Mixed-frequency medium-voltage aging analysis of epoxy in the absence of partial discharges and dielectric heating

Premature failures of polymeric insulation under inverter-type electrical stress are predominantly associated with partial discharge (PD) erosion or dielectric heating. In the present contribution, an approach for aging analysis in the absence of the aforementioned mechanisms is proposed and applied to anhydride-cured epoxy samples, which are designed with a recessed shape to achieve PD-free aging. Dielectric heating was found to be negligible under all applied experimental conditions. Aging of samples was performed with a specialized setup for the generation of mixed-frequency medium-voltage (MF-MV) waveforms under controlled temperature and humidity conditions. The health state of samples was evaluated before and after different aging sequences by analysis of potential aging markers, namely the short-term AC breakdown strength, the complex dielectric permittivity (real and imaginary part), the volume resistivity, the glass transition temperature and the characteristic absorbance peaks obtained by Fourier-transform infrared spectroscopy (FTIR). Of these, only the breakdown strength exhibited significant aging effects under hygroelectric stress, which is hypothesized to be attributed to localized microcracking caused by electromechanical stress. Pure electrical MF-MV stress (i.e. at room temperature and dry conditions) was not found to be critical under the applied experimental conditions. By means of FTIR, hydrolysis was excluded as a possible aging mechanisms. In summary, the proposed aging analysis approach was found to be suitable to reveal aging effects empirically as well as to give indications about the underlying aging mechanisms without the need for excessively long or accelerated lifetime testing.


Introduction
The growing contribution of power electronic devices in medium-voltage (MV) and high-voltage (HV) systems is driven by current trends in electric energy supply. They enable the integration of renewable energy sources [1,2] and allow increased converter power densities in areas where space or weight limitations apply, such as traction [3] and electric aircraft [4,5] applications. For example, solid-state transformers allow a more flexible power conversion at up to 100fold increased power densities and higher efficiencies compared to their low-frequency counterparts [3,6]. Similarly, inverter-fed MV rotating machines allow more flexible and efficient power conversion [7]. An example for the trend towards increasing voltage levels is the recent step for electric vehicles from 400 V to 800 V systems [8,9].
A main enabler for the increasing penetration of power electronic devices into new areas, as the MV and HV sector, is the recent progress in wide bandgap semiconductor technologies (SiC and GaN). It allows for reduced switching losses by increasing the switching speeds (>10 kV µs −1 ) [10,11] as well as for higher conversion power densities by increased switching frequencies (>10 kHz) [12]. Furthermore, higher blocking voltages of SiC-and GaN-based devices (>2 kV) pave the way for a growing number of MV and HV applications [13][14][15].

Review of failure mechanisms under inverter-type stresses
The aforementioned maturation in power semiconductor technologies, however, comes with challenges for the involved insulation systems and materials [2] which need to be able to withstand novel types of electrical stresses with respect to higher switching frequencies, voltage levels and switching speeds. Moreover, the latter might lead to transient overvoltages if the slew rate dV/dt is high enough. In this context, three main aging regimes are identified.

Partial discharge (PD) erosion.
First of all, PDs, if incepted, lead to the erosion of the insulation material over time [16][17][18]. As a consequence, the insulation lifetime will decrease dependent on the repetition frequency of the PD events that mainly occur during the pulse slope [18][19][20][21][22][23]. In addition, it is reported that the PD amplitudes increase with increasing slew rate [20,24]. As systemic overvoltages might occur, e.g. at cable terminations, PDs might incept at nominal voltages lower than the PD inception voltage (PDIV) [25]. Furthermore, the PDIV decreases significantly with decreasing pressure, which leads to the risk of overestimation of the PDIV with respect to its true value in low-pressure applications, such as in aircrafts [26].

