Analysis of Microphone Coupling and Zero-Point Calibration Model for Non-Resonant Photoacoustic Spectroscopy

Dissolved Gas Analysis (DGA) of transformer insulation oil is an effective method for monitoring transformer operating conditions and diagnosing faults. Photoacoustic spectroscopy (PAS) is widely employed for online dissolved gas analysis in transformer oil. The positioning of the pressure equalization hole within the sound field significantly impacts the microphone’s sensitivity when coupled with the photoacoustic cell in non-resonant photoacoustic spectroscopy. The static temperature and humidity characteristics inside the photoacoustic cell also have a notable influence on the microphone’s output signal. Consequently, an analysis is performed to explore the relationship between the sensitivity of the photoacoustic spectrometer and temperature/humidity, leading to the optimization of the system configuration based on the microphone parameters. Moreover, the photoacoustic zero-point signal is influenced by the temperature and humidity levels within the photoacoustic cell. To address this problem, air mixtures at different humilities are measured, resulting in the establishment of a zero-point model for the background signal in Photoacoustic Spectroscopy (PAS). Subsequently, the experimental detection of acetylene under various humidity mixtures is conducted, successfully extracting effective signals for the measurement of 5 ppm acetylene gas. These results serve as evidence showcasing the efficacy of both the proposed structural optimization and zero-point model put forth in this study.


Introduction
With the development of the ubiquitous power Link of Things (LoT), China is gradually establishing a smart energy system characterized by comprehensive state awareness and efficient information processing.Intelligent sensing serves as the core foundational technology for the ubiquitous power LoT, enabling real-time online diagnosis of electrical equipment faults and aging, which is crucial for ensuring grid safety and achieving efficient equipment maintenance.Dissolved Gas Analysis (DGA) of large-scale transformer insulation oil has proven to be an effective method for monitoring the operating condition and diagnosing faults in transformers [1][2][3][4][5] .Currently, one commonly used technique in power systems for online transformer monitoring is the online analysis and monitoring of dissolved gases in transformer oil based on the principle of photoacoustic spectroscopy (PAS) [6] .
Non-resonant PAS provides the advantage of not requiring gas separation and allows for the detection of various characteristic gas components such as acetylene (C2H2), ethylene (C2H4), and methane (CH4).This technique possesses a simple structure, multiple measurement capabilities, and relatively low cost.By simply changing the filter, it enables the detection of various gases.Mature commercial instruments used internationally include GE's Tranfix series of transformer oil online instruments and Innova's 1412 series gas analyzers from the Netherlands.Notable applications of these instruments include Bertrand et al.'s experiment using the Innova photoacoustic spectrometer to conduct nitrogen gas monitoring on a farm, where they successfully established a model for the distribution of atmospheric nitrogen content.GE's Tranfix instrument has been widely adopted for online monitoring of transformer oil DGA and has also been promoted and utilized in Chinese substations.Although some relevant instruments have been developed domestically, such as Zhang et al.'s non-resonant spectrometer for detecting fire-characteristic gases and exhaled ammonia, there still exists a gap compared to mature commercial instruments available overseas.As part of our research, we have developed a photoacoustic spectroscopy module specifically for transformer oil DGA and conducted validation experiments specifically targeting acetylene [7] .
During the online detection of dissolved gases in oil by using a photoacoustic spectrometer, it is necessary to flush the photoacoustic cell with air to ensure the absence of residual characteristic gases inside the cell.Additionally, since fewer gases are released from the oil sample, it becomes essential to supplement the air to maintain consistent pressure inside the photoacoustic cell and its surroundings.Consequently, the presence of water vapor in the air directly interferes with the accuracy of measuring the characteristic gas concentration.The nonresonant PAS employs a thermal radiation light source, and heat conduction from the light source results in an increase in temperature within the photoacoustic cell during the measurement process [8][9][10] .This temperature variation affects the photoacoustic signal.Therefore, the photoacoustic spectroscopy signal is susceptible to environmental factors such as temperature and humidity, leading to changes in the background signal.To ensure the stability and reliability of the photoacoustic spectroscopy system, calibration of the background signal becomes imperative.

PAS detection model
The received electrical signal of non-resonant PAS is expressed as follows: (1) where S represents the voltage output of the microphone in millivolts (mV); A is the sensitivity of the microphone (mV/Pa); I is the power of the light source (W); Ccell represents the acousto-optic cell constant (Pa•cm/W), which generally depends on the size of the acoustooptic cell and the physical constants of the background gas; N denotes the gas number density (molec/cm 3 ), and σ represents the gas absorption cross-section (cm 2 /molec), where their product gives the absorption coefficient α (cm -1 ).
The structure of the condenser microphone is depicted in Figure 1, comprising a diaphragm, a condenser plate, a back electrode, and a pressure equalization hole.The microphone receives incoming sound waves, which cause mechanical movement of the diaphragm and subsequently convert it into an electrical signal.The relative sensitivity (dB) of the microphone can be expressed as: where out V is the output voltage, in P is the input pressure.The sensitivity of the microphone varies with changes in relative humidity and temperature.The humidity coefficient of the selected microphone is -0.001 dB/%RH, and the temperature coefficient is -0.01 dB/℃.To assess the impact of these two factors on sensitivity changes, an analysis is conducted as shown in the following figure 3. It can be observed that there is an inverse relationship between sensitivity and both temperature and humidity.Temperature has a more significant impact on sensitivity compared to humidity, which has a relatively smaller effect.These findings highlight the importance of considering the effects of temperature and humidity when optimizing the performance of the condenser microphone.
We assume a reference filter that is used to measure water vapor with output as

