JOU RN AL O F CHI NA OR DNAN CE
Modeling and Performance Prediction of Induction Motor Drive System for Electric Drive Tracked Vehicles
CHEN Shu yong( 陈树勇) 1, CH EN Quan shi(
陈全世) 1 , SUN F eng chun( 孙逢春) 2
1 T he State Key L aboratory of Automobile Safety and Energy, T singhua U niversity , Beijing 100084, China; 2 Schoo l of M echanical and V ehicular Engineer ing , Beijing Institute of T echno logy, Beijing 100081, China Abstract: T he principle of rotor flux orientation v ector control on 100/ 150 kW three phase AC induction motor for electric drive tracked vehicles is analyzed, and the mathematic model is deduced. T he drive system of induction motor is modeled and simulated by M atlab/ Simulink. T he character istics of motor and drive system are analyzed and evaluated by practical bench test. T he simulat ion and bench test results show that the model is v alid, and t he driving control system has constant tor que under rated speed, constant torque above rated speed, widely variable speed range and better dynamic character is tics. In order to evaluate the practical applications of high pow er induction mo to r driving system in electr ic driv e tr acked v ehicles, a collaborative simulation based on interface technology of M atlab/ Simulink and mult i body dynamic analysis softw are known as Recur Dyn is done, the vehicle performances ar e predicted in the acceler at ion time ( 0 32 km/ h) and turning characteristic ( v = 10 km/ h, R = B) . Key Words: electric engineering; electric dr ive; rotor flux orientation v ector control; simulation; bench test; performance prediction CLC Number: T J81+ 0 323 Document Code: A Article ID: 1673 002X( 2007) 03 0172 07
Introduction
T he t raction mot or and it s cont roller are t he core of electric vehicle powertrain drive syst em. T he pow ertrain drive system is required to have t he follow ing charact erist ics: w ide variable speed rang e, large st art ing t orque, high backup power, high power den sity, w ide hig h ef ficient area, high reliability , con st ant torque under the rat ed speed and const ant pow er above t he rat ed speed. T ract ion mot or and it s con t roller have a direct impact on vehicle driving perfor mances. T he three phase AC squirrel cage t ype in duct ion mot or is widely used as t he tract ion motor for elect ric vehicles. Based on the analysis of the mat he mat ical model of AC induct ion mot or, a simulation model of 100/ 150 kW hig h power three phase AC in duct ion mot or drive system is built in virtue of a pow erful simulation modeling ability of M at lab and the funct ional elements of Simulink in conjunct ion wit h
Recei ved 2006 12 28
t he vector control t heory . It s dynam ic response abilit y is analyzed. T he characterist ics of t he whole drive system are analyzed and evaluat ed by bench t est. Finally t he act ual vehicle performances are pre dict ed by using t he int erface t echnolog y of control simulat ion soft ware Mat lab/ Simulink and dy namic simulat ion soft w are RecurDyn/ Cont rol.
[ 1 3]
1
Modeling of Induction Motor Drive System
T he left and right side sprocket s of an elect ric drive t racked vehicle are propelled by t wo squirrel cage induct ion motors. T he vehicle drives along t he beeline when t he rot at ing speed of left side mot or is t he same as that of right side mot or, and t he st eering of vehicles is cont rolled by the speed dif ference be tw een the left and right side tract ion motors. A rot or f lux orient at ion vector cont rol ( RFOC) is int roduced int o t he induction mot or drive system. T he rot or f lux orientation has a good decoupling performance.