Dielectric heating.
Another aging regime is caused by excessive heating of the insulation due to dielectric losses generated by high-frequency switching of high voltages [16,22,[27][28][29]. This phenomenon is especially pronounced for polar materials [28]. If the generated heat is not dissipated effectively enough, a thermal breakdown by thermal runaway occurs [30,31]. Even in cases without a thermal runaway, the heating of the insulation might enhance thermally activated aging processes [23,32] or, as in the Eagle Pass incident [33], cavities are opened due to drying of silicone grease, which leads to PD inception. 1.1.3. Electromechanical aging. Much less is known about aging of polymeric insulation under inverter-type voltage stress in the absence of PDs and/or dielectric heating. However, empirical observations of aging in this regime exist [34][35][36][37][38], but the underlying mechanisms are not yet fully understood. Some authors state a potential contribution of space charges to the observed aging mechanism [19,22,[36][37][38]. It is demonstrated by [36] that space charges are not only relevant at direct current (DC), but also at alternating electric field stress. Even if their density is shown to decrease with increasing frequency [39], the local electric field might be increased at increasing frequencies due to space charges [40].
The interaction of an applied electric field with (space) charges generates an electromechanical force in a solid dielectric material. Based on Griffith's theory of fracture mechanics [41], different models were developed to describe electromechanical aging in dielectrics [42][43][44][45]. These models have in common to describe microscopic morphological material changes, such as the formation and growth of microcracks in the (sub-)µm range, caused by the energy dissipation due to long-term electromechanical stress. These effects occur primarily in amorphous regions of a polymer [46,47]. As a direct breaking of intermolecular bonds such as covalent bonds is unlikely due to high energy barriers, it is rather a deformation/breaking of intermolecular van der Waals bonds with much lower energy barriers which is responsible for the onset of aging [44,47,48]. The energy barrier which has to be exceeded for bond breaking can be lowered by an applied electric field and space charges [43,47]. The broken bonds as well as possibly created free radicals are favorable to react with charges and dipoles, such as water [47][48][49]. Where voids/cracks reach a size that allows the inception of PDs, aging will be dominated by PD erosion with electrical treeing [42]. Thus, the electromechanical stress acts as the initiator for fatal aging.
Alternating electric field stress introduces cyclic stress into the dielectric, which causes a fraction of polymer chains to occupy conformational states other than their equilibrium under constant stress. This might increase the free volume in parts of the polymer, thus leading to an acceleration in void formation in amorphous regions. The mechanical energy dissipation associated with this cyclic stress is proportional to the excitation frequency and the fourth power of the electric field [48]. In addition, charge trapping/detrapping can create microcracks due to the vibrational energy which is released during the capturing and escaping of charge carriers in and from traps, respectively. This effect is enhanced under alternating electric fields due to the additional repulsive field of trapped charges [49].
In addition to electric field and space charge, higher temperatures enhance the described (thermally activated) electromechanical aging processes [43,45,47]. Humidity, i.e. absorbed water, can be responsible for lowering of the activation energy for bond breaking and it is speculated that the highly polar water molecules accelerate fatigue processes due to alternating electric field oscillations [47]. [48] concludes that 'ingress of water [. . .] under the influence of the electric field, may induce some kind of mechanical cracking' (p 209-210). Formation of microcracks in polymers in the presence of absorbed water might also be caused by hydraulic pressure induced by alternating electric fields on water droplets [50] or by plasticization (which is typically reflected by a reduction in the glass transition temperature) [51]. If microcracks are filled with a (semi-)conductive medium, such as water, a (field-assisted) crack propagation can occur [42,52]. Furthermore, water-treeing in amorphous phase after stress-cracking is reported [45,53], and it is observed to be faster at higher frequencies [50,54].

Aim and procedure of this work
In order to study aging effects of inverter-type stress on polymeric materials, epoxy is a suitable sample candidate due to its long-term use, e.g. as machine insulation of inverter-fed drives [23,55]. Considering the aforementioned aging mechanisms, stronger PD aging of epoxy insulation with increasing frequency was measured by other authors [56,57]. Thermal breakdowns for epoxy insulation were predicted [27,30,59] and observed [60,61] under high-frequency stress.
Since much less is known about aging in the absence of PDs and dielectric heating, the focus of the present study is on aging of epoxy insulation under inverter-type stress in the absence of the aforementioned mechanisms. For this purpose, an approach for aging analysis of polymeric insulation materials is proposed and applied to anhydride-cured epoxy samples. It is noteworthy that extrapolation of typical lifetime-curves from high stress conditions for accelerated aging tests to lower stress conditions is questionable, as different aging processes might be at play [49]. This yields a challenge for realistic aging tests as failure times are expected to be considerably long. Consequently, in the present contribution a different approach is chosen, which is not based on failure time analysis, but on the analysis of (destructive or non-destructive) potential aging markers prior and after non-destructive aging sequences. Aging markers are selected which might reveal important physical properties of epoxy insulation, such as short-term AC breakdown strength, complex relative permittivity (real and imaginary part), volume resistivity, glass transition temperature as well as spectra obtained by Fourier-transform infrared spectroscopy (FTIR) in order to detect changes in the chemical composition, e.g. from hydrolysis [58][59][60][62][63][64][65][66][67][68][69].
The goal of the present contribution is to evaluate the usefulness of the proposed approach for aging analysis in the absence of PDs and dielectric heating with proof-of-concept measurements. The design and manufacturing process of suitable epoxy samples for PD-free aging is shown in section 2.1. Detailed information about an aging test bench designed for inverter-type stress with controlled ambient conditions is found in section 2.2, whereas the stress profiles are described in section 2.3. Moreover, thermoelectrical simulations are carried out to evaluate whether dielectric heating effects are relevant (section 2.4). The different diagnostic tools (built in-house and commercial) for the analysis of potential aging markers are described in section 2.5.

