Reliability of PEA Measurement in Presence of an Air Void Defect

This paper deals with the reliability of the Pulsed Electro-Acoustic (PEA) technique in the case of a specimen containing an air layer. The first approach to this study has been proposed by the authors in previously published works. In these papers, the mathematical description, the PEA cell simulation model, and some experimental tests have been reported. In this work, a more accurate description of the acoustic wave behavior within the PEA cell and specimen with and without an air layer is given. Moreover, the comparison between simulation and experimental tests for both cases (specimen with and without air layer) allowed the validation of the previously developed PEA cell simulation model. The latter was previously validated only for a single layer specimen, here the good performances of the model have also been confirmed in the case of a multilayer specimen, also with an air layer. Experimental and simulation results show that the air layer acts as a barrier for the acoustic signal, due to the different acoustic impedance between the air and the solid dielectric material which constitute the specimen. Therefore, the aim of the present work is to demonstrate that in the case of a three-layers specimen, composed as dielectric-air-dielectric, the PEA cell is not able to provide the complete profile of the entire specimen under test.


Introduction
The Pulsed Electro-Acoustic (PEA) is the most used technique for measuring the accumulation of space charge in solid dielectrics [1]. This measurement technique is quite consolidated especially for testing single layer specimens [2]. Nevertheless, during the years, several experimental tests were carried out in specimens composed of multiple layers [3][4][5]. This was with the aim to analyze the accumulation of space charge in samples simulating the different High Voltage Direct Current (HVDC) components, e.g., cables and joints [6][7][8].
However, measurements in real components have also been made with different types of PEA cells. Hozumi in [9] measured the space charge in a cable specimen, while Takeda in [10] proposed the measure of space charge in a full-size cable. Further PEA cell types, named 2-D and 3-D PEA, have been developed for testing other kinds of specimens, e.g., the joints [1].
With reference to the space charge measurement in multilayer flat specimens, two-or three-layered samples are typically tested. In these specimens, due to the different acoustic impedances between the multiple layers placed in contact with each other, careful attention must be paid to the reflection phenomenon of the acoustic waves [11,12]. If the reflected waves are not taken into account, the obtained space charge profile could be incorrectly interpreted [13].
Based on the reflection phenomenon mentioned above, the authors proposed several works, as well as a MATLAB model simulating the acoustic wave behavior within the PEA cell [13][14][15][16][17][18].
In the previously published works, authors have shown that each PEA cell (on the basis of its ground electrode and absorber thicknesses) is suitable to measure space charge on dielectrics with sound velocity and thickness in a fixed range of values [18,19]. If the sample's features fall outside the range allowed by the adopted PEA cell, a certain amount of reflected signals are present within the main space charge profile. Therefore, the PEA cell output signal results are disturbed and the real charge distribution is difficult to interpret. This aspect has also been recently demonstrated by several studies in [20,21].
As is well known, over the space charge phenomenon, the partial discharge phenomena represent the further main degradation factor for the insulators employed in the field of High Voltage Direct Current (HVDC) systems. Considering that the trigger of the discharge needs the availability of electrons, both of the above-mentioned phenomena are strongly correlated [22][23][24][25][26][27][28].
In recent papers, with the aim to simultaneously measure space charge and partial discharge, specimens containing an air layer have been investigated. In particular, the study of the acoustic wave behavior followed by experimental tests has been carried out in specimens with a configuration of dielectric-air-dielectric [13,29].
In these works, authors found that due to the reflection and transmission coefficients of the air layer in contact with a dielectric material, the reflection phenomenon is strongly accentuated.
What was previously obtained has been confirmed in the present paper, where was also found that the air layer acts as a barrier for the acoustic wave.
Based on the above, the aim of this work is to demonstrate that in the case of a specimen containing an air layer, it is not possible to perform the measurement of the space charge with the PEA method. Compared to the previously published works [13,29] where only experimental tests and a brief theoretical description were given, here a detailed study and analysis of the behavior of the wave are provided, as well as simulations and experimental tests for different multilayer specimens configurations, in order to confirm the predicted behavior.
Concerning the PEA cell simulation model, it has already been widely explained and validated for a single layer specimen [14]. In the present work, it is used to confirm the predictable and obtainable experimental behaviors, thus only the simulation results are reported.
In this way, the validation of the developed model in the case of a multilayer specimen has also been carried out.

Mathematical Model
In Figure 1, the block diagram of the PEA cell with a multilayer specimen composed of three layers is reported.
The generators HVDC and e p (t) are the high voltage and the pulse voltage sources, respectively. The resistor R is inserted for the protection of the HVDC generator, while C is the decoupling capacitor between the two generators. The HVDC generator, applied by means of the HV and ground electrode, is used to promote the charge accumulation, while e p (t) allows the charges vibration. Due to the charges vibration, acoustic waves are generated from each charge.
These waves travel within the PEA cell and reach the sensor which converts the acoustic wave into the electrical signal. The latter has a very low magnitude, thus an amplifier is used to increase its voltage level. The absorber component, which is mechanically protected by the bottom electrode, has the task of absorbing the waves passing through the sensor, with the purpose of attenuating the magnitude of reflected waves [1,2].

