A Three-Phase Induction Motor Problem

Ansoft RMxprt Application Note

A Three-phase Induction Motor Problem Problem This application note describes how to set up, solve, and analyze the results of a tw o-pole, three-pha se indu ction ction m otor using RMxprt. The The mod el create created d by RMxprt will then be used as an inp ut for EMpulse as a basis for performing m ore detailed analysis and for increasing the accur accur acy of the perform ance predictions. RMxprt Mxprt uses uses a combinati ombination on of analyti analyticcal and magneti magneticc circuit rcuit equati equations ons to predic predictt the performa performanc ncee of this this three three--phase inductio nduction n motor motor. EMpulse Mpulse is a nonline nonlinear ar timetime-domai domain n finite finite eleme element nt analys analysiis (FEA) sof software tware package th at solves electromagn electromagn etic field equ ations, electric electric circuit circuit equations, an d eq uation s of motion. You can create the project project from scratch scratch or op en th e p re-solved re-solved project project called called 3ph.pjt, 3ph.pjt, in the /ansoft/examples/rmxprt/ dire ples/rmxprt/ direct ctory ory.. If you are creat creating ing a projec projectt from from scratc scratch, h, selec selectt Three Phase Induction Motor a s t he he motor type in RMxprt. This project project w as created u sing version 2.3 2.3 of RMxprt RMxprt a nd version 7.0 of the Maxw ell 2D 2D Field Field Simu lator. lator.

Application Note

AP067-9911

General Data Use the General w indow to specify specify the motor char acteristics. acteristics. ➤

Define the general data: 1. En te te r 70.87 kW in the Rated Output Power field field for this tw o -pole motor . This is is equ al to a 95 horsepower motor. 2. En te te r 460 V in th e d riving RMS line-to-line line-to-line Rated Voltage field. 3. En te te r 60 Hz in the Frequency field. 4. En te te r 3502 rpm in the Rated Speed field. 5. En te te r 1276 W in th th e Stray Loss field. field. If the m easured stray load loss is unav ailable, ailable, NEMA M G1 G1 [1], p a ra ra gr gr ap ap h 20.52, s ta ta te te s t h at at t h is is v al alu e s ha ha ll ll b e a ss ss u m ed ed t o b e 1.2% o f t h e r at at ed ed o u tp tp u t for motors ra ted less than 2500 2500 hp and 0.9% 0.9% for motors ra ted 2500 hp and greater. IEEE IEEE St an an d a rd rd 112 [2] g iv iv es es d if iffe re re nt nt a ss ss u m ed ed s tr tr ay ay lo ad ad lo ss ss v a lu lu e s fo r m o to to rrss r at at ed ed le ss ss t h an an 2500 hp . They They are as follows: 1-125 hp

1.8%

126-500 hp

1.5%

501-2499 hp

1.2%

In this examp le, follow follow the IEEE IEEE guidelines and use 1.8% or 1276 1276 watts. 6. En te te r 700 W in the Friction Loss field. field. This value contains both the friction friction an d w ind losses. 7. C h oo oo se Tools/Model Units, select Inches as the un its. Choose OK to accept accept the u nits and Units, and select close close the window . 8. En te te r 9.5 inches in the Iron Core Length field field to d efine efine the length of the stator. 9. En te te r 0.95 in t he he Stacking Factor fie ld ld . Th is is g iv iv es es a v al alu e o f 9.025 in ch ch es es a s t h e n et et le ng ng th th o f t h e steel, after taking lamina tion into account. 10. Select Select D23 as the nonlinear Steel Type used in the m anufacturing of the stator lamination. lamination. To examine th e mater ial BH-curv BH-curv e for D23, D23, choose Materials/BH, Materials/BH, and then, in the Material Data Open, a n d s el D23.h-b. O n ce window, choose hoose Open, ele ct ct D23.h-b. ce t he he d a ta ta is lo ad ad ed e d in t he he le ft w in in d ow ow , y ou ou ca n plot the B-H B-H cu rve for this material. The The stand ard loss and sp ecifi ecificc weight of the material are also displayed . This information information is necessary necessary to calculate the iron core loss. Exit Exit this wind ow, and continue the general data inpu t. 11. Select Select Wye as the Winding Connection. Connection. 12. Select Select Constant Power as the Load Type. Type.

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Three-phase Induction Motor Problem

Stator Data Use the Stator1 an d Stator2 wind ows to define the stator dimensions and stator windings.

