Mounir et al 2023b - Revision history

Rimni at 14:45, 22 May 2023

2023-05-22T14:45:15Z

Rimni at 14:43, 22 May 2023

2023-05-22T14:43:05Z

Rimni at 10:08, 22 May 2023

2023-05-22T10:08:58Z

Rimni at 09:41, 22 May 2023

2023-05-22T09:41:40Z

Rimni at 09:41, 22 May 2023

2023-05-22T09:41:00Z

Rimni: /* Appendix */

2023-05-22T09:39:57Z

‎Appendix

Rimni at 09:37, 22 May 2023

2023-05-22T09:37:42Z

Rimni at 09:34, 22 May 2023

2023-05-22T09:34:18Z

Rimni at 09:33, 22 May 2023

2023-05-22T09:33:25Z

Rimni at 09:22, 22 May 2023

2023-05-22T09:22:08Z

@@ Line 502: / Line 502: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\left[ \begin{matrix}{v}_{ds}\\{v}_{qs}\\0\\0\end{matrix}\right] =</math><math>\, \left[ \begin{matrix}{R}_{s}+p{L}_{s}&-{\omega }_{r}{L}_{s}&p{L}_{m}&\, \\{\, \omega }_{r}{L}_{s}&{R}_{s}+p{L}_{s}&{\omega }_{r}{L}_{m}&\, \\p{L}_{m}&0&{R}_{r}+p{L}_{r}&\, \\0&p{L}_{m}&0&\, \end{matrix}\begin{matrix}{-\omega }_{r}{L}_{m}\\p{L}_{m}\\0\\{R}_{r}+p{L}_{r}\end{matrix}\right] \left[ \begin{matrix}{i}_{\begin{matrix}ds\end{matrix}}\\{i}_{qs}\\{i}_{dr}\\{i}_{qr}\end{matrix}\right]</math>
+| <math>\left[ \begin{matrix}{v}_{ds}\\{v}_{qs}\\0\\0\end{matrix}\right] =</math><math>\, \left[ \begin{matrix}{R}_{s}+p{L}_{s}&-{\omega }_{r}{L}_{s}&p{L}_{m}&\, \\{\, \omega }_{r}{L}_{s}&{R}_{s}+p{L}_{s}&{\omega }_{r}{L}_{m}&\, \\p{L}_{m}&0&{R}_{r}+p{L}_{r}&\, \\0&p{L}_{m}&0&\, \end{matrix}\begin{matrix}{-\omega }_{r}{L}_{m}\\p{L}_{m}\\0\\{R}_{r}+p{L}_{r}\end{matrix}\right]\,\, \left[ \begin{matrix}{i}_{\begin{matrix}ds\end{matrix}}\\{i}_{qs}\\{i}_{dr}\\{i}_{qr}\end{matrix}\right]</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (38)

