## 2 Characterization of Baffle Motion Due to Inrush Current
### Dynamic Characteristics of the Gas Relay Baffle Plate  
Suppose that the baffle of a gas relay is a rigid body rotating around an axis. At this time, the baffle is subjected to three main torques: gravity torque, resistance torque of the spring on the baffle, and impact torque of the oil flow on the baffle [8], as shown in Figure 3:  
Figure 1: Physical diagram of gas relay. Figure 2: Schematic diagram of gas relay. (1) Gravity moment \(M_{g}\)  
In reality, the center of gravity of the gas relay baffle is directly below the rotating shaft, and the gravitational moment of the baffle can be obtained as  
\[M_{g}=mgb\sin\theta \tag{1}\]  
where \(m\) is the mass of the baffle of the gas relay, \(g\) is the acceleration of gravity, \(b\) is the vertical distance from the center of gravity of the baffle of the gas relay to the rotating axis, and \(\theta\) is the angle of deflection of the baffle of the gas relay. (2) The moment of resistance of the spring to the baffle plate \(M_{\rm s}\)  
As shown in the Figure 3, when the baffle is impacted by the oil flow horizontally to the right, the baffle starts to rotate around the O from the starting vertical state. The AB segment indicates the immediate position of the spring after stretching, and the length is \(l\), which can be changed with the rotation of the baffle to change its size, and let the initial value be \(l_{0}\), and the change amount is \(\Delta l\). The expression of the spring's resisting moment on the baffle is  
\[M_{\rm s}=C_{1}(1-\frac{C_{2}}{\sqrt{C_{3}-\cos(\theta+\theta_{1})}}\sin( \theta+\theta_{1}) \tag{2}\]  
where \(\theta_{1}=\arccos(\frac{c^{2}+d^{2}-l_{1}^{2}}{2 cd})\), indicates the starting position of the \(\beta\) size; \(C_{1}=ckd\); \(C_{2}=\frac{l_{1}-\Delta l}{\sqrt{2 cd}}\); \(C_{3}=\frac{c^{2}+d^{2}}{2 cd}\); \(k\) is the stiffness coefficient of the spring. (3) Impact moment of oil flow on baffle \(M_{\rm f}\)  
The expression of the impact moment \(M_{\rm f}\) of the oil flow on the baffle is  
\[M_{f}=M_{p}+M_{\rm v} \tag{3}\]  
where  
\[M_{p}=\oiint p(x-x_{0})dS_{y}-p(y-y_{0})dS_{x} \tag{4}\]  
\[ \begin{array}{l}M_{\rm v}=\oiint\biggl{(}-(x-x_{0})\biggl{(}\frac{\partial v }{\partial x}+\frac{\partial u}{\partial y}\biggr{)}-(y-y_{0})\biggl{(}- \frac{4\partial u}{3\partial x}+\frac{2\partial v}{3\partial y}+\frac{2 \partial w}{3\partial z}\biggr{)}\biggr{)}dS_{x}\\ +\oiint\biggl{(}-(x-x_{0})\biggl{(}\frac{2\partial u}{3\partial x}-\frac{4 \partial v}{3\partial y}+\frac{2\partial w}{3\partial z}\biggr{)}+(y-y_{0}) \biggl{(}\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}\biggr{)} \biggr{)}dS_{y}\\ +\oiint\biggl{(}-(x-x_{0})\biggl{(}\frac{\partial w}{\partial y}+\frac{\partial v }{\partial z}\biggr{)}+(y-y_{0})\biggl{(}\frac{\partial w}{\partial x}+\frac {\partial u}{\partial y}\biggr{)}\biggr{)}dS_{z}\end{array}  \tag{5}\]  
where \(M_{p}\) is the pressure moment of the oil flow impacting on the baffle, \(M_{\rm v}\) is the viscous resistance moment of the baffle; \(p\) is the pressure of the oil flow impacting on the baffle; \((x\), \(y\), \(z)\) is the coordinate of a point on the baffle; \((x_{0}\), \(y_{0}\), \(z_{0})\) is the coordinate of the center of  
Figure 3: Schematic diagram of baffle dynamic characteristics. the rotation of the baffle; \(u\), \(v\), and \(w\) are the velocity components in the direction of \(x\), \(y\), and \(z\), respectively. (4) Total moment \(M_{t}\)  
The total moment of the baffle of the gas relay consists of the above three moments, and its expression is  
\[M_{t}=M_{f}-M_{s}-M_{g} \tag{6}\]  
In practical engineering, the impact moment of the oil flow on the gas relay baffle is related to the oil flow surge characteristics inside the converter transformer under the excitation surge. Therefore, it is necessary to obtain the oil flow velocity through the gas relay under the inrush current through finite element simulation experiments, and use it as an excitation to obtain the corresponding degree of deflection of the gas relay baffle.