Define the Dimensions Use the Stator1 wind ow to define the stator dimensions. ➤

Define the stator: 1. Enter 5.525 inches in the Inner Diameter field. 2. Enter 10.125 inches in the Outer Diameter field. 3. Enter 36 in the Number of Slots field. 4. Select 2 as the Slot Type for the shap e of the slot. 5. D es ele ct Auto Design if it is selected, an d enter th e follow ing Slot Dimensions (inch): • Enter 0.055 in the Hr0 field. • Enter 0.065 in the Hs1 field. • Enter 0.698 in the Hs2 field. • Enter 0.16 in the Bs0 field. • Enter 0.309 in the Bs1 field. • Enter 0.432 in the Bs2 field.


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Define the Windings Use the Stator2 wind ow to define the stator windings. ➤

Define the w indings: 1. Select 21 in the Winding Type field. The w inding is a d ouble layer lap w inding. 2. En ter 0 in b ot h t he Top Spare Space an d Bottom Spare Space fie ld s . Th e s p ar e s p ace s in t h e s lo t are 0% of the slot's area. 3. En ter 0.01 inches in the Slot Insulation field. The slot insu lation is the thickness on one sid e of the stator slot. 4. En ter 0 in the End Adjustment field. The end adjustment is the length that the stator w indings extend beyond th e end of the stator. For this motor, the windings d o not extend beyond the stator. 5. En ter 1 in th e n u mb er of Parallel Branches fie ld . Th is m e an s t h e co ils m a kin g u p o n e p h a se a re connected in series. 6. En ter 11 in the number of Conductors per Slot field. 7. En ter 16 in the Coil Pitch field. Had the stator used a full pitch win ding , then the coil pitch w ould b e 18 slots (36 slots/ 2 poles). The w ind ing is woun d 2 slots shorter, wh ich resu lts in a coil pitch of 16 slots. 8. En ter 4.378 in the number of Wires per Conductor field. This is not the actual num ber but th e e qu iv ale nt n u m b er t h at g iv es t h e t ot al w i re cr os s-s ect io n al a re a. (O n e co n d u ct or is m a d e u p o f tw o 15 AWG w ires and of three 16 AWG wires.) 9. En ter 0.01 inches in the th ickness of the Wire Wrap field. 10. Enter 0.05708 inches in the Wire Diameter field. 11. Enter 15 in the Gauge field. Gauge settings are given in A WG.

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Rotor Data Use the Rotor1 an d Rotor2 wind ows to define the rotor.

Define the Slot Data Use the Rotor1 wind ow to define the rotor measurements and the characteristics of the rotor slots. ➤

Define the rotor measur emen ts and r otor slot characteristics: 1. Enter 0.046 in ch es in t h e Air Gap fie ld t o d efin e t he w id t h o f t h e a ir g ap b et w een t he r ot or a nd the stator. 2. Enter 1.875 inches in the Inner Diameter field to d efine the inn er diam eter of the rotor. This value is the same as th e diam eter of the shaft. 3. Enter 28 in the Number of Slots field to d efine the n um ber of rotor slots. 4. Select 6 as the Slot Type.

Define the Vent Data Use the Rotor2 wind ow to define th e rotor vent characteristics and other rotor measurements. ➤

Define the rotor vent characteristics and rotor measurements: 1. Enter 0 in the Numbers of Vents field. There are no vents in th e rotor. 2. Und er Skew Width, select Other, and enter 0 inches as the skew. 3. Enter 0.815 inches in the End-Ring Height field. 4. Enter 1.276 inches in the End-Ring Width field. 5. Und er Conductor Resistivity, select Aluminum to define the resistivity. This is the material used in manu facturing the bars and the end ring.


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Process the Analytical Design With the m otor data d efined, you are ready to generate the m odel. ➤

Generate the mod el: 1. Ch oose Tools/Options t o m a ke ce rt ain t h at t h e Wire Setting is American, a nd t hen ch oo se OK to close the window . 2. Ch oose Analysis/Analytical Design. RMxprt calculates the moto r perform ance param eters for this design.

Displaying the Lamination Once the an alysis is comp leted, you can d isplay the laminations on the objects. ➤

Display the laminations: 1. Ch oose Tools/Options/Lamination and make sure that all the items are checked. Choose OK to close this window wh en you are finished. 2. Ch oose Post Process/View Lamination to examine the cross-section of the motor. Choose OK to close the window wh en have finished viewing. 3. Ch oose Post Process/View Winding Layout to see the wind ing arrangement. 4. Ch oose Exit wh en you hav e finished viewing.

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Design Output Choose Post/Process/Design Output to examine the motor's parameters. The Design Output w in d o w is b ro ken d ow n into the following sections: General Data, Stator Data, Rotor Data, Rated-Load Op eration, NoLoad Operation, Break-Down Operation, Locked Rotor Operation, Detailed Data at Rated Operation, Wind ing Arrangem ent, and Transient FEA Inpu t Data.

