Dual Inverter Control Strategy for High Speed Operation of E

Dual Inverter Control Strategy for High Speed Operation of EV

Dual Inverter Control Strategy for High Speed Operation of EV Induction MotorsJunha Kim and Kwanghee NamDepartment of Electrical Engineering, POSTECH University, Hyoja San-31, Pohang, 790-784 Rcpublic of Korea. Tel:(82)54-279-2218, Fax: (82)54-279-5629, E-mail:kwnam@postech.ac.kr .Abstract- ISA (integrated starter/alternator) will be used for cars soon with 42 volt system. ISA is a multi-functional integrated device t h a t functions as starting motor, generator, flywheel, or torque assist t o combustion engine. But, other than thermal and cost problem, there is an inherent difficulty in t h e design of motor-inverter system. Specifically, it should produce 150 N m starting torque and also generate electricity while engine is running 6000 rpm. To produce t h e required torque, ISA has normally as many as 12 poles. A great problem is t h a t t h e generated voltage must be limited t o under 42 volt even when 12 pole ISA is running 6000 rpm. Hence, t h e recent ISA design shows t h a t it has as much as 1O:l speed range, i.e., t h e field weakening operation should be extended t o 10 times higher than t h e rated speed. In this work, we are considering t h e use of induction machine instead of permanent synchronous machine. As an idea for solving t h e voltage limit problem, we a r e utilizing two inverters. Sharing t h e voltage requirements by dual inverters is t h e main idea. But, t h e secondary inverter only takes care of t h e reactive voltage component which grows very large in high speed operation. Therefore, t h e secondary inverter does not require t h e use of extra voltage source. Capacitor bank suffices the purpose of t h e secondary inverter. Finally, both simulation and experiment for confirmation are presented.Inverter

I

Inverler 2

Fig. 1. Dual Inverter System for ISA.

tem integrated starter/altcrnator (ISA). According to the performance specification devcloped by several automotive manufacturcrs, ISA needs to supply 150 N . m of starting torque and to deliver 42 V powcr to the automotive accessories over a 1 O: l speed range extending 4 IW at 600 rpm C to 6 kW at 6000 rpm. Thc interior permanent magnet (IPM) machine is an attractive candidate for this application[3][4][5][6]. However, the IPM machine must havc a special structure so that a large rcluctance contribution plays a role in high speed range[6]. Further, due to the use of permanent magnets, cost of IPM is higher than that of induction machine. Another disadvantage of IPM is that back-emf voltage does not disappcar as far as the rotor is running, which is sometimes fatal to the inverter in the case of unexpcctcd shut down at high spccd. Induction machine is an alternative for ISA[7]. Though the cost is cheaper, it requires more volume. Further, since the magnetizing current has to be supplied from the stator side, its constant power range is not wide if thc source voltage is low such as 42V.

NOMENCLATURE stator voltagc(currcnt) vector. rotor flux vector. ang

lc of A,. angular (rated angular) frequency of A,. actual rotor spccd. angular frcquency at which thc ficld weakening control is activatcd. d-axis rotor flux in the rotor flux reference frame (RFRF). d(q)-axis voltage in the RFRF. d(q)-axis stator current in thc RFRF. stator (rotor) rcsistancc. stator(rotor, mutual) inductance. total leakage coefficient (A 1- L;/(L,L,)). rotor time constant (A L~/ R~ ) . gcnerated torque. numbcr of pole.

Tr

Te P

I. INTRODUCTIONDue to the increase in electrical cquipments in a car, the powcr demand grows steadily. Today, the clcctrical power dcmand is around betwecn 750 W and 1 k W . However, in luxury cars in 2005 to 2010, the auxiliary electric power requirement is cxpccted to increase to 4 to 6 kW[2]. This turns out to bc one motivation to adopt 42 V sys-

s In this work, induction machine was considered a a candidate of ISA. With an objectivc of the enlarging constant powcr region up to 1 O: l under 42 V source, a dual inverter system is considered here. Dual inverter system is shown in Fig. 1 in which thc other ends of phase windings, instead of being shorted, are connccted t o the secondary inverter. Pulse width modulation (PWM) stratcgy for dual inverter system was studied in[8][9]. Howevcr, it should be emphasized that the sccondary inverter docs not requirc any powcr source in the DC-link. It just have a capacitor bank which makes a great difference from the previous dual inverter[8][9]. Thc dual invcrtcr systcm also enhances an redundancy provision in emergency cases if wc add somc by-pass switches.