Methods
In the following section, the sample manufacturing, preparation and conditioning is explained. Subsequently, the simulation and measurement principles as well as the aging analysis and experimental tools are described.

Sample manufacturing, preparation and conditioning
A three-component epoxy system, consisting of unfilled epoxy resin, anhydride-based hardener and catalyst (ratio 100:85:0.5), provided as raw materials by ELANTAS, was used. The sample shape was chosen in a way that a recessed plate-to-plate geometry with a thickness of 200 µm and a diameter of 5 mm (of the flat sample part) is achieved, see figure 1. The recessed sample side was designed with a 5 mm radius. This ensured, after applying silver conductive paint (SCP Electrolube) on both sides, a high and uniform electric field stress at the recessed sample part during aging and breakdown tests. Furthermore, mechanical support from the thicker regions around the recessed area was achieved in this way. A cross-section of the designed mold with thickness adjustment steps as well as pictures of the recessed samples are shown in figure 1.
All manufacturing steps were carried out under clean room conditions to minimize the amount of impurities in/on the sample. The mixed components were stirred for 5 min and degassed under vacuum (1 . . . 10 mbar) for 15 min. Afterwards, the mixture was filled in the mold, which was cleaned with ethanol and prepared with a silicone-based releasing agent (Huntsman QZ 13) beforehand. This was followed by another period of degassing under vacuum for 15 min with subsequent curing in an oven (6 h at 80 • C + 6 h at 160 • C) and demolding thereafter. Samples were cleaned with silicone cleaner (Silikon-EX 2609) in an ultrasonic bath for 10 min to remove potential residuals of the releasing agent. The thickness of every sample was measured individually (Sylvac Hi-Cal 300) and samples not within 200 µm ± 10 µm were discarded. Samples were subsequently dried at 50 • C for >24 h (according to ISO 62:2008 [70]) and conditioned at the desired humidity conditions for >24 h. In a last step, silver painting of samples with subsequent humidity conditioning for >24 h was carried out. It was found by gravimetric analysis (not shown here) that the used SCP is permeable to water.
Gravimetric water absorption measurements at plane samples of 500 µm thickness allowed the calculation of the diffusion coefficient D = 8.64 × 10 −9 cm 2 s −1 , which in turn allowed the estimation of the water absorption saturation time of 6.5 h for the recessed samples of a thickness of 200 µm. This confirms that conditioning of the samples for >24 h is sufficiently long for saturated water absorption. The measurements and calculations followed the procedure described in [70,71].

Mixed-frequency medium-voltage (MF-MV) and ambient stress setup
Multilevel inverter-type (or converter-type) voltage stress was synthesized by superimposing a low-frequency alternating current (AC) (50 Hz) sinusoidal voltage and a high-frequency pulse-width modulated (PWM) voltage, which resulted in socalled MF-MV stress. This voltage shape was chosen to enable systematic variations of the sinusoidal AC and the rectangular PWM voltage components. Simultaneous aging of eight samples was achieved with the setup shown in figure 2, which is based on the setup initially designed by Färber et al [19], and was modified during this work. It consists of a BEHLKE HTS 41-06-GSM half-bridge metal-oxide-semiconductor fieldeffect transistor (MOSFET) switch, which generates a unipolar PWM voltage from a DC source V p and a DC link capacitor C 1 = 1 µF. The PWM signal is supplied by an Arduino Yún. With the help of a coupling capacitor C 2 = 2.7 nF, the unipolar PWM voltage becomes bipolar and a 50 Hz AC voltage can be superimposed onto the PWM voltage at the device-under-test (DUT), i.e. the eight epoxy samples in parallel. The resistor R 1 = 220 Ω protects the internal diodes of the switch by forcing the current flow through D 1 /D 2 in case of a sample breakdown, which is detected by a current transformer (CT). The rise time of PWM voltage pulses can be varied by changing the value of R 2 (currently R 2 = 90 Ω) and decoupling of the AC and PWM voltages is achieved by R 3 = 600 kΩ. The capacitance of a total of eight samples was measured by means of dielectric spectroscopy (also see section 2.5) as C DUT ≈ 68 pF.
The samples were placed inside a test cell with a temperature-controlled heating sleeve. The relative humidity (RH) inside the test cell can be varied between RH = 0 . . . 80% at ambient temperature (22 ± 1 • C). The desired RH level was set by a dried air flow that is separated in two branches out of which one is directed into a mixing chamber with an RH sensor, while the other passes a bath of de-ionized water beforehand. By adjusting the volume flow of both branches, the RH level can be controlled, see figure 2. The samples were conditioned according to the procedure described in section 2.1. Subsequently, they were placed inside individual sample holders with holes for air passage between two Aluminum electrodes with spring contacts for defined contact pressure. Note that the RH values in this work are given as fixed values, e.g. RH = 0%, even if slight differences cannot be fully excluded due to the inaccuracy (±3%) of the RH sensor. The MF-MV stress setup specifications are given in table 1.