Acoustic Wave Behavior Within the PEA Cell
The acoustic wave behavior within the PEA cell is characterized by the reflection phenomenon. When an acoustic wave, starting from the deposited charges, reaches an interface, the behavior changes due to the resulting partial transmission and partial reflection of the acoustic wave. This is caused by the mismatch of different acoustic impedance Z values (given by the product between the sound velocity v and density ρ) of the different materials placed in contact with each other [11].
In each PEA cell components interface, included the specimen, the transmission , and the reflection coefficients are calculated as: where, the subscript i indicates the material from which the wave is generated or comes from, while the subscript j indicates the material the wave is traveling to.
To evaluate the presence of reflected waves in the main charge profile, the time t (depending on the sound velocity v and thickness d) needed across each PEA cell component and specimen also has to be taken into account.
The knowledge of the acoustic wave behavior within the PEA cell, as well as inside the specimen under test, is important for the correct interpretation of the obtained space charge profile. Thanks to this preliminary study, the reflected waves can be identified and separated from the main space charge signal. The main charge distribution, considering only the accumulated surface charge in the dielectric interfaces, is composed of only two peaks in the case of a single layer specimen. For two or three layers specimens, instead, the number of main charge peaks is equal to three or four, respectively. If some reflected waves fall inside the main charge profile, further peaks will be present in the PEA cell output signal. This phenomenon occurs for two main causes, such as the PEA cell components dimensions (ground electrode, sensor, and absorber thicknesses) and the specimen features, such as thickness and sound velocity. However, each PEA cell allows us to correctly measure the accumulated charge (without reflected signal) in specimens of dielectric material with features in a specific range of values. To facilitate the choice of sample features based on the used PEA cell, some useful graphs have been reported in a previously published work [18,19].
Moreover, a simulation model of the acoustic wave behavior within the PEA cell has been realized and proposed in [14]. It is able to provide the PEA cell output signal composed of the main charge peaks and, if present, the reflected waves. This simulation model will be used in the present work in order to compare simulation results with experimental tests for the different specimen configurations.

Acoustic Wave Behavior Within the PEA Cell
The acoustic wave behavior within the PEA cell is characterized by the reflection phenomenon. When an acoustic wave, starting from the deposited charges, reaches an interface, the behavior changes due to the resulting partial transmission and partial reflection of the acoustic wave. This is caused by the mismatch of different acoustic impedance Z values (given by the product between the sound velocity v and density ρ) of the different materials placed in contact with each other [11].
In each PEA cell components interface, included the specimen, the transmission K T , and the reflection K R coefficients are calculated as: where, the subscript i indicates the material from which the wave is generated or comes from, while the subscript j indicates the material the wave is traveling to.
To evaluate the presence of reflected waves in the main charge profile, the time t (depending on the sound velocity v and thickness d) needed across each PEA cell component and specimen also has to be taken into account.
The knowledge of the acoustic wave behavior within the PEA cell, as well as inside the specimen under test, is important for the correct interpretation of the obtained space charge profile. Thanks to this preliminary study, the reflected waves can be identified and separated from the main space charge signal. The main charge distribution, considering only the accumulated surface charge in the dielectric interfaces, is composed of only two peaks in the case of a single layer specimen. For two or three layers specimens, instead, the number of main charge peaks is equal to three or four, respectively. If some reflected waves fall inside the main charge profile, further peaks will be present in the PEA cell output signal. This phenomenon occurs for two main causes, such as the PEA cell components dimensions (ground electrode, sensor, and absorber thicknesses) and the specimen features, such as thickness and sound velocity. However, each PEA cell allows us to correctly measure the accumulated charge (without reflected signal) in specimens of dielectric material with features in a specific range of values. To facilitate the choice of sample features based on the used PEA cell, some useful graphs have been reported in a previously published work [18,19].
Moreover, a simulation model of the acoustic wave behavior within the PEA cell has been realized and proposed in [14]. It is able to provide the PEA cell output signal composed of the main charge peaks and, if present, the reflected waves. This simulation model will be used in the present work in order to compare simulation results with experimental tests for the different specimen configurations.

Measurement Procedure and Specimens Under Test
As reported in the introduction section, the aim of this work is to show that the PEA method is not suitable to measure space charges in the case of multilayer specimens containing an air void. This is because the air layer acts as a barrier for the acoustic waves and thus some charge signals are not able to be detected by the piezoelectric sensor.
In order to demonstrate this, specimens with and without air layers have been considered. Firstly, the acoustic wave behavior has been analyzed in a three-layer PET-PET-PET specimen. This specimen has been investigated for two main reasons, such as the validation of our PEA cell simulation model for three layers specimens and for the comparison with the specimen having an air void. After that, in order to show the inability of the PEA method to measure space charge in case of a specimen containing an air void, a three-layer PET-AIR-PET specimen has been analyzed.
In the proposed study, the presence and the position of the main charge peaks (such as those due to the charge accumulated in the specimen interfaces) and their reflection have been widely investigated. Therefore, the specimens under test have been subjected to the DC voltage with a magnitude value able to generate only the interfacial charges. The applied DC stress is 13 kV for both specimen configurations, while the magnitude of the pulse voltage is fixed to 500 V.
For each specimen, the mathematical description of the acoustic wave behavior and the obtained PEA cell output signal in both experimental and simulation tests have been reported.

