Cécilien Thomas
email: cecilien.thomas@laplace.univ-tlse.fr

Gilbert Teyssedre

Christian Laurent

A new method for signal averaging resorting to space charge measurements by the pulsed electro-acoustic method under AC stress

A new method for space charge measurement resorting to the pulsed electroacoustic (PEA) method under periodic stress of arbitrary waveform is presented. The originality of the work resorts to the use of a long memory digital oscilloscope combined to the method used to sample one period of the HV stress into several profiles. There is no need for synchronization between pulse generation and HV stress and hence no hardware change of classic PEA system. The pulse generator provides a probing pulse of 5 ns duration, at a maximum frequency of 1 kHz. With these features, one period of the AC frequency can be resolved into 200 profiles by frequency adjustment of the pulse generator. The typical measurement time is less than 20s for f > 0.2 Hz. Preliminary results obtained on a crosslinked polyethylene film under 50Hz ac stress are shown to demonstrate the feasibility.

INTRODUCTION

Most of the experimental studies resorting to space charge profile measurements have focused on DC stress conditions. There is comparatively much less attempts to investigate dynamic stresses such as AC or impulse. The reason is actually not in the lack of interest of having information on charge dynamics in these conditions since space charge could constitute an ageing driving mechanism through associated energetic processes. In fact, rather sophisticated experimental tools are necessary for implementing such measurements. The pulsed electroacoustic -PEAmethod has been used for this purpose as it combines the possibility of high acquisition rate for charge profiles and measurement under applied high voltage. The principle of the PEA technique consists, in brief, in detecting acoustic waves generated by internal charges under the Coulombic influence of a pulsed electric field. To obtain an exploitable signal, the response is averaged applying several voltage pulses. The time for a profile acquisition, and hence the frequency of profile acquisition depend directly on the frequency of the pulse generator (generally in the kHz range). Under DC stress, as the applied voltage is constant, signal averaging can be easily achieved by internal functions of most of numeric oscilloscopes. However, under AC stress, the applied voltage can not be necessarily considered as constant during the averaging time, especially when relatively high frequency is applied.

Several set-ups for space charge measurement under AC stress have been reported in the literature [1][START_REF] Montanari | Proc. Conference on Electrical Insulation and Dielectric Phenomena[END_REF][START_REF] Fukuma | [END_REF][START_REF] Wu | Proc. Conference on Dielectric Materials, Measurements and Applications[END_REF]. PEA systems generally use a digital oscilloscope for data systems. However, limitations readily occur which such systems due the low data transfer rate of the GBIB bus. Therefore, alternative strategies have been developed based on a 16Mb memory data acquisition -DAQcard [START_REF] Wu | Proc. Conference on Dielectric Materials, Measurements and Applications[END_REF] or on a box-car system that allows real time data acquisition and transfer at a high rate [1]. In all of these systems, the pulse generation must be triggered at specific positions (called point on wave) of the AC cycle. Generally, a limited number of these positions are used (to our knowledge, up to 16 so far). Burst of pulses are generated at the measurement point. The measurement time depends on the resolution expected on the phase of the signal and on the number of records to average. The advantages of DAQ or box-car systems rely on their ability to handle a large amount of data and on the possibility to trigger the pulse generation. However, they do not use the pulse generation at its full capacity (which is therefore detrimental to the measurement time), the control of the ensemble is rather complex, and the position of points on wave are fixed. Also the application to non-sinusoidal stress is not straightforward. Digital oscilloscopes offer now large storage capabilities, and therefore the problem of slow data transfer rate can be overcome by proceeding to data upload once the full measurement has been carried out. For the problem of overall synchronization, we propose an alternative method wherein the novelty comes from data processing: the hardware is essentially the same as that used for standard PEA systems.

IMPLEMENTATION OF THE METHOD

Our method combines a long memory (digital oscilloscope, model LT374L from Lecroy (16 Mb memory, 500MHz bandwidth, 4GS/s sampling rate), with simultaneous measurement of both the piezoelectric signal and the applied voltage for each voltage pulse. With this method, the AC stress and the pulse generation need not to be synchronized and account is taken about the actual AC voltage provided by the source. Also, the method can be easily extended to periodic arbitrary voltage waveforms.

Hardware

The PEA cell is installed in a thermostated oven in order to carry out measurements at controlled temperature. The HV-AC stress (up to 10kV peak) is generated by a Trek amplifier (model 609A) with an input signal produced by an arbitrary function generator. The pulse generator (5ns duration, 300 to 1500V peak, 40Hz to 1kHz frequency), has been developed in the lab. The applied voltage is read directly at the output of the amplifier by means of an HV probe integrated in the amplifier. Care has to be taken about adaptation of the PEA cell to non-DC stress. The consequence of miss-adaptation is a phase shift and attenuation of the voltage applied to the sample in respect to that provided by the amplifier. The choice of the components must also maintain the 50 adaptation of the pulse circuit and avoid over consumption of the current provided by the amplifier (source limited to some mA). Acceptable values of R and C are 470k and 150pF [START_REF] Fukuma | [END_REF]. A graphic interface has been fully developed on purpose. It controls the form and the frequency of the input signal of the HV amplifier along with the number of period of the HV stress. Data storage in the oscilloscope, acquisition, averaging and processing are carried out by this interface providing so space charge, field and voltage profiles along one period of the HV stress based on data acquired in one or several periods of the HV-AC signal. The advantages of the method are: the control of the HV stress, an estimation of the error bar on the voltage for each profile, the measurement time and resolution in time: one period of the AC stress can be resolved into up to 200 profiles in an acquisition time not exceeding 20s at 50Hz. Finally, mathematical treatments applied to rough data for extracting charge and field profiles are incorporated.