0-7803-7474-6/02/$17.00 02002 IEEE

163

Dual Inverter Control Strategy for High Speed Operation of EV

I

l

l

1

I

Fig. 4. Two phase equivalent circuit of dual inverter system in stator reference frame. Fig. 2. Basic idea.

B. Motivation for the Dual InverterWe call dual inverter system the induction motor control system shown in Fig.1. In the dual inverter, two inverters are connected a t both ends of stator phase windings. This connection topology appears in the previous work[8][9]. But, this dual inverter system is different from the previous onc in that the second inverter does not have any voltage source other than capacitor bank. The basic rationalc is that only the reactive power is handled in the second inverter. In the high speed region, the reactive voltage develops a lot so that it takes a significant portion of thc: limited source voltage, making hard to produce torque. If the reactive voltage part is covered by the second inverter, the primary inverter reserves more voltagc t o extend operating speed. Thus, the objective of this topology is to increase the operation speed range where source voltage it; limited at the expense of utilizing two inverter. In the following, we describe in detail how big the reactive voltage is and how the secondary inverter gives room for speed extension. Writing (l),(2) and (3) in the steady statc in thc form of complex numbers, we obtain

Fig. 3. Phasor diagrams showing back-emf voltage and coupling voltagc a

t w e= 303 r a d/ s e c, w e= 757 r a d/ s e c and we= 3142 rad/sec.

11. PROBLEM STATEMENT AND MOTIVATION THE FOR DUALINVERTER

A . Induction Motor ModelIn the rotor flux oriented frame, thc dynamics of induction motor are described as follows:

where is+, is= are projections of is onto A, and jX,, respectivcly. Bascd on Kim. et al.[lo], we obtain three pha.sor diagrams from (5)-(7), as shown in Fig. 3, at the base speed Wbase= 303 rad/sec, we= w1= 757 rad/sec, and we= 10 x w,,,,t= 3142 radlsec. Note that w1 is the boundary value between the constant power region and the constant power times speed region[lo]. Machine parameter in Tablc I were used. Note that the voltage jw,uL,iSj is orthogonal to the stator current is, making a reactive power. The reactive component jweuLsi, is small compared with thc back emf jwe(Lrn/Lr)X, a t the base speed. But as the specd gocs up the reactive component becomes largcr and largcr, and finally it exceeds the magnitude of thc back cmf, taking a major portion of the source voltagcVs

.As shown in Fig. 2, the basic idea is to let the secondary

invertcr (Invertcr 2) produce the reactive voltage term which canccls out jw,uL,i,. Then, the primary inverter (Invertcr 1) can take carc of the rest component. More (4) spccifically, thc back emf j u e(L,/L,)A, is supplied from the primary inverter, while the coupling voltage gw,aL,i,, whcrc p 4 d/ d t is a differential operator, and the super- is compensated by thc sccondary inverter. By dividing the script"e" implies a variablc in thc rotor flux oricntcd frame. rolcs of cach inverter, we can manage the magnitude of the (3)

164

Dual Inverter Control Strategy for High Speed Operation of EV

TABLE I LIST OFTHE MACHINE PARAMETERS USED IN SIMULATION.

4

pole

wherc v;,~,vqeSl are d-axis voltage, q-axis voltage of the Invertcr 1, respectively, and U&, v&2 are d-axis voltage, q-axis voltage of the Inverter 2, respectively. Inverter 2 is supposcd to supply exactly the same voltage quantities as the coupling terms, i.e.