Experimental Test
The PEA cell adopted in our experimental test is represented by the block diagram reported in Figure 1. For the knowledge of the acoustic wave behavior, some geometrical dimensions and physical features of the PEA cell components need to be taken into account. This information, also for the specimen under test, is reported in Table 1. As can be seen, the HV and Bottom electrodes are not inserted in Table 1, this is because the acoustic waves affecting these components do not influence the main PEA cell output signal. This aspect will be more comprehensible in the later paragraphs. For a complete description of the wave behavior, the time τ needed for the acoustic waves to travel within each PEA cell component and dielectric layer must be taken into account. Therefore, it has also been inserted in the last row of Table 1.
Based on the information above, the description of each acoustic wave, which starts from the different interfaces between two materials placed in contact with each other, can be easily done. In fact, it is only necessary to know the time, indicated with τ in the table, and the transmission K T and reflection K R coefficients (calculated as in Equation (1)) of each interface.

Three Layers Specimen, the PET-PET-PET Configuration
The three layers specimen is widely employed by researchers to measure the charge accumulation in configurations simulating cables, joints, and terminations. For the partial discharge analysis, instead, an air layer is inserted between two layers of solid dielectric in order to simulate internal discharges. In a recent paper published by the authors, as well as in other works present in technical literature, the three layers specimen with an air void defect has been adopted to simultaneously measure the partial discharge and the space charge [29]. In literature, this type of specimen configuration has been inserted in the PEA cell in order to measure the accumulated charge before, during, or after the discharges events [30,31]. As reported in the introduction section, the aim of this work is to demonstrate that in the case of an air layer the PEA cell output signal does not represent the real accumulated charge. This can be confirmed for two reasons, such as the barrier effect of the air layer for the acoustic waves and the very low acoustic wave generation coefficient in the dielectric/air interface.
Initially, the acoustic wave behavior was investigated for the three layers PET-PET-PET specimen, without the presence of air void. Despite multilayer specimens made of the same dielectric material not typically being investigated, in our work the results are useful for the comparison with the PET-AIR-PET configuration. In this way, the effect of the air layer on the PEA cell output signal is more understandable.
The scheme of the specimen under test inserted between the electrodes of the PEA cell is shown in Figure 2, while the experimental PEA cell output signal is reported in Figure 3.
the dielectric/air interface.
Initially, the acoustic wave behavior was investigated for the three layers PET-PET-PET specimen, without the presence of air void. Despite multilayer specimens made of the same dielectric material not typically being investigated, in our work the results are useful for the comparison with the PET-AIR-PET configuration. In this way, the effect of the air layer on the PEA cell output signal is more understandable.
The scheme of the specimen under test inserted between the electrodes of the PEA cell is shown in Figure 2, while the experimental PEA cell output signal is reported in Figure 3.
As is well known, in the case of a specimen made of the same dielectric material, in the ideal case the interfacial charges should be equal to zero. However, due to the use of silicon oil and the imperfect contact between the dielectric layers, a certain amount of interfacial charge has been observed.
For a better interpretation of the PEA output signal of Figure 3, an analysis of the acoustic wave is needed. First of all, the transmission and reflection coefficients in each PEA cell components and specimen interfaces have been calculated by means of equation 1 and reported in Figure 4.
Based on these values, including those reported in Table 1, the acoustic wave behavior within the PEA cell and the specimen can be described as shown in Figure 5. As can be seen in Figure 4, due to the same dielectric material used for the specimen, the transmission coefficient between each PET/PET interface is equal to 1. This means that the acoustic wave passing through the two layers of PET in contact with each other is totally transmitted. Meanwhile, the reflection coefficient in the same PET/PET interfaces is equal to 0. By observing Figures 3 and 5, the first acoustic wave reaching the sensor is provided by the charges accumulated in the PET-3/Ground electrode interface. In particular, it needs a time equal to  = 1.56 μs to reach the sensor, which is the time needed to cross the ground electrode of the PEA cell (see Table 1), while the waves named and , due to the interfacial charges accumulated in the PET-2/PET-3 and PET-1/PET-2 interfaces, are sensed by the sensor after  +  = 1.6 μs and  +  +  = 1.64 μs, respectively. The last acoustic wave, named , reaches the sensor at 3 +  = 1.68 μs.  Based on this study it is possible to confirm that our PEA cell (with its specific components features) is able to correctly measure the space charge in a three layers specimen. The obtained charge distribution and the study of the acoustic wave behavior result are simply to be carried out thanks to the specimen made of the same dielectric material. In the case of a layer different from the other two characterizing the three layers specimen, the reflection phenomenon occurs and thus the charge pattern interpretation results more complicated. As is well known, in the case of a specimen made of the same dielectric material, in the ideal case the interfacial charges should be equal to zero. However, due to the use of silicon oil and the imperfect contact between the dielectric layers, a certain amount of interfacial charge has been observed.
For a better interpretation of the PEA output signal of Figure 3, an analysis of the acoustic wave is needed. First of all, the transmission K T and reflection K R coefficients in each PEA cell components and specimen interfaces have been calculated by means of equation 1 and reported in Figure 4.
Based on these values, including those reported in Table 1, the acoustic wave behavior within the PEA cell and the specimen can be described as shown in Figure 5.
As can be seen in Figure 4, due to the same dielectric material used for the specimen, the transmission coefficient K T between each PET/PET interface is equal to 1. This means that the acoustic wave passing through the two layers of PET in contact with each other is totally transmitted. Meanwhile, the reflection coefficient in the same PET/PET interfaces is equal to 0.
Based on this study it is possible to confirm that our PEA cell (with its specific components features) is able to correctly measure the space charge in a three layers specimen. The obtained charge distribution and the study of the acoustic wave behavior result are simply to be carried out thanks to the specimen made of the same dielectric material. In the case of a layer different from the other two characterizing the three layers specimen, the reflection phenomenon occurs and thus the charge pattern interpretation results more complicated. In order to investigate and validate, for multilayer specimens, the previously realized PEA cell simulation software [14] has been employed, and in Figure 6 the simulated PEA cell output signal for the specimen configuration, described in Figures 2 and 5, is reported.
By making a comparison between Figures 3 and 6 (taking also into consideration the waves, named in Figure 5) a good similarity can be observed. In particular, the validation of the model can be confirmed because the polarity and the position of the charge peaks are the same in both patterns.
The differences in the magnitude of the peak do not represent a problem for our aims. However, it could be overcome by knowing the correct attenuation coefficient value of the dielectric material under test. In addition, it is possible to see that in the experimental pattern of Figure 3, the signal between two peaks is different from zero. This is the signal depicted by the oscilloscope, where the deconvolution process has not been applied. On the contrary, in our model, the effect of the RC filter that causes the signal distortion was not implemented, therefore, in the pattern of Figure 6, the signal between two peaks is equal to zero [32].  The distribution of the charge and its sign, found in both experimental and simulation tests, have been validated by making a comparison with the charge profile detected in a multilayer specimen by R. Zou et al. in [33].   By observing Figures 3 and 5, the first acoustic wave reaching the sensor is provided by the charges accumulated in the PET-3/Ground electrode interface. In particular, it needs a time equal to τ GR = 1.56 µs to reach the sensor, which is the time needed to cross the ground electrode of the PEA cell (see Table 1), while the waves named p 2−3 and p 1−2 , due to the interfacial charges accumulated in the PET-2/PET-3 and PET-1/PET-2 interfaces, are sensed by the sensor after τ A + τ GR = 1.6 µs and τ A + τ A + τ GR = 1.64 µs, respectively. The last acoustic wave, named p + , reaches the sensor at 3τ A + τ GR = 1.68 µs.