@@ Line 785: / Line 785: @@
 [5] Mirošević M.,  Maljković Z., Pavlinović D. The dynamics of diesel-generator unit in isolated electrical network. International Journal of Renewable Energy Research (IJRER),  1(3):126-133, 2011. doi: 10.5923/j.eee.20120204.03
-[6] Marija M., Zlatko M., and Ivan G., Effects of Interruption in Power Supply of Induction Motors in Isolated Electrical Grid, Acemp - Electromotion, 732-735, 2011.
+[6] Mirošević M.,  Maljković Z., Gašparac I. Effects of  interruption in power supply of induction motors in isolated electrical grid. International Aegean Conference on Electrical Machines and Power Electronics and Electromotion, Joint Conference, Istanbul, Turkey, pp. 732-735, 2011.
-[7] M. MiroSevid, Z. Maljkovid, and M. MilkoviC, Dynamics of Generator-Units During the Start-up of the Induction Motor Drives, IEEE Melecon, 1109-1112, 2004
+[7] MiroSevid M.,  Maljkovid Z.,  MilkoviC M. Dynamics of generator-units during the start-up of the induction motor drives. Proceedings of the 12th IEEE Mediterranean Electrotechnical Conference, Vol. 3, 1109-1112, Dubrovnik, Croatia, 2004.
-[8] Nashwa M., Mohamed E., and Fathy E., Dynamic operation of isolated self-excited synchronous generator under static loads, Journal of Electrical Systems,  17(3),  310-323, 2021.  [http://www.journal.esrgroups.org/jes/ www.journal.esrgroups.org/jes/]
+[8] Mounir N., Enany M., El-Said F. Dynamic operation of isolated self-excited synchronous generator under static loads. Journal of Electrical Systems,  17(3):310-323, 2021.  [http://www.journal.esrgroups.org/jes/ www.journal.esrgroups.org/jes/]
-[9] E. J. Akpama, K. M. Udoka, and O. I. Okoro., Dynamic Modeling of Induction Machine Incorporating Transmission Line Impedance, International Journal of Recent Development in Engineering and Technology,  7(6),  7-13, 2018.   [http://www.ijrdet.com www.ijrdet.com]
+[9]  Akpama E.J.,  Udoka K.M.,   Okoro O.I. Dynamic modeling of induction machine incorporating transmission line impedance. International Journal of Recent Development in Engineering and Technology,  7(6):7-13, 2018.   [http://www.ijrdet.com www.ijrdet.com]
-[10]  Pema D. and Bevek S, D-Q Mathematical Modelling and Simulation of Three-Phase Induction Motor for Electrical Fault Analysis, International Advanced Research Journal in Science, Engineering and Technology,  7(9),  38-46, 2020.  [http://doi: http://doi:] 10.17148/IARJSET.2020.7909
+[10]  Pema D., Bevek S. D-Q Mathematical modelling and simulation of three-phase induction motor for electrical fault analysis. International Advanced Research Journal in Science, Engineering and Technology,  7(9):38-46, 2020.  [http://doi: http://doi:] 10.17148/IARJSET.2020.7909
-[11] Pratyusha B. D. and Sudhangshu S., Dynamic Model Analysis of Three Phase Induction Motor Using Matlab/Simulink, International Journal of Scientific & Engineering Research, 7(3),  572-577, 2016.  [http://www.ijser.org http://www.ijser.org].
+[11] Pratyusha B.D.,  Sudhangshu S. Dynamic model analysis of three phase induction motor using Matlab/Simulink. International Journal of Scientific & Engineering Research, 7(3):572-577, 2016.  [http://www.ijser.org http://www.ijser.org].
-[12] Onofre A. M., Carlos E. C., Riemann R. C., Fredy A. V. Miguel A. M., Abel E. Q., and Nahitt P., The Squirrel-Cage Induction Motor Model and Its Parameter Identification Via Steady and Dynamic Tests, Electric Power Components and Systems,  0(0),  1-14, 2018.  [https://doi.org/10.1080/15325008.2018.1445140 https://doi.org/10.1080/15325008.2018.1445140]
+[12] Morfín O.A., Castañeda C.E., Ruiz-Cruz R.,  Valenzuela F.A., Murillo M.A., Quezada A.E., Padilla N.  The squirrel-cage induction motor model and its parameter identification via steady and dynamic tests. Electric Power Components and Systems,  46(3):302-315, 2018.  [https://doi.org/10.1080/15325008.2018.1445140 https://doi.org/10.1080/15325008.2018.1445140]
-[https://www.tandfonline.com/loi/uemp20 https://www.tandfonline.com/loi/uemp20]
+[13] Kim S.-H., Electric motor control DC, AC, and BLDC motors. Published by Elsevier Inc., pp. 438, 2017.  [http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0 http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0]
-−
-[13] Sang-H. K., Electric Motor Control DC, AC, and BLDC Motors, Published by Elsevier Inc. 2017.  [http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0 http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0]
-−
-[14] Reuben J., Onah C. O., and J. U. Agber, Modeling and Simulation of Three Phase Induction Motor Electrical Faults Using Matlab/Simulink, International Journal of Modern Trends in Engineering and Research (IJMTER),  5(5),  176-187, 2018.
 [http://doi.10.21884/ijmter.2018.5158.zxudq http://doi.10.21884/ijmter.2018.5158.zxudq]
-[15] Martin. K., Anastázia M., and Michal K., Modeling of Synchronous Machines Including Voltage Regulation, Przegląd Elektrotechniczny, R. 95 NR 7,  125-132, 2019.  [http://doi:10.15199/48.2019.07.26 http://doi:10.15199/48.2019.07.26]
+[15] Kanálik M., Margitová A., Kolcun M, Modeling of synchronous machines including voltage regulation. Przegląd Elektrotechniczny, R. 95 NR 7,  125-132, 2019.  [http://doi:10.15199/48.2019.07.26 http://doi:10.15199/48.2019.07.26]
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@@ Line 773: / Line 773: @@
 ==References==
-[1] B. T., Jaykishan R., Jay D., and Kamlesh S., “Soft Start of Induction Motor Using TRIAC Switching”, ''International Journal of Engineering Development and Research (IJEDR)'', Vol. 5(2), pp. 1635-1639, 2017. [http://www.ijedr.org www.ijedr.org]
+[1] Trivedi B., Raval J., Desai J.,  Sonwane K. Soft start of induction motor using TRIAC switching. International Journal of Engineering Development and Research (IJEDR),  5(2):1635-1639, 2017. <!-- [http://www.ijedr.org www.ijedr.org]-->
-[2] Mahmoud M.S. A., “Development of the system of preemptive control over excitation of a synchronous generator to reduce voltage dips when starting-up asynchronous motors”, ''Przegląd elektrotechniczny,'' R. 94, NR 10, pp. 210- 215, 2018. doi:10.15199/48.2018.10.49
+[2] Alsuod M.M.S. Development of the system of preemptive control over excitation of a synchronous generator to reduce voltage dips when starting-up asynchronous motors. Przegląd Elektrotechniczny, R. 94, NR 10, 210-215, 2018. doi:10.15199/48.2018.10.49
-[3] Guogang W., Shiyu S., and Jinning L., “Influence of Motor Starting on The Operating Characteristics of Diesel Generator Sets”, ''Advances in Computer Science Research, ''Vol. 71
+[3] Wei G., Sun S., Liu J. Influence of motor starting on the operating characteristics of diesel generator sets. Advances in Computer Science Research,  71:105-109,  2016.
-[4] Marija M., and Zlatko M., “Torsional Dynamics of Generator Units During Sudden Impact Load”, ''Electrical and Electronic Engineering, ''Vol''. ''2(4), pp.183-191, 2012. doi: 10.5923/j.eee.20120204.03
