This article was downloaded by: [University of Auckland Library]On: 18 December 2014, At: 14:43Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Electric Machines & Power SystemsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/uemp19

A NUMERICAL APPROACH FOR THE ANALYSIS OFINVERTER-FED INDUCTION MOTOR SCHEMESV. V. SASTRY a & K. R. RAO ba Professor of Electrical Engineering Indian Institute of Technology , Kanpur, Indiab Department of Electrical Engineering , Benaras Hindu University , Varanasi, IndiaPublished online: 07 May 2007.

To cite this article: V. V. SASTRY & K. R. RAO (1979) A NUMERICAL APPROACH FOR THE ANALYSIS OF INVERTER-FED INDUCTIONMOTOR SCHEMES, Electric Machines & Power Systems, 3:2, 157-170, DOI: 10.1080/03616967908955335

To link to this article: http://dx.doi.org/10.1080/03616967908955335

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

A NUMERICAL APPROACH FOR THE ANALYSISOF INVERTER-FED INDUCTION MOTOR SCHEMES

V. V. SASTRY

Professor of Electrical EngineeringIndian Institute of TechnologyKanpur, India

ABSTRACT

K. R. RAO

Department of Electrical EngineeringBenaras Hindu University

Varanasi, India

The steady-state analysis of an induction motor when fedfrom a voltage-source invsrter for varied types of operationusing a numerical approach is presented in contrast to the exist­ing theoriss such as instantaneous symmetrical component trans­formation and ths state-variable technique. This approach hasths added advantage over that of the state variable technique inthat there is no change in the elements of the machine-matrixwhen more than one state exists, in addition to that of Obtainingdirectly the nature of variation of currents, voltages and torqueWith respect to time.

NOMENCLATURE

List of symbols

E

VR,Vy,VBiR,iy,iBVdp'Vqp

idP,iqpidr,iqrvp1,vp2'v r 1 It v r2Rp,LpRr , Lr

xp

Inverter d.c. link voltage3-phase inverter phase voltages

3-phase inverter phase currents

stator phase voltages resolved to 2-phase quantities

stator phase currents resolved to 2-phase quantities

rotor phase currents resolved to 2-phase quantities

Transformed voltage quantities related to

idP,iqp,idr,iqr,Xm' xp and Xr2-phase stator resistance and self-inductance

2-phase rotor resistance and self-inductancereferred to stator turnsMagnetising reactance per phase resolved to a2-phase machinePrimary stator (self-) reactancs

Electric Machines and Electrornechanics : An International Quarterly, 3: 157-170Copyright © 1979 by Hemisphere Publishing Corporation 0361-6967179/010157-14$2.25

157

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

158

D

Subscriptsprdq

V. V. SASTRY AND K. R. RAO

Secondary rotor (self-) reactanceslipPeriod over which a phase current is zero dUringmode -II operation, raddd(wt)

primary or stator windingrotor windingdirect axisquadrature axis

1. INTRODUCTIONInduction motors fed from volta~e source, static

force-commutated inverters with laOo [1,2 J and 1200 1),4,5}gating logic could be considered in which the period of conduc­tion of each main thyristor is maintained at 1800 and 1200

respectively over each half-cycle. The control logic and gatepulsing circuit of a 1200 - mode inverter is simpler and reliablecompared to the laOo-mode. .Although the effective fundamentalvoltage is reduced in the 1200 mode the harmonic content and thecorresponding losses associated with it are reduced for an induct­ion motor-inverter drive system. In Eddition if the timing ofthe gate pulses to the main and auxiliary thyristors of a 1800

square wave inverter is not carefUlly timed, it will result in'shoot-throughs'. In addition as seen from the literature 1200

mode inverter seems to be of some significance in relation tobattery-powered vehicles @, 7 ,8J •

The analysis of a lao~ square wave inverter fed indu­ction motor is fairly simple and has been accomplished by severalmethods for example: i) boundary value approach utilising theconcept of super-position 01], ii) method of multiple referenceframes [l4J and iii) state-transition matrix [13J. In contrastthe more difficult analysis of a 1200 square-wave inverter feedinga poly-phase induction mechine has been analysed using instant­aneous symmetrical componen~ ~heory by Sabhag & Shewan 04J •Further, Lipo and Turnbull 1151 considered this scheme togetherwith the effect of d.c. link-pllrameters by state variable approach,avoiding the tedious frequency domain techniques. In contrastHeers jl6J analysed this problem using a.Laplace transformationapproach by reducing the order of the matrix during the disconti­nuous region for -the current, instead of the elements beingaltered without changing the order as adopted by Lipo and'l.'urnbull.