Three Layers Specimen, the PET-AIR-PET Configuration
Based on this study it is possible to confirm that our PEA cell (with its specific components features) is able to correctly measure the space charge in a three layers specimen. The obtained charge distribution and the study of the acoustic wave behavior result are simply to be carried out thanks to the specimen made of the same dielectric material. In the case of a layer different from the other two characterizing the three layers specimen, the reflection phenomenon occurs and thus the charge pattern interpretation results more complicated.
In order to investigate and validate, for multilayer specimens, the previously realized PEA cell simulation software [14] has been employed, and in Figure 6 the simulated PEA cell output signal for the specimen configuration, described in Figures 2 and 5, is reported.

Three Layers Specimen, the PET-AIR-PET Configuration
As previously explained, the three-layer specimen made of two layers of solid dielectric and a layer of air interposed between them is a configuration widely investigated by researchers. With reference to the measure of space charge, this specimen configuration has been used to evaluate the effect of charges on the partial discharge, and vice-versa. However, considering the different acoustic impedance of the air layer with respect to other dielectric materials that make up the specimen, the wave reflection phenomenon is strongly present. Therefore, an accurate study of the acoustic wave behavior is essential to avoid an incorrect interpretation of the obtained charge distribution.
Based on the above, in the following three-layer PET-AIR-PET specimen, with configuration reported in Figure 7, has been investigated.
The PEA cell output signal provided by the oscilloscope is shown in Figure 8. By observing the pattern of Figure 8, seems that the four peaks are associated with the charges accumulated in the four specimen interfaces, as in Figure 5 but with different charge signs. In reality, some peaks are reflected signals that can be easily confused with the accumulated charge. In particular, the first and the second peak are due to the interfacial charge accumulated in the PET/Ground electrode and AIR/PET interfaces, while, the other two peaks are due to the reflection of acoustic waves within the PET layer in contact with the ground electrode. A detailed explanation is given below. By making a comparison between Figures 3 and 6 (taking also into consideration the waves, named in Figure 5) a good similarity can be observed. In particular, the validation of the model can be confirmed because the polarity and the position of the charge peaks are the same in both patterns.
The differences in the magnitude of the peak do not represent a problem for our aims. However, it could be overcome by knowing the correct attenuation coefficient value of the dielectric material under test. In addition, it is possible to see that in the experimental pattern of Figure 3, the signal between two peaks is different from zero. This is the signal depicted by the oscilloscope, where the deconvolution process has not been applied. On the contrary, in our model, the effect of the RC filter that causes the signal distortion was not implemented, therefore, in the pattern of Figure 6, the signal between two peaks is equal to zero [32].
The distribution of the charge and its sign, found in both experimental and simulation tests, have been validated by making a comparison with the charge profile detected in a multilayer specimen by R. Zou et al. in [33].