+[4] Mirošević M.,  Maljković Z. Torsional dynamics of generator units during sudden impact load. Electrical and Electronic Engineering,  2(4):183-191, 2012. doi: 10.5923/j.eee.20120204.03
-[5] Marija M., Zlatko M., and Daniel P., “The Dynamics of Diesel-Generator Unit in Isolated Electrical Network”, ''International journal of renewable Energy Research, IJRER, ''Vol''. ''1(3), pp.126-133, 2011. doi: 10.5923/j.eee.20120204.03
+[5] Mirošević M.,  Maljković Z., Pavlinović D. The dynamics of diesel-generator unit in isolated electrical network. International Journal of Renewable Energy Research (IJRER),  1(3):126-133, 2011. doi: 10.5923/j.eee.20120204.03
-[6] Marija M., Zlatko M., and Ivan G., “Effects of Interruption in Power Supply of Induction Motors in Isolated Electrical Grid”, ''Acemp - Electromotion'', pp.732-735, 2011.
+[6] Marija M., Zlatko M., and Ivan G., Effects of Interruption in Power Supply of Induction Motors in Isolated Electrical Grid, Acemp - Electromotion, 732-735, 2011.
-[7] M. MiroSevid, Z. Maljkovid, and M. MilkoviC, “Dynamics of Generator-Units During the Start-up of the Induction Motor Drives”, ''IEEE Melecon, ''pp.1109-1112, 2004
+[7] M. MiroSevid, Z. Maljkovid, and M. MilkoviC, Dynamics of Generator-Units During the Start-up of the Induction Motor Drives, IEEE Melecon, 1109-1112, 2004
-[8] Nashwa M., Mohamed E., and Fathy E., “Dynamic operation of isolated self-excited synchronous generator under static loads”, Journal of Electrical Systems, Vol. 17(3), pp. 310-323, 2021.  [http://www.journal.esrgroups.org/jes/ www.journal.esrgroups.org/jes/]
+[8] Nashwa M., Mohamed E., and Fathy E., Dynamic operation of isolated self-excited synchronous generator under static loads, Journal of Electrical Systems,  17(3),  310-323, 2021.  [http://www.journal.esrgroups.org/jes/ www.journal.esrgroups.org/jes/]
-[9] E. J. Akpama, K. M. Udoka, and O. I. Okoro., “Dynamic Modeling of Induction Machine Incorporating Transmission Line Impedance”, ''International Journal of Recent Development in Engineering and Technology,'' Vol. 7(6), pp. 7-13, 2018.   [http://www.ijrdet.com www.ijrdet.com]
+[9] E. J. Akpama, K. M. Udoka, and O. I. Okoro., Dynamic Modeling of Induction Machine Incorporating Transmission Line Impedance, International Journal of Recent Development in Engineering and Technology,  7(6),  7-13, 2018.   [http://www.ijrdet.com www.ijrdet.com]
-[10]  Pema D. and Bevek S, “D-Q Mathematical Modelling and Simulation of Three-Phase Induction Motor for Electrical Fault Analysis”, ''International Advanced Research Journal in Science, Engineering and Technology'', Vol. 7(9), pp. 38-46, 2020.  [http://doi: http://doi:] 10.17148/IARJSET.2020.7909
+[10]  Pema D. and Bevek S, D-Q Mathematical Modelling and Simulation of Three-Phase Induction Motor for Electrical Fault Analysis, International Advanced Research Journal in Science, Engineering and Technology,  7(9),  38-46, 2020.  [http://doi: http://doi:] 10.17148/IARJSET.2020.7909
-[11] Pratyusha B. D. and Sudhangshu S., “Dynamic Model Analysis of Three Phase Induction Motor Using Matlab/Simulink”, ''International Journal of Scientific & Engineering Research,'' 7(3), pp. 572-577, 2016.  [http://www.ijser.org http://www.ijser.org].
+[11] Pratyusha B. D. and Sudhangshu S., Dynamic Model Analysis of Three Phase Induction Motor Using Matlab/Simulink, International Journal of Scientific & Engineering Research, 7(3),  572-577, 2016.  [http://www.ijser.org http://www.ijser.org].
-[12] Onofre A. M., Carlos E. C., Riemann R. C., Fredy A. V. Miguel A. M., Abel E. Q., and Nahitt P., “The Squirrel-Cage Induction Motor Model and Its Parameter Identification Via Steady and Dynamic Tests”, ''Electric Power Components and Systems'', Vol. 0(0), pp. 1-14, 2018.  [https://doi.org/10.1080/15325008.2018.1445140 https://doi.org/10.1080/15325008.2018.1445140]
+[12] Onofre A. M., Carlos E. C., Riemann R. C., Fredy A. V. Miguel A. M., Abel E. Q., and Nahitt P., The Squirrel-Cage Induction Motor Model and Its Parameter Identification Via Steady and Dynamic Tests, Electric Power Components and Systems,  0(0),  1-14, 2018.  [https://doi.org/10.1080/15325008.2018.1445140 https://doi.org/10.1080/15325008.2018.1445140]
 [https://www.tandfonline.com/loi/uemp20 https://www.tandfonline.com/loi/uemp20]
-[13] Sang-H. K., “Electric Motor Control DC, AC, and BLDC Motors”, ''Published by Elsevier Inc.'' 2017.  [http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0 http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0]
+[13] Sang-H. K., Electric Motor Control DC, AC, and BLDC Motors, Published by Elsevier Inc. 2017.  [http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0 http://dx.doi.org/10.1016/B978-0-12-812138-2.00004-0]
-[14] Reuben J., Onah C. O., and J. U. Agber, “Modeling and Simulation of Three Phase Induction Motor Electrical Faults Using Matlab/Simulink”, ''International Journal of Modern Trends in Engineering and Research (IJMTER)'', Vol. 5(5), pp. 176-187, 2018.
+[14] Reuben J., Onah C. O., and J. U. Agber, Modeling and Simulation of Three Phase Induction Motor Electrical Faults Using Matlab/Simulink, International Journal of Modern Trends in Engineering and Research (IJMTER),  5(5),  176-187, 2018.
 [http://doi.10.21884/ijmter.2018.5158.zxudq http://doi.10.21884/ijmter.2018.5158.zxudq]
-[15] Martin. K., Anastázia M., and Michal K., “Modeling of Synchronous Machines Including Voltage Regulation”, ''Przegląd Elektrotechniczny,'' R. 95 NR 7, pp. 125-132, 2019.  [http://doi:10.15199/48.2019.07.26 http://doi:10.15199/48.2019.07.26]
+[15] Martin. K., Anastázia M., and Michal K., Modeling of Synchronous Machines Including Voltage Regulation, Przegląd Elektrotechniczny, R. 95 NR 7,  125-132, 2019.  [http://doi:10.15199/48.2019.07.26 http://doi:10.15199/48.2019.07.26]
-−
-−
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@@ Line 687: / Line 687: @@
 The specifications of the synchronous generator as well as the induction motors applied in the simulation were as follows:
 '''''Synchronous generator specifications'''''
 The synchronous generator applied in this work was 100 KVA, 460 V, 125.5-A, 60 Hz, 4 pole 3-phase cylindrical pole synchronous generator, star-connected:
 : Per phase stator resistance (Rs): 0.055 &#x03a9;
@@ Line 704: / Line 704: @@
 : Rated rotor Speed =1800 r.p.m.
 '''''Induction motor 1 specifications'''''
 Three-phase squirrel cage &#x03a5;connected, 20 HP, 460-V, 23.4 -A, 60 Hz, 4 poles:
 : Speed (N):1760 rpm
@@ Line 725: / Line 725: @@
 : Friction factor (F): 0.01771 N m s
 '''''Induction motor 2 specifications'''''
 Three-phase squirrel cage &#x03a5;connected, 50 HP, 460-V, 52-A, 60 Hz, 4 poles:
 : Speed (N):1780 rpm
@@ Line 746: / Line 746: @@
 : Friction factor (F): 0.02187 N m s
 '''''Induction motor 3 specifications'''''
 Three-phase squirrel cage &#x03a5;-connected, 100 HP, 460-V, 117-A, 60 Hz, 4 poles:
 : Speed (N): 1780 rpm

