## 3 New Strategy to Avoid the Impact on GC: Three-Point Climbing Algorithm  
The traditional sampling method when GC exists is shown in Figure 3. In the \(M_{1}\) phase, \(v_{1}\) decreases slowly, and \(v_{2}\) increases slowly. Sampling continues for \(v_{1}\) and \(v_{2}\) until \(t_{11\_n}\) and \(t_{12\_n}\), respectively; \(v_{1}\) falls to stable value \(v_{dc}X_{11}\), and \(v_{2}\) rises to stable value \(v_{dc}X_{12}\). After stabilization, the final \(v_{11}\) and \(v_{12}\) are obtained. The method switches to the \(M_{2}\) phase until \(v_{1}\) and \(v_{2}\) reach stable values \(v_{dc}X_{21}\) and \(v_{dc}X_{22}\), respectively, and the controller obtains the final \(v_{21}\) and \(v_{22}\). One sampling period \(T_{C}\) ends, and the insulation resistance values \(R_{f2}\) and \(R_{f1}\) are calculated by \(v_{11}=v_{dc}X_{11}\), \(v_{12}\) = \(v_{dc}X_{12}\), \(v_{21}=v_{dc}X_{21}\), and \(v_{22}=v_{dc}X_{22}\). The resistance values of \(R_{11}\), \(R_{12}\), \(R_{21}\), and \(R_{22}\) are large, so the charging time of the capacitor is long. Sampling and calculation should be performed after GC charging is completed; hence, the measurement time of the traditional method is long and unable to meet the real-time requirements of EVs. To avoid the measurement overtime caused by GC, a new insulation resistance monitoring method, namely, three-point climbing algorithm, is proposed.  
Figure 2: Equivalent circuit of unbalanced bridge with GC. (**a**) The circuit of \(M_{1}\) phase. (**b**) The circuit of \(M_{2}\) phase. (**c**) The equivalent circuit of \(M_{1}\) phase. (**d**) The equivalent circuit of \(M_{2}\) phase.  
Figure 4 shows that each phase is sampled three times, and the sampling intervals are equal. With \(v_{11}\) as an example, the three sampling times are \(t_{11\_1}\), \(t_{11\_2}\), and \(t_{11\_3}\); the sampling voltage values are \(v_{11\_1}\), \(v_{11\_2}\), and \(v_{11\_3}\), respectively, and the time intervals are \(\Delta t\). Similar definitions of \(v_{12}\), \(v_{21}\), and \(v_{22}\) are provided to facilitate the calculation, and \(E_{1}\) and \(E_{2}\) are used to present natural exponential function. The following equation is then obtained from (5).  
\[\left\{\begin{array}{l}\frac{v_{11\_1}-v_{11\_2}}{v_{11\_2}-v_{11\_3}}=e^{- \frac{\Delta t}{v_{1}}}=E_{1},\quad\frac{v_{12\_1}-v_{12\_2}}{v_{12\_2}-v_{12 \_3}}=e^{-\frac{\Delta t}{v_{1}}}=E_{1}\\ \frac{v_{21\_1}-v_{21\_2}}{v_{21\_2}-v_{21\_3}}=e^{-\frac{\Delta t}{v_{2}}}= E_{2},\quad\frac{v_{22\_1}-v_{22\_3}}{v_{22\_2}-v_{22\_3}}=e^{-\frac{\Delta t}{v_{2}}}= E_{2}\end{array}\right. \tag{6}\]  
\(t_{11\_1}\), \(t_{12\_1}\), \(t_{21\_1}\), and \(t_{22\_1}\) are set as initial times for the first-order circuit full response curve, and the curve Equation (5) is converted into Equation (7).  
\[\left\{\begin{array}{l}v_{11\_2}=v_{dc}X_{11}+(v_{11\_1}-v_{dc}X_{11})E_{1} \\ v_{12\_2}=v_{dc}X_{12}+(v_{12\_1}-v_{dc}X_{12})E_{1}\\ v_{21\_2}=v_{dc}X_{21}+(v_{21\_1}-v_{dc}X_{21})E_{2}\\ v_{22\_2}=v_{dc}X_{22}+(v_{22\_1}-v_{dc}X_{22})E_{2}\end{array}\right. \tag{7}\]  
Equation (7) is converted into Equation (8).  
\[\left\{\begin{array}{l}X_{11}=\frac{v_{11\_2}-v_{11\_1}E_{1}}{v_{dc