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Unbalanced Voltage Impacts and its Analysis on an Induction Motor
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 167 Unbalanced Voltage Impacts and its Analysis on an Induction Motor Vyshnav S B1, Abhishek Vinod2, Denil Paul3, Karthik R Ashok4, Sudheer P N5 1,2,3,4 Student, Dept. Of mechanical Engineering, Alva’s Institute Of Engineering and Technology, Karnataka, India 5 Professor Dept. Of mechanical Engineering, Alva’s Institute Of Engineering and Technology, Karnataka, India ---------------------------------------------------------------------***-------------------------------------------------------------------- ABSTRACT Lacks like unequal voltages in the voltage source could bring about issues like extreme misfortunes, overvoltage mechanical motions, and impedance with control hardware. Recognizing these unique machine situationsis crucial in the electrical machine's collaboration with the power matrix. This investigation studied the influence of unequal voltages on motor execution. Then, at that point, checking this unfortunate condition utilizing electrical machine boundaries is done. For this situation, the motor itself can go about as the sensor that distinguishesunusual circumstances. Furthermore, this paper studies the detrimental impactsofunevenThis representsa sinusoidal voltage which is frequently seen in powersuppliesvoltage, on acceptance motor presentation in terms of line flows, power element, and proficiency. Keywords- Unbalanced voltage, Induction motor, Derating Curve. 1. INTRODUCTION Induction motors are frequently employed in commercial and industrial settings. Ventures incorporate vehicle and semiconductor fabricating plants, emergency clinics, broadcasting offices, and so on. Uneven stock voltage makes unfriendly impacts on the electrical mechanical assembliesparticularlytheelectrical motors.Asymmetrical transformer winding, unbalanced loads, or huge single- stage loads can all create voltage unbalance. Albeit the voltage unbalances is little, huge uneven current streams because are of moderately little negative arrangement impedance. This high current produces overheating, further accidents, vibrations, auditory disturbance, a loss in force, and a decrease in the life of an induction motor [6, 7]. The effects of uneven voltage on induction motor torque, speed, and current when the voltage size, stage point, or both are modified at the same time are discussed in this paper. The NEMA, IEEE, and power local area networks have specified the voltage imbalance.Oneofthedefinitions is frequently used for the induction motor test, and they are all presented here. At this point when no less than one of the stockpile qualities(abundanceaswell asstagepoint) goes amiss from the guidelines, the electrical framework is impacted by the unbalance voltage [11]. The induction motor (IM) is broadly utilized in the industry since it gives great execution as well as high unwavering quality and solidness [1, 2]. IMscanbelocated in numerous applications which makes strenuous conditions. Working under these circumstances antagonistically influences IMs execution [3].IMs shortcoming finding is vital, as it keeps away from sensational outcomes to the actual machine and to the general climate. The following are a some of the important flaws that can affect the operation of electrical machines: (1) problems with the stator, caused by the opening or loosing of at least one turn; (2) unexpectedaffiliationofthe stator windings; (3) broken rotor bars or broke rotor end- rings; (4) static or potentially strong air-hole impetuousness; (5) twisted shaft (similar to dynamic whimsy), which can cause serious damage to the stator core and windings; (6) shorted rotor fieldwinding;and(7) failures with the headings and gearbox This essay focuses on the stator deficits, which are caused by a few various stressors and are primarily grouped into four categories. [5] The legitimate utilization of the power by the induction motor as a framework to encounter burden prerequisites is always a subject of extreme interest [1]-[13]. Most modern motors have intended for 460 V activity, still, the utilization of the dissemination framework to intend for 480 V. So the reasoning over here is that the link voltage drop will permit the legitimate voltage of 460 V which is present at the motor load points.Estimationshasappeared to be disregarding the link falls, the motor terminal voltages can be considerably more than the 460V in firm modern frameworks, while it could bewell underneaththe ostensible voltage, where the framework is vigorously stacked in powerless business 2. Losses in electric motor By using the proper, similar circuitcomputations,thesame stator and rotor flows and corresponding copper losses at each heap or slipknot are completely fixed. This contact and wind age losses which generally 1-2%oftheevaluated output. The no heap primary losses are especially subject to quite a large number of highlights of the plan, yet an unpleasant normal 2-3% of the examined output is this number. In general, the rate of core losses decreaseswhen the space openings, the ratio of the rotor to stator spaces, or the length of the air hole are reduced. A huge extent of this center malfunction and the wanderer load losses is J.