@@ Line 690: / Line 690: @@
 '''''Synchronous generator specifications'''''
-The synchronous generator applied in this work was 100 KVA, 460 V, 125.5-A, 60 Hz, 4 pole 3-phase cylindrical pole synchronous generator, star-connected
+The synchronous generator applied in this work was 100 KVA, 460 V, 125.5-A, 60 Hz, 4 pole 3-phase cylindrical pole synchronous generator, star-connected:
 : Per phase stator resistance (Rs): 0.055 &#x03a9;
@@ Line 706: / Line 707: @@
 '''''Induction motor 1 specifications'''''
-Three-phase squirrel cage &#x03a5;connected, 20 HP, 460-V, 23.4 -A, 60 Hz, 4 poles
+Three-phase squirrel cage &#x03a5;connected, 20 HP, 460-V, 23.4 -A, 60 Hz, 4 poles:
 : Speed (N):1760 rpm
@@ Line 726: / Line 728: @@
 '''''Induction motor 2 specifications'''''
-Three-phase squirrel cage &#x03a5;connected, 50 HP, 460-V, 52-A, 60 Hz, 4 poles
+Three-phase squirrel cage &#x03a5;connected, 50 HP, 460-V, 52-A, 60 Hz, 4 poles:
 : Speed (N):1780 rpm
@@ Line 746: / Line 749: @@
 '''''Induction motor 3 specifications'''''
-Three-phase squirrel cage &#x03a5;-connected, 100 HP, 460-V, 117-A, 60 Hz, 4 poles
+Three-phase squirrel cage &#x03a5;-connected, 100 HP, 460-V, 117-A, 60 Hz, 4 poles:
 : Speed (N): 1780 rpm

