## 1 Introduction  
Second-generation (2G) high-temperature superconducting (HTS) generators are promising because they can achieve a higher power density compared to conventional generators [1]. For synchronous generator applications, HTS coils placed in the stator have an advantage in terms of static cooling, but HTS coils will suffer AC loss because they are under alternating magnetic fields and currents.  
The AC loss of an isolated HTS coil has been studied by many groups [2; 3; 4; 5; 6]. To calculate the AC loss of HTS coils in the actual generator environment, a two-stage segregated model consisting of a machine model and an AC loss model has been proposed [7] and used [8; 9]. The rotating machine is first simulated by the A-formulation, and then the HTS coil is simulated by the H-formulation [10], with the boundary condition calculated from the A-formulation model.  
The T-A formulation model [11; 12] can fully couple the A-formulation model of the generator and the HTS coil model. The efficiency of the T-A formulation model is higher than the H-formulationmodel due to the decrease in the degrees of freedom [11]. Moreover, the T-A formulation model can directly achieve the fully coupled simulation of the HTS coils under the generator's electromagnetic environment because rotating generators are usually simulated by the A-formulation [13].  
When a short circuit fault happens, the magnetic field on the surface of the HTS coils and the current flowing in the coils will change drastically and cause a greater AC loss. The ohmic loss also occurs when the current exceeds the critical current of the coils. If the cooling capacity of the cryocooler is not enough to remove the heat immediately, the HTS coils may be permanently damaged [14]. To understand whether the short circuit fault will cause permanent damage to HTS coils, conducting an electromagnetic thermal coupling simulation is of great importance. It should be considered that these factors will have an effect on HTS materials, including the magnetic field, the current and the temperature.  
To date, some numerical simulations of the short circuit faults of HTS generators have been done [15; 16; 17; 18; 19]. However, none of these simulations achieves fully coupled simulations, considering the dependence of the critical current density on the temperature and the magnetic field.  
The main novelty of this paper is to conduct an electromagnetic-thermal coupling numerical study of a synchronous generator with 2G HTS armatures. In Section 2, the field-circuit thermal coupled model is introduced. In Section 3, the parameters of the HTS generator and the HTS coils are introduced. In Section 4, the model is first used to calculate the AC loss of the stator HTS coils under the rated condition of the generator. Then, the transient electromagnetic-thermal behavior of the HTS coils under a sudden three-phase short circuit fault at the no-load operation will be studied. This situation causes a maximum peak short circuit current, which is the worst case for the HTS coil. Moreover, the effects of the copper stabilizer thickness on the thermal stability of the HTS coil at the worst short circuit fault will also be investigated. Finally, our conclusions are drawn in Section 5.