## 4 Experimental Tests
### Experimental Results  
Numerous tests have been conducted to verify that the measured exciter field current (\(I_{fe}\)) must be significantly increased in BSMs under warm conditions to maintain a constant reactive power delivered by the machine. The tests involve initially setting an operating point for the BSM in terms of active and reactive power, and then allowing the machine to operate as it warms up, while continuously keeping the reactive power constant. To maintain constant \(Q\) as the temperature rises, it is necessary to increase the exciter field current (\(I_{fe}\)).  
All the aforementioned electrical variables (\(P\), \(Q\), \(U\), \(U_{fe}\), \(I_{fe}\), \(I_{f}\), and \(U_{f}\)) and the rotor and stator temperatures are continuously monitored. Figure 9 illustrates the increase in the exciter field winding current due to the rising rotor temperature during a test.  
Since it is impossible to access the voltage and current of the field winding of the main machine in industrial BSMs and consequently to calculate the rotor temperature, the stator temperature was measured to assess whether it could be used instead of the rotor temperature to estimate the excitation current (\(I_{fe}\)).  
Figures 10 and 11 show the exciter field winding current variation with the increment of the stator and rotor temperatures, respectively. It can be seen that, in this BSM, the exciter field current (\(I_{fe}\)) consumption increases by 0.75% every 10 K degrees of temperature rise. Thus, to develop a model capable of estimating the excitation current consumption at an electrical operating point of the machine, in the case of BSMs it is necessary to add the machine temperature variable in the estimation model, as said above.  
Figure 10: Exciter field current rise (\(\Delta I_{fe}\)) with respect to stator temperature rise during a 2 h operation test (\(P\) = 2.9 kW, \(Q\) = 2.3 kvar, \(U\) = 400 V).  
Figure 9: Exciter field current (\(I_{fe}\)) with respect to rotor temperature during a 2 h operation test (\(P\) = 2.9 kW, \(Q\) = 2.3 kvar, \(U\) = 400 V).  
Comparing Figures 10 and 11, it is verified that the variation in excitation current consumption with increases in stator and rotor temperatures is very similar. Importantly, the slope remains constant with both temperatures, indicating that it is feasible to use the stator temperature in the estimation model.  
Additionally, Figure 12 displays the rotor and stator temperatures during a constant reactive power test. The difference between them is also represented. This difference is not constant and varies depending on the machine temperature.  
As described in Section 4, to validate that this method is significantly more efficient when using temperature as an input to the model, a DNN was trained with real operating points measured using the experimental system described in the previous subsection.  
Figure 13 shows the measured excitation current, \(I_{fe,mean}\) (in blue), and the calculated excitation current, \(I_{fe,cal}\) (in orange), for all test operational points. The calculated excitation current value is derived from the DNN previously trained with the machine operational data under healthy conditions.  
As shown in Figure 13, the DNN excitation current prediction is highly accurate, with a maximum error of 3 mA, which is an error of 1.5%. The MSE obtained is 0.5%, which means that the minimum detectable fault severity is 0.5%, considering the fault severity of Equation (2).  
Figure 11: Exciter field current rise (\(\Delta I_{fe}\)) with respect to rotor temperature rise during a 2 h operation test (\(P=2.9\) kW, \(Q=2.3\) kvar, \(U=400\) V).  
Figure 12: Temperature variations during a 2 h operation test (\(P=2.9\) kW, \(Q=2.3\) kvar, \(U=400\) V).