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 168 Faiz et al. /Energy Transformation and The board 47 (2006) 289-302 291 ordinarily because of space recurrence throb losses, with the goal thatexcellentsilicon steel is generally utilized for center laminations. Typical upsides of stray center malfunction are 1-2% of the result [8, 9]. 3. Effect of Unbalanced Voltage on Losses Voltage unbalances and mechanical over-burden create extreme overheating on acceptance motors [12, 13]. The overheating brought about by these two peculiarities is created by the addition of current in the motor windings [14, 15]. This augmentation is requested by the actual motor to keep up with the force in the rotor [5, 7]. Moreover, a decrement in the rotor speed is gotten, creating a deficient cooling [7]. The warm addition adversely influences the motor lifetime, rotor and stator guides, center, protection, and orientation, creating irreversible harm when the motor warms past its plan limits. Voltage unbalance condition is introduced when the voltage sizes of a three-phase framework are inconsistent as well as vary from one another by a phase’s point of 120 degrees [13]. Voltage unbalance can be assessed utilizing the voltage unbalance rate (%UNB) as indicated by the IEEE standard [7]. It is characterized as follows: Where U+ and U-are the positive and negative balanced parts, individually, which are gotten through the Quick Fourier Change (FFT) and the Fortescue change. Not with tending the positive succession part, the negative arrangement part of this current furthermore, one of the main causes of the increase in machine losses is the differentiation of the phase flowsinthesituationofuneven voltage. If the entire losses of an acceptance machine are separated into three groups, such as the copper losses (stator and rotor), core losses, and mechanical losses, the inconsistent voltage has the biggest effect on the copper losses and the smallest effect on the mechanical losses. To examine this exhibition motor with three stages provided by an uneven voltage, what’s more, envision its impact Based on the machine'slosses,a 7.5kW three-phase enlistment motor with the specified specifications is suggested. Summarizes the exhibition circumstances while the motor operates with 4% slip and estimated yield power. Stator copper losses, rotor ohmic losses, core losses, mechanical losses (contact and windage), and stray losses have all beentakenintoaccount in the malfunction evaluation for the unequal voltage supply. The manufacturerhastakenintoconsideration100 W in mechanical losses. Given that the core losses opposition is also well understood, its variations under balanced and unbalanced situations may be taken into consideration In light of the complex voltage unbalance factor, or CVUF, definition, the proposed motor is broken down over full load and 0-6% unbalanced voltage, and the different losses are assessed. Naturally, with the meaning of CVUF, guarantee of the normal line voltage is necessary to provide precise results from the analysis, disregarding the imbalance point. With a point = 120 and a normal voltage corresponding to 380 V, the imbalance of the terminal voltage will be taken into consideration in this case. As regular, it has expected that this normal terminals voltage in modern plants is lower than the evaluated esteem. This builds the warm stress in the machine and will prompt malfunction throughout everyday life, while perhaps not an early disappointment. Thisis expectedfirst and foremost are decrease over the size wherethepositive arrangement voltage is contrasted with the uneven contributed voltage. Furthermore, the existence of this negative grouping moving charge makes a negative grouping force which deducts from the positive grouping force to relent a net force which is the more modest. 