36.86

mH

36.86

mH

primary inverter voltage within a given limit, while achieving a wide speed operation range. It should be emphasized that since the secondary inverter takes care of the reactive power, it can be opcrated with only capacitors in the DC-link.111. DUALINVERTER SYSTEM MODEL

Note that the coupling terms (14), (15) correspond t o the reactive voltage component jw,aL,i, as shown in Fig. 3, Fig. 2. Substituting (14), (15) into (12), (13), we have voltage equations for Inverter 1 such that

Fig. 5 shows rotor flux oriented controller with flux regulation and current control, reactive voltage compensator, Vaal= Rsias~ L s i a s e,, (8) DC-link voltage regulator of Inverter 2, and how voltage of vbb’= UL,ibs ebs (9) invcrters is shared. v,,~= R,i,, aLsdcs e,, (10) A . Inverter 1 where ea,, eb,, e,, are voltage components that include Thc rotor flux oriented control is basically the same as back-cmf of a, b, c windings, respectively. Summing up[lo] othcr than the voltage parti

tion rule. Thus, we have (8), (9) and (lo), d-axis currcnt command i:: and d(q)-axes voltage commands (v&*,‘U&*) such that (vao U60 vco) - (va/o’ -fvb’o’ v d d ) 3uoo’

It follows from Fig. 1 that the voltage cquations for thc dual inverter system are expressed as

+++

+++

+

=

Rs(ias i b s 2,s) aLs(ba,+(ea,+ ebs+ ecs)

+++

+

+

+++ ibs+its)

zzs*

===

(kpx

+ kzx

Notc that ias i b s+a,,= 0, and e,, eb, ecs= 0 due to the symmetry of induction motor. Furtherrnorc, v,, v,,= 0, and va/ol vb’o’ v,,,,= 0 for the fundamental voltage componcnts. Thus, we have woo/= 0. It follows obviously that o and 0’ are virtually equipotential. Hcncc, we obtain a two phasc cquivalcnt circuit as shown in Fig. 4 and a voltagc cquation such that

+

++

t)

(AS:- z&)

-

Asr)

(18)(19)

+

+

v,;*

(ICp(kp

+ ka;)(i::

+

1 kzi)(z;s* - i t s )

+ we(Lm/Lr)Xzr (20)

v,where

A v,1

- v,2= R,i,

+ aL,i,+ e,

(11)

whcre kPxI k,x arc proportional and integral gains of the flux PI rcgulator, rcspcctivcly, and i&* is a q-axis current command, and ICp, k, are proportional and integral gains of the currcnt controller, rcspcctively. Note that d(q)-axes s, rcactivc voltages ( -~ e u L s i~w,uL,z~,) are supplied by Invertcr 2.

v,

a (2/3)(va,+ ejzTI3. vbs+ ej4K/3. v,,)

B. Inverter 2When Invertcr 2 supplies only the reactive voltage componcnts (14), (15), no real powcr is generated by Inverter 2 since v,2 . i,= 0. Thus, the DC-link voltage of the Inverter 2 v d c 2 stays unrcgulated, starting from its initial charging state. However, the DC-link voltage must be controllable and sufficiently high so that Inverter 2 supplies thc rcquircd reactive voltage components (14), (15). Thus, V d c 2 must satisfy thc following inequality such that V d c 2 2 fi we,maxoLsImax whcre is a maximum angular frequency. Drawing some real powcr as shown in the lowcr part of Fig. 5, the DC-link voltagc can bc regulated. Using a PI rcgulator, wc obtain voltagc magnitude for regulating the

is A (2/3)(ias+ e j 2 n/ 3. i b se,

+ ej4n/3. i,,) (2/3)(ea,+ e j 2 n/ 3. eb,+ ei4n/3 . e,,).