MF-MV and ambient stress
Changes of the health state of the samples due to MF-MV and ambient stress were investigated by evaluation of potential aging markers (see section 2.5) before and after aging. At each aging sequence, eight samples were stressed simultaneously in the setup shown in figure 2. An example MF-MV waveform with special focus on the rise time of the PWM voltage pulses with frequency f PWM = 10 kHz and duty cycle D c = 0.5 is shown in figure 3. According to the measured rise time τ r ≈ 90 ns (time between 10% and 90% of the maximum voltage value) and the peak-to-peak PWM voltage V PWM,pp = 3.5 kV, the slew rate could be calculated as dV/dt = V PWM,pp /τ r = 38.9 kV µs −1 . The superimposed AC peak voltage was V AC,p = 5.75 kV, such that the total peak voltage was V p = 7.5 kV and the root-mean-square (RMS) voltage was V p = 5.3 kV for a duty cycle D c = 0.5 (represents the time fraction D c T p during a full PWM period T p for which a positive PWM voltage is applied). The aging sequences used in this work are listed in table 2, wherein t d is the aging duration, T the temperature and RH the RH inside the test cell (also applied during conditioning according to section 2.1). Aging was carried out under two different electric stresses and both dry (D) and high humidity (H) conditions. In case of an early breakdown, i.e. during intended nondestructive aging, the silver paint of the sample was removed and the sample surface was searched for PD traces. This indicates whether the failure was caused by PD erosion in an air gap between the sample surface and the potentially delaminated electrode or if the breakdown was due to one or more PD-free aging mechanism(s) (see section 3.2 for further analysis).

Thermoelectrical simulations
Two-dimensional thermoelectrical simulations were carried out with COMSOL Multiphysics. In general, the total dielectric losses P loss,sin are defined for a sinusoidal voltage of angular frequency ω and RMS value V RMS as In order to simulate the dielectric losses in the case of MF-MV stress, it is useful to describe the voltage waveforms by a Fourier series [30]. However, COMSOL Multiphysics can only simulate dielectric heating at a single frequency at a time.
For this reason, an approach was chosen in the present work to split the total dielectric losses generated under combined AC (50 Hz) and PWM voltage stress P loss into a single term for the AC component and a sum term for the harmonics of the PWM voltage as wherein ω 0 = 2π · 50 Hz, C 0 is the vacuum capacitance, ε ′ ′ r the imaginary part of the complex relative permittivity. Due to the linearity of the Fourier series and by introducing a function g(n) as well as a factor c = (V PWM,pp /2)/V AC,RMS to relate the RMS values of the PWM and AC voltages, the coefficients V n,RMS read With the help of a frequency relation factor k and formulation of ω n = knω 0 , equation (2) can be written as which formally equals equation (1). Thus, introducing an equivalent imaginary part of the complex relative permittivity ε ′ ′ r,eq enabled us to enter the whole sum of equation (4) into the COMSOL model. The function g(n) was calculated according to [30] as by assuming a low-pass characteristic of the PWM voltages with the measured rise time τ r = 90 ns with The values of ε ′ ′ r at different frequencies, temperatures and humidities were measured by dielectric spectroscopy, whereas the volume resistivity values at different temperatures and humidities were obtained by polarization-depolarization current (PDC) measurements (both not shown here). The heat transfer properties of the epoxy samples were measured with a heat transfer analyzer (Isomet 2114) which resulted in the values shown in table 3.
By using the approach and input values described above, it was straightforward to perform two-dimensional thermoelectrical simulations of the sample-electrode configuration shown in figure 5 under all possible MF-MV and ambient stress conditions. This reveals the loss density and temperature (increase) inside the epoxy sample.
However, the calculated temperature increase in the epoxy sample (with rather low thickness and low dielectric losses) was very small and thus hard to measure experimentally. In order to validate the simulation model experimentally, an approach similar to [72] was applied. For this purpose, phenolic paper (Tufnol SRBF) samples of 400 µm thickness were used, as they exhibit much higher dielectric losses (e.g. by a factor of 30 . . . 66, measured at 1 kHz and 25 . . . 125 • C). It was   expected that this leads to significantly higher dielectric heating, which might be easier to measure experimentally with a thermal camera. As for epoxy samples, the temperature-and humidity-dependent permittivities, dielectric losses and resistivities as well as heat transfer properties of phenolic paper samples were measured experimentally as input for the thermoelectrical simulation. The comparison between simulated and measured dielectric heating of phenolic paper samples is shown in section 3.1.

