## 3 Model of the Variable-Speed Pumped Storage Unit
At present, the stator internal CT of the large generator is mainly the TPY type. TPY is a current transformer considering transient characteristics for protection applications; its core has an air gap. The core of the TPY current transformer has an air gap, so the reluctance is large, and the saturation time is prolonged; that is, there is a longer time to maintain the linear transformation, which greatly improves the transient characteristics. Therefore, a TPY current transformer has a strong anti-saturation ability, which can effectively avoid transient maloperation. The error of the TPY current transformer under rated primary current should be less than \(\pm 1\%\). The measurement accuracy is high. In addition, CT2 and CT3 are the same type current transformers, which can overcome the measurement error caused by non-fault factors to a certain extent. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Stator** & **Rotor** \\ \hline Slot number (\(Z\)) & 252 & 294 \\ Winding form & Double-layer lap winding & Double-layer wave winding \\ Number of parallel branches & 4 & 2 \\ Number of coils per branch & 21 & 49 \\ First pitch (\(y_{1}\)) & 15 & 21 \\ Second pitch (\(y_{2}\)) & 14 & 21 \\ Rated current/A & 12317 & 6400 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The basic parameters of a variable-speed pumped storage unit. Figure 2: Stator winding branch wiring diagram. The protection object of split-phase transverse differential protection is the short-circuit fault of the stator winding, and the fundamental frequency effective value of circulating current is extracted as the action quantity of split-phase transverse differential protection. However, the protection object of the proposed method is the rotor winding short-circuit fault, and the comprehensive effective value of the characteristic frequency components of the circulating current is extracted as the protection action. In summary, this method does not need additional measurement devices in the industrial environment and only needs to add a set of protection algorithms in the microcomputer protection device to realize the protection of the rotor winding short-circuit fault of the variable speed pumped storage unit. When the slip ratio \(s\) is 0.1, the theoretical characteristic frequency of the circulating current between stator branches can be calculated according to Equation (7), and the calculation results are shown in Table 2.  
It is assumed that a short-circuit fault occurs in the 32 nd turn coil of branch A2 (the second branch of phase A in rotor winding) and the 34 th turn coil of branch A2; the turn difference is 2 turns, and the fault time is 35 s. The analytic model constructed by the multi-loop method is used for simulation calculation, and the transient current waveforms of stator branches are obtained as shown in Figure 3. The abscissa of Figure 3 is time, and the ordinate is the normalized unit value of the current. The reference value of current normalization is the amplitude of the 50 Hz stator phase current. In normal operation, the amplitude of the normalized current of each stator branch is about 0.25 p.u (the stator winding is a four-branch structure in each phase, 1/4 = 0.25 p.u). p.u is the abbreviation of per unit, which is a numerical labeling method used in power system analysis and engineering calculation. It represents the relative value of a physical quantity or a parameter that can be considered dimensionless. Since the physical position of each stator branch winding is different, the transient current of each stator branch is different. It can be found that the stator branch current distortion is obvious, with a large number of harmonic components after the fault occurs.