4. Derating Curve of the IM Working a motor for an extended length of time in an imbalanced voltage state exceeding 5% "is not recommended," according to NEMA standards. The imbalance state causes a motor to operate blazing. The NEMA standard states that damagepreventionisnolonger required when the imbalance hits 5% since the temperature begins to increase so quickly at that point. The most fundamental protection,accordingtoNEMA,isto de-rate the motor — to lower the result draw load so that it is able to withstand the additional heat produced by the imbalanced accumulation. That has various ways to encourage a derating curve. Based on several experiments with various motors and adjusted voltages, one of them claims that when voltages are imbalanced, the % increment in temperature climbing climbs to almost twice the square of the percentage voltage imbalance. According to one of them, when voltages are unbalanced, the temperature increases by a percentagethatisalmosttwice the square of the percentage of the voltage imbalance. In the end, it is still uncertain what derating will be neededto keep the machine's temperature rising. This imbalance derating curve (NEMA definition) Fig 1. The motor shouldn't run at more than 77% of its predicted power,for example, with a 5% imbalance. In ideal supply circumstances, Comparing LSPMM improvements to IE2 and IE3 class motors, lower operating temperatures are achieved. Large current unbalances areformedunderVUcircumstances,increasing motor losses and hence the temperatures inside and outside. To investigate the VU influence on motor
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 169 temperature with under and over voltage, thermo graphic pictures indicating Figures 18 and 19 illustrate the results for each VU condition for the LSPMM for the expansion of this parameter in the motor end shield The images demonstrate the behavior of 1% of VU at low and high voltage. Causes no obvious changes in LSPMM temperature, proving that motor output power should not be reduced. Fig; 1 Derating curve of the IM [16]. 5. Consideration of Overvoltage and under voltages in the Derating Curve Overvoltage andUndervoltageontheNEMAderatingcurve were accommodated by the electrical and heated models. Motor losses are calculated using the electrical model. To account for these losses and anticipate the increase in motor temperature. Fig2. Inclusion of overvoltage’s and undervoltage on the derating curve [16]. The no-heap and locked rotor tests have left the motor spinning. The core losses werecorrectedtentatively. When used in conjunction with over- or under-voltage. As the voltage imbalance grows, the center issue intensifies. The warm model, which was introduced, was favorably appreciated. Simple tests were performed to detect warm boundaries, rather than motor plan information. In the instance presentation the heated model performed admirably in testing with variable voltages, uneven voltages, and over- and under voltages. Both fleeting and recurring occurrences might be predicted by the model. Temperatures at the exactness of case 2. The derating curve takes into account overvoltage and undervoltage. The curves were created by carrying out the three following scenarios: In Case 1, a motor was subjected toan imbalanced voltage at the normal voltage. If both 2 and a 10% overvoltage in addition to up to 5% in unbalanced voltages were applied to the motor. In Example 3, 10% undervoltage and up to 5% irregularvoltages wereapplied to a motor. When supplied by adjusted assessed voltages, the motor's evaluated temperature was known at full load the motor connections received the selected voltages. At full load, a high stator twisting temperature was anticipated. To keep the temperature at the appraised level, the motor yield power was lowered for temperature values over the assessed level. The derating still up in the air as the proportion of the determined yield capacity that evaluated power The motor is supposedto beprotectedby the derating's 100 percent curve when it receives Case 1 voltages. As might be predicted, the NEMA curve and this curve are extremely similar. When Case 2 voltages are applied, the 110% curve will protect the motor. Less than 1% of an imbalance allows the motor to operate at maximum power. This is equivalent to the NEMA curve. The motor cannot be run at more than 71% of its rated power with a 5% imbalance. When working with Case 3 voltages, the 90% curve is the derating curve that will prevent motor twisting from overheating. Regardless of voltage imbalance, the 90% curve recommends that a motor be derated if it is anticipated to operate at full load when under 10% Undervoltage. The derating for the 90% Undervoltage and 100%evaluatedvoltagecurvesisalmost the same at 5% imbalance. This is expected because the Undervoltage scenario’s bigger and lower core losses compensate for the analyzed case's lower and higher core losses, resulting in the corresponding derating at thattime [16].
