# Electrical Monitoring under Transient Conditions:
## 2 Foundations of the Transient Analysis of Electrical Quantities
### Transient Analysis of Stray Fluxes  
During these recent years, the transient-based methodology approach that had been successfully applied to motor currents (and, more specifically, to starting currents) was extrapolated to the analysis of other electrical quantities, such as stray fluxes. Since the early 2000s, it had been observed that the installation of external coil sensors attached to the motor frame and the further analysis of the electromotive force (emf) signals that the stray flux induces in these sensors is a powerful source of information for the diagnosis of many faults [25; 26; 27]. Different authors demonstrated the theoretical expressions of the harmonics that were amplified by rotor damages, eccentricities, stator faults, and even coupling system problems at the induced emf signals under the steady-state regime. Most of these harmonics are slip-dependant, and many of them are coincident with those appearing in the  
Figure 2: Theoretical evolutions of the most relevant harmonics associated to rotor damages (denoted by \(f_{\rm rot}\)) and eccentricities/misalignments (denoted by \(f_{\rm ee}\)) that are present in the motor starting current, considering a simulated direct on-line starting on an induction motor. stator current spectra. Therefore, the analysis of steady-state stray flux signals became an interesting alternative for the diagnosis, following a similar procedure than that employed for MCSA. With the advent and development of the transient-based diagnosis approaches and the better knowledge of the signal processing tools that are available for the analysis of non-stationary signals, some works proposed the use of this technology for the diagnosis of emf signals that were induced by the stray flux under the transient operation of the machine. Some authors [28; 29; 30] deepened the study of the transient emf signals that were induced under starting, proving that this analysis is a robust source of information for the diagnosis of many faults such as rotor asymmetries (both in cage and in wound rotor induction motors), eccentricities, and misalignments. In comparison with the current analysis, the advantages of analyzing stray flux signals rely on the much richer harmonic content of the registered signals (this means that many more evolutions can be identified in the time-frequency maps and employed to diagnose the fault) and the lower influence of load-related problems, a fact that may help to discriminate between motor and load-related anomalies (e.g., eccentricities and misalignments) [31; 32]. Moreover, some motor manufacturers are incorporating embedded flux sensors in their machines, which will enhance the potential penetrability of the technique in the industry in the near future [33; 34]. However, the technique relying on the analysis of the stray flux has drawbacks also. One of them is the strong influence of the sensor position in the results; it has been proven that depending on the sensor location, the flux captured can be primarily radial or axial, and hence, the corresponding components (axial/radial) will be more observable in the resulting time-frequency maps. The point is that combining the information coming from different sensor locations can enhance the diagnosis, since more fault components of different nature can be identified [35]. On the other hand, the fault severity thresholds based on flux analysis are still less mature than those based on currents, which have been validated over the years. Usually, the most common locations for the stray flux sensors are those depicted in Figure 3. As reported in several works [36; 37], depending on the sensor position, a higher portion of axial or radial flux will be captured, and therefore, the corresponding components (axial or radial) will be present in the results of the analyses of the corresponding signal. In this regard, at Position A, the sensor mainly captures axial flux. On the contrary, the flux captured at Position C is primordially radial. Finally, Position B captures a portion of axial and a portion of radial flux.