## 3 Protection Method Combining the Stator and Rotor Currents
### Calculation Method of the Protection Setting Value  
The actual VSPSGM may have a slight negative-sequence component in normal operation [25], which is mainly caused by the structural asymmetry, unbalanced voltage, and sensor measurement error, so the \(g(t)\) is not exactly 0. Considering that the VSPSGM will undergo strict performance index detection before leaving the factory, the negative-sequence component generated by structural asymmetry is much smaller than that generated by a large unbalanced voltage. Therefore, the influence of unbalanced voltage and sensor measurement error is mainly considered in the protection setting value calculation. The influence of unbalanced voltage is simulated by the random voltage drop of stator and rotor single-phase voltage, and the influence of the sensor measurement error factor is simulated by adding noise to each phase current obtained by simulation. The maximum action value \(S_{op,normal}\) under normal operating conditions is simulated and multiplied by the reliability coefficient greater than 1 to obtain the protection setting \(S_{set}\).  
Taking the VSPSGM shown in Table 1 as an example, it is assumed that the single-phase voltage of the stator side drops by 1-40% randomly, and the single-phase voltage of the rotor side also drops by 1-40% randomly. A large unbalanced voltage will lead to zero-sequence voltage protection action, so the more serious voltage drop is not considered. A total of 10 dB Gaussian white noise is added to the simulated phase currents. When the slip ratio \(s\) is 0.01, the maximum action value of the normal running state \(S_{op,normal}\) obtained in the above scenarios is shown in Figure 4. It can be found that when the voltage drops on the stator and rotor sides, the unbalanced voltage generated will increase the protection action value \(S_{op,normal}\), and the maximum value of \(S_{op,normal}\) in each scenario is 0.0184. When \(s\) is 0.1, the protection action value \(S_{op,normal}\) in each scenario is shown in Figure 5, and the maximum value of \(S_{op,normal}\) is 0.0179. It can be found that under different rotor speeds, the difference of the maximum action value \(S_{op,normal}\) caused by unbalanced voltage and sensor measurement error is small, and it can be considered that the maximum \(S_{op,normal}\) is almost unaffected by the rotor speed. The maximum value is selected to set the protection setting value \(S_{set}\).  
Figure 4: The action value \(S_{op,normal}\) with different phase voltage drops when the slip ratio \(s\) is 0.01.  
After the above analysis, \(S_{set}\) can be set to:  
\[S_{\text{set}}=K_{rel}\cdot\max(S_{\text{op.normal}}) \tag{20}\]  
where \(K_{rel}\) is the reliability coefficient. To give the protection setting value \(S_{set}\) high reliability, the value of \(K_{rel}\) is set as 1.5. Then, the protection setting value \(S_{set}\) is calculated to be 0.0276.  
It should be noted that this method is applicable to VSPSGMs of different types, different capacities, and different winding connection forms. Of course, the protection setting values of different units are different, which need to be set according to their specific parameters, but the calculation method of protection setting values in Section 3.2 is universal. More specifically, the proposed method can be extended to the motor with three-phase AC excitation, and cannot be applied to the motor with single-phase DC excitation.