Sponsored by Ordnance S cience and Technology Pre research Project of China( 40402070101) Biography CH EN Shu yong( 1972 ) , assist ant researcher, shuyongchen@ sina. com
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CH EN Shu yong , et al . / Modeling and Perf or mance Prediction of I nduction Motor Dr ive System f or Electric Dr ive T r acked Ve hicles
By transformation and calculat ion of coordinates, the st ator current of induct ion motor can be decoulped in t o f ield current and t orque current w hich are con t rolled, respect ively. T he cont rol charact eristic of the induct ion mot or is similar to t hat of separat ely excited DC mot or. T herefore, the system has preferable dy namic perf orm ance. 1 1 Vector Control Motor Governor System Struc tural Principle According to t he mag netic f ield equivalence prin
loop circuit . We must abide by t he follow ing principle in vect or control system design: firstly current loop, secondly speed loop. 1 2 Modeling of Induction Motor We must build a dynamic model of induct ion mo tor in order to att ain high dy nam ic perf orm ance. T he dynam ic mat hemat ical model of induction motor is non linear and m ulti variable, its input variables are st ator volt age and frequency, and it s output variables are rotating speed and magnetic chain. For t he induc t ion motor, t he dynamic m at hemat ical model based on RFOC is as follows. Volt age equat ion u sM u sT 0 0 R s+ L sp
cL s
ciple, the induction motors can be equivalent t o DC mot or af ter Clark and P ark t ransformat ions. Ref er ring to DC motor control met hod, t he cont rol variable of equivalent DC motor can be used t o control t he in duct ion motor af ter t he corresponding inverse trans f orm at ion. T hrough the above t ransformat ions, the st ator current of induct ion motor can be equiv alent to field current and torque current , t he direct ion of field current vector is t he same as t hat of rotor f lux vector, w hich achieves t he decoupling control of induction mot or f lux and torque. A constant t orque must be maint ained to keep the st at or M axis inst ant aneous current unchanged at a rat ed speed, t he different torques can be output by adjusting t he stator T ax is instant aneous current; t he st ator current must be kept unchanging in order t o maintain a const ant pow er w hen t he voltage arrives at rated volt ag e and keeps const ant above t he rat ed speed. T he st ruct ure of in duct ion motor driving vect or control syst em is show n in F ig . 1. T he g overnor syst em is controlled by t hree regulat ors, i. e. rotat ing speed regulat or ASR, w hich achieves speed adjustment , M axis current regulator AMCR achieves t he adjust ment of t he equivalent field loop current , T ax is current regulat or AT CR achieves t he adjustment of t he equivalent arm at ure
isM = i sT ir M i rT L Mp
cL M

eL s

cL M
Rs + L s p 0 0
L Mp 0 Rr
L Mp LM
R r+ L r p Lr
,
( 1) w here u sM , u sT are the inst antaneous volt ages of st a tor M axis and T ax is respectively; i sM , i sT are t he inst antaneous current s of st ator M ax is and T ax is; i rM , i rT are t he inst ant aneous currents of rot or M axis and T ax is; p is the dif ferent ial operator; R s, R r are the phase w inding resist ances of stator and ro tor; L s, L r are the w inding self inductances of st at or and rot or phase; L m is mut ual inductance w hen rotor axis coincides w it h st ator axis; e is t he ang ular ve locit y of pow er; r is the angular velocit y of rot or; = ( e  r ) is the angular velocity difference of e and r. Flux formula
sM= sT
L s i sM + L M i rM , L M i sM + L r i rM =
r,
= L s i sT + L M i rT ,
rM=
( 2)
0= L M i sT + L r i rT , w here sM , sT are t he flux of stator M axis and T axis; rM is t he flux of rotor M ax is, i. e. t otal rot or f lux r . T he st ator current is controlled in t he vector con 173
Fig. 1
Structure of vector control system
JOU RN AL O F CHI NA OR DNAN CE, 2007, Vol. 3, N o. 3
t rol syst em. T herefore, t he relat ionship bet w een the tw o component s of the st at or current and ot her physi cal parameters must be founded from the mathemati cal model. T he dynam ics relation betw een t he st at or current i sM and t he rotor t otal f lux ( 3) i sM = 1+ T r p r, LM ( 3)
r
rules: if V ref1 > 0, A = 1, else A = 0; if V ref2 > 0, B = 1, else B = 0; if V ref3 > 0, C = 1, else C= 0. T here fore, sector N = A + 2B + 4C . 1 3 2 Calculat ion of X , Y , Z and acting t ime t x , ty of tw o adjacent vectors
of M axis meets Eq.
Defi nition X = 3 V !t s/ V dc , Y = ( 3 V !/ 2+ 3 V ?/ 2) t s / V dc, Z = ( 3 V! / 2 3 V ?/ 2) t s/ V dc . t x and ty of the different sect ors are evaluated according t o T able 1. However, af ter t he assig nment t o t x and ty , their saturation capacity is still judged. If tx + ty > t s , t s = t x t s / ( tx + ty ) , t y = ty t s / ( tx + t y ) .
Table 1
sector No. tx 1 Z Y
w here T r = L r / R r is the excit ing t ime constant of ro t or. T he dynam ics relation betw een t he st at or current i sT and the rot or current i rT of T axis meets Eq. ( 4) i sT = T orque equat ion T e= n p M ovement equat ion T e= T L + J d r , n p dt ( 6) LM i L r sT
r.