General Data This information is the same as the data you entered in the General window.

Stator Data Th is in fo rm a tio n is g en er ally t h e s am e a s t h e d a ta y ou e nt er ed in t h e Stator1 an d Stator2 windows.If Auto Design was selected, RMxprt displays the optimized values for the windings.

Rotor Data This information is the same as the data you entered in the Rotor1 an d Rotor2 windows.

Rated-Load Operation This section displays information about the main performance parameters in the steady state: current, losses, mechanical torque, and input power, as well as the parameters of the one-phase equivalent circuit: resistance and leakage reactance for the stator w indin g, and mag netizing reactance for the rotor.

No-load, Break-Down, and Locked Rotor Operation These sections display information about the motor parameters at different operating conditions.

Detailed Data at Rated Operation The detailed d ata includes the slot, end -wind ing, differential, and skewin g leakage reactance for the stator w inding an d th e rotor. The sum of these values gives the main leakage reactance as displayed in the Rated-Load Op eration section. Other d ata listed in this area includ e the wind ings factor; the flu x density for the stator-teeth, rotor-teeth, stator-yoke, rotor-yoke, and air gap ; and m agnetom otive force: Slot Fill Factor

The percentage of the av ailable slot area (total slot area minu s slot insulation) that is filled with th e wire (copp er plus insu lation).

Correction Factor

The correction factor for the magnetic circuit length for the stator yoke and rotor yoke.

Saturation factor

The satu ration factor for the Teeth an d the Teeth an d Yoke fields.

Stator Current Density

The current d ensity of the stator.

Specific Electric Loading The amp ere-conductors per m eter of armature p eriphery. Mean Half-Turns Length The mean n um ber of half-turns for the main an d auxiliary phases. Stator Thermal Load

The current density in each slot multiplied by the Specific Electric Loading.

Half-Turns Length of Stator Winding

The half-turn s length of the stator w indings.


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Winding Arrangement This is the w inding arrangem ent for one full A phase, B ph ase, and C p hase wind ing. Only one layer arran gemen t is disp layed; the second can be ded uced rap idly from the coil pitch. For this examp le, the wind ing arrangement is:

Top layer: Bottom layer:

AAAAAAZZZZZZBBBBBBXXXXXXCCCCCCYYYYYY YYAAAAAAZZZZZZBBBBBBXXXXXXCCCCCCCYYYYYAA

The Winding Arrangement section also disp lays the following values (in electrical d egrees): Angle per slot

180 electrical degrees divid ed by th e nu mber of slots per pole.

Phase-A axis

The center of the A p hase wind ing with respect to the ph ase first slot.

First slot center

The reference used to calculate p hase.

Transient FEA Input Data This information is used wh en calculating the m otor perform ance using the 2D time transient finite elemen t field solver. For the main and auxiliary windings, this section displays:

• • • •

the nu mbers of turns, as seen from the terminal. the nu mber of p arallel branches. the term inal resistance. the end leakage ind uctance.

For the rotor end ring, this section displays both the end ring resistance and the end ring indu ctance between two bars at one of the ends. When you hav e reviewed the outp ut d ata, choose Exit to exit the w indow and begin plotting the p erformance curves.

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Plotting the Performance Curves ➤

Plot the cur ves: 1. Ch oose Post Process/Performance Curves. The PlotData window appears, with an Open wind ow v isible. The follow ing plot titles are available to open: n_curr.dat

Input Cu rrent vs Speed

n_effi.dat

Efficiency vs Sp eed

n_pow2.dat

Outp ut Power vs Speed

n_powf.dat

Pow er Factor vs Speed

n_torq.dat

Outp ut Torque vs Speed

2. Select the name of the plot to view. 3. Ch oose OK. Th e p lo t a p pe ar s in t he PlotData w i nd o w . A ft er y ou ’v e o p en e d o n e p lo t, t o o p en a different plot, choose Plot/Open. The speed is measured per un it of the synchronous speed. The following figures show the performance plots for the sample problem:


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4. When you have finished viewing the performance curves, choose File/Exit to exit PlotData.

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Create the Maxwell 2D Project N ow y ou can create the Maxw ell 2D project. ➤

Create th e Maxwell pr oject: 1. Ch oose Tools/Options, and m ake certain that the Periodic an d Teeth-Teeth options are selected, and th en choose OK to close the wind ow. These options allow you to take advan tage of the motor symmetry. 2. Ch oose Analysis/View Geometry. The Maxw ell 2D Modeler app ears, displaying the geom etry. 3. Ch oose File/Exit to exit the Maxw ell 2D Mod eler. 4. Ch oose Analysis/Create Maxwell 2D Project. A message wind ow ap pears, informing you that the Maxw ell 2D pr oject has been created. 5. Ch oose OK to close the message window . 6. Re tu r n t o t h e P ro je ct M an a ge r t o co n tin u e w i th t h e r es t o f t h is e xa m p le . Le av e RM xp r t o p en t o refer to later in the examp le.

