# Development of an Online Detection Setup for Dissolved Gas in Transformer Insulating Oil
## 2 Principles of Detection
### TDLAS Detection Theory  
Different molecules need to absorb different wavelengths of light to achieve vibration. Therefore, every gas has its own characteristic spectrum. The TDLAS technique uses both the narrow line width and the tunable features of the laser to scan a single characteristic absorption line of the target gas, as shown in Figure 3.  
Figure 3: Schematic diagram of laser absorption spectrum detection.  
Figure 2: Schematic diagram of degassing time.  
The intensity of the laser light passing through the target gas can be expressed by the Beer-Lambert law:  
\[I_{t}(v)=I_{o}(v)exp[-\alpha(v)CL] \tag{6}\]  
where \(I_{o}(v)\) is the incident light intensity; \(I_{t}(v)\) is the transmitted light intensity; \(\alpha(v)\) is the absorption coefficient at frequency \(v\) per unit concentration and per unit length; \(C\) is the volume fraction of the gas; and \(L\) is the length of the optical path.  
Wavelength modulation and harmonic detection techniques are used to improve detection sensitivity. A high-frequency sinusoidal modulation signal is superimposed on the laser scanning signal. The instantaneous frequency of the laser can be expressed as:  
\[v(\mathrm{t})=\overline{v}+a\cos(2\pi ft) \tag{7}\]  
where \(a\) represents the modulation amplitude and \(\overline{v}\) is the laser center frequency. The incident light intensity was assumed to remain essentially constant with sufficiently minor modulations. Therefore, the modulated input intensity \(I_{o}[v(t)]\) is equivalent to the intensity at the center frequency of the absorption spectrum \(I_{o}(v_{o})\). As a result, the high-frequency modulated transmitted light intensity can be calculated as follows:  
\[\begin{split} I_{t}[v(t)]=I_{o}[(v(t)]exp\{-\alpha[\overline{v}+ a\cos(2\pi ft)]CL\}\\ =I_{o}(v_{o})\sum\limits_{n=0}^{\infty}H_{n}(\overline{v})\cos(2 \pi fnft)\end{split} \tag{8}\]  
where \(H_{n}(\overline{v})\) is the Fourier coefficient with a modulated absorption factor; and \(H_{n}(\overline{v})\) can be demodulated by a lock-in amplifier. [PERSON] et al. determined that the magnitude of the second harmonic amplitude is related to the gas concentration. As a result, the second harmonic amplitude was used to calculate the gas concentration. Figure 4a depicts the signal received by the photoelectric detector in the absence of gas absorption. With the onset of gas absorption, the sunken shape of the signal appeared, as shown in Figure 4b. In Figure 4c, the second harmonic signal was obtained by demodulating the concave region.  
The presence of baseline drift and residual amplitude modulation caused the second harmonic to appear asymmetrical, which occurred during the detection and modulation processes. Consequently, to suppress this phenomenon, the second harmonic amplitude was defined as the sum of the absolute values of the maximum and minimum of the second harmonic. The definition of the second harmonic amplitude is shown in Figure 5.  
Figure 4: Process of TDLAS gas detection: (**a**) Original signal; (**b**) absorption signal; (**c**) second harmonic.