Evaluation of t x , t y
2 Y  X 3  Z X 4  X Z 5 X  Y 6  Y  Z
Lr i . L M rT
( 4)
ty
( 5) 1 3 3 Calculation of vector sw itching point s t cm1 , t cm2 and t cm3 ta = ( t s t x  t y ) / 4, t b = ta + t x /
Defi nition
w here T L is the load torque; J is the t otal moment of inert ia from load t o the mot or axis; n p is t he pole pairs of motor. According t o t he above mathematical models, a dynamic model of induction motor under MT coordi nat e system is est ablished by using Matlab/ Simulink, w hich is show n in F ig. 2.
2, t c= t b + ty / 2. t cm1 , t cm2 and t cm3 of dif ferent sec tors are evaluated according t o T able 2.
Table 2
sector No. t cm1 t cm2 t cm3 1 tb ta tc
Evaluation of t cm1 , t cm2 , t cm3
2 ta tc tb 3 ta tb tc 4 tc tb ta 5 tc ta tb 6 tb tc ta
1 3 4 SVPWM implement ed by Matlab/ Simulink According t o the above alg orit hm, SVPWM simulat ion model built by Matlab/ Sim ulink is show n in Fig. 3.
Fig. 2
Dynamic model of induction motor
1 3
Modeling of SVPWM Judgement of sect or in w hich vector V ref is locat ed Definition V ref1 = V!, V ref2 = (  V!+ 3 V?) / 2,
Fig. 3 Model of SVPWM
1 3 1
V ref3 = (  V ! 3 V ?) / 2. By analyzing the relat ion ship betw een V ? and V !, w e can f ind t he follow ing 174
1 4 Modeling of Inverter By t aking t wo power sw itches of t he up dow n
CH EN Shu yong , et al . / Modeling and Perf or mance Prediction of I nduction Motor Dr ive System f or Electric Dr ive T r acked Ve hicles
sam e arm t o be equiv alent t o an ideal sw itch, six IG BT s of invert er are simulated w ith t hree ideal sw it ch es. T he simulation model is shown in Fig. 4. 1 5 Simulation Model of Single Side Induction Mo tor Vector Control System According t o the above depict ions, t he simula t ion model of induction mot or vect or control system is built in M at lab/ Simulink block diagram f orm by us ing the packaged subsyst em models, which is show n in Fig. 5.
Fig. 4 Model of inverter
Fig. 5
Simulation model of induction motor vector control system
2
Collaborative Simulation Model of Electrical Mechanical System Based on Matlab/ Simulink
T he motor load is generally nonlinear w hen the vehicle travels actually. T racked vehicles are a very complicat ed variable and nonlinear system. In order to accurat ely assess and evaluat e the act ual change w it h load on t he ent ire drive syst em charact erist ics, and to provide an object ive basis for est ablishing a reasonable w hole vehicle cont rol strategy [ 4 5] , so it is necessary to establish the induction motor load model that can accurate response t o syst em driv ing charac t erist ic. T herefore, we build a t racked vehicle dy namics model based on mult i body dynam ics soft ware nam ed RecurDyn/ T rack H M, the whole vehicle dy namics model is regarded as t he induction motor load model. T he propulsion system of elect ric drive tracked vehicle consists of t w o track chain systems. Each track chain system includes one sprocket, one idler, six road rollers, t hree support rollers and 96 t rack links. T he st ruct ure of track link is double pins, the st ruct ure of road roller is single flang e. T he suspen 175
sion unit is a torsion independent suspension, t he lim iter is spiral spring , t he cylindrical hydraulic shock absorber is installed on t he top of front behind road roller. T he hull is im port ed from 3 D solid modeling soft ware Pro/ E as a hull. st p f ile. T he sprocket s, idlers, and support rollers are connected t o t he chassis by revolute joints. A simula t ion can be performed af ter apply ing t orque or kine mat ics on t he sprockets. T he road w heels are con nected t o the hull by the road arms, one end of t he road arms is connect ed to t he road w heels by revolute joints, t he other end is fixed in t he t orsional bar axis of hull. T he suspension unit is simulat ed by a rota t iona1 spring damper actuator ( RSDA) . Each t rack chain syst em has it s ow n geomet ry and t he parame ters of t he pavement, t he cont act pressure bet ween t he ground and t rack is det ermined by the ground col lision paramet ers. According to t he original design parameters and 3 D solid model of vehicles, t he geometric parameters and performance parameters of t he whole vehicle and t he various com ponents are confirmed. T he vehicle dynam ic model is built, as show n in Fig. 6. T here are 34 joints and 1 196 degrees of f reedom in t he model.