Exporting the BH-Curve Once the p roject has been created, you can export th e BH-curv e for the magn etic mater ial HP76F to use for the m aterials in the Maxw ell project. ➤

Export the BH-curv e: 1. Ch oose Materials/BH. The Material Data window app ears. 2. Ch oose Open. A file brow ser app ears. 3. Locate and select the D23.h-b file. 4. Ch oose Open. The d ata for the material app ears. 5. Ch oose Save as and save the file as a .bh file (not an .h-b file). This file can be directly used by the 2D transient solver. 6. Ch oose OK to save the file and close the brow ser. 7. Ch oose Exit to close the Material Data window.

This file can now be directly used by th e 2D transient solver.


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Some Exercises This section provides some useful exercises for analyzing changes in the motor's performance in different situations.

Y - Delta Switching Create an indu ction m otor designed for a delta armatu re connection. Examine the starting torque and current for the tw o cases of the Y connection and the d elta conn ection. You sh ould obtain the following results:

• For the delta connection, the torque is 535 Nm, and the phase current is 512 A. • For the Y connection, the torque is 125 Nm, and the phase current is 247 A.

Multiple Parallel Circuits The wind ings forming on e ph ase may be connected in series or in p arallel, providing m ultiple parallel circuits (par allel bran ches). Examine the chang es in the wind ing resistance and the ph ase current at the rated -load op eration. You sh ould o btain the follow ing results:

• For one parallel branch, the resistance is 0.232 ohms, and the phase current is 64 A. • For two parallel branches, the resistance is 0.058 ohms, and the phase current is 214 A.

Influence of Rotor Resistivity on Locked-Rotor Torque Change the m aterial for the rotor bar. Use copper instead of aluminum , and examine the changes in the v a lu e o f t h e lo ck ed -r ot or t or qu e . Ke ep t h e Y co n ne ct io n a n d t w o p a ra lle l p a th s. Yo u s ho u ld o bt ain t h e fo llowing results:

• For aluminum, the locked-rotor torque is 753 Nm. • For copper, the locked-rotor torque is 582 Nm.

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Three-Phase Induction Motor Simulation Using EMpulse N ow th at the Maxwell 2D project is created, use the EMPulse environmen t to pred ict the operating p erformance of the motor. EMpulse is a nonlinear time-domain FEA software package that analyzes the electromag netic (plane p arallel) phen omen a in electromagnetic devices, combined w ith electric circuits and motion. If you w ant to simp ly open and inspect the finished p roject, the pre-solved p roject is includ ed in 3ph_fea.pjt. If you wa nt to step throu gh the p roject you rself, open the p roject you p reviously exported from RMxprt.

Set Up the Geometry The geometry of the mod el is already created by RMxprt. ➤

Open the project, and set up th e geometry: 1. Fr om t h e P ro je ct M an a ge r in t h e M axw e ll C on t ro l P an el, o p en t h e M axw e ll 2D p r oje ct t h at w a s created in th e prev ious section. If using the p re-solved project, its name is 3ph_fea.pjt. Upon open ing the p roject, notice that the Transient solver, the XY draw ing plane, and Define Model are already set. 2. Ch oose Define Model/Draw Model to open th e Maxwell 2D Modeler. 3. Ch oose View/Zoom In, and zoom in on th e air gap. There is an add itional object in the air gap called Band. This object is used du ring the solution p rocess to d etermine w hich objects are stationary and wh ich objects rotate. 4. Ch oose

File/Save ,

and then File/Exit, to save the file and exit the Maxwell 2D Modeler.

5. Ch oose Define Model/Group Objects, and group the objects that belong to the same w inding. RMxprt assigns names to all of the objects in the geometry. Group the objects as follows (notice the abbreviations for the names of the windings): Bar

objects Bar0-Bar13

PhA

objects PhA0-PhA11

PhB

objects PhB0-PhB11

PhReB

objects PhReB10, PhReB11

PhReC

objects Ph Re0-PhRe11

N ote that the stator w inding s of an indu ction m otor can be grou ped into six different objects. Since the FEA mod el is only half of the full mod el, group s PhReA an d PhC are not in the samp le drawing. If you assu me that th e rotor rotates coun terclockwise (positive torque), the stator wind ings have to be grou ped counterclockw ise in the same sequ ence. In this examp le, that ord er is PhA (represented as A), PhReC (represented as C-), PhB (represented as B), and PhReB (represented as B-).