Three Layers Specimen, the PET-AIR-PET Configuration
As previously explained, the three-layer specimen made of two layers of solid dielectric and a layer of air interposed between them is a configuration widely investigated by researchers. With reference to the measure of space charge, this specimen configuration has been used to evaluate the effect of charges on the partial discharge, and vice-versa. However, considering the different acoustic impedance of the air layer with respect to other dielectric materials that make up the specimen, the wave reflection phenomenon is strongly present. Therefore, an accurate study of the acoustic wave behavior is essential to avoid an incorrect interpretation of the obtained charge distribution.
Based on the above, in the following three-layer PET-AIR-PET specimen, with configuration reported in Figure 7, has been investigated.  For this specimen, as in the previous case, the transmission and reflection coefficients have been calculated in each interface. For the entire PEA cell, the values of and are the same as those reported in Figure 4. The same is also the values of and , calculated in the HV/PET and PET/Ground electrode interfaces. In the PET/AIR and AIR/PET interface, instead, the values are different from the previous case and they are reported in Figure 9.
The analysis of the values reported in Figure 9 confirms that the air layer acts as a barrier for the acoustic waves. In particular, in the PET-1/AIR interface, is equal to 2.3•10 −4 for the acoustic waves coming from the PET-1 and directed towards the AIR layer. This means that only 0.023% of the wave is transmitted in the sensor direction, while, 99% is reflected in the opposite direction, due to the value of = −0.99. The negative sign of means that when the wave is reflected, it goes back in the opposite direction with respect to the incident wave.
In the AIR/PET-3 interface, for the wave coming from the AIR layer and directed towards the PET material, = 2 and = 0.99. Therefore, the part of the acoustic wave able to cross this interface is given by − = 1.01, such as 101%. This means that the wave is totally transmitted and a bit amplified, thus this interface result is not influential for the wave behavior.
Based on the explanation above, the complete acoustic wave behavior in the PET-AIR-PET specimen can be schematically described as in Figure 10.
By observing Figure 10 and taking into account the time values reported in Table 1, the sequence of the acoustic waves that reach the piezoelectric sensor can be described as follows.
First of all, as in the previous case of Figure 5, the acoustic wave generated in the PET-3/Ground electrode interface, named , reaches the sensor at a time τ =  = 1.56 μs. After that, the green acoustic wave, which is due to the charge accumulated in the AIR/PET-3 interface, is sensed by the sensor after τ =  +  = 1.60 μs.
Before describing the behavior of the other acoustic waves, it is important to explain the acoustic wave generation. In particular, when a charge is subjected to vibrations, two acoustic waves with opposite polarity are simultaneously generated. If the charge has a positive sign, a positive acoustic wave is generated and directed toward the sensor. Simultaneously, a negative acoustic wave is generated and directed in the opposite direction. On the contrary, if the accumulated charge has a negative sign, the wave directed towards the sensor is negative, while that directed in the opposite direction is positive. For this last case, Figure 11 can be observed. The PEA cell output signal provided by the oscilloscope is shown in Figure 8.  For this specimen, as in the previous case, the transmission and reflection coefficients have been calculated in each interface. For the entire PEA cell, the values of and are the same as those reported in Figure 4. The same is also the values of and , calculated in the HV/PET and PET/Ground electrode interfaces. In the PET/AIR and AIR/PET interface, instead, the values are different from the previous case and they are reported in Figure 9.
The analysis of the values reported in Figure 9 confirms that the air layer acts as a barrier for the acoustic waves. In particular, in the PET-1/AIR interface, is equal to 2.3•10 −4 for the acoustic waves coming from the PET-1 and directed towards the AIR layer. This means that only 0.023% of the wave is transmitted in the sensor direction, while, 99% is reflected in the opposite direction, due to the value of = −0.99. The negative sign of means that when the wave is reflected, it goes back in the opposite direction with respect to the incident wave.
In the AIR/PET-3 interface, for the wave coming from the AIR layer and directed towards the PET material, = 2 and = 0.99. Therefore, the part of the acoustic wave able to cross this interface is given by − = 1.01, such as 101%. This means that the wave is totally transmitted and a bit amplified, thus this interface result is not influential for the wave behavior.
Based on the explanation above, the complete acoustic wave behavior in the PET-AIR-PET specimen can be schematically described as in Figure 10.
By observing Figure 10 and taking into account the time values reported in Table 1, the sequence of the acoustic waves that reach the piezoelectric sensor can be described as follows.
First of all, as in the previous case of Figure 5, the acoustic wave generated in the PET-3/Ground electrode interface, named , reaches the sensor at a time τ =  = 1.56 μs. After that, the green acoustic wave, which is due to the charge accumulated in the AIR/PET-3 interface, is sensed by the sensor after τ =  +  = 1.60 μs.
Before describing the behavior of the other acoustic waves, it is important to explain the acoustic wave generation. In particular, when a charge is subjected to vibrations, two acoustic waves with opposite polarity are simultaneously generated. If the charge has a positive sign, a positive acoustic wave is generated and directed toward the sensor. Simultaneously, a negative acoustic wave is generated and directed in the opposite direction. On the contrary, if the accumulated charge has a negative sign, the wave directed towards the sensor is negative, while that directed in the opposite direction is positive. For this last case, Figure 11 can be observed. By observing the pattern of Figure 8, seems that the four peaks are associated with the charges accumulated in the four specimen interfaces, as in Figure 5 but with different charge signs. In reality, some peaks are reflected signals that can be easily confused with the accumulated charge. In particular, the first and the second peak are due to the interfacial charge accumulated in the PET/Ground electrode and AIR/PET interfaces, while, the other two peaks are due to the reflection of acoustic waves within the PET layer in contact with the ground electrode. A detailed explanation is given below.
For this specimen, as in the previous case, the transmission and reflection coefficients have been calculated in each interface. For the entire PEA cell, the values of K T and K R are the same as those reported in Figure 4. The same is also the values of K T and K R , calculated in the HV/PET and PET/Ground electrode interfaces. In the PET/AIR and AIR/PET interface, instead, the values are different from the previous case and they are reported in Figure 9.  The analysis of the values reported in Figure 9 confirms that the air layer acts as a barrier for the acoustic waves. In particular, in the PET-1/AIR interface, K T is equal to 2.3·10 −4 for the acoustic waves coming from the PET-1 and directed towards the AIR layer. This means that only 0.023% of the wave is transmitted in the sensor direction, while, 99% is reflected in the opposite direction, due to the value of K R = −0.99. The negative sign of K R means that when the wave is reflected, it goes back in the opposite direction with respect to the incident wave. In the AIR/PET-3 interface, for the wave coming from the AIR layer and directed towards the PET material, K T = 2 and K R = 0.99. Therefore, the part of the acoustic wave able to cross this interface is given by K T − K R = 1.01, such as 101%. This means that the wave is totally transmitted and a bit amplified, thus this interface result is not influential for the wave behavior.