Note that v,1, v,2 rcprcscnt voltagc vcctors supplicd by Invertcr 1 (primary invcrtcr) and Inverter 2 (secondary inverter), rcspectively. With definitions vi, ZI;,~ - v&~v&, vqesl - vqes2 in the rotor flux oricnted frame, wc havev;,~w;,~= R~~~,+ u L,~~, -~,~ L,~;,+ ( L,/ L, ) X~, -

(12) (13)

vqeSl - v&~ R,i;,=

Lm+ aLsiz,+ weaLsi&+ w,-A& Lr

165

Dual Inverter Control Strategy for High Speed Operation of EV

DC-link voltage such that

is where VtC2 a DC-link voltage command of Inverter 2, and k p,, kiv are proportional and integra1 gains, respectively. Then, multiplying the voltage magnitude in (21) to normalized d(q)-axes currents, we obtain d(q)-axes voltage commands for drawing some real power such that

N

~K,maxIs,max

3

n

(31 I

a;,;

-e * Wqs2

==

v; (~~,/llLaIl) e (i;s/llisll)

(22) (23)

Note that once the dc-link voltage is regulated, i$,f= i& j;= 0. Note that

inverter 2 must supply the reactive voltages (14), (15) as well as the voltages (22), (23) for DC-link voltage regulation. Combining (14), (15), (22) and (23), we obtain the total d(q)-axes voltage commands of Inverter 2 such that

Note that the approximations in (30), (31) are based on the fact that I,,,,,> L> 42 * and we x w, in the field weakening region. Thus, it follows from (30), (31) that tho maximum torque is approximately inversely proportional to we, and that the maximum power is approximately constant a t unity power factor and independent of we.

VI. SIMULATION AND

EXPERIMENTAL

RESULTS

Tablc I shows parameters used in both simulation and experiment. In the simulation, by using C-language a PWbl voltage pattern was generated and applied to the rnathematical motor model[l].We set the switching frequency w,;;= a;,; weaL,i;, (24) 5 k H z and dead-time 3 ps in both simulation and experiment. The induction motor dynamics were calculated evwy U,",;= ij,",. - w,uL,i~, (25) 0.5 ps by using Runge-Kutta 4th order method. Current v. THEORETICAL MAXIMUM TORQUE MAXIMUM control routine was carried out every 200 p, and both the AND rotor flux regulation and speed control routines were actiPOWER vatcd every 800 ps. A 1800 p F of capacitor was used in the is limited The maximum voltage of Inverter 1, DC-link of Inverter 2. Instead of battery, as a DC voltage under v d c/& by the available DC-link voltagc, and u;,~, source, a diode rectifier with capacitor bank was used. For u&l must satisfy simplification, no magnetic saturation and iron loss were considercd in both simulation and experiment. Thc simulation rcsults in Fig. 6 show responses of rotor flux,A,; torque T,, current magnitude Ili,(( and mechanNeglecting the voltage drops on the stator resistancc R, ical power P, vs. rotor speed w, when the speed comin the field weakening region, and assuming that the rotor mand changcs stepwisc from 0 to 7 p . U . In the convenflux magnitude A&. is sufficiently slowly varying, it follows tional method[lo] shown in Fig. 6(a) I,,,,,= 31.8 A, from (16), (17), and (26) in the stcady statc that v d c= 245 V, while in the proposed method shown i n= 31.8 A, v d c= 245 v d c 2= 450 v . Fig. 6(b) I,,,,,~e(Lrn/Lr)X:r I V1,max. (27) Notc from Fig. 6(a) (conventional method) that magnitude Note from (3) that Xi,= Lrni2, in the stcady statc. of thc current is kcpt constant only up to w,= 2.1 p . U, and that the mechanical output power P, is less than the Thus, thc inequality (27) is rcwrittcn as rated valuc (5.5 k W ), furthcrmore dramatically decreases 22, 5 (Lr/Lk)(Vl,rnax/we). (28) invcrsely proportional to rotor specd in the speed range over 2.1 times rated specd. But, note from Fig. 6(b) that In general, the stator current must bc also limited by the the proposcd method is capable of keeping the mechanical inverter current rating as well as the thermal rating of thc output power constant over the rated value (5.5 k W ) u p induction motor.