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Setup Materials After grouping the objects, you can now assign material properties. Because this example requires materials not includ ed in the m aterial database, you m ust create them in the Material Manager. Choose Setup Materials to access the Material Manager and assign material properties to all of the objects.

Add a New Material Ad d a n ew n onlinear ma terial called D23 to the local material data base. ➤

Add a new material: 1. Ch oose Material/Add, and enter D23 in the nam e filed below Material Attributes. 2. Select Nonlinear Material, and choose B H Curve. The B-H Curve Entry window ap pears. 3. Ch oose Import from the The B-H Curve Entry window. The Import File window ap pears. 4. Se le ct t h e D23.bh file that was created w ithin RMxprt. Make certain that th e bh button is selected before imp orting. In m ost cases, this file is located in c:\ansoft\rmxprt\matlib. 5. Ch oose OK to import the file and return to the B-H Curve Entry window. 6. Ch oose Exit to exit the wind ow an d retu rn to the Material Manager. The new material is now available in the d atabase.

Derive a New Material Derive a new cond uctor mater ial called Alu miniu m_115. ➤

Derive the new material: 1. Select aluminum from the Materials list. 2. Ch oose Material/Derive. 3. En ter Aluminum_115 in the nam e field below Material Attributes. 4. En ter 2.304e7 S/ m in the Conductivity field. 5. Ch oose Enter to enter the new material in the local material database.

Assign the Materials Now assign material properties as follows. ➤

Assign the mater ials: Assign vacuum to the AirGap an d Band. ■ Assign Aluminum_115 to the Bar group. ■ Assign copper to groups PhA, PhB, PhReB, PhReC. ■ Assign D23 to the Rotor an d Stator. ■ Assign steel_stainless to the Shaft. ■ Exclud e the background from the mod el. ■

No te that the rotor bar cond uctivity is set up for a wo rking temp eratu re of 75 degrees Celsius. The condu ctivity of the stator windings w ill not be taken into account if the w indings are set up as a strand ed condu ctor. The resistances of the stator w ind ings w ill be specified in th e Source Setup .

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Setup Boundary / Sources Th e fi rs t s te p in d e fin in g t he b ou n d a ry co n d it io n s is t o d e fin e t h e M as te r/ Sla ve b ou n d a ry. Yo u t h en n ee d to setup the source and assign the end ring parameters. First, choose Setup Boundaries/Sources. The 2D Boundary/Source Manager appears.

Define the Master Boundary ➤

Define the master bound ary: 1. Ch oose Window/New to open an add itional window . Once the wind ow is open choose Window/Tile to arrange the w indow s in a tile format. 2. Ch oose Edit/Select/Edge, and select the curved edge of the outside d iameter of the stator. 3. Ch oose Assign/Boundary/Value, and assign to it a value bound ary of 0. 4. Ch oose View/Zoom In, and zoom in on th e air gap so that the area where the Band and the inside d iameter of the stator cross the x-axis can easily be seen. 5. Ch oose Edit/Select/Trace. St ar tin g in t h e w i nd o w w i th t h e fu ll m o d el s ho w n , click o n t he ce n te r axis of the motor (u=0, v=0), and then click on the following intersection: • Rotor Inside Diameter (u=23.8125, v=0) 6. Switch to the window wh ere the air gap is enlarged, and click on the following intersections: • Rotor Ou tside Diameter (u=68.9991, v=0) • Band (u=69.5833, v=0) • Stator Inside Diameter (u=70.1675, v=0) 7. Switch back to the window with the full mod el, and dou ble-click on the Stator Outside Diameter (u=128.5875, v=0) to end th e master b oun da ry d efinition. 8. Ch oose Assign/Boundary/Master, and th en choose Assign.

The master boundary is now assigned.

Define the Slave Boundary Again, use the Edit/Select/Trace command to define the slave bound ary. ➤

Define the slave bound ary: 1. Ch oose Edit/Select/Trace. St ar tin g in t h e w i nd o w w i th t h e fu ll m o d el s ho w n , click o n t he ce n te r axis of the motor (u =0, v=0), and th en click on the following intersection: • Rotor Inside Diameter (u=0, v=23.8125) 2. Switch to the window wh ere the air gap in enlarged, and click on the following intersections: • Rotor Outside Diameter (u=0, v=68.9991) • Band (u=0, v =69.5833) • Stator Inside Diameter (u=0, v=70.1675) 3. Switch back to the window with the full mod el, and dou ble-click on the Stator Outside Diameter (u=0, v=128.5875), to end the slave bou nd ary d efinition. 4. Ch oose Assign/Boundary/Slave, and select Slave = –Master. When solving for an od d n um ber poles of an electrical machine, u se the Slave = –Master symmetry. When solving for an even num ber of poles, use the Slave = +Master symmetry. 5. Ch oose Assign.