@@ Line 703: / Line 703: @@
 : Rated rotor Speed =1800 r.p.m.
 '''''Induction motor 1 specifications'''''
@@ Line 709: / Line 708: @@
 Three-phase squirrel cage &#x03a5;connected, 20 HP, 460-V, 23.4 -A, 60 Hz, 4 poles
-Speed (N):1760 rpm
+: Speed (N):1760 rpm
-Per phase stator resistance (R1): 0.2761&#x03a9;
+: Per phase stator resistance (R1): 0.2761&#x03a9;
-Per phase stator reactance (X1):0.82598 &#x03a9;
+: Per phase stator reactance (X1):0.82598 &#x03a9;
-Referred rotor per phase resistance (R2): 0.1645 &#x03a9;
+: Referred rotor per phase resistance (R2): 0.1645 &#x03a9;
-Referred rotor per phase reactance (X2): 0.82598 &#x03a9;
+: Referred rotor per phase reactance (X2): 0.82598 &#x03a9;
-Magnetizing inductance (Xm): 28.704 &#x03a9;
+: Magnetizing inductance (Xm): 28.704 &#x03a9;
-Moment of inertia (J): 0.1 kg m2
+: Moment of inertia (J): 0.1 kg m2
-Friction factor (F): 0.01771 N m s
+: Friction factor (F): 0.01771 N m s
 '''''Induction motor 2 specifications'''''
@@ Line 729: / Line 728: @@
 Three-phase squirrel cage &#x03a5;connected, 50 HP, 460-V, 52-A, 60 Hz, 4 poles
-Speed (N):1780 rpm
+: Speed (N):1780 rpm
-Per phase stator resistance (R1): 0.09961 &#x03a9;
+: Per phase stator resistance (R1): 0.09961 &#x03a9;
-Per phase stator reactance (X1): 0.32685 &#x03a9;
+: Per phase stator reactance (X1): 0.32685 &#x03a9;
-Referred rotor per phase resistance (R2): 0.05837 &#x03a9;
+: Referred rotor per phase resistance (R2): 0.05837 &#x03a9;
-Referred rotor per phase reactance (X2): 0.32685 &#x03a9;
+: Referred rotor per phase reactance (X2): 0.32685 &#x03a9;
-Magnetizing inductance (Xm): 11.4567&#x03a9;
+: Magnetizing inductance (Xm): 11.4567&#x03a9;
-Moment of inertia (J): 0.4 kg m2
+: Moment of inertia (J): 0.4 kg m2
-Friction factor (F): 0.02187 N m s
+: Friction factor (F): 0.02187 N m s
 '''''Induction motor 3 specifications'''''
@@ Line 749: / Line 748: @@
 Three-phase squirrel cage &#x03a5;-connected, 100 HP, 460-V, 117-A, 60 Hz, 4 poles
-Speed (N): 1780 rpm
+: Speed (N): 1780 rpm
-Per phase stator resistance (R1):  0.03957 &#x03a9;
+: Per phase stator resistance (R1): 0.03957 &#x03a9;
-Per phase stator reactance (X1): 0.146649 &#x03a9;
+: Per phase stator reactance (X1): 0.146649 &#x03a9;
-Referred rotor per phase resistance (R2): 0.02215 &#x03a9;
+: Referred rotor per phase resistance (R2): 0.02215 &#x03a9;
-Referred rotor per phase reactance (X2): 0.146649 &#x03a9;
+: Referred rotor per phase reactance (X2): 0.146649 &#x03a9;
-Magnetizing inductance (Xm):  6.2731322 &#x03a9;
+: Magnetizing inductance (Xm):  6.2731322 &#x03a9;
-Moment of inertia (J):1.3 kg m2
+: Moment of inertia (J): 1.3 kg m2
-Friction factor (F):0.05543 N m s
+: Friction factor (F): 0.05543 N m s
 ==Acknowledgment==