JOU RN AL O F CHI NA OR DNAN CE, 2007, Vol. 3, N o. 3
Not e that t he cent er of sprocket is selected as a fixed coordinat e syst em .
ed volt age V eAC = 300 V, rat ed current I e = 264 A, rat ed torque T e = 514 N m, rated speed n e = 1 860 r/ min, pole pairs n p = 3, L s = 2 351 8 mH, L r = 2 372 1 mH , L m= 2 28 mH, R s= 0 007 1 # , R r = 0 004 2 # and J = 0 8 kg m 2 . T he main parameters of whole vehicle are vehicle mass m = 14 000 kg, t he cont act lengt h of each of t he t wo tracks L = 3 547 m, t he tread of vehicle B = 2 547 m, final t ransmission ratio i f = 13 2, sprocket radius r s= 0 313 m and heig ht of gravit y cent er H = 0 945 m. 3 1 Study of Single Side Induction Motor Driving Control System Simulation T o verify t he st at ic and dynamic characterist ics of simulat ion model of induct ion motor vect or control syst em, the follow ing condit ions are assum ed. Idling st arter is used as induct ion mot or; object ive rotating
Fig. 6 Model of tracked vehicle virtual prototype
On the basis of the above models, t he motor load model ( 3 D virtual prot oty pe) and induct ion motor vect or cont rol syst em simulation model based on M at lab/ Simulink are combined f or the collaborat ion simu [ 6] lat ion of mechanical system and cont rol syst em by using the int erface t echnology of RecurDy n/ Cont rol. T he collaboration simulat ion model is shown in Fig. 7. Since t here is a f inal drive betw een induction mo t or fan out and sprocket , 4 gains are set up in the model.
Fig. 7 Model of collaborative simulation
It must be ensured t hat the dynamics model of tracked vehicles is correct before building t he collabo rative simulat ion model. First ly define t he input vari ables 1 , 2 and out put variables T L1 , T L2 of the 3 D w hole vehicle model in RecurDyn/ Control, and tank. m file w hich links RecurDyn and Matlab/ Simulink. Secondly close RecurDy n program and st art M at lab/ Simulink prog ram so t hat a masked con t rol subsystem model is correct ly linked up w it h Re curDyn subsystem model t hat has been est ablished. F inally run Matlab/ Simulink program and set up the simulation parameters, RecurDyn program w ill be au t omat ically run for collaborat ive simulation.
3
Simulation and Test
T he main parameters of induction mot or are rat 176
Fig. 8
Curves of induction motor rotating speed, torque, phase currents with time
CH EN Shu yong , et al . / Modeling and Perf or mance Prediction of I nduction Motor Dr ive System f or Electric Dr ive T r acked Ve hicles
speed of the induction motor is 195 rad/ s; the motor load T L = 514 N m is applied suddenly af ter 0 5 s. T he simulation and test curves of motor rot at ing speed, t orque and a, b, c phase currents are show n in F ig. 8( a)  ( c) . From F ig. 8, it is known t hat the simulation data and t est dat a are f it w ell, t he rot at ing speed and t orque respond quickly and st eadily, and the change in t he phase current is more acute w hen mot or st arts at idling, but the phase current can quickly reach t he st eady state. T hus it can be seen that t he syst em has a good performance. 3 2 Bench Test of Single Side Induction Motor Drive System
A 100/ 150 kW induct ion mot or driving cont rol syst em is used for a real prot otype vehicle, w hich is based on t he vect or control principle of induct ion mo t or. T he mechanical propert ies and system ef ficiency of t he real mot or driving control syst em are t ested in the t est bench of elect ric vehicle pow ert rain driving syst em . Fig. 9( a)  ( e) shows the curves of induction mot or out put t orque, induct ion mot or out put pow er, induct ion motor and it s controller overall ef ficiency, cont roller ef ficiency and induction eff iciency under different rotating speeds, respectively. From the bench test, it is known t hat the mot or drive syst em developed based on the vector cont rol principle has w ell performance. T he motor has a const ant t orque under t he rated speed and a const ant pow er above the rated speed. It s eff iciency is low at low speed and high speed operat ion, but its ef ficiency is higher at rated speed operat ion. T he ef ficiency fluct uation is high at some point s at T 1 = 100 N m, w hich results from DC bus current and volt age f luctuat ion from the test pow er supply cabinet m ainly. 