It is intended in this paper to develop a numericalapproach for the analysis of an induction motor fed from eitherof the two types of inverters considered, which gives the solutiondirectly with respect to time. In addition, according to thisapproach the elements and the order of the matrix representingthe induction machine during the various states will not changealthough there is a change in the forcing voltages. Further this

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES

analysis is proved to be equally valid for a current-controlledvoltage forced inverter - a hybrid between voltage forced andcurrent forced inverters feeding an induction motor.

2. ANALYSIS OF THE SYSTEM

159

The system considered basically has a rectifier bridge,filter capacitor and an inverter feeding the three-phase star­connected induction motor as in Fig.1. In addition it is assumed

that no saturationof the magnetic circuitexists and the corelosses of the indu­ction motor arenegligible.

FIG.1 Block diagram for a Voltage-Source Inverter-tedinduction motor drive.

2.1 Machine Equations:

The differential equations describing the three-phaseinduction motor are expressed by transforming the stator androtor phase variables to d-q axes fixed on to the stator and arerepresented in matrix notation as

Vdp Rp+XpD 0 -X .D 0 i dpmVqp = 0 Rp+~.D 0 -X .D i qpm

0 -X .D -X (l-s) Rr+Xr·D X (l-s) i dr(1 )

m m m0 X (l-s) -X .D -X (l-s) Rr+X~ i qrm m m

Let us define variables vp1' vp2' vr 1 and vr 2 to take care of anydiscontinuities in the stator currents in the following way

vp1 = Xp i d Xm i dr

vp2 = Xp i qp ~ i qr (2)vr 1 = Xr i dr Xm i dp

vr 2 = Xr i qr X i qpm

Eqn. ( 1) can be expressed in terms of these variables and rewri-tten as

'Vp1 -Ivp1 Vdpvp2 Vqp -I-A 1

Vp2 1

O}D =V r 1 0 V r 1

v 0 !r2_L r2

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

160 V. V. SASTRY AND K. R. RAD

whereRpXr 0 RX 0

- J 1Pm

I_A = X X _X2 0 Rp Xr 0 RpXmp' r m RX 0 RrXp (l-s)(X X _X2)

rm p r m

0 RX -(l-s)(X X - RrXpr m 2 p rXm)

In addition the expression for the instantaneous torque, Te isgiven by

Te = Xm (idP' i qr - i qp' i dr) (4)

Equation (3) can be written in vector matrix form as

D [xj = LvJ - LA) LxJ (5)and the boundary condition when written in matrix formconforms to

Xl (0) ! i }3/2 0 0 -I Xl ( Ii /3)i

I

-/3/2 iX2(0): 0 0 X2(i(/3)-' (6)=X

3(0). 0 0 i }3/2 X

3( 'ii/3)

X4(0) ; 0 0 -:/3/2 t • X4( Tl! 3 } ',_ .J ....i L .J

2.2 Solution according to Numerical Approach

The equations (5) and (6) together constitute a boun­dary value problem for which the solution can be obtained using'Harner's teohnique Q6] for steady-state operation as disoussedbelow.

Let Xi' i=1,2, ••••m be the unknown initial values of x which isa function of the known final values yi, i=1,2, •••m at the endof a time period T. Thus we oan write

Xi = Xi [y~, y~, ••••• y;] (7)

Now let xi1) be an initially assumed guest for Xi correspondingto whioh the final values are called as Y11) . Defining

"y(l) (1) T"i = Yi - Y1

eqn.(7) oan be expressed by Taylor's series around the guess x(l),1

negleoting terms of second order and higher, i.e.,

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES

Rewritting (8)

161

(8)

(9)(1) J!l -oXi

xi ::Xi + L --TJ=l ~YJ

Let x12) be another initial guess for Xi' then

( 2 ) -.!!L ;;'Xi (2)x =X + > --T ",Y

i i j';T 'JYJ J

One requires (m+1) such initial guesses, each guess having theform of eqn.(9) with a view to determine the best possiblestarting vector Xi. For the analysis of a voltage source inver­tsr-fsd induction motor, the value of m becomes 4. Hence re­arranging the guesses neatly all the five sets for this problemmay be written as follows:

~yP) '6y~l) cy(l)y(l) Xl X2 X3 X4'" 3 '0 4

1 _p) y(2) ~y(2) ,y(2) ,)X1 ,)X2 ')X, ,) X4b 1 "2 3 "4 ---or -T- --T --T

.;"yO) ~(3) 'yO) _yO) ,j Yl -JYl 'i Y1 -JYl- 1 2 ." 3 b 4 -)X1 ,)X2 ')X3 5 1-L\1by~4) ;,y~4) y(4) _y(4)

--T -T- -T- T"3 "4 'i Y2 '';Y2' -JY2 'i Y2<=,y(5) >.y(5) ~y~5) >syi5)_ 0X1 ,)X2 ,)X