Based on the explanation above, the complete acoustic wave behavior in the PET-AIR-PET specimen can be schematically described as in Figure 10.  Based on the above, it is possible to say that the negative interfacial charge deposited in the PET-3/Ground electrode interface generates a positive acoustic wave which travels in the opposite direction. This wave, depicted in orange color, when reaches the AIR/PET-3 interface is for the 99% reflected in the sensor direction. Moreover, the negative value of = −0.99 (see Figure 9) means that during the reflection the sign of the wave is also inverted. To better understand what happened in this interface the screenshot of the dynamic simulation provided by our PEA cell model, is shown in Figure 12 [34]. In particular, the simulation has been stopped and printed at time zero (such as the same time instant of Figure 11) and after 0.064 μs (such as the time needed for the acoustic wave to reach the interface and be reflected).
However, the orange acoustic wave with negative polarity, named , reaches the sensor after τ = 2 +  = 1.64 μs.   Table 1, the sequence of the acoustic waves that reach the piezoelectric sensor can be described as follows.
First of all, as in the previous case of Figure 5, the acoustic wave generated in the PET-3/Ground electrode interface, named p − , reaches the sensor at a time τ = τ GR = 1.56 µs. After that, the green acoustic wave, which is due to the charge accumulated in the AIR/PET-3 interface, is sensed by the sensor after τ = τ A + τ GR = 1.60 µs.
Before describing the behavior of the other acoustic waves, it is important to explain the acoustic wave generation. In particular, when a charge is subjected to vibrations, two acoustic waves with opposite polarity are simultaneously generated. If the charge has a positive sign, a positive acoustic wave is generated and directed toward the sensor. Simultaneously, a negative acoustic wave is generated and directed in the opposite direction. On the contrary, if the accumulated charge has a negative sign, the wave directed towards the sensor is negative, while that directed in the opposite direction is positive. For this last case, Figure 11 can be observed.  Based on the above, it is possible to say that the negative interfacial charge deposited in the PET-3/Ground electrode interface generates a positive acoustic wave which travels in the opposite direction. This wave, depicted in orange color, when reaches the AIR/PET-3 interface is for the 99% reflected in the sensor direction. Moreover, the negative value of = −0.99 (see Figure 9) means that during the reflection the sign of the wave is also inverted. To better understand what happened in this interface the screenshot of the dynamic simulation provided by our PEA cell model, is shown in Figure 12 [34]. In particular, the simulation has been stopped and printed at time zero (such as the same time instant of Figure 11) and after 0.064 μs (such as the time needed for the acoustic wave to reach the interface and be reflected).
However, the orange acoustic wave with negative polarity, named , reaches the sensor after τ = 2 +  = 1.64 μs.  Based on the above, it is possible to say that the negative interfacial charge deposited in the PET-3/Ground electrode interface generates a positive acoustic wave which travels in the opposite direction. This wave, depicted in orange color, when reaches the AIR/PET-3 interface is for the 99% reflected in the sensor direction. Moreover, the negative value of K R = −0.99 (see Figure 9) means that during the reflection the sign of the wave is also inverted. To better understand what happened in this interface the screenshot of the dynamic simulation provided by our PEA cell model, is shown in Figure 12 [34]. In particular, the simulation has been stopped and printed at time zero (such as the same time instant of Figure 11) and after 0.064 µs (such as the time needed for the acoustic wave to reach the interface and be reflected).
Energies 2020, 13, x FOR PEER REVIEW 10 of 14 Finally, the fourth peak in the pattern of Figure 8 is due to the reflection within the PET-3 layers of the acoustic wave generated by the positive charge deposited in the AIR/PET-3 interface. In Figure  10, this wave is highlighted in the brown color and named . By observing Figure 10, when the green acoustic wave reaches the PET-3/Ground electrode interface, it is partially transmitted and partially reflected. The reflected part is equal to 66% (see Figure 4) of the incident wave. Therefore, it goes back to maintaining the positive polarity (as the generated wave) and when it reaches the AIR/PET-3 interface is reflected again in the sensor direction. In this interface = −0.99 and thus, as for the previous orange wave, the polarity of the wave is inverted. In conclusion, after τ = 3 +  = 1.68 μs, the brown acoustic wave, with negative polarity, reaches the sensor. As can be seen, the calculated value (1.68 μs) is a bit different from that observed in the oscilloscope, which is around 1.69 μs (see Figure 8). This difference can be attributed to the wave propagation delay during the reflection, which is not taken into account in our calculations. With reference to the acoustic wave generated by the charge deposited in the PET-1/AIR interface, based on the time values reported in Table 1, it should reach the sensor after τ =  +  +  = 1.91 μs. However, we use the dashed (and violet) line because no peaks were observed in that instant of time. This is due to the acoustic wave generation coefficient , calculated as in equation 2, which for the PET-1/AIR interface is equal to 0.00012. However, the generated acoustic wave in this interface has a very low magnitude and thus, due to the attenuation coefficient of the materials involved in the wave path, no signal is sensed by the sensor. On the contrary, in the AIR/PET-3 and PET-3/Ground electrode interface, the values of are equal to 0.99 and 0.82, respectively.
Concerning the acoustic wave generated by the charge deposited in the HV electrode/PET-1 interface, the value of is equal to 17% of the incident pulse voltage. Despite this value being low, the generated wave is able to be detected by the sensor. However, as previously widely explained, the barrier effect of the air layer forces the acoustic wave to reflect itself within the PET-1 layer. Therefore, this wave, depicted in the dashed red line, also cannot reach the sensor.
The PET-AIR-PET specimen above described has been implemented in the PEA cell simulation model. The simulated result is reported in Figure 13. The comparison between the simulated and experimental (see Figure 8) profiles confirms the good performances of the developed model for specimens in which an air layer is present. The differences between the simulated and the experimental patterns have been already explained for the previously analyzed PET-PET-PET specimen. However, the orange acoustic wave with negative polarity, named p R − , reaches the sensor after τ = 2τ A + τ GR = 1.64 µs.
Finally, the fourth peak in the pattern of Figure 8 is due to the reflection within the PET-3 layers of the acoustic wave generated by the positive charge deposited in the AIR/PET-3 interface. In Figure 10, this wave is highlighted in the brown color and named p R A−3 . By observing Figure 10, when the green acoustic wave reaches the PET-3/Ground electrode interface, it is partially transmitted and partially reflected. The reflected part is equal to 66% (see Figure 4) of the incident wave. Therefore, it goes back to maintaining the positive polarity (as the generated wave) and when it reaches the AIR/PET-3 interface is reflected again in the sensor direction. In this interface K R = −0.99 and thus, as for the previous orange wave, the polarity of the wave is inverted. In conclusion, after τ = 3τ A + τ GR = 1.68 µs, the brown acoustic wave, with negative polarity, reaches the sensor. As can be seen, the calculated value (1.68 µs) is a bit different from that observed in the oscilloscope, which is around 1.69 µs (see Figure 8). This difference can be attributed to the wave propagation delay during the reflection, which is not taken into account in our calculations.
With reference to the acoustic wave generated by the charge deposited in the PET-1/AIR interface, based on the time values reported in Table 1, it should reach the sensor after τ = τ B + τ A + τ GR = 1.91 µs. However, we use the dashed (and violet) line because no peaks were observed in that instant of time. This is due to the acoustic wave generation coefficient K G , calculated as in equation 2, which for the PET-1/AIR interface is equal to 0.00012. However, the generated acoustic wave in this interface has a very low magnitude and thus, due to the attenuation coefficient of the materials involved in the wave path, no signal is sensed by the sensor. On the contrary, in the AIR/PET-3 and PET-3/Ground electrode interface, the values of K G are equal to 0.99 and 0.82, respectively.

