Abstract: Background and Objective: The condition of electrical insulation in transformers is one of the most important factors that govern transformer life. Different factors influence the aging of the transformer insulation and one of the most important factors is the occurrence of partial discharge (PD). Frequent occurrence of PD can cause damage to the insulation which may eventually lead to its failure. Among the PD detection techniques, there is increased interest in the PD acoustic detection method because it overcomes several disadvantages inherent in electrical methods. The main objective of this work is to introduce mathematical model of partial discharge and study the effect of its travelling path on its arrival time to detect its location. Materials and Methods: A complete setup was examined to get the experimental results by creating PD in transformer oil and collecting the produced acoustic waves via different sensors through different paths. Results: The proposed model presents the propagation of acoustic wave with direct and indirect path which helps in calculating arrival time. This will identify the location precisely by detecting the peak value from the modelled signals. Conclusion: The output acoustic wave received by the PD AE sensor can be analyzed by the mathematical model. The attenuation of each component can be understood to calculate the real arrival time of peak value. The location will be determined by comparing with the experimental one.
INTRODUCTION
Monitoring of PD is the indispensable and primary tool of determining the health of transformer insulation. When PD is initiated, the resulting energy is transformed into mechanical, electrical and chemical energy. A wide range of sensors and techniques can be used to detect PD as depicted in Fig. 1. Acoustic Emission (AE) sensors within a transformer are considered as one of the most promising techniques for the detection of waves that propagate from the PD origin to the tank through the dielectric medium and specify its location1.
In addition, AE sensors are also cost effective compared to conventional methods. Furthermore, the installation of AE sensors is non-invasive as they are attached magnetically to the outside of the transformer tank while the transformer is energized and the sensors are not susceptible to external electrical and electromagnetic interference. However, the major disadvantages of AE sensors is that AE waves are greatly attenuated within the transformer and also multiple reflections occur while travelling from the source to the sensors.
Both impact negatively on the ability of using the AE method to detect, classify and localize PD sources. Hence, there is a need to understand the behaviour of the AE PD signal while travelling from its source to the sensor.
The measured acoustic wave that is generated from the release of the mechanical energy from PD can be considered as a pulse that propagates within the transformer oil. As acoustic sensors are usually connected to the wall of the transformer tank, it is extremely difficult to trace the AE waves experimentally. As an alternative, modelling of the AE wave can help to understand the main factors that influence the AE PD signal.
A mathematical model of acoustical PD detection in a transformer was introduced by Akumu et al.2 using the finite difference technique to solve the acoustic wave propagation equations taking multiple paths through the oil and iron, detecting the arrival times of the wave peaks at various sensor locations within the tank. This approach falls short of being able to provide a high degree of approximation to solve the acoustic wave equations in complex transformer geometries and in particular, providing suitable boundary conditions at critical surfaces. These disadvantages were overcome by Ashraf et al.3 by solving the propagation equations using the finite element technique whereby contour plots where used to show the attenuation at different locations. Moreover, the model examined the propagation properties under the effect of oil density and temperature. On the other hand, the study did not represent the details of the PD acoustic wave to understand the degree of attenuation, reflection and refraction of the acoustic wave. Also, the impact of PD frequency on the wave propagation in transformer oil was not considered. In both studies of Akumu et al.2 and Ashraf et al.3, the velocity of the acoustic wave was assumed to be constant in transformer oil which is not accurate as discussed by Kundu et al.4 as the sound velocity changes with the travelled distance and increases from around 600 m sec–1 at a distance of 0.1 m to 1400 m sec–1 at about4 1.0 m. The sound velocity is critical to understand the wave propagation as it controls the arrival time of the wave and hence the ability to correctly determine the location of the PD. In addition, the effect of frequency on acoustic PD attenuation was studied in Kundu et al.4 by applying pulses with different widths showing increased attenuation with increased frequency of the PD pulse.
| Fig. 1: | Partial discharge detection techniques for transformers |
An important factor discussed in Lundgaard5, needs to be highly considered to understand the behaviour of acoustic wave. It has been mentioned that each frequency component of the PD wave will travel with different velocity and hence will arrive to the tank wall at different time which will lead to a higher degree of distortion of the received PD wave. The author considered two factors that will influence the acoustic wave attenuation and dispersion. The attenuation will be much greater for the high frequency component than the low frequency components. Also, the velocity of high frequency will be higher than the lower one which will result in more dispersion. These two effects will be combined together to contribute to the complete distortion of the wave5.
This understanding of acoustic PD behaviour is important in predicting the actual frequency range of the PD generated pulse based on the received one. Wotzka et al.6 presented the PD pulse as a multiple of sine waves of different frequencies to reconstruct the generated pulse based on the received one. However, in this approach, all of the sine waves were considered to travel at the same velocity which is not accurate as each frequency component will travel at a different velocity.
As each frequency component of the acoustic PD wave travels at a different velocity and is subjected to a different attenuation, the wave that arrives at the sensor location is distorted from the starting wave. Hoek et al.7 examined how propagation velocity and attenuation of the component frequencies shapes the received pulse. In this study, the main objective is to understand the propagation of PD acoustic waves in transformer oil by considering the changes in its velocity. Also, it will show the attenuation of the received signal and how the travelled distance effects on the received pulse and its arrival time. In addition, the effect of reflections within the steel enclosure on the received pulse is also studied and helps to understand the PD propagation and predicting the location of PD.
