1. Introduction
Transformers play an important role in power transmission systems. Partial discharge inside the transformer may cause insulation failure, and even catastrophic accidents in severe cases [
1]. The detection of partial discharge is widely used in insulation diagnosis for electrical equipment. The insulation failure can be found immediately by monitoring the evolution of discharge process, and the online detection can act as a preventive role before failure occurs [
2].
Ultrasonic detection method has become one of the most important methods for online partial discharge detection because it can effectively resist electromagnetic interference in transformers [
3]. Nowadays, piezoelectric ceramic sensor is the most popular external ultrasonic sensor [
4]. Although the external sensor is convenient to install, it is sensitive to the influence of the external environment. Besides, ultrasonic waves that were generated by partial discharge will be attenuated when they transmit through transformer oil or a transformer oil tank wall, and multipath transmission will cause positioning difficulties. These shortcomings would greatly hinder the application of external sensors [
5]. As for the built-in sensor, it has many advantages, such as no chemical reaction with insulating medium, good insulation, stable operation and small size, etc. [
6] Recently, the extrinsic Fabry-Perot interferometer (EFPI) sensor has become one of the most popular built-in sensors due to its advantages, such as anti-electromagnetic interference, small size, easy signal processing, flexible application and operation in extreme environments [
7]. It is found that, the Fabry-Perot membrane has a remarkable effect on both the amplitude-frequency characteristics and sensitivity of the sensor.
At present, there are many pieces of research on the design of sensor membranes. For example, Jiang et al. [
8] developed highly sensitive sensor membranes by changing the membrane radius and thickness. In their study, in order to avoid a signal interference caused by magnetic vibration of internal winding in the transformer and noise generated by the cooling oil circulation, the membranes natural frequency was controlled within an appropriate range. A cantilever beam sensor membrane was designed by Su et al. [
9], and the effect of thermal stress on the natural frequency, sensitivity and stability for the membrane was analyzed. Ghildiyal et al. [
10] manufactured a metal membrane with a measurement range of 0–100 mbar by stretching membrane and changing stress. Liu et al. [
11] developed a high sensitivity membrane by etching permanent ripples on the membrane. The mechanical property of this membrane would change as the ripple depth changes. Yu and Zhou [
12] used a controlled thermal bonding technique to process EFPI sensors that can work at 300 ℃, which further increases the application range of the EFPI sensors. Bo et al. [
13] used polyethylene oxide (a strongly hydrophilic material) to fabricate sensors for detecting humidity variations. Liao et al. [
14] used polyethylene terephthalate as the membrane material and it was applied to highly sensitive acoustic detection. Liu et al. [
15] deposited a perylene diimide derivative as a sensitive film on the membrane, and developed a new type of optical fiber sensor with a temperature sensitivity of 9.8 pm/℃ by using the change in the refractive index of the membrane under hydrazine vapor. Kendir and Yaltkaya [
16] used magnetostrictive material as the sensor membrane and successfully fabricated fiber optic magnetic field sensors that can sense changes in the magnetic field. Li et al. [
17] demonstrated through experiments a low-cost fiber optic accelerometer based on a polyethylene membrane, and the measured sensitivity was 135 mV/g, which greatly reduced the production cost of the probe.
The above references mainly optimize the performance of the sensor membrane from the aspects of the shape of the membrane, manufacturing materials, processing technology, and application scenarios. However, when the sensor is arranged in the transformer, the membrane is surrounded by transformer oil, and the oil around the membrane will affect the vibration characteristics, causing the design deviations from the actual application. Some scholars have performed related researches on the relationship between membrane vibration and surrounding medium. Kilic et al. [
18] analyzed the influence of static pressure fluctuation on the vibration performance of the sensor membrane. The results show that the influence of static pressure fluctuation could be ignored when the cavity was interconnected with the transformer oil. Lesieutre [
19] conducted a corresponding study on the influence of load on structural modal damping and found that an increase in tensile load will increase the natural frequency, but reduce the modal damping. Minami [
20] studied the vibration of the membrane structure in the air environment. Under the assumption that air is an incompressible fluid, the additional mass of air is derived as a coefficient related to the air density and the shape of the membrane. Sygulski [
21] used the boundary element method to establish the discrete dynamic equation of the free vibration of the membrane structure in the air environment, and numerically analyzed the influence of air on the membrane vibration. Henn et al. [
22] simulated the fluid dynamics of transient fluid-structure interaction, and the results showed that there is a clear flow velocity in a narrow area close to the membrane surface, and the additional mass layer has no clear boundary. These studies have analyzed the influence of air on the vibration characteristics when the membrane is vibrating in the air. However, in these applications, the effect of viscosity during the vibration process is negligible and does not reveal the effect of viscous damping on the vibration characteristics. In working media with non-negligible viscosity (such as transformer oil), viscosity will cause viscosity loss and heat loss, thereby affecting vibration characteristics. Changes in vibration characteristics will cause the sensor’s signal reception deviations from the design target.
Therefore, in the present paper, the EFPI membrane vibration performance in transformer oil was numerically studied, and a membrane vibration model that couples thermal viscosity and flow heat transfer was established. The effects of viscous damping and mass damping on the natural frequency, sensitivity, amplitude-frequency characteristics and time domain response of the membrane were analyzed. This study is meaningful for understanding the influence of transformer oil on membrane vibration and the design of membranes arranged in transformer oil.
5. Conclusions
In the present paper, the EFPI membrane vibration performance in transformer oil was numerically studied based on the finite element method. The effects of transformer oil on the natural frequency, sensitivity, amplitude-frequency characteristics and time domain response of the membrane were analyzed. Meanwhile, both the mass damping and viscous damping of transformer oil were considered during the simulation process. The main conclusions are as follows:
For the first-order vibration mode, the membrane has the same phase point, which would be beneficial for prediction membrane vibration through the intensity of output light. As the membrane vibration mode order increases, the membrane vibration amplitude decreases gradually, and the membrane sensitivity should be the highest for the first-order vibration mode. The effect of transformer oil on the natural frequency of membrane vibration is remarkable, especially for the lower-order vibration modes. In the present study, the first-order natural frequency of membrane vibration is reduced by 60% in transformer oil.
As the membrane vibrates, the oil velocity gradient near the surface of membrane is relatively large, which will lead to a viscous loss for membrane vibration, and its vibration amplitude is reduced to one-fifth of that for the non-viscous vibration. When the vibration frequency of the membrane is close to its natural frequency, the vibration amplitude of the membrane is larger, and the effect on the oil velocity field caused by the vibration is wider and more significant. As compared with oil velocity distributions around the membrane, the variations in oil temperature are relatively small as the vibration frequency changes.
The effect of transformer oil viscosity on the time domain response of membrane vibration is remarkable. When the membrane vibrates in viscous oil, mechanical energy is converted into thermal energy during the vibration and its vibration amplitude will decrease gradually with time. Therefore, when we design the membrane, the effect of oil viscosity on the membrane vibration displacement attenuation should be considered.
Since the natural frequency will affect the signal detection for the sensor, the amplitude-frequency characteristics and the time domain response will affect the sensitivity of the sensor. In practical applications, it is necessary to combine the design requirements based on original membrane, and fully consider the impact of viscous damping and mass damping caused by transformer oil on vibration characteristics. This work should be performed in the near future.