Rough data acquisition.

Two methods are used for rough data acquisition, depending on the frequency of the HV-AC stress.

-When the frequency is low, i.e. less than typically 50mHz, the variation of the applied voltage is small within the measurement time (defined as the time required for averaging a minimum of 50 records): the same method as for measurement under DC stress is applied. The oscilloscope proceeds to averaging of records. The measurement time is just the period of the AC stress, ranging from 20 to 1000s for frequencies in the range 50mHz to 1 mHz. In order to limit the amount of data to be stored, the pulse frequency is reduced when going to low frequency for the HV stress. The applied voltage is measured using the second channel of the oscilloscope.

-For higher frequency, acquisition over several periods of the HV stress is necessary. The oscilloscope, which is set into the sequential trigger mode [START_REF] Fukuma | Proc. International Symposium on Electrical Insulating Materials[END_REF], acquires the signal in the form of sequences, each of them containing 4000 segments. A segment represents the response to a single pulse, i.e. a record. Two input channels of the oscilloscope are used: one for the acoustic signal and one for measuring the applied voltage. Once a pair of sequences has been acquired, they are transferred into memory blocks of the oscilloscope. Four memory blocks are available, plus the information stored in recording channels. In this way, 3 pairs of sequences can be acquired representing 12000 records. The time necessary for the measurement is in the range 18 to 70s representing 3.5 to 1800 periods of the HV stress when going from 50mHz to 100Hz. Afterwards, the data are transferred to the PC and processed as detailed below. An important point is that the pulse frequency must not be a multiple of the frequency of the HV stress.

Averaging of raw data

The main problem for treating data consists in identifying, for each record, the corresponding phase in the HV stress. In case of the AC stress, it can be easily deduced from the measured voltage and the corresponding derivative in time. However, for a square signal for example, it is no longer valid since a point on wave is not unequivocally defined by V and dV/dt. An alternative procedure based on the properties of the Hilbert transform has been developed. The Hilbert transform has many applications in digital signal processing and a conspicuous literature is available around it. Here, we use a quite straightforward property of this function, which is to enable to transform a real data sequence v(t) in an analytic signal s(t) that contains the information on the original phase signal, see for example ref. [START_REF] Rosenblum | Analysing Synchronization Phenomena from Bivariate Data by Means of the Hilbert Transform[END_REF].

) ( ) ( ) ( ) ( ) ( t j e t A t v j t v t s     (2) where
) ( ˆt v corresponds to the Hilbert transform of v(t):

    d t v t v       ) ( 1 ) ( ˆ (3)
As one can see from equation (2), the Hilbert transform of v(t) corresponds to the convolution of the functions v(t) and 1/t:

) ( 1 ) ( ˆt v t t v    (4)
For application to the present problem, we essentially need the phase corresponding to a given voltage value (v in the above expressions), which is obtained from:

) ( ) ( ârctan ) ( t v t v t   (5)
Figure 1 illustrates the form of the phase obtained for a truncated triangle signal. All the numeric treatment is carried out using Matlab® in-built functions. The phase does not vary linearly in time (it would be linear only for a pure sinusoidal signal). However, each data point value is identified by a unique value of the phase, and hence the time in a period at which a given profile has been acquired can be unambiguously identified considering (t). Figure 1d shows the phase values, after sorting them out, as a function of the cumulated number of records: several criteria can be used for averaging data. One can either average a fixed number of records, in which case the error interval on the phase (and hence on the voltage) will vary along the period, or consider equally spaced intervals along the phase, in which case the number of records taken in each interval varies. This is to be appreciated depending on the shape of the arbitrary waveform and on the expected resolution on the voltage. There are a number of limitations to the procedure, which however can be easily handled: i/ a minimum number of 2 periods of the stress in a given sequence is needed. This is not really a problem here since low frequency measurements can be treated using the standard method. Alternatively, the frequency of pulse generation can be lowered.

ii/ the beginning and end of a sequence are erroneously treated in the Hilbert transform. This concerns at most 1/2 period of the stress. Therefore, the corresponding records have to be discarded.

iii/ the function s(t) must occupy the 4 quadrants of the complex plane, meaning that the voltage values must change sign within the period: an offset can be introduced on the voltage for data treatment purpose.