MATERIAL AND METHODS
The experimental setup is shown in Fig. 2. A high voltage electrode immersed in transformer oil in a steel tank is used to generate the PD acoustic signals. The electrode is connected to a 40 kV, 50 Hz AC supply. Two AE sensors are held magnetically to the tank and have a silicone grease layer between the sensor and the tank to improve the signal transmission and to reduce reflections. The sensors have a bandwidth of 100-450 kHz and resonate at 150 kHz.
The location of the PD source and AE sensors is depicted in Fig. 3. The received acoustic wave can take different forms according to the input pressure (PD source) and have different paths. These paths can be either direct through oil (solid line in Fig. 3) or through the steel by conduction and reflection (dashed lines). These paths give rise to a complicated waveform received by the sensors and hence it is imperative to understand the effect of the various paths on the shape of the received signal.
The PD signal can be considered as a point source of acoustic emission with a very short duration in the range5,8 20 kHz to 1 MHz. The propagation of the acoustic emission is evaluated by solving partial differential equations using the finite element technique. The standard partial differential equation that governs the propagation of an acoustic wave within a 2-D homogeneous media is given by Markalous et al.8 and Tsang and Radar9:
where, P is the pressure wave field in Pa, t is the time in sec, C is the acoustic wave velocity in m sec–1 and δ is the Dirac Delta function associated with the position of the PD source. The dimensions of the steel tank is 100 cm×100 cm, the transformer oil density is 899 kg m–3 and the PD source is assumed to be 25 cm away from the wall.
| Fig. 2: | Experimental setup for PD acoustical wave generation and measurement |
| Fig. 3: | Schematic view for acoustic wave propagation inside tank with possible propagation paths until reaching sensors S1 and S2 |
| Fig. 4(a-b): | AE PD signals received by sensors (a) S1 and (b) S2 |
In the experimental setup, both the PD source and the acoustic sensors are mounted at the same height to minimize the effect of the third dimension (Z-direction) which will complicate the acoustic wave propagation. Hence, the proposed model will be considered as a two dimensional problem.
RESULTS AND DISCUSSION
Figure 4 shows an example of signals received by sensors S1 and S2. It is apparent from Fig. 5 that there are multiple of AE waves that are received by sensors S1 and S2. As such, it will be extremely difficult to identify the AE signal that results from the direct or the indirect path of the PD signal which will complicate the process of PD localization. To better understand the behaviour of the AE PD signal, modelling the propagation of the signal is investigated.
Similar to the measured signals, the modelled acoustic PD signals showed that multiple waves arrived at both S1 and S2 as depicted in Fig. 5. As mentioned earlier, the AE PD signal can take different paths to reach the sensor. For better understanding of the effect of the AE PD path on the received signal, two paths will be considered, i.e., direct and indirect path as depicted in Fig. 3. The direct distances from sensor S1 and S2 to the PD source are 0.25 and 0.559 m, respectively. Moreover, the distance as indirect path from the PD source to S1 and S2 through steel is 0.5 and 1 m, respectively.
| Fig. 5(a-b): | Modelled AE PD signals received by sensors (a) S1 and (b) S2 |
| Table 1: | Arrival time for the AE waves for both the direct and indirect paths |
The speed of acoustic wave is assumed to be 1400 and 5950 m sec–1 in oil and steel, respectively. The calculated arrival times for both the direct and indirect paths for S1 and S2 are shown in Table 1. Furthermore, the received AE waves at both S1 and S2 are shown in Fig. 5. It is apparent from Fig. 5a, that the peak value of the received AE signal arrives to sensor S1 at around 180 msec while the arrival time of the indirect path of the AE wave is 262 msec. On the other hand, the AE signal through the indirect path arrives before the direct path. However, in both cases the largest peak corresponds to the direct path and hence its time of arrival should be considered to determine the AE arrival time. This could be attributed to the fact that the attenuation of AE signal is more significant in steel as opposed to oil.
It is clear that the measured signal are consistent with the calculated ones that it will help to detect the location of the PD. The location can be precisely predicted by taking the correct arrival time from the signal. It is obvious that the largest peak comes directly in the direct path without much reflections and attenuated waves. Otherwise, the peak value of the wave from the indirect path comes after reasonable time from starting and a lot of attenuated signal because of large attenuation in steel. Based on that, the location of PD based on the arrival time of the largest peak is 0.249 m and the exact location is 0.25 m in the real setup. It means that the error will be around 0.4% and the accuracy is highly accepted.
CONCLUSIONS
The output acoustic wave received by the PD AE sensors can be analyzed using its individual travelling paths. By collecting all received waves, the distortion and the attenuation can be understood and the PD location can be precisely detected by selecting the exact peak and the its corresponding arrival time.
SIGNIFICANCE STATEMENT
This study discover the factors that affect on the propagation of partial discharge acoustic wave that can be beneficial for determining the location of partial discharge based on detecting the travelled direct path of the signal. This study will help the researcher uncover the critical area of receiving a lot of signal without understanding the correct peak location with a lot of attenuated signals based on their path.
ACKNOWLEDGMENT
This work was made possible by NPRP 5-044-2-016 grant from Qatar National Research Fund (a member of Qatar Foundation).