Experiment and results analysis
We have developed a PAS module and constructed a testing system comprising of the following components: (1) PAS module, (2) Humility generator, and (3) Dew point detector.
The photoacoustic spectroscopy module includes a power supply, a non-resonant photoacoustic spectroscopy measurement unit, and data acquisition software.It can measure six typical dissolved gases in oil (CO2, CH4 C2H2, CO, C2H4, and C2H6).The dew point detection system manufactured by Nanjing Sigma Instruments Company has a measurement range of -100°C to +20°C dew point, with an accuracy of ±1°C dew point and a maximum pressure of 30 MPa.
In our testing system, water vapor and acetylene are mixed by using the gas mixing apparatus to generate mixed gases with different humidity levels.These mixed gases are then introduced into the PAS module for concentration testing.The system configuration is illustrated in the figure 4. The selected water vapor and acetylene filters are shown in Figure 2. The filter parameters are as follows: the center wavelength of the water vapor filter is 5.0847 μm with a full width at half maximum (FWHM) of 0.1037 μm, and the acetylene filter has a center wavelength of 3.066 μm with an FWHM of 0.0766 μm. Figure 5 displays the absorption coefficient spectra of water vapor and acetylene.In actual air samples, the concentration of water vapor is much higher than that of the measured acetylene, resulting in significant interference with the acetylene signal.By introducing different water vapor/acetylene gas mixtures and measuring the voltage changes in the photoacoustic cell with varying temperatures, the zero-point calibration model can be obtained by using Equation (3).Under a specific gas mixture ratio, continuous measurements are conducted at room temperature, where the temperature of the photoacoustic cell is gradually increased from the ambient temperature and then stabilized to obtain the temperature variation.By repeating experiments with different gas mixtures, the voltage values are obtained to establish the zero-point model for water vapor concentration and temperature.The result is depicted in the figure 6.Based on the data obtained from various gas mixture ratios, the zero-point calibration model for the acetylene filter can be established as follows:  Figure 7 demonstrates the zero calibration effect with air mixture, simulating real operating conditions.The lower graph displays the results after zero calibration.Notably, a concentration of 5ppm of C2H2 can be distinguished from the air, and the air data is predominantly calibrated to near-zero levels.Calibration results may still exhibit noise.To further enhance gas detection stability and sensitivity, it is recommended to employ techniques such as averaging or other filtering methods through multiple measurements.These approaches help reduce the impact of noise and improve the overall performance of gas detection.

Conclusion
The impact of temperature and humidity on the non-resonant photoacoustic spectroscopy signal is analyzed.The uniform pressure hole position of the microphone is theoretically simulated.It shows that the sensitivity of the photoacoustic spectroscopy is better outside the acoustic field than inside.Simulations are performed to examine the influence of temperature and relative humidity on the microphone sensitivity, revealing a negative correlation between the two factors and the microphone sensitivity.A dedicated optical filter is designed to measure water vapor.The study utilizes laboratory equipment to detect photoacoustic signals under different humidity and environmental temperature conditions.A model correlating zero signals with temperature and humidity is established.By measuring acetylene signals under various environmental conditions, both zero-point correction and microphone calibration effectively distinguish the background from acetylene signal effective values.These experiments demonstrate the effectiveness of zero-point correction and microphone calibration discussed in this paper.

Figure 1 .
Figure 1.Electret microphone structure.Based on the selected parameters of the condenser microphone, the sensitivity of the pressure equalization hole at different positions is simulated, as illustrated in the following figure.It can be observed that for low-frequency signals, placing the pressure equalization hole outside the sound field results in higher sensitivity.The positioning of the pressure equalization hole has a more significant impact on low-frequency signals.For low-frequency signals with sound frequencies between 15-30 Hz in PAS, placing the pressure equalization hole outside the sound field yields higher sensitivity.

Figure 2 .
Figure 2. The sensitivity of the pressure equalization hole, both inside and outside the sound field, varies with frequency.

Figure 3 .
Figure 3.The sensitivity varies with temperature (left) and relative humidity (right).

S
and the temperature, pressure, and concentration of water, regression coefficients B can be obtained to calibrate the zero point.The zero-point signal can be written as follows: obtaining the regression coefficients (j) B by using the least squares method, the zero- point photoacoustic signal of the -th j filter can be determined based on the voltage value of the water vapor filter and the temperature.Subtracting the background () 0 j S from the measured values gives us a useful signal.

Figure 4 .
Figure 4. Different water vapor experiments using the PAS module.

Figure 6 .
Figure 6.Measurements of acetylene and water vapor filters under different water vapor concentrations and photoacoustic cell temperature conditions.The first graph represents the variation in the photoacoustic cell temperature.The second and third graphs display the voltage values obtained for acetylene and water vapor, respectively.The fourth graph shows the water vapor concentration values measured by using a dew point detector.
Using the aforementioned model, measurements are conducted on air samples with different humidity levels and acetylene gas at varying concentrations.The calibrated acetylene voltage values are obtained.In the graph below, the horizontal axis represents different water vapor concentrations and various samples of water vapor/acetylene gas mixtures.The gas mixing apparatus is used to prepare different concentrations of water vapor and acetylene gas for each sample.The zero reference value for each measurement is calculated by using the zero-point model mentioned earlier.After subtracting the zero reference value, the acetylene voltage values are corrected.

Figure 7 .
Figure 7.The horizontal axis represents different water vapor concentrations and various samples of water vapor/acetylene gas mixtures.The upper graph represents the voltage values of acetylene and the calculated zero reference values based on the model.The horizontal axis indicates different samples, which are prepared by introducing varying proportions of air and C2H2 into the instrument.The lower graph displays the results after zero calibration.It can be observed that a concentration of 5 ppm of C2H2 is distinguishable from the air, and the air data is mostly calibrated to near-zero levels.