Aging evaluation
As mentioned in sections 1.2 and 2.3, the health state of the epoxy samples was assessed before and after each aging sequence described in table 2. It is emphasized that samples aged under high RH levels were dried at RH = 0% for >48 h at room temperature before measuring the potential aging marker in order to reveal irreversible instead of reversible aging effects. For this purpose, the following markers were tested for their suitability in the context of aging under MF-MV and ambient stress: short-term AC breakdown strength, relative permittivity (real and imaginary part), volume DC resistivity, glass transition temperature as well as FTIR spectra. The corresponding experimental setups and measurement procedures are explained in the following.  breakdown. The samples and electrodes were immersed in insulating oil (Shell Diala S4 ZX-1) to prevent surface discharges. Note that the electrodes used for breakdown testing posses a plate-to-plate shape with the smaller electrode having a diameter of 5 mm and an edge radius of 5 mm. The resulting uniform electric field stress was assumed to lead to a rather high scattering of the breakdown strength data, which, in general, makes it difficult to detect small changes in the breakdown strength. In addition, the volume/thickness effect of the breakdown strength of solid insulation materials had to be considered. Consequently, the measured breakdown strength V bd,m for each sample with slightly varying thickness d m = 200 µm ± 10 µm was related to a thickness of 200 µm by [75] V bd,200 µm = Note that the thickness-related voltage differences corrected by equation (8) were a maximum of 5% for the sample thicknesses used in this work. Statistical analysis of breakdown strength measurements was carried out by representing the data as box plots, consisting of median, boxes between the 25th and 75th percentiles with whiskers up to 1.5 times the interquartile distance. Values outside of this range are separately shown as outliers.

Dielectric permittivity measurements.
Measurements of the real (ε ′ r ) and imaginary (ε ′ ′ r ) part of the complex relative permittivity at varying frequency, temperature and RH were performed by means of dielectric spectroscopy. For this purpose, a setup with guarded test cell and electric supplies was designed and built by Färber and Franck [76] and the measurement procedure is described in [71,77]. The silver electrodes used during aging were removed with ethanol and new electrodes with diameter D el = 4.18 . . . 4.54 mm were applied only at the flat part (thickness d = const.) of the plate-toplate sample to exclude any influence of the edges, where d ̸ = const.. The diameter of the new electrodes was measured by an image processing program (ImageJ) for each sample. This value was needed for a correct estimation of the sample capacitance and thus the absolute value of the complex relative permittivity. Reference measurements with and without guard ring electrode at the sample surface confirmed that the additional guard ring introduced no changes to the measurements (not shown here). It was thus justified to perform further measurements in this work without an additional guard ring.

Volume DC resistivity measurements.
Volume DC resistivity was determined by PDC measurements, for which a test bench was designed and built in an earlier work [78]. The measurement procedure consisted mainly of the measurement of the polarization current i p (d) during an applied DC voltage V DC = 1 kV over the course of 1 h with subsequent measurement of the depolarization current i d (t) for the same time. Their absolute difference i pd,1h ≈ |i p (1 h)| − |i d (1 h)| is related to the so-called apparent DC resistivity (after 1 h) ρ v,1h as described in [78]. Measurements were performed at RH = 0% and 90 • C. The elevated temperature led to higher current signals, which otherwise were too low to be measured at room temperature for epoxy samples of the used geometry. Example measurements for samples aged at different stress conditions are shown in figure 4. The solid lines represent the currents filtered with a moving median (ten data points) to eliminate the transient current signals (shown in lighter color), caused e.g. by switching events of the temperature controller. Note that the filtered current signals before application of the DC voltage were always below ±10 fA (not shown here), which confirms that no significant offset current component was present in the measurements shown in figure 4.

Glass transition temperature measurements.
The glass transition temperature T g was determined by means of differential scanning calorimetry (DSC). For aged samples, the silver electrodes were removed with ethanol before each measurement. A METTLER TOLEDO DSC 1 device was used at a heating rate of 10 K min −1 in the range 25 . . . 180 • C with two cycles per sample. For all DSC measurements, a small fraction of the sample material (4 . . . 6 mg, measured with a scale of 0.01 mg accuracy for each sample) was extracted from the flat inner part of the sample in order to evaluate the location of the highest electrical stress during aging.

FTIR measurements.
The chemical composition of the non-aged and aged materials was analyzed by FTIR. Measurements were carried out with a diamond attenuated total reflection type device (Varian 640 Fourier Transform Infra Red Spectrometer) in the wavelength range 750 . . . 4000 cm −1 . For aged samples, the silver electrodes were removed with ethanol before each FTIR scan. Reference measurements (not shown in this work) confirmed that this did not lead to measurable changes in the FTIR spectrum. As the absorbance might vary between different FTIR scans, it is recommended to use reference peaks which are known to be (almost) unaffected by aging. For anhydride-cured epoxy, the absorbance around 1608 cm −1 is reported to be the most stable and independent of aging due to its correspondence to the aromatic structure in epoxy [63]. Thus, all FTIR spectra were related to this absorbance peak.

