## 3 Remanence Measurement Method Based on Degaussing Hysteresis Loop
### Determination of the Size of Capacitor Energy Storage  
According to the capacitor energy calculation in Formula (9), the energy stored in the capacitor is determined by the voltage across both sides of the capacitor and the capacitance itself. When the energy storage of the capacitor is too low, it can result in incomplete degaussing, which compromises measurement accuracy. \[W_{C}=\frac{1}{2}{C}{U_{C}}^{2} \tag{9}\]  
To ensure the accuracy of the remanence measurement, it is essential to address the issue of capacitor charge in advance, specifically by determining the capacitor's energy storage size based on the maximum saturation level of the converter transformer core. Regardless of the remanence present at this moment, it can be mitigated by the damping oscillation current released by the capacitor, thereby facilitating precise measurement. However, indiscriminately increasing the capacitance size \(C\) or the voltage \(U_{C}\) across the capacitor will result in prolonged degaussing hysteresis loop shrinkage or prevent the circuit current from diminishing oscillation. Thus, a method is required to establish the relationship between saturation flux, stored electrical energy, and voltage. The factory report of the converter transformer contains the B-H hysteresis curve of the silicon steel sheet used in the transformer's core, or the technical report for the hysteresis curve specific to the material of the silicon steel sheet in the core can be referred to [28]. In the _B-H_ curve, coercivity is defined as the reverse magnetic field strength \(H_{c}\) required to reduce the magnetic induction intensity B from saturation to zero. Specifically, in the hysteresis loop, coercivity corresponds to the strength of the reverse magnetic field when the magnetic induction intensity B reaches zero. In the diagram, this is typically represented in the demagnetization curve, which illustrates the process of reverse demagnetization from the saturation state, and when the value of the B-axis is zero, the value of the H-axis represents the coercivity \(H_{c}\)[15; 29; 30]. Figure 3: The equivalent circuit diagram. From Formula (10) for the calculation of energy density, it can be seen that the energy per unit volume in the core of the converter transformer must meet the following conditions:  
\[u=\frac{1}{2}B_{\mathrm{r}}H_{c} \tag{10}\]  
Here, \(u\) denotes energy per unit volume in joules per cubic meter (J/m\({}^{3}\)). If it is necessary to calculate the total energy \(W_{\mathrm{demag}}\) required for the whole magnetic core, the energy per unit volume shall be multiplied by the volume \(V\) of the magnetic core, and the result is shown in Equation (11):  
\[W_{\mathrm{demag}}=u\times V=\frac{1}{2}B_{\mathrm{r}}H_{c}V \tag{11}\]  
The available capacitance energy must satisfy Equation (12):  
\[W_{c}\geq W_{\mathrm{demag}}+W_{R} \tag{12}\]  
where \(W_{R}\) is the energy dissipated by the resistor during this period, and its magnitude is presented in Equation (13). \[W_{R}=I_{C}^{2}R_{2} \tag{13}\]  
Simultaneously with the above formula, Equation (12) can be rewritten as Equation (14):  
\[\frac{1}{2}CUL_{c}^{2}\geq\frac{1}{2}B_{\mathrm{r}}H_{c}V+e^{-\frac{R_{2}}{L} t}\frac{U_{C}(0)^{2}R_{2}}{L^{2}(\frac{1}{LC}-(\frac{R_{2}}{2L})^{2})}\sin^{2}( \sqrt{\frac{1}{LC}-(\frac{R_{2}}{2L})^{2}t}) \tag{14}\]  
The range of values for \(C\) of the energy storage capacitor is as follows:  
\[C\geq\frac{B_{\mathrm{r}}H_{C}V}{U_{c}(0)^{2}(1-\frac{2R_{2}}{L})} \tag{15}\]  
In the case of unknown remanence, in order to ensure that the energy of the energy storage capacitor can fully meet the needs of remanence measurement and demagnetization, the remanence magnitude \(B_{\mathrm{r}}\) is replaced with the saturation magnetic induction intensity \(B_{\mathrm{s}}\).