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Source Setup W h en s p ecify in g t h e s ou r ce , y ou n ee d t o co n sid e r t w o o p tio n s in EM p u ls e: co ils ca n b e e it h er cu r re nt s u p plied or voltage supplied. In the electric motors, windings are generally voltage supplied, with the resulting currents d epen den t on the w indin g's resistance and b ack electromotive force (emf). EMpu lse can calculate the currents from the field solution and the terminal data.

Phase A Winding ➤

To set up th e Phase A winding p arameters: 1. Ch oose Edit/Select/Object/By Clicking, and then select the object grou p PhA. Click th e right mou se button to stop selecting. 2. Ch oose Assign/Source/Solid. New fields appear below the view w indow . 3. Select Voltage an d Strand. 4. Ch oose Functions, and ad d th e following three new fun ctions: • Ph aseA = 460*sqr t(2/ 3)*cos(360*60*T) • Ph aseB = 460*sqr t(2/ 3)*cos(360*60*T-120) • Ph aseC = 460*sqr t(2/ 3)*cos(360*60*T-240) 5. When you have finished entering the fun ctions, choose OK to accept th e functions and close the window. 6. Ch oose Options and select Function in the window that app ears. Choose OK to accept a functional value for the voltage and close the w indow . 7. En ter PhaseA in the valu e field. 8. Ch oose Winding. The Winding Setup for Boundary window app ears. 9. Assign a positive polarity to the object group PhA. 10. Under Terminal Attributes, enter the following values, which w ere derived using the transient FEA inpu t data from RMxprt Design Ou tput: • Enter 0.231977 ohms in the Resistance field. The resistance is the total resistance of the wind ing at the working temperature • Enter 0.000441694 henries in the Inductance field. The ind uctance is only the end -wind ing leakage ind uctance, which can not be d edu ced from th e 2D field solution. • Enter 66 in the Total turns as seen from terminal field. • Enter 1 in the Number of Parallel Branches field. 11. Choose OK to accept the settings and return to the 2D Bound ary/ Source Manager. 12. Enter PhaseA in the Name field, and th en choose Assign.

The PhaseA wind ing parameters are now d efined.

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Phase B Winding ➤

To set up the Phase B wind ing param eters: 1. Ch oose Edit/Select/Object/By Clicking, and th en select the object group s PhB an d PhReB. 2. Ch oose Assign/Source/Solid. New fields appear below the view w indow . 3. Select Voltage an d Strand. 4. Ch oose Options, and select Function for the voltage. Choose OK. 5. Enter Voltage in the Value field. 6. Ch oose Winding. The Winding Setup for Boundary window app ears. 7. Assign a positive polarity for PhB and a negative polarity for the group PhReB. 8. Und er Terminal Attributes, define the follow ing valu es: • Enter 0.231977 ohms in the Resistance field. The resistance is the total resistance of the wind ing at the working temperature. • Enter 0.000441694 henries in the Inductance field. The ind uctance is only the end -wind ing leakage inductance, which can not be deduced from the 2D field solution. • Enter 66 in the Total turns as seen from terminal field. • Enter 1 in the Number of Parallel Branches field. 9. Ch oose OK to accept the settings and return to the 2D Bound ary/ Source Manager. 10. Enter PhaseB in the Name field, and th en choose Assign.

Phase C Winding ➤

To set up th e Phase C winding p arameters: 1. Ch oose Edit/Select/Object/By Clicking, and then select object group PhReC. 2. Ch oose Assign/Source/Solid. New fields appear below the view w indow . 3. Select Voltage an d Strand. 4. Ch oose Options, and select Function for the voltage. Choose OK. 5. Enter Voltage in the Value field. 6. Ch oose Winding. The Winding Setup for Boundary window app ears. 7. Assign a negative polarity for group PhReC. 8. Und er Terminal Attributes, define the follow ing valu es: • Enter 0.231977 ohms in the Resistance field. The resistance is the total resistance of the wind ing at the working temperature • Enter 0.000441694 henries in the Inductance field. The ind uctance is only the end -wind ing leakage inductance, which can not be deduced from the 2D field solution. • Enter 66 in the Total turns as seen from terminal field. • Enter 1 in the Number of Parallel Branches field. 9. Ch oose OK to accept the settings and return to the 2D Bound ary/ Source Manager. 10. Enter PhaseC in the Name field, and th en choose Assign.


