect of variable pressure in aircraft or intermittent PD activity, as is often experienced in electrical apparatus), the specification lifetime of 30 years at 1% failure probability is achieved with E_D = 7.0 kV/mm. If PD is active at all times, Equation (13) can be considered and E_D becomes 6.4 kV/mm. Finally, employing the NCR material (with n = 5.4 from Table 2 and Table 3), the same condition as for CR above is reached at E_D = 3.2 kV/mm with $\delta$ = 1 and E_D = 2.8 kV/mm for permanent PD activity. Thus, the possibility of achieving feasibility is higher in the case of CR when compared with NCR material. This reflects a larger mean insulation thickness, in a percentage roughly proportional to the design field ratio, thus lower power density for an electrical apparatus component.

Finally, and specifically for surface insulation design: variation in pressure and contamination will likely change the PDIV, such that PD can be occurring during service in a PD-free design. Even if the reliability redundancy concept is used, which will be able to endure the needed reliability, the risk here is flashover, which cannot be contrasted by CR materials. However, PD activity and consequent erosion bringing about volume breakdown can be strongly delayed by CR materials, as discussed above and shown in [27]. This is why, downstream of the design process, health condition monitoring systems constitute a further level of reliability redundancy. They, indeed, can call for maintenance before any significant slow or fast degradation processes may occur. Such monitoring systems could be focused on PD detection and analytics, dynamic health index estimation, environmental quantity recording (e.g., pressure, humidity, contamination). PD analytics must be able to identify the type of defect generating the PD [16,39,40,41], in relation to its harmfulness and location, since, e.g., surface discharges can be less harmful than internal discharges and the type of maintenance action could be completely altered (e.g., even cleaning could be sufficient to remove/reduce surface discharges).

4. Conclusions

There are, hopefully, valuable contributions in this paper, which could become a reference for insulation system design, especially in electrified transportation where high specific power (in weight and volume), different types of power supply (which may trigger unpredictable aging processes), and harsh environmental conditions that are not represented in long-term, on-field experience feedback for insulation reliability and resilience.

In contrast to traditional accelerated life tests, which take longer to reach specimen breakdown, a new approach for the quick assessment of insulating material endurance has been proposed and validated, which can estimate the voltage endurance coefficient, n, under surface partial discharge activity in a shorter amount of time. Furthermore, it is demonstrated that this testing process can be readily adapted to any pressure level, thus, it can be used to determine the PD resistance of materials used in aircraft/aerospace vehicles. Interestingly, the findings presented in this paper highlight that the PD endurance of corona-resistant material remains sufficient (compared to Kapton NCR) even at reduced pressure levels.

On the whole, basic life modeling in the presence of PD, even intermittent, could enable a PD-free design approach, powered by the possibility to generate additional (redundant) reliability in order to account for unpredictable (or partially predictable) extrinsic aging mechanisms. PD monitoring based on the identification of the root cause of PD can support both design and condition maintenance plans. The feasibility of such an approach, also at reduced atmospheric pressure, may expand the reliability redundancy paradigm to applications in electrical aircraft and aerospace, including the design of vehicles for planets at reduced pressure. Notably, the same approach can also possibly work for increased pressure, which will be the contribution of this research work.