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Concerning the acoustic wave generated by the charge deposited in the HV electrode/PET-1 interface, the value of K G is equal to 17% of the incident pulse voltage. Despite this value being low, the generated wave is able to be detected by the sensor. However, as previously widely explained, the barrier effect of the air layer forces the acoustic wave to reflect itself within the PET-1 layer. Therefore, this wave, depicted in the dashed red line, also cannot reach the sensor.
The PET-AIR-PET specimen above described has been implemented in the PEA cell simulation model. The simulated result is reported in Figure 13. The comparison between the simulated and experimental (see Figure 8) profiles confirms the good performances of the developed model for specimens in which an air layer is present. The differences between the simulated and the experimental patterns have been already explained for the previously analyzed PET-PET-PET specimen.

Results Discussion
It has been shown by means of the presented study that the PEA technique is not suitable for testing multilayer specimen in which an air layer is present. This is due to the barrier effect of the air material. In particular, the strongly accentuated acoustic wave reflection phenomenon in the air/solid dielectric interfaces is caused by the high difference of the acoustic impedance Z. In fact, in our case, Zair = 421.4 kg/m 2 s while ZPET = 3.5 × 10 6 kg/m 2 s. These values, in turn, generate a high acoustic wave reflection coefficient and a very low acoustic wave transmission coefficient , in the same interface. Therefore, for the acoustic waves traveling within the PEA cell, it is difficult to reach the piezoelectric sensor because they are reflected in the opposite direction. Despite not being demonstrated in this work, the same phenomenon can be also observed when the air layer is placed in contact with the ground electrode of the PEA cell. This is because the acoustic impedance of the aluminum material is much higher than that of air (Zaluminum = 17 × 10 6 kg/m 2 s).
Based on the obtained results, in order to avoid incorrect interpretation of the charge distribution provided by the PEA cell, the authors suggest that the PEA is a preliminary evaluation of the acoustic wave behavior.