EXPERIMENTAL RESULTS

Some preliminary measurements are reported in the following in order to demonstrate the potentialities of the method. Experiments were carried in crosslinked Polyethylene (XLPE) samples in film form that were cut from HV-AC cables [START_REF] Fothergill | [END_REF] aged for 10 000 h under a field of ≈13kV/mm at room temperature. The sample thickness was about 150µm. Rolls have been stored for several years at room temperature. Without applying any stress, we observed that charges were present close to the surface of the investigated films (positive charge on one side; negative on the other side). For measurements, the films were not metallized; the electrodes used were formed by those of the PEA system, being a carbon-black reinforced PE for the upper electrode (put at HV) and aluminium for the lower electrode (at ground). The applied voltage was 6kV peak (representing a r.m.s. field of 28kV/mm). The pulse amplitude was set at 300V. The pictures shown in Figure 2 are 3-D plots of space charge profiles along one period of the AC stress, for frequencies of 0.5 and 50Hz. The measurement time was 18s for all. The method described above, based on Hilbert transform was used for data treatment. For the pattern obtained at 50Hz shown in Figure 2.b, one observes a negatively charged region close to the lower electrode (LE), and a positively charged region close to the upper electrode (UE). The amount of charge detected does not vary much along the period (this is visible here considering for example the negative charge density close to the LE when the latter is anode). When turning the sample over, Figure 2.c, we observe a change in the sign of charge (positive charge close to the LE, negative charge close to the UE), thus demonstrating that it is related to sample features and not to measurement artifacts. In addition, the polarity and position of the charges correspond to that measured before application of the stress.

When decreasing the AC frequency to 0.5Hz (Figure 2.a), the situation changes. When the LE is cathode, one observes a transit of negative charges towards the bulk of the insulation, which might correspond to negative charge injection during this half-period. At the crossover point at a phase of 180°, the density of negative charge is higher than at the same phase for a 50Hz stress. For the phase in the range 180 to 270°, the negative charge density progressively decreases, and finally vanishes during the end of the half-period (270-360°). It can therefore be concluded that, as expected, charge are generated and drift in the insulation all the more that the frequency is lower.

CONCLUSION

A method based on the pulsed electroacoustic technique for measuring space charge distribution under AC stress, and more generally under periodic stress of arbitrary waveform, at variable temperature and frequency has been settled. The main advantages of the method in respect to existing solutions are as follows:

-It can be readily applied to any periodic stress of arbitrary waveform; -It provides a very good resolution along the phase of the signal. Whereas previous reports refer to 16 points at most, we present here results with 200 points, a number which can be extended without difficulty.

-It can be applied to standard PEA test cells, without hardware modification and could find application to other techniques such as the PIPWP (Pressure-induced wave propagation method).

-There is no synchronization between pulse generation and HV stress, which provides flexibility when changing waveform; -The measurement time is minimized (and depends on the frequency of the pulse generator) since the pulse generator is used at his nominal frequency and all pulse responses are exploited. This opens the way to measurements for investigating the influence of the stress duration on the response. With the current hardware configuration, measurement along a single period is readily feasible only at low frequency (up to 50mHz), an upper limit that could be extended to 2.5Hz by using a higher frequency pulse generator (50 kHz instead of 1kHz) and still further by broadening the error interval set on V.

A wealth of new routes is open by measurements of space charge under non-DC stress: a better resolution of processes at play at the interfaces, the dynamic aspects associated with carriers, the low frequency limit and its implication for the DC situation, the impact of non sinusoidal stresses on materials being examples.

  Cite as: C. Thomas, G. Teyssedre, C. Laurent, "A new method for signal averaging resorting to space charge measurements by the pulsed electroacoustic method under AC stress", 9 th Int. Conf. on Solid Dielectrics (ICSD), Winchester, UK, 8-13 July 2007. Proc. ICSD-2007, pp. 490-493, 2007. DOI: 10.1109/ICSD.2007.4290857

  Cite as: C. Thomas, G. Teyssedre, C. Laurent, "A new method for signal averaging resorting to space charge measurements by the pulsed electroacoustic method under AC stress", 9 th Int. Conf. on Solid Dielectrics (ICSD), Winchester, UK, 8-13 July 2007. Proc. ICSD-2007, pp. 490-493, 2007. DOI: 10.1109/ICSD.2007.4290857

Figure 1 :

 1 Figure 1 : Principle of the Hilbert transform. (a) example of 1 Hz frequency HV stress applied to the sample; (b) representation of the function s(t) in the Nyquist plane. (c) Phase of data shown in (a) as a function of time; (d) Phase vs. cumulative number of records obtained in a full sequence.

Figure 2 :

 2 Figure 2 : 3D space charge distribution under AC voltage (peak voltage Vp=6kV) obtained on XLPE. (a) f=0.5Hz; (b) f=50Hz; (c) f=50Hz after turning the sample over. LE and UE refer to lower (at ground) and upper (at HV) electrodes, respectively. At phase 90°, the voltage on the UE is at +Vp. The bar indicates charge density (in C/m³).

LE

  Cite as: C. Thomas, G. Teyssedre, C. Laurent, "A new method for signal averaging resorting to space charge measurements by the pulsed electroacoustic method under AC stress", 9 th Int. Conf. on Solid Dielectrics (ICSD), Winchester, UK, 8-13 July 2007. Proc. ICSD-2007, pp. 490-493, 2007. DOI: 10.1109/ICSD.2007.4290857