Results
In the following section, the thermoelectrical simulation results as well as the aging evaluation results are presented.

Thermoelectrical simulation results
At the highest possible MF-MV stress, the maximum temperature increase at dry conditions and room temperature is shown in figure 5. The influence of the AC voltage on dielectric heating for the given sample-electrode configuration was almost negligible and also the high-frequency PWM voltage pulses introduced only a maximum temperature increase of 0.75 K. Note that the different ∆T values at each V 2 PWM,pp · f PWM value reflect the measured frequency-dependent dielectric losses, i.e. ε ′ ′ r (ω) as well as the different number of dielectric loss terms in equation (4) for different fundamental frequencies.
For example, V 2 PWM,pp · f PWM = 48 kV 2 kHz can be achieved with V PWM,pp = 1 kV and f PWM = 48 kHz or with V PWM,pp = 3.5 kV and f PWM = 3.9 kHz, but the dielectric losses measured at 3.9 kHz and 48 kHz, respectively, are not the same, thus leading to slightly different ∆T values in figure 5.
Elevated temperatures up to 125 • C and relative humidities up to 80% led to maximum dielectric heating of 0.75 K and 1.2 K, respectively (not shown here). Thus, the effect of dielectric heating for the used sample-electrode configuration in this work is considered negligible.
However, the same simulation model developed in this work was capable of revealing considerably higher dielectric heating in the case of much higher voltages and frequencies than possible with the used setup. For example, the glass transition temperature T g ≈ 123 • C of the tested epoxy sample was exceeded at V PWM,pp /f PWM combinations of about 25 kV/50 kHz or 100 kV/2.75 kHz. Note that under the latter condition, i.e. V PWM,pp = 100 kV, the short-term breakdown strength might be exceeded even before a thermal breakdown can take place. Moreover, a higher sample thickness with associated poorer heat dissipation might as well lead to a higher risk for excessive dielectric heating.
In order to verify the correctness of the developed simulation model experimentally, phenolic paper samples with much higher dielectric losses were used, which in turn caused higher dielectric heating. In figure 6, the measured (with standard deviation) as well as the simulated temperatures are shown at different time steps after applying of voltage stress for 30 min. The measurements and simulations were evaluated at the same location in proximity to the electrodes. It was found that due to heating of the nearby MOSFET switch during operation, the ambient air heated up additionally, which was also included in the simulation model. From figure 6, it is evident that a good agreement between measured and simulated values of dielectric heating and the subsequent temperature decay existed. The same test was carried out at different voltage levels (not shown here), which resulted in a similar agreement between experiments and simulations.

Analysis of pre-breakdowns
In case of a pre-breakdown, i.e. a sample breakdown occurring before the end of the intended 48 h of aging, the failed sample was removed from the test cell and the silver paint was removed with ethanol. Each sample was optically examined for PD traces. If present, PD occurred at the sample edges, probably caused by a delamination of the silver paint with associated formation of a small air gap in which PD inception was possible. The failure times of all pre-breakdowns at the corresponding RMS voltage stress levels are given in figure 7. Note that therein, the pre-breakdowns of more aging studies than presented in this contribution were included. A clear distinction in terms of failure times between samples with and without PD traces can be observed. When a sample breakdown occurred in the first 10 h of aging, traces of PD were always observed. In turn, for later breakdowns, no PD traces were found. This was further confirmed by optical analysis of aged, non-failed samples, which consistently exhibited no PD traces.

AC breakdown strength measurement results
Measurement results of the short-term AC breakdown strength E bd of a set of epoxy samples before and-for a different but identically manufactured set-after aging at the conditions described in table 2 are given in figure 8. Whereas no clear  aging effect was visible for samples aged at dry conditions, a clear decrease in E bd was observed under same electric stress, but additional high RH. In other words, the electrical stressing is observed to lead to a reduction in the short-term AC breakdown strength only in the presence of (absorbed) water.
In order to rule out that humidity alone had a significant influence on E bd , sample conditioning for different periods of time at the same RH level was applied to non-aged samples. Subsequent measurement of E bd either at wet conditions or after drying resulted in figure 9. From this representation, it is clear that only the combined humidity and electric stress (here called hygroelectric stress) had such a tremendous influence on the breakdown strength.