Conclusions
The purpose of this work was to demonstrate that for a specimen containing an air layer, the space charge measurement with the PEA method cannot be correctly made. The motivation that pushed the authors to this study derived from several failed attempts in which the simultaneous detection of the space charge and partial discharges was attempted. In particular, we published some papers in which the charge signal has been detected in a specimen containing an air void. However, after further subsequent studies where the acoustic wave behavior has been widely investigated, it was understood that the previously obtained and published charge profiles were not correctly interpreted. In reality, as reported in the present work, we found that the air layer acts as a barrier for the acoustic wave due to its acoustic impedance values. In the proposed experimental test, in fact, by taking into consideration the generation , transmission and reflection coefficients calculated in each specimen interface the following numerical values have been found. In the PET-1/air interface = −0.99 and = 2.3 × 10 −4 , this means that the acoustic wave reaching this interface is almost totally reflected in the HV electrode direction. In the AIR/PET-3 interface, instead, = 0.99 and = 2, therefore − = 1.01 is the total transmitted wave, which is equal to 101%. This means that in this interface there is no acoustic wave propagation problem. Despite the acoustic wave being able to easily across the AIR/PET-3 interface, no charge peak coming from the PET-1/AIR Figure 13. Simulated PEA cell output signal for the PET-AIR-PET specimen.

Results Discussion
It has been shown by means of the presented study that the PEA technique is not suitable for testing multilayer specimen in which an air layer is present. This is due to the barrier effect of the air material. In particular, the strongly accentuated acoustic wave reflection phenomenon in the air/solid dielectric interfaces is caused by the high difference of the acoustic impedance Z. In fact, in our case, Z air = 421.4 kg/m 2 s while Z PET = 3.5 × 10 6 kg/m 2 s. These values, in turn, generate a high acoustic wave reflection coefficient K R and a very low acoustic wave transmission coefficient K T , in the same interface. Therefore, for the acoustic waves traveling within the PEA cell, it is difficult to reach the piezoelectric sensor because they are reflected in the opposite direction. Despite not being demonstrated in this work, the same phenomenon can be also observed when the air layer is placed in contact with the ground electrode of the PEA cell. This is because the acoustic impedance of the aluminum material is much higher than that of air (Z aluminum = 17 × 10 6 kg/m 2 s).
Based on the obtained results, in order to avoid incorrect interpretation of the charge distribution provided by the PEA cell, the authors suggest that the PEA is a preliminary evaluation of the acoustic wave behavior.

Conclusions
The purpose of this work was to demonstrate that for a specimen containing an air layer, the space charge measurement with the PEA method cannot be correctly made. The motivation that pushed the authors to this study derived from several failed attempts in which the simultaneous detection of the space charge and partial discharges was attempted. In particular, we published some papers in which the charge signal has been detected in a specimen containing an air void. However, after further subsequent studies where the acoustic wave behavior has been widely investigated, it was understood that the previously obtained and published charge profiles were not correctly interpreted. In reality, as reported in the present work, we found that the air layer acts as a barrier for the acoustic wave due to its acoustic impedance values. In the proposed experimental test, in fact, by taking into consideration the generation K G , transmission K T and reflection K R coefficients calculated in each specimen interface the following numerical values have been found. In the PET-1/air interface K R = −0.99 and K T = 2.3 × 10 −4 , this means that the acoustic wave reaching this interface is almost totally reflected in the HV electrode direction. In the AIR/PET-3 interface, instead, K R = 0.99 and K T = 2, therefore K T − K R = 1.01 is the total transmitted wave, which is equal to 101%. This means that in this interface there is no acoustic wave propagation problem. Despite the acoustic wave being able to easily across the AIR/PET-3 interface, no charge peak coming from the PET-1/AIR interface has been observed in the obtained charge distribution due to the low acoustic wave generation coefficient (K G = 0.00012) of the PET-1/AIR interface. However, as a conclusion, it is possible to confirm that the signal displayed by the oscilloscope is only due to the acoustic waves and their reflections generated by the charge accumulated in the PET-3 layer interfaces.
In summary, the air layer does not allow the charge signal coming from the dielectric layer placed in contact with the upper electrode of the PEA cell to reach the sensor. Moreover, we also found that the acoustic wave generation coefficient in the PET/AIR interface is very low. This means that the waves generated in this interface, due to the attenuation phenomenon, are not able to reach the sensor. Therefore, the only acoustic wave correctly detected and observed by the oscilloscope are those due to the charge accumulated in the layer of PET placed in contact with the ground electrode.
In conclusion, it is essential to highlight the importance of the developed PEA cell model for understanding acoustic wave behavior. In particular, the dynamic simulation, which is able to show as a video of the acoustic wave traveling within the PEA cell, results in a very useful tool. However, in the proposed work, the previously developed PEA cell simulation model has been validated for the three layers specimen with the presence of an air void.
In future work, we will focus on the design of a new PEA cell able to measure the space charge in a multilayer specimen with the presence of an air layer.