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 170 Fig.3 (a) Positive sequence equivalent circuit By breaking down a three-phase imbalanced system into two sets of balanced signals and a set of single phase phasors or symmetrical components, symmetrical component analysis makes fault analysis simpler. The positive, negative, and zero sequence components refer to these stages. The use of symmetrical components in relation to three-phase electric power networks facilitates the investigation of imbalanced situations. A large induction motor is especially susceptible to supplyvoltage imbalance. A defect in voltage imbalance is significant because an imbalanced voltage source can produce excessive losses, heating, noise, and vibration. It is necessary to resolve the problem of unbalance in the voltage supply. This study analysis of an induction motor operating in an unbalanced voltage supply is possible (b) Use a NEMA [32] negative sequence equivalent circuit [16] for this VU situation. The worst recorded conditions are 3% and 4% overvoltage unbalances (Figure 19, c-f), which are more harmful to the temperature of this motor than the VU with Undervoltage. Figure 20 depicts the temperature fluctuationforthethree IMs in the six situations studied. The IE2 class motor has an insulation class (maximum temperature of 130 C), whereas the IE3 and IE4 class motors have insulationclass F (maximum temperature of 155 C), indicating a better tolerance for temperature rises. The results, however, show that the IE4 and IE2 class motors have lower operating temperatures than the IE3 class motor. Figure 20(a, c, and e) demonstrates that the VU with low voltage does not result in an IE4 class motor. DIFFERENT LOSSES IN 3-PHASE INDUCTION MOTOR Copper loss: This copper loss happensmostlyinthestator and rotor windings. It is the I^2R loss in winding in the winding resistive components that are present. In which the current passes where I^2R loss will occur in terms of heat in the winding. This loss is variable loss due to load varying the current varies and I^2R also varies. Due to the length coil extension, this loss can be included and due to the loss of copper wire in the slot copper loss is more proven to occur. In the copper losses, there are stator copper losses and rotor copper losses in the 3-phase induction motor where these stator copper losses are calculated according to the IEC norm by using an equation of the test resistance RH and current IH rate [25, 26]. Ps= 1.5 RHI^2H = 3RPH I^2H In this example, IH denotes the stator phase current and RH denotes the winding line-to-line resistance, as both equations provide the same answer when the phase resistance RPH is used. These rotor winding losses areslip (s) related and are generally calculated usingthe equation. Pr= (P1-PS-PFe) S P1 represents the electric input power, PS represents the stator winding losses, PFe represents theno-loadironloss, and S represents the slip. [26] Iron or core or Magnetic loss: This iron or core loss occurs mostly on an induction motor's stator and rotor cores. This type of loss is sometimes referred to as core loss or magnetic loss. A core loss or magnetic loss is another name for this kind of loss. Eddy current loss and hysteresis are combined in this situation. The supply frequency, as well as the flux densityinthestatorandrotor cores, influence both of these losses. The hysteresis loss (considering an iron core with a winding and connected to an AC supply using the right-hand thumb rule the current passes anti-clockwise direction and magnetic flux is upward. In the negative half cycle, the situation has reversed the Sis on the right and north on the left. The situation is called magnetic reversal it is a land of work done when the energy loss takes place. This energy loss is called hysteresis loss [23, 24, 28]. In the eddy current loss when the AC supply happens flux is generated the AC flux due to AC flux the EMF (electromagneticflux)isinducedon the iron core surface. This EMF causes an eddy current core surface. Due to this I^2R loss and resistive loss is occurred in form of heat this loss is called eddy current loss. A laminated core can be used to