**5. Validation**

Validation of the RTDT was performed by comparing its real-time outputs to measurements available on the physical WRIM during operation. Waveforms shown below are real-time raw data acquired by an oscilloscope. For comparison purpose, a dq model of the WRIM was also implemented on another core of the DRTS for parallel execution alongside the CFE-CC model.

For the first setup, shown in Figure 6a, the WRIM's stator windings were connected to a three-phase 60 Hz autotransformer. It was used as an induction motor, so rotor terminals were short-circuited. The WRIM was mechanically coupled to a synchronous generator loaded by resistors. Figures 7 and 8 show waveform comparisons between measurements, CFE-CC model and dq model. Only winding *a*

is shown because *b* and *c* were only 120◦ phase-shifted. Both models yielded good accuracy, but it was possible to draw more conclusions from the frequency decomposition. Tables 3–5 show the notables frequencies of the spectra. As expected, the CFE-CC model approximated well higher frequencies which were related to the geometry of the machine, whereas the dq model only computed harmonics related to input voltage.

**Figure 6.** WRIM setups used for validation. (**a**) Balanced; (**b**) With rotor unbalance; (**c**) With TRIACs.

**Figure 7.** Stator current in winding *as* during load operation, enlarged on right side.

**Figure 8.** Rotor current in winding *ar* during load operation, enlarged on right side.


**Table 3.** Main frequency components of stator input voltage.



**Table 5.** Main frequency components in rotor current.


Geometric irregularities of the machine had an impact on the torque as well, as seen from Figure 9. By analysing the electromagnetic torque of a machine, one can draw many conclusions about its condition.

**Figure 9.** Electromagnetic torque during load operation, enlarged on right side.

Figure 10 shows the clear congruence between real-time output of the search coil voltage and its measured counterpart. Search coil voltage gave a good indication of local magnetic flux linkage. Using Equation (11), any number of search coils could be directly added to the machine's winding configuration without restarting the FEM process. This also proved to be an interesting tool for online fault monitoring.

**Figure 10.** Search coil voltage during load operation, enlarged on right side.

Figure 11 shows the dynamic response of rotor currents when the mechanical load was suddenly disconnected from the shaft. Here, the position tracking control loop played an important role. It needed to be fast enough to minimize the error during speed variations.

**Figure 11.** Rotor current in winding *ar* starting from load operation and suddenly disconnecting the load.

The following Figures 12–14 show the RTDT's current outputs when a phase imbalance was introduced. The setup is depicted at Figure 6b. A resistor was connected to winding *ar* of the physical machine, and the same was done to the RTDT. While the frequency content was accurate, a small phase discrepancy was present at winding *br* and *cr*. The cause could be related to the methodology employed to compute [*L*] in Appendix A, such as the way the coil end inductances were added. Many assumptions were made. Magnetic saturation could also play a role since it was not taken into account in the model.

**Figure 12.** Stator current in winding *as* during load operation with 12 ohm resistor on winding *ar*, enlarged on right side.

**Figure 13.** Rotor current in winding *ar* during load operation with 12 ohm resistor on winding *ar*, enlarged on right side.

**Figure 14.** Rotor current in winding *br* during load operation with 12 ohm resistor on winding *ar*, enlarged on right side.

Finally, TRIACs were added inside the delta configuration as depicted in Figure 6c. It demonstrated the RTDT's behavior under switching converter's voltage input for an unusual phase configuration. Figures 15 and 16 show currents flowing in windings *as* and *ar*. The RTDT yielded accurate estimations.

**Figure 15.** Stator current in winding *as* during load operation and fed through TRIACs, enlarged on right side.

**Figure 16.** Rotor current in winding *ar* during load operation and fed through TRIACs, enlarged on right side.
