Figure 1.
Faulty phase equivalent circuit.
Figure 2.
T2-FL–EKF conceptual model. PMSM, permanent magnet synchronous motor; T2-FL–EKF, type-2 fuzzy logic–extended Kalman filter.
Figure 3.
EKF flow diagram. EKF, extended Kalman filter.
Figure 4.
T2-FL estimator configuration. T2-FL, type-2 fuzzy logic.
Figure 5.
T2-FL estimator structure. T2-FL, type-2 fuzzy logic.
Figure 6.
T2-FL membership functions configuration. T2-FL, type-2 fuzzy logic. (a) Input variables and (b) Output variable.
Table 1.
T2-FL rule set for Rs determination.
| E/E′ | NM | NS | Z | PS | PM |
|---|---|---|---|---|---|
| NM | NM | NM | NS | Z | PS |
| NS | NM | NS | Z | PS | PM |
| Z | NS | Z | Z | Z | PS |
| PS | Z | PS | PS | PM | PM |
| PM | PS | PM | PM | PM | PM |
Figure 7.
Dynamic speed regression.
Figure 8.
Rotor angular velocity.
Figure 9.
Angular position.
Table 2.
Indication of ITSC severity.
| µ (%) | Tfault | Severity | Indication | |
|---|---|---|---|---|
| Rf = 1 Ω | µ = 25 | 40 turns | High | Poor visibility |
| µ = 50 | 80 turns | Extremely high | Higher visibility |
Figure 10.
Iabc stator currents.
Figure 11.
Vector control currents.
Figure 12.
Stator resistance measurements. (a) μ = 25% and (b) μ = 50%.
Figure 13.
Fault current measurements. (a) μ = 25% and (b) μ = 50%.
Table 3.
ITSC fault current values.
| For Rf = 1 Ω | Estimated If moy | Measured If moy | RMSE |
|---|---|---|---|
| μ = 25% | 0.0182 | 0.0216 | 0.2303 |
| μ = 50% | 0.0321 | 0.0416 | 0.5513 |
Figure 14.
Rs estimation precision: (a) EKF approach, (b) FL–EKF approach and (c) T2-FL–EKF approach. T2-FL–EKF, type-2 fuzzy logic and extended Kalman filter; FL–EKF, fuzzy logic–extended Kalman filter.