## 2 Methods
### Test Bench for Loss Studies in HTS Winding  
The special test bench was developed to test HTS winding in a magnetic circuit equivalent to an electric machine. It consists of the generator with HTS annular winding, motor drive, and a set of sensors. The rotor of the generator was driven by an external electric motor (Figure 3a,b).  
In general, the experimental setup can be considered as a synchronous electric machine with excitation from permanent magnets. Its peculiarity is that it has two phases with the number of slots per pole and phase equal to 2. The HTS coils are cooled to a superconducting state by using liquid nitrogen (LN\({}_{2}\)) (77 K), which is poured into the body  
Figure 2: Inverter simulator for HTS devices. 1—microcontroller, 2—transistor drivers, 3—transistor assemblies with built-in protection diodes, 4—feedback sensor, (_DC_)—laboratory power source, (_Rs_)—noninductive current shunt, (_L_)—device under test, and (_DAQ_)—data acquisition system.  
of the electric machine. This is the simplest, most reliable, cheapest, and fastest cooling method suitable for laboratory testing. The enclosure of the machine is a single volume with an LN\({}_{2}\) inlet on the side and with output at the highest point of the structure to ensure that the volume is completely filled with coolant. The inlet is connected to the LN\({}_{2}\) tank with excessive pressure and the flow is controlled by a manual valve installed on the tank. The coolant from the output port is collected in an open dewar. This method does not require any additional cryogenic recuperation systems or pumps. As follows from the description, the rotor is also located in the nitrogen. The rotating sealing of the machine uses a technical solution similar to the pumps for liquefied natural gas: a spring loaded PTFE seal. The mechanical part of the stand consists of a drive (_D_) with a control system, the device under test (_G_), and a sensor Magtrol TMHS 307 (Magtrol SA, Rossens / Fribourg, Switzerland) that registers the torque (_M_) and speed (\(\omega\)) of rotation of the shaft. In the electrical part, the data acquisition system receives the electrical parameters of both phases (current and voltage), as well as the voltages proportional to the rotor speed and torque. All data are written to a file for further analysis on the PC.  
Thus, the assembled system can be tested as an electrical two-phase generator. Winding losses (\(P_{HTS}\)), in that case, can be determined via power balance:  
\[P_{input}=P_{no\ load}+P_{load}+P_{HTS}. \tag{2}\]  
The input power is equal to mechanical power:  
\[P_{input}=M\cdot\omega, \tag{3}\]  
where \(M\) and \(\omega\) are the torque and the speed of the shaft, respectively, recorded by the sensor. For a two-phase electric machine, the active output power (\(P_{load}\)) can be calculated as  
\[P_{load}=\frac{1}{t_{\rm m}}\int\limits_{0}^{t_{\rm m}}{\rm u_{1}}{\rm i_{1}} \rm{dt}+\frac{1}{t_{\rm m}}\int\limits_{0}^{t_{\rm m}}{\rm u_{2}}{\rm i_{2}} \rm{dt}, \tag{4}\]  
where \({\rm u_{1}}{\rm i_{1}}\) and \({\rm u_{2}}{\rm i_{2}}\) are the instantaneous values of the voltages and currents in the phases, and \(t_{\rm m}\)--integration period equal to the phase voltage period. No-load losses are equal to the sum of mechanical and magnetic losses \(P_{no\ load}=P_{mech}+P_{mag}\) for each rotation speed.  
Initially, no-load tests were carried out at various frequencies, which made it possible to determine the mechanical and magnetic losses in the system from the readings of the speed and torque sensor (\(P_{input}=P_{no\ load}\) in that case). After that, an identical, discrete variable load was connected to the phases, and the voltage and the current of each phase were recorded by the data acquisition system.  
Figure 3: (**a**) Schematic of the test site; (**b**) Photo of the mechanical part of the bench. 1—HTS generator, 2—torque and rotation speed sensor, and 3—variable speed motor drive.