## 3 Remanence Measurement Method Based on Degaussing Hysteresis Loop  
### Principle of Attenuation Oscillation of Energy Storage Capacitors  
When there is remanence in the transformer core, the internal remanence can be considered remanence energy, and the excess energy is dissipated in the form of RLC oscillation due to the mutual cancellation of the applied energy and the initial remanence energy. In the degaussing process, voltage and current curves are collected, the flux is calculated through voltage integration, and the degaussing hysteresis loop diagram of the flux and current is plotted. In the case of sufficient degaussing, the initial remanence measurement is determined by calculating the difference between the starting point and the endpoint before and after degaussing [26; 27].  
The method proposed in this paper includes a remanence measurement circuit consisting of an energy storage capacitor, a transformer core, and its windings. This method connects an energy storage capacitor that stores charge with a coil of a converter transformer. When the circuit current is low, the electric field energy within the capacitor is converted into the magnetic field energy of the core. When core saturation is reached, indicating that the magnetic field energy is fully stored, the remaining energy is reabsorbed into the capacitor. Oscillation is generated by the mutual conversion between the electric field energy of the capacitor and the magnetic field energy of the core. The oscillation period depends on the equivalent inductance of the coil of the converter transformer core, resulting in domain deflection between the attenuated magnetic field generated by the coil and the transformer core. A capacitor is connected to the transformer to form an RLC oscillation circuit.  
The equivalent circuit diagram is shown in Figure 3, and based on the relationship between voltage and current for capacitance and inductance, the circuit equation forms the RCL differential equation, as shown in Equation (1).  
\[LC\frac{\mathrm{d}^{2}U_{C}}{\mathrm{d}t^{2}}+R_{2}C\frac{\mathrm{d}U_{C}}{ \mathrm{d}t}+U_{C}=0 \tag{1}\]  
Let \(U_{c}=Ae^{at}\) substitute Equation (1) to obtain the characteristic Equation (2):  
\[LC\alpha^{2}+R_{2}C\alpha+1=0 \tag{2}\]  
When an attenuated oscillation occurs in a circuit, the condition of Equation (3) is satisfied:  
\[\zeta=\frac{R_{2}}{2}\sqrt{\frac{C}{L}}<1 \tag{3}\]  
The current change in the line should be as shown in Equation (4):  
\[I_{C}=e^{-\frac{R_{2}}{2L}t}(A_{1}\cos(\omega_{\mathrm{d}}t)+A_{2}\sin(\omega_ {\mathrm{d}}t)) \tag{4}\]  
Wherein \(\omega_{\mathrm{d}}=\sqrt{\frac{1}{LC}-(\frac{R_{2}}{2L})^{2}}\), \(A_{1}=I_{C0}=0\)\(A_{2}\). Specifically:  
\[A_{2}=\frac{\mathrm{d}I_{C}}{\mathrm{d}t}(0)+\frac{R_{2}}{2L}A_{1}\omega_{ \mathrm{d}} \tag{5}\]  
Simplify Equation (5) to obtain:  
\[A_{2}=\frac{U_{C}(0)}{L\omega_{\mathrm{d}}} \tag{6}\]Equation (4) can be reduced to:  
\[I_{c}=e^{-\frac{\hbar\omega_{\rm d}}{2\hbar}t}\frac{U_{C}(0)}{\omega_{\rm d}L} \sin(\omega_{\rm d}t) \tag{7}\]  
After obtaining the relevant data of the voltage and current transformers, the voltage and current are exported at each time, the current change curve is drawn, and the magnetic flux change curve is obtained according to Equation (8).  
\[\psi(t)=\int_{t_{0}}^{t}u_{L}(t)\mathrm{d}t+\psi(t_{0}) \tag{8}\]