reduce eddy current loss [29, 30]. Mechanical losses: mechanical losses in a three-phase induction motor mainly occur due loss due to friction and loss of windage. In this friction loss, these losses occur when the two surfaces are in contact with each other and have relative motion with each other. This frictional loss mainly occurs in the bearing of the motor and this loss can be reduced with the help of good lubrication. And the windage losses are caused by the air disturbance in the moving parts of the induction motor. By replacing the old parts with a cylindrical design of the moving partsthisloss can be minimized. In the cylindrical parts, air disturbance is less so windage loss can be reduced. Mechanical loss is
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 171 constant, the magnetic losses are also constant this mechanical plus magnetic loss creates a stray loss all these losses occurs in term of heat [31]. And other additional load losses are also found in the three-phase induction motor due to the unbalanced condition. CONCLUSION Voltages this research investigated the derating of acceptance machines when supplied by unevenvoltagesin combination with over-and-under.Abroadinvestigation of the unique meanings of unequal inventory has uncovered that the distinctions in the definitions don't bring about critical derating contrasts at the point when worked by unequal supplies in the 5% territory. Positiveandnegative succession circuits were introduced and the effect on the general force speed curve made sense. The negative grouping force diminishes the beginning, pinnacle and full burden appraised force, in this way expanding beginning time, lowering the motor's list-cyclingspeed,andmakingit operate at a higher slip. For derating acceptancemachines, the NEMA curve has been expanded to accommodate overvoltage and Undervoltage. Themis voltage and temperature data have beencomputedindependentlyfora machine running with 10% overvoltage or 10% under voltage using the electrical and heated models. The derating factor for safe activities is not absolutely fixed. There were also two contextual studies. REFERENCES [1] P. Pillay, “Practical considerations in applying energy efficient motors in the petrochemical industry,” IEEE IAS Mag., vol. 3, pp. 32–40, Jan. /Feb.1997 [2] R. F. Woll, “Effect of unbalanced voltage on the operation of polyphase Induction motors,” IEEETrans. Ind. Applicant., vol. IA-11, pp. 38–42, Jan. /Feb. 1975. [3] Williams. Operationofthree-phaseinduction motorson unbalanced voltages.AIEE Trans, Pt-III-A, and Power Apparatus Syst 1954; 73(April):125–33. [4] Gafford WC, Duestenhoef, Mosher CC.Heating of induction motors on unbalanced voltages.AIEE Trans, Pt- IIIA, Power Apparatus Syst 1959; PAS-78(June):282–97. [5] “Comparison of applicationcapabilitiesofUandTrated motors,” IEEE Trans. Ind. Applicat., vol. IA-11, pp. 34–39, Jan. /Feb. 1975. [6] Ana Barbara Fernandes Neves,AnesiodeLelesFerreira Filho, MarcusVinicius Borges de Mendonca, “Effects of Voltage Unbalance on Torque and Efficiency of a Three- phase Induction Motor”, 16th IEEE conf.onHarmonicsand Quality of Power, May 2014, pp. 679 – 683 [7] Enrique C. Quispe, Ivan D. Lopez,“EffectsofUnbalanced Voltages on the Energy Performance of Three Phase Induction Motors”, IEEE conf. on Power Electronics and Power Quality Applications, July 2015, pp. 1- 6 [8] Spooner T, Kincaid CW.No load induction motor core losses. Trans AIEE 1928; 48(April):645. [9] Spooner T.Squirrel-cage induction motor core losses. Trans AIEE 1925; 44:155. [10] Nandi, S.; Toliyat, H.A.; Li, X. Conditionmonitoringand fault diagnosis of electrical motors—A review. IEEETrans. Energy Convers. 