*5.5. Robustness Test*

As in the simulation, the machine was tested using different load conditions; this approach tested the parameter estimation response to various load conditions. The tests are listed as following:

Test 1: Variation of frequency from 20 Hz to 50 Hz with a 10 Hz step.

Test 2: Variation of load Current variation from 0.72 A to 2.25 A by 0.75 A step at a constant frequency of 30 Hz.

The EKF showed a constant response in assays with different frequencies (20 Hz, 30 Hz, 40 Hz and 50 Hz) in the presence of 4%, 8%, 12%, and 16% stator inter-turn fault in phase A, and a load current of 0.72 A in a healthy state (Table 2). This emphasized the robustness of this technique when there was a variation in frequency. Moreover, the results confirmed the simulation results for the same machine during the same operating and fault conditions.


**Table 2.** EKF estimation response with different frequencies at constant load current in phase A.

Besides, the estimation response was tested when exposed to variations in the current (1.5 A and 2.25 A) and at a constant frequency of 30 Hz. Again, the response of the EKF technique showed a robust estimation in load current variation at a constant frequency, (Table 3). For safety conditions, it was not able to emulate short circuit inter turns fault more than 12% as the current in the faulty state went over 5 A; 5 A being the maximum load current for this machine.


**Table 3.** EKF estimation response with different load currents in phase A at a constant frequency.

#### *5.6. Decision-Making Process*

The decision was taken based on the estimated total internal current in all three phases of the machine. The loads were divided into two groups: critical loads and uncritical loads were connected through contactors K2 and K1, respectively. To prevent the propagation of internal inter-turn faults inside the machine, there are two proposed scenarios:


Figure 32 shows the flowchart presenting the FDS EKF technique and the proposed scenarios based on the operator's choice.

### 5.6.1. Scenario 1: The Disconnection of the Machine

This solution provides for the safety of the machine and prevents the propagation of the fault to other turns and phases. However, this solution affects the reliability of the operation, and it requires a backup for the disconnected generator.

This scenario is presented in the experimental work at RMS load current of 1.5 and 30 Hz frequency, in a healthy state the machine gives *nA s*/*<sup>c</sup>* = 0, *nB s*/*<sup>c</sup>* = 0 and *nC s*/*<sup>c</sup>* = 0. At *t* = 0.5 s. A 4% inter-turn fault exists in phase A, the estimated parameter *nA s*/*<sup>c</sup>* = 4.1% and the total estimated internal current reached an RMS value of 2.8 A. As the FDS works in parallel with the protection system of the machine, the disconnection of the machine will be based on the extremely inverse time (EIT) thermal characteristics curve of overcurrent relay based on IEEE standard [46], the expected time to disconnect the machine is 17 s, at TDS = 0.1 s. Figure 33b,c show the detection time and disconnection time of contactor K1 and contactor K2 after detecting the presence of a fault. An LCD was used to monitor the situation of the machine in both the healthy and faulty states; it also shows the expected disconnection time of both contactors and the position of the loads' contactor to inform the operator about the situation.

#### 5.6.2. Scenario 2: Load Shedding

The second scenario is the disconnecting of some uncritical loads (contactor K1) to decrease the total current of the machine allowing it to run under the fault condition. This solution offers the reliability for the process; the machine can continue running in the presence of a fault but with partial loading. This solution does not solve the main problem of internal fault, but it gives the operator a suitable time to take corrective action; the fault may propagate for other turns or phases, respectively, increasing the internal short circuit current, causing a severe fault.

This scenario was implemented at RMS load current of 1.5 A and 30 Hz frequency; at *t* = 0.5 s, 2% inter-turn fault was emulated in phase C, which caused an increase in the total estimated internal current to 2 A. The fault was indicated, and the first group of loads (the uncritical loads) connected through contactor K1 was disconnected (Figure 34a). The disconnection of K1 decreased the current in the machine, and the total current became 1.25 A, allowing the machine to return to its normal state for a definite time and consequently canceling the alarm indication. After a time, the fault percentage increased to 8%, causing an increase in the internal current. In this case, the right decision was to disconnect the machine to solve the internal fault problem. The machine was disconnected after the estimated time based on the EIT characteristics of the overcurrent relay.

**Figure 32.** Decision-making process scenarios flowchart.

**Figure 33.** Scenario 1 Alarm indication and machine disconnection.

**Figure 34.** Scenario 2 Alarm indication and contactors disconnection.

#### **6. Conclusions**

The paper presents the detection and isolation of PMSG stator windings faults using the EKF and the UKF, which are model-based techniques. The model of the faulty machine was implemented in the state-space model using the machine equations in the dq-frame. The estimated states of the EKF and the UKF techniques were the short circuit turns ratio in each phase. It was noted that the proposed techniques have the following advantages:


On the other hand, the UKF technique overcomes the EKF technique drawback of the inaccuracy of the technique in case of severe faults, as it is a nonlinear system and it was linearized around a definite operating point, and so the error of estimation increased as the value of the short circuit turn ratio increased.

Also, the tuning of the weighting matrices (*Q* and *R* ) has a great impact on the estimated parameters. As indicated in the result, an increase in *Q* implies an acceleration of the dynamic response of the fault indicator with an increase in noise sensitivity, however, decreasing *Q* implies better filtering with a decrease in the dynamic response.

The results of this paper point to several exciting directions for future research work. The proposed technique can be used on FD of different types of faults such as bearing, eccentricity, and demagnetizations faults in machines. Moreover, other types of FD techniques may be used, such as artificial intelligence-based techniques and signal-based techniques, and comparing their results with the results of the EKF Technique. This result raises the ability to implement the fault tolerant control (FTC) technique in case of faults such as using the model predictive control (MPC) [47], which would increase the reliability of the machine safety-critical applications.

**Author Contributions:** Conceptualization, W.E.S., M.A.E.G. and A.L.; methodology, W.E.S. and M.A.E.G.; software, W.E.S.; validation, W.E.S., M.A.E.G. and A.L.; formal analysis, W.E.S., M.A.E.G. and A.L.; investigation, W.E.S., M.A.E.G. and A.L.; resources, W.E.S. and M.A.E.G.; data curation, W.E.S. and M.A.E.G.; writing—original draft preparation, W.E.S. and M.A.E.G.; writing—review and editing, W.E.S. and M.A.E.G.; visualization, W.E.S.; supervision, M.A.E.G. and A.L.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Nomenclature**


#### **References**


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