@@ Line 678: / Line 678: @@
 In this study, the mathematical dynamic model of the synchronous generator direct-on-line by an induction motor is analyzed in case of rotoa r reference frame. The modeling of an isolated synchronous generator direct-on-line by different sizes induction motors (20, 50, 100 Hp) was performed using MATLAB /SIMULINK software package with constant and adjusted the excitation voltage at (3.35, 4.55 an,d 6.21V), respectively. The generator parameters were experimentally measured and the generator simulated values (terminal voltage, current, output power, electromagnetic torque and, load angle as funca tion of time) were subsequently calculated.
-The obtained results show that the current, the output power, the electromagnetic torque and the load angle increased with increasing the load torque at ca onstant speed. While,the terminal voltage decreased with increasing the load torque at ca onstant speed. In case of sa udden decrease in the rotor speed at full load torque, only the load angle increased.  In this study, the voltage dip may be due to
+The obtained results show that the current, the output power, the electromagnetic torque and the load angle increased with increasing the load torque at ca onstant speed. While,the terminal voltage decreased with increasing the load torque at ca onstant speed. In case of sa udden decrease in the rotor speed at full load torque, only the load angle increased.  In this study, the voltage dip may be due to:
 ) The load torque was greater than the generation torque,

@@ Line 643: / Line 643: @@
 Conversely, as the rotor speed decreased, the load angle (<math>\delta</math>) increased from 7.6, 14.48, and 24.73° to 8.18, 15.95, and 28.34° where <math display="inline">\frac{d\delta }{dt}={\omega }_{e}-p{\omega }_{m}</math>, reaching thereafter a stable condition in two sized induction motors of 20, 50 Hp. However, it increased greatly versus the dip in the voltage in the 100 Hp- induction motor ([[#img-6|Figure 6]](f)).
-<div id='img-5'></div>
+<div id='img-6'></div>
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