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End Ring Parameters ➤

Define the end connection: 1. U se th e Edit/Select comm and s, and select the object group Bar. 2. Ch oose Assign/End Connection. New fields appear below the view w indow . 3. Se le ct t h e Passive end-connected conductor box. 4. En ter 7.5856e-7 ohms in the End Resistance between adjacent conductors field. 5. En ter 1.47364e-9 henries in the End Inductance between adjacent conductors field.

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Setup Solution Since ad aptive refin emen t is not available for the tr ansient solver, the qu ality of the m anu al mesh is critical to the accur acy and th e convergen ce of the field solution. The mesh mu st be fine in regions w here a large magn etic field grad ient occur s (such as air-gaps an d rotor bars) and larger elsewh ere. For pr actical use, generating a mesh th at is too fine can result in excessive comp utation al time.

Manual Mesh ➤

Manually create the m esh: 1. Select Setup Solution/Options from the Executive Command s menu . The Solve Setup window appears. 2. Ch oose Manual Mesh. The 2D Meshmaker ap pears. 3. Ch oose Mesh/Seed/QuadTree. The QuadTree Seed wind ow ap pears. Accept 6 as the Number of levels, and choose OK. 4. Ch oose Mesh/Make. The basic mesh is generated for the mod el. This mesh is too coarse to provide the most accurate solution and mu st be refined. To refine the mesh, you need to take into account th ose areas w hich are critical for solution accuracy. In this examp le, the critical areas are the band , the air-gap, and the rotor bars. During the m anual refinement, you can specify the d esired nu mber of triangles in each object. 5. Ch oose Refine/Object. The Object Refinement wind ow ap pears, allowing you to refine the mesh fur ther. The goal is to hav e a uniform m esh with a su fficient num ber of elements in the air gap:. 6. Make certain the following nu mber of triangles appear in the Refine Number field for each object: AirGap

2000

Band

1000

Bars

50

PhA, PhB

40

PhReB, PhReC

40

Rotor

1300

Shaft

150

Stator

2000

If t h e n u m b er o f e le m en ts fo r a n o bje ct d o es n o t fa ll w i th in a fe w p e rce n t o f t h a t lis te d , s ele ct it s name from the Object Name list, and enter its app ropriate value in the Refine Number field. Choose Accept to accept the n ew v alue. Values for the air gap, ban d, and stator require the greatest nu mber of elements to obtain the most accurate solution. 7. Ch oose OK w hen finished refining the objects.


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Refine the Mesh You can mod ify the m esh still further by ad ding ind ividu al points with the m ouse. In this step, pay p articular attention to the region surround ing the air gap and the top of the rotor bars because this region w ill experience the high est rate of error, requiring th e most refinem ent. ➤

Refine the m esh: 1. Ch oose Refine/Point. The Point Refinement window ap pears. 2. Leav e Circumcircle selected an d choose OK to accept th is style of point refinemen t. The wind ow closes. 3. Add triangles where they are needed to further refine the mesh, if necessary. Click the right mou se button to exit. 4. Ch oose Mesh/Line Match and select the ed ges of both the master and slave boundaries, to e ns u re t h at t he m e sh in g p o in t s w i ll m a tch a t y ou r m a tch in g b ou n d a r ie s. C lick t h e r ig h t m o u se button w hen d one selecting. If the m eshing p oints do not match at m atching bou ndaries, you w ill receive an error m essage about a m issing tran script file du ring the nom inal solution. 5. Ch oose File/Exit, and save the changes to the mesh as you exit from the wind ow.

W hen y ou re tu r n t o t he Solve Setup window, the Starting Mesh o pt io n is ch an ged t o u se t he Current mesh.

Solution Options for the Transient Analysis For this examp le, use the following settings to defin e the solution op tions for the transient an alysis. ➤

Define the solution op tions: 1. Leav e Starting Mesh set to Current. 2. Accept the default value in the Solver Residual field. This value has n o effect when the d irect solver is used . 3. Select Direct as the Solver Choice. Use this option w henever you generate a solution u sing the transient solver. 4. Select Start from time zero as the Solution starting point. 5. En ter 0.10 seconds in the Stop time field. You w ill only gener ate a solution for the first 0.1 seconds of motion. 6. En ter 0.00015 in the Time step field. This instructs th e solver to calculate th e fields every 150 microseconds of the solution process. For fixed time steps, such as these, typically use 50 steps per electrical cycle. The resulting rotor d isplacement per on e time step shou ld be a m aximum of 3 mechanical degrees. 7. En ter 0.05 in the Save fields time step field. This instructs the solver to w rite the field solution out every 50 milliseconds. 8. En ter 241.3 mm in the Model depth field. 9. En ter 2 in t he Symmetry multiplier field. Because you are modeling only one-half of the model, use this mu ltiplier to generate a solution for the entire geometry. 10. Choose OK to accept the values and return to the Executive Command s menu .