Dielectric permittivity measurement results
A comparison of non-aged epoxy samples and the same aged (H: 5.75/3.5/10/0.5) samples for ε ′ r and ε ′ ′ r measurements at different frequencies and temperatures is presented in figure 10. For the shown two samples, no significant differences were observed and also evaluation of all eight samples (in figure 10 for instance at 10 3 Hz) revealed no aging-induced changes. It is noteworthy to mention that dielectric spectroscopy measurements of PD-aged samples exhibited distinct changes in ε ′ r as the sample thickness had been reduced (but not considered in the calculation) due to material erosion (not shown here). This is another indicator that samples aged in this work were aged in the non-PD regime.

Volume DC resistivity measurement results
The measurement results of PDCs of differently aged samples are shown in figure 11. From the current difference i pd,1h , the apparent volume DC resistivity ρ v,1h was calculated according to the procedure described in section 2.5.3 and presented for non-aged and aged (H: 5.75/3.5/10/0.5) samples in figure 11. It is evident that aging under these conditions caused no measurable changes in the DC resistivity.

Glass transition temperature measurement results
DSC measurements of non-aged and aged (H: 5.75/3.5/10/0.5) epoxy samples resulted in the glass transition temperature T g values, which are shown as box plots in figure 12. The absolute value was reproducibly around T g ≈ 123 • C, but the relative difference between non-aged and aged samples was negligible. Thus, hygroelectric aging under the conditions applied in this work had no influence on T g .

FTIR measurement results
The recorded FTIR spectra of two (out of a total eight) nonaged and aged (H: 5.75/3.5/10/0.5) epoxy samples are shown in figure 13. Note that the absorbance peak at 1608 cm −1 was taken as a reference value due to its reported independence on aging, as described in section 2.5.5. The focus was on the hydroxyl group between 3400 . . . 3520 cm −1 as well as the ester groups between 1680 . . . 1780 cm −1 and between  1100 . . . 1300 cm −1 , respectively [63,64,79,80]. As seen from figure 13, no evidence for the existence or change of the hydroxyl peak was found. Furthermore, no strong changes of both ester-related peaks were observed for samples aged under pure electric stress, pure humidity stress as well as under hygroelectric stress, see figure 13).