Hcncc, the d-axis and q-axis currcnts to 6:l speed rangc with VdcZ= 450 V . must also satisfy Thc expcrimcntal results in Fig. 7 show responses of rotor spccd w,., rotor flux,,A torque T,, electrical power Pt.,; (29) currcnt magnitude IJi,11, maximum inverter voltage w,,,~~, magnitude of motor phase voltage llvsll when the speed Under thc limitations (28) and (29) in thc ficld wcakcning command changcs stcpwise from 0 to 6500 rpm. In the region, it Follows from (4) that the maximum torquc T e, m a x= 31.8 A, convcntional mcthod shown in Fig. 7(a) I,,,,, and thc maximum output power, Po.,,, arc cxprcsscd as v d c= 290 V, whilc in the proposed method shown in Fig. 7(b) I,,,,,,= 31.8 A, v d c= 290 v, v d c 2= 350 Notc that the motor phasc voltage llvsll is approximately same a thc maximum invcrter voltagc in both convcntional s and proposcd method, i.e., JJv,JJ Ws,ma,, IIv,III M W l, r n a s - . x This statcs that thcrc is no extra voltagc to use. Thc fluc-

+

v,

v.

166

Dual Inverter Control Strategy for High Speed Operation of EV

I

I

Current& Flux Controller

I

{

Voltage Partition

I

I

Fie. 5. Overall control block diagram with current controllers. a flux regulator, a rcactive voltage compensator, a DC-link voltage regulator c 0.423 Web 0.4-

- of the Inverter 2.0.4

L

_

_

_

~

~

DC -~~ Regulator _ Link~ - _~

~

~

_

-

_

I

_

_

_

0,

r o t o r f l u (Web)

r o t o r f l u (Web)

0.2-

A&torque

30-

r,

( N.m )

0

0 30-'

currenl ( A )

rated curenl

_f

0

__. -. _ . .~ pouer(kW) 5.5kW ( RoIedPower)

___

16

_

0

llisll_

4( a )Convenlionai Method

2

4

I 6

Speed(p")

( b ) Proposed Method

Roror

('

'

")

currcnt rnagnitudc (Ili.ll) and mechanical powcr P, vs. rotor speed (w,) when the Fig. 6. Simulation rcsults - rotor flux (A&), torque ( T e ),= rated current= 31.8 A, vdc= 245 V speed command changes stcpwise from 0 t o 7 p . U. (a) Convcntional method[lo] under I,,,,, (b) Proposed method undcr I,,,,,= rated current= 31.8 A, vdc= 245 V and vdc2= 450 v.

tuation of the DC-link voltage is due to thc usc of thc diode rectifier. To draw a comparison for powcr capabilities between thc conventional and proposed method, electrical 1.5(vs . is) is used instcad of thc mechanical power P, power P,= (2/P)Tew,, which could bc incorrcct duc t o the iron loss and inductancc variation in thc ficld wcakcning region. In similar to thc simulation rcsults shown in Fig. 6, the proposed method is capablc of kccping the clcctrical output power constant ovcr the rated value (5.5 ICW) up to 6500 rpm with Vd&= 350 V, whilc in thc case of thc conventional method (Fig. 7(a)) thc electrical powcr is lcss than thc ratcd valuc, and dramatically dccrcascs inversely proportional to rotor spced as the spced goes up. Notc that the higher the electrical powcr is, the fastcr thc spccd rcsponse is. Note again that the theoretical maximum power value based on (31) is approximatcly 7.2 I W with the rcC duced Z J~,,~~ by 10% duc to DC-link voltagc drop, whilc thc expe

rimental clcctrical powcr is approximatcly 7.0 ICW. The cxperimental rcsult shown in Fig. 8 shows rotor spced w,, currcnt magnitudc llisll, maximum voltage of thc~~, Invcrtcr2 T J Z,~ output voltage magnitudc of Invcrtcr 2 IIvspII when thc spccd command changes stcpwise from 0 to 6500 rpm. Notc from thc bottom trace of Fig. 8 that