3 3 Research on Col laborative Simulation In order to f urt her evaluat e the applicat ion of high pow er induct ion motor drive system in electric vehicles, the vehicle performances are predicted based on the collaborat ive simulat ion technology. F ig. 10 shows t he curves of velocit y vs. time f rom 0 t o 32 km/ h on the good level road. T he accelerat ion time is 5 8 s, w hich shows t hat the accelerat ion perf orm ance using t he elect ric drive syst em is bet ter t han t hat of the tradit ional mechanical transmission. Figs. 11 and 177
Fig. 9 Test curves
12 show t he curves of each side sprocket rotating speed w ith t ime and each side sprocket torque w ith
JOU RN AL O F CHI NA OR DNAN CE, 2007, Vol. 3, N o. 3
time for electric driving t racked vehicle using inde pendent st eering mechanism, t he vehicle beg an to shift a large radius steering R = B on t = 0 75 s ( Ve locity is 10 km/ h before steering. ) , w here t he solid lines means inside, t he dott ed line means outside, the neg at ive sign means clockw ise direction. T he sprock et torque has t he signif icant fluctuat ions before steer ing , w hich is mainly due t o overcome larger resist ance at t he moment of vehicle steering, the sprocket torque becom e st able aft er 1 s.
phase AC induct ion motor mathemat ical model. T he simulat ion and t est results show t hat the elect ric drive t racked vehicle wit h 100/ 150 kW induct ion mot or drive syst em can be operat ed smoot hly, and also has bett er dynamic and st at ic charact erist ics. 2) In order t o furt her show the act ual situat ion on the motor loads on bot h sides, the protot ype model of vehicle is built , vehicle dy nam ic charact eristics are studied in t he diff erent cases of velocit ies, loads and use requirements accurately. T he collaborative simu lat ion and predicat ion of 0 32 km/ h acceleration per formance are done based on interface technology of M at lab/ Simulink and RecurDyn/ Cont rol, and also t he steering performance at 10 km/ h velocity and large radius. T he predict ion result s meet t he whole vehicle driving demand. T he research period can be short ened and the cost is reduced by using the method of collaborat ive simulat ion.
Fig. 10
Curve of velocity vs. time from 0 to 32 km/ h
References
[ 1] F AN Zheng qiao. Pow er transmission and automatic con trol system[ M ] . Beijing: Beijing U niversity of Aeronau tics and Astronautics Press, 2004: 212  238. ( in Chi nese) [ 2] F AN Han rong, Dawson G E, Eastham T R. M odel of electric vehicle induction motor drive system[ J] . Electri cal and Computer Engineering, 1993: 1045 1048. [ 3] F AN Y ing le. Detail explanation of M atlab simulation application [ M ] . 2nd ed. Beijing : Posts & T elecom Press, 2002: 257 295. ( in Chinese) [ 4] L U Lian jun, SU N Feng chun, ZHA I L i. Steering per formance simulation for electric dr ive tracked vehicle based o n M atlab/ Simulink [ J ] . A cta A rmamentar ii, [ 5] 2006, 27( 1) : 69 74. ( in Chinese) WANG G G, WANG S H, CH EN C W. Design of turn ing co ntrol for a tracked vehicle [ J ] . Contro l Systems M agazine, 1990, 10( 3) : 122 125. [ 6] X ION G Guang leng, GU O Bin, CHEN Xiao bo , et al. Collabo rative simulat ion and virtual prototy ping [ M ] . Beijing: T singhua U niversit y Press, 2004: 134  141. [ 7] ( in Chinese) WANG M ing de, ZHA O Yu qin, ZHU Jia guang. T ank drive theor y [ M ] . Beijing : N ational Defense I ndustry Press, 1983: 103 123. ( in Chinese)
Fig. 11 Curves of sprocket rotating speed with time ( R= B)
Fig. 12 Curves of sprocket torques with time ( R = B)
4
Conclusions
1) T he mot or drive syst em model is built using vect or cont rol theory based on the analysis of a t hree
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