Discussion
Experimentally validated thermoelectrical simulations of the used electrode-sample configuration showed only a maximum temperature increase due to dielectric heating of <1.2 K, even at the highest possible stress conditions (see section 3.1). These results clearly confirm that dielectric heating for the used sample-electrode configuration cannot lead to a thermal breakdown or other heating-related degradation mechanisms. It should be noted that a thermal breakdown can still occur for the same insulation material if either the switching losses (P l,PWM ∝ ε ′ ′ r V 2 PWM,pp f PWM ) are large enough or the heat dissipation of the insulation system is poor enough.
Furthermore, the analysis of pre-breakdowns demonstrates that PD-related aging occurs on a much faster timescale than PD-free aging, see figure 7. It ensures that samples aged for 48 h (without pre-breakdown) were not aged by PD erosion. In addition, permittivity measurements revealed no aginginduced changes in ε ′ r which, in contrast, were observed if PD erosion was present during aging. These observations indicate that indeed no PD was present at the investigated sample area under MF-MV and ambient stress for the studies in this work. Thus, it verifies the suitability of the used sample design for aging analysis below the PDIV.  MF-MV aging at RH = 0% showed no effect on any of the evaluated potential aging markers. Thus, it is assumed that the electric stress conditions used in this work were too low to activate a detectable aging mechanism in the epoxy sample in the absence of humidity, or, more precisely, in the absence of absorbed water.
In the case of combined electric and humidity stress, a significant reduction of the short-term AC breakdown strength  was observed (about 25% at H: 4.35/3.5/10/0.9 and about 56% at H: 5.75/3.5/10/0.5). A dominant influence of humidity alone is ruled out by the aging analysis after pure humidity stress. However, interestingly, other potential aging markers such as the real or imaginary part of the relative permittivity, the volume DC resistivity, the glass transition temperature and FTIR spectra are unable to detect the aging-induced changes that lead to a significant reduction of the material's electric strength. Whereas these parameters reflect macroscopic material properties representing an average over the sample's volume, the breakdown strength is by its very nature also sensitive to highly localized changes (weakest link theory). Thus, it is hypothesized that the underlying aging mechanism occurs in a small partial volume of the sample, potentially influenced by changes on a microscopic scale. Similar observations were made in [81] by (online-)monitoring of the dielectric permittivity of polyethylene terephthalate (PET) during voltage stress until a breakdown occurred. Similar as in the present work, no changes in the permittivity were observed despite the apparent aging that led to a sample breakdown.
Moreover, the non-existing alterations of the glass transition temperature further confirm that no plasticization due to the hygroelectric stress occurs. Hydrolysis is excluded as possible aging mechanism by the FTIR spectra, as no increase in the absorbance peak associated with the hydroxyl group was observed.
As can be seen from figure 8 and table 2, the breakdown strength reduction is more significant for larger applied RMS voltage stress (for a constant peak voltage stress). This points towards an aging mechanism which is dependent on the dissipated energy in the sample during aging. Moreover, the results indicate that no uniform aging with changes on a macroscopic scale takes place under the studied experimental conditions. Consequently, the electromechanical aging models described in section 1.1.3 are suited to explain this observation as they all have in common the formation and growth of microcracks caused by and dependent on the amount of dissipated energy. The fact that this aging mechanism appears to occur only in the presence of water/humidity can also be explained within these models. For example, water is reported to lower the activation energy for breaking of intermolecular van der Waals bonds [47]. In addition, the propagation of microcracks under an applied electric field is described to be more pronounced if they are filled with a conductive medium, such as water [42,52].
In order to connect these hypothesized aging-induced material changes and the observed reduction in the AC breakdown strength, the breakdown criterion as described in [82] can be used. It states that a breakdown is possible when the voltage drop V x = E x x over the longest free path length x, where electrons can be accelerated by the electric field E x , attains the value W b /e, i.e.
Therein, W b represents the height of the energy barrier that needs to exceeded by an electron to contribute to hopping charge transport and e = 1.602 × 10 −19 C the elementary charge of an electron. The formation of voids/microcracks in amorphous regions of the polymer by an alternating electric field stress due to movement of polymer chains leads to an increase of the free volume in fractions of the polymer [48]. As this increases also the longest free path for an electron to be accelerated by an electric field, electrons of higher potential energy are present in fractions of the polymer when an electric field is applied. These electrons are thus capable of hopping over larger energy barriers. Moreover, the energy barrier W b depends only on the chemical structure of the polymer [82] and is reported to be lowered by electromechanical stress, especially in the presence of water [47]. Thus, it seems plausible that localized microcracking leads to a local reduction in the energy barrier W b and, according to equation (9), to a reduction in the breakdown strength as the breakdown path always follows the weakest path. In other words, the observed reduction in the AC breakdown strength after hygroelectric aging can be explained both by a higher probability of high-energy electrons as well as by a (local) reduction in the energy barriers for electron hopping charge transport during the applied AC voltage ramp used for short-term AC breakdown strength testing in this work. The present contribution thus demonstrates how aging of solid insulation materials can be analyzed in the absence of PDs and dielectric heating. Even though the stress conditions applied in this work are higher than in real applications, the approach can be applied to lower and more realistic stress conditions. As a consequence, it provides an effective method for aging analysis under more realistic stress conditions compared to destructive lifetime testing, which inherently needs much higher stress conditions in order to generate a premature failure in reasonable time.
However, the results demonstrate that aging markers that reveal the macroscopic material properties are not suited to detect aging in the absence of PDs and dielectric heating. Only the AC breakdown strength, i.e. a destructive aging marker, was found to indicate aging effects. This is also of practical relevance as it points out that the observation of classical nondestructive aging markers (e.g. the dielectric permittivity) during operating conditions is not sufficient to detect early signs of critical aging in the absence of PDs and dielectric heating.

Conclusion and outlook
In the present contribution, an approach for the aging analysis of polymeric insulation under combined MF-MV and ambient stress in the absence of PDs and dielectric heating is presented. For this purpose, a specialized MF-MV aging test bench is used and potential aging markers are evaluated before and after different aging sequences. The key findings of this work are as follows: • The proposed non-destructive aging analysis approach is applicable to recessed epoxy samples and reveals aging effects in the absence of both PDs and dielectric heating without the need for excessively accelerated or long destructive lifetime testing, but only the destructive aging marker (AC breakdown strength) is able to indicate aginginduced changes. • The results confirm that PD-related aging occurs on a significantly shorter timescale than non-PD aging. sible aging mechanisms as well as degradation due to PDs or dielectric heating. • The dominant aging mechanism rather influences the material on a localized rather than a uniform scale (as of all potential aging markers, only the breakdown strength changes due to aging). • The observed reduction in breakdown strength can be explained both by a higher probability of highenergy electrons due to increased free volume caused by electromechanically-induced microcracking as well as by a (local) reduction in the energy barriers for bond breaking.
The measurements carried out throughout this work have a proof-of-concept intention. As the applicability of the aging analysis approach is successfully verified (however only for a destructive aging marker), the next step is to conduct a broad study with focus on different stress parameters, such as the RMS and peak voltage stress, the PWM frequency, slew rate and temperature. In terms of material optimization, it seems promising to modify the material with respect to its performance in the presence of water. Approaches in this direction will be part of future work. Since at the present time, only indications of the hypothesized electromechanical aging mechanism involving microcracking exist, it is recommended to investigate this further with the help of other diagnostics, e.g. microscopic tools. This will enable a better understanding of MF-MV aging mechanisms in the absence of PDs and dielectric heating, a topic, which is still underrepresented in current research activities.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).