the voltage magnitude IIv,z(( of Inverter 2 is proportional to both the rotor speed w, M we and the current magnitude is, according to (14) and (15), which are reactive voltagc components. Notc&gain that the DC-link voltage of Inverter 2 is regulated without fluctuation by using the DC-link voltage regulator (??). Thc experimental result shown in Fig. 9 shows DC-link voltage ( V d c z ) of Invcrtcr 2 bcing rcgulatcd after building up thc rotor flux. To prcvcnt thc instantaneous high pcak powcr from bcing drawn from the voltage sources such as rcctificr or battcry, thc voltage command is programmed to change slowly from 0 t o the setting value. VII. CONCLUSIONS A dual invcrtcr control strategy for high speed operation of EV induction motors was proposed. The reactive voltage componcnt which is dominant in high speed region is compcnsatcd by Inverter 2. Since Inverter 2 takes care of only reactive powcr, thc dc-link needs not to be connected a dc voltage source. Just only capacitors suit the purpose. Through thc sharc of voltage rcquirements, the proposed dual inverter schcmc cnablcs ISA to work in 1 O: l speed rangc with 42 volt systcrn.

167

Dual Inverter Control Strategy for High Speed Operation of EV

o o oI I

Fig. 7. Experimental results - rotor speed U,., rotor flux (Xzp), torque (Te), electrical power P,, current magnitude (Ili.ll), maximuin~ ), inverter voltage ( v~,~, magnitude of motor phase voltage (llv.II) when the spced command changes stepwise from 0 t o 6500 rpm. (a) Conventional method[lo] under I,,,,,= rated current= 31.8 A, v c= 290 V (b) Proposed method under I,,,,, d= rated c u r r e n t:= 31.8 A, v c= 290 v and vdcz= 350 v. d

age magnitude of Inverter 2 (IlvszII) when the speed command changes stcpwise from 0 t o 6500~ p m .[6] S. Morimoto, M. Sanada and Y . Takcda,“Performance of PMAssisted Synchronous Reluctance Motor for High-Efficiency and Widc Constant-Power Opcration,” IEEE Trans. on Ind. Applicat.,, vol. 37, pp. 1234-1240, 2001.[7] J.M. Millcr, A.R. Gale, P.McClecr, F. Lconardi and J . Lang,“Startcr-Alternator for Hybrid Electric Vchiclc: Comparison of Induction and Variable Rcluctance Machines and Drives,” IEEE Industry Application Society Annual Meeting, pp. 513-523, 1998.[8] E.G. Shivakumar, K. Gopakumar, S.K. Sinha, A. Pittet and V.T. Ranganathan,“Space vector P W M control of dual inverter fed open-end winding induction motor drive,” Applied Power Electronics Confercncc, vol.1, pp. 339-405, 2001.[9] E.G. Shivakumar, V.T. Somasekhar, K. Krushoa, K. Mohapatra, K. Gopskumar, L. Umanand and S.K. Sinha,“A multi level space phasor based P W M strategy for an open - end winding induction motor drive using

two inverters with different D C link voltages,” Power Elcctronics and Drive Systems, vol. 1, pp. 169-175, 2001.[lo] S.H. Kim and S.K. Sul,“Maximum Torque Control of an Induction Machinc in t h e Field Weakening Region,” IEEE Trans. on I n d . Applicut., vol. 31, pp.787-794, 1995.

REFERENCESAndrzet M. Trzynadlowski,“The Field Orientation Principlc in Control of Induction Motors,” pp. 1-41, 1994. J.G. Kassskian, J.M. Millcr and N.‘Ikaub,“Autornotivc Elcctronics Powcr Up,” IEEE Spcctrum, pp. 34-39, May 2000. E.C. Lovelace, T.M. Jahns, J.L. Kirtlcy J r . and J.H. Lang,“An Interior P M Starter/Altcrnator For Automotive Applications,” in Proc of Intl/Conf. on Elec. Machznes, Istanbul, Turkey, pp. 1802-1808, 1998. W.L. Soong, N. Ertugrul, E.C. Lovelace and T . M . Jahns,“Investigation of Interior Permanent Magnet Offset-Coupled Automotive Integrated Startcr/Altcrnator,” Industry Applications Conferencc, vol. 1, pp. 429-436, 2001. J . Wai and T.M. Jahns,“A Ncw Control Tcchniquc for Achicving Widc Constant Powcr Spccd Opcration with an Interior P M Altcrnator Machinc,” IEEE Industry Application Socicty Annual Meeting, vol. 2, pp. 807-814, 2001.

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