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Motion Setup Wit h t h e s olu t io n p a r am e te rs d e fin ed , y ou ca n n o w d e fin e t h e m o tio n p a ra m et er s fo r t h e t ra n sie nt m o d el. ➤

Define the m otion setup : 1. Ch oose Setup Solution/Motion Setup from the Executive Comm ands menu . The Motion Setup window ap pears. 2. Select t he Band object, and then choose Set Band. Th e b an d is d e fin ed a s a s ta tio n ar y o bje ct t h at contains all mov ing objects. 3. Select Rotation as the Type of Motion. 4. Ch oose Set Position, and select (0,0) as the center of ro tation. 5. Ch oose Mechanical Setup. The Mechanical Setup window app ears. 6. D es ele ct Consider Mechanical Transient, and enter 3502 in the Constant Angular Velocity field. Make sur e the u nits list beside the field is set to rpm. 7. Ch oose OK to close the window . 8. Ch oose Exit to exit the Mechanical Setup wind ow. Save the changes as you exit.

Solve the Nominal Problem Choose Solve/Nominal Problem fr om t h e Exe cu t iv e C om m a n d s m e nu . Th e p r og re ss b ar in fo rm s y ou o f t h e status of the solution. Solving the p roblem takes abou t 8 hours on a 400 MHz PC. If you w ant to disp lay the transient d ata, such as voltages, currents, torque, and pow er loss, choose Solutions/Transient Data. If you choose Refresh du ring the solution p rocess, the plots will be refreshed a fter completing th e current time step.


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Post Processing ➤

Access the Fields Post Processor: 1. Ch oose Post Process/Fields. The Post-Process Saved Fields wind ow ap pears, listing the time steps. 2. Select the time step to plot, and choose OK. The 2D Post Processor open s.

Calculate the Flux Density Calculate the flux d ensity in the air gap . First, you m ust id entify a line in the air gap , then load th e B vector and calculate the ma gnitu de of B, map th e magn itud e of B onto this line, and then take its average value. ➤

Calculate the flux density: 1. Ch oose Post/Line/Define. The Line Segment Menu window app ears. 2. Zoom into the air gap so that the band can be selected. 3. En ter Object in the Line segment name field. 4. Select the band object. 5. Ch oose Display and then Return. 6. Ch oose Calc/Plane to enter the p lane calculator. 7. Und er Transient, choose B_Vector to load the B vector into the calculator. 8. Und er Vector, choose magnitude to calculate th e magn itud e of B. 9. Ch oose Line to the r ight of the calculator to access the line calculator. 10. Under Register, choose enter. Set lineseg1 to Yes, and choose Execute. 11. Under Operations, choose value, and enter 1000 in the blank field. This map s the value of the mag nitud e of B onto the line. 12. Under Operations, choose integrate. Set Enter in number calculator to Yes. 13. Choose Plane to return to the plane calculator. 14. Under Scalar, choose constant, and enter 1.0 in the field. 15. Choose Line to return to the line calculator. 16. Under Register, choose enter. Set lineseg1 to Yes, and choose Execute. 17. Under Operations, choose value. 18. Under Operations, choose integrate, and set Enter in number calculator to Yes. This calcula tes the length of the line. 19. Choose Number to enter the num ber calculator. 20. Under Operations, choose divide to divide ou t the length of the line. Follow ing is the equation w e just solved:

∫

B • d l B( avg) = ----------------d l

∫

The value in the top register of the calculator stack is the value in tesla of the avera ge flux d ensity in the air gap, w hich shou ld be ap proximately 0.412 tesla. The valu e calculated by RMxpr t is 0.447 tesla. Exit from th e calculator, and choose Post/Plot to view field qu antities such as flux, B, and H .

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Results Your values m ay d iffer slightly from th ese, but sh ould still be close:

• Phase Current = 30 A rm s (comp ared to 31 A rms in RMxprt) • Torque = 58.5 Nm (comp ared to 56.6 in RMxprt) • Pow er Loss = 2230 W The following figures show the transient plots for the samp le problem:


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References [1] NEMA Stand ards Pub lication N O. MG1, National Electrical Manufacturers Association (NEMA), Washington D.C.,1993. [2] IEEE Standard Test Procedu re for Polyph ase Ind uction Motors and Generators, IEEE Stand ard 1121991, 1991.


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A Three-Phase Induction Motor Problem

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