2005, 20, 719–729. [11] Alwash, J.H.H.; Ikhwan, S.H. Generalised approach to the analysis of asymmetrical threephaseinductionmotors. IEEE Electr. Power Appl. 1995, 142, 87–96. [12] J. L. Gonzalez-Cordoba, D. Granados-Lieberman, R. A. Osornio-Rios, R. J. Romero-Troncoso, J. J. De Santiago- Perez, and M. Valtierra-Rodríguez, “Methodology for overheating identification on induction motors under voltage unbalance conditions in the industrial process,” J. Sci. Ind. Res., vol. 75, no. 2, pp. 100-107, Feb. 2016. [13] P. Gnacinski, “Windings temperature and lossoflifeof an induction machine under voltage unbalance combined with over- or under voltages,” IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 363-371, Apr. 2008. [14] R. M. Tallam, B. L. Sang, G. C. Stone, G. B. Kliman, Y. Ji- Yoon, T.G. Habetler, and R. G. Harley, “A survey of methods for detection of stator-related faults in induction machines,” IEEE Trans. Ind. Appl., vol. 43, no. 4, pp. 920- 933, July 2007. [15] A. Siddique, G. S. Yadava and B. Singh, “A review of stator fault monitoring techniques of induction motors,” IEEE Trans. Energy Convers., vol. 20, no. 1, pp. 106-114, Feb. 2005. [16] Derating of Induction Motors Operating with a Combination of Unbalanced Voltages and over or under voltages Pragasen Pillay, Senior Member, IEEE, Peter Hofmann, and Marubini Manyage. 17. Venkataraman, B.; Godsey,B.;Premerlani,W.;Shulman, E.; Thaku, M.; Midence, R. Fundamentals of a motor thermal model and Its applications in motor protection. In Proceedings of the 58th Annual Conference for Protective Relay Engineers, Jacksonville, FL, USA, 5–7 April 2005. 18. Lei, G.; Zhu, J.; Guo, Y.; Liu, C.; Ma, B. A Review of Design Optimization Methods for Electrical Machines. Energies 2017, 10, 1962. [CrossRef]
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of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue 02|Feb 2023 www.irjet.net p-ISSN: 2395-0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 172 19. Bouzid, S.; Viarouge, P.; Cros, J. Real-Time Digital Twin of a Wound Rotor Induction Machine Based on Finite Element Method. Energies 2020, 13, 5413. [CrossRef] 20. Gnaci nski, P. limczak, P. High-Power Induction Motors Supplied with Voltage Containing Subharmonics. Energies 2020, 13, 5894. 21. Asad, B.; Vaimann, T.; Belahcen, A.; Kallaste, A.; Rassõlkin, A.; Iqbal, M.N. The Cluster Computation-Based Hybrid FEM–Analytical Model of Induction MotorforFault Diagnostics. Appl. Sci. 2020, 10, 7572. [CrossRef] 22] A. M. Bazzi and P. T. Krein, "Review of methods for real-time loss minimization in induction machines, "IEEE Trans. Ind. Appl., 2010. Rated Load. Energies 2018, 11, 2024. 23. Jeong-Jong Lee, Soon-O Kwon, Jung-Pyo Hong, Ji-Hyun Kim, Kyung-Ho Ha, " Core Loss DistributionofThree-Phase Induction Motor Using Numerical Method", IEEE Conferences, INTELEC-31st international telecommunications energy conference, pp.1 – 4, 2009. 24. T. Marcic et al" The impact of different stator and rotor slot number combinations on iron losses of a three-phase induction motor at no-load" Journal of Magnetism and Magnetic Materials, vol.320, no20, pp. 891- 895, 2008. 25. Estimation of Copper and Iron Losses in a Three Phase Induction Motor using Finite Element Analysis 574–583. 26. A. G. Yepes, J. Doval-Gandoy and H. A. Toliyat, "Strategy with smooth transitions and improved torque-speed region and stator copper loss for two-level asymmetrical six-phase induction motor drives under switch faults", IEEE Trans. Power Electron., vol.36,no.2,pp.1954- 1969, Feb. 2021. 27. Cardoso, A.J.M.; Cruz, S.M.A.; Fonseca, D.S.B. Inter-turn stator winding fault diagnosis in three-phase induction motors, by Park’s vector approach. IEEE Trans. Energy Convers. 1999, 14, 595–598. 28. D. M. Ionel, Mohammed H. Yasen, M. Popescu, “Factors Affecting the Accurate Prediction of Core Losses in Electrical Machines", IEEE International Conference on Electric Machines and Drives, pp. 1625 – 1632, 2005. Trans. Power Deliv. 2015, 30, 693–703. [CrossRef] 29. Tong Yang; Libing Zhou; WeiJiang," CalculationofEddy Current Losses in a Solid-Rotor Cage Induction Motor by Finite Element Analysis", IEEE Conferences on Electrical Machines and Systems, pp. 3656 - 3659, 2009. 30. atsumi and Noriaki, “Iron Loss Model for Rotating Machines Using Direct Eddy Current Analysis in Electrical Steel Sheets ", IEEE transactions on energyconversion,vol. 25, no. 3, 2010. 31. Konrad Dabala, " Analysisofmechanical lossesinthree- phase squirrel cage induction motors "IEEE Conferences, electrical machines andsystems,ICEMS,proceedingsofthe fifth international conference, vol.1, pp.39-42, 2001
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