3 JX4- 1 - 2T T T T

cJ Y3 ,lY3 ')Y3 'i Y3I

.) Xl ,)X2 '~ r~ ( 10)-T- ~ T

where":"-)Y4 -JY4 ·.JY4 :;Y4 -

( 1) (1 ) (1) (1)xl x2 x3 x4x(2) x(2) x(2) (2)

1 2 3 x4

~J -= x(3) x(3) x(3) xO)1 2 3 4

x(4) x(4) x(4) x(4)1 2 3 4

x(5 ) x(5) x(5) x(5)_ 1 2 3 4

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

162 V. V. SASTRY AND K. R. RAD

Rewritting eqn.(lO) one has

Xl X2

oX,,1X2--T --::--¥

;)Yl ()Y,

:] Xl ,)X2--T- ~')Y2 a Y2

.) Xl aX2--T- ~oY3 ')Y3

)X1 .]X2

----y- --:-r~Y4 ()Y4

X3

~')Yl

~T

oY2

.~T

,)Y3

;~3Y4

X4dX 4

J;rdX~=oY2

~T

.)Y3

'~()Y4

-1

~y~l)bY~l) by~l) ~yi')

, by(2)t3(2) by(2) 6y(2)1 - 2 3 4

Now Xl' X2' X3 and X4 are the best starting values 01' X at leastto the tirst order. This requires one matrix inversion and asimple partial multiplication as the first row of the matrix onthe left hand side of eqn.(ll) needs to be evsluated. Khans [17]applied this method by correcting the error at each stsp fornon-linear differential equations, where the tinal values at oneend of the boundary are known. The problem that one generallyencounters in an inverter fed induction motor analysis is thatneither the initial values nor the final values are known at theboundaries. The only condition known is the relationship betweenthe variables at the beginning and at the end of one-sixth of acycle such as that given in equation (6). In such cases thismethod is extended by assuming the final values at the end of 1/6of a cycle to be definite such as zeros. Solution of eqn.(ll)gives a good guess for Xl' X2, X3 and X4• Using these valuesalong with eQns.(3) and ~6), the exact values can be readilyobtained by using any of the known iterative techniques.

A quick but a good guess is made in respect of theinitial values of the variables by using five di1'ferent startingvectors and an iterative procedure. Accordingly this method isreterred as 'numerical approach' for this class of two-pointboundary value problems.

3. COMPUTATION ASPECTS

In order to solve equation (11), five sets of initialguesses are made. The initial guesses assumed but expressed in

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES

per unit notation are:

0 0 0 0

LtJ1 0 0 0

= 0 1 0 00 0 1 00 0 0 1

163

This corresponds to the second ety~ent on t~! righthand side of eqn.(ll). In order to find yi to ·yi ,thefinal values of yI at the end of a one-sixth cycle are to bedefined. As these are not known, these are assumed in this caseto be equal to zeros. HaVing defined eqn.(11), completely, theinitial guesses obtained by this equation are utilised along witheqn.(3) and (6) and an iterative procedure is adopted to find theinitial values of the variables [X] i.e. vp1' Vp2 ' v rl and v r 2'

With these starting vectors, one more integration bya fourth order Ranga-Kutta method of eqn.(3) yields the timesolution of the variables Vp1 ••• vr2 over the one sixth cycle.Using these values, the d-q component currents can be calculatedbased on the transformation adopted. Phase quantitiee over thecomplete cycle can be constructed using the standard procedures,while eqn.(4) gives the instantaneous electro-magnetic torquedeveloped having known the d-q component currents.

4. COMPARISON OF ANALYTICAL AND EXPERIMENTAL RESULTS

It is widely known that there are two modes of condu­ction while considering a 120o-square wave inverter feeding astar-connected induction motor. These are

i) mode I - Continuous current conductionii) mode II -Discontinuous current conduction

Hence the results relating to these shall be considered sepsratelywith a view to check the generality of the analysis.

4.1 Mode 1- Continuous Current Conduction

In order to verify the analysis presented the forcingvoltages represented ae VdP' Vqp in eqn.(3) have to be defined.Typical Phase Voltages together with their counter-part 2-phaseequivalent wave shapes are shown in Pig.2. These forCing voltagesare identical to those obtained when a A-connected induction motoris fed from a 180o-square wave inverter. For the 0 to 60 0 periodthat is to be considered, the values of Vdp and Vqp are

2Vdp = -3- E

Vqp =.0

Knowing thus the forcing voltages, the rest of the equations areprogrammed on a digital computer, the block diagram of which is

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

164

i'P=tu=F-\' '.

FIG. 2 Phase voltage. d-q Voltage Mode Iconductlon-Vst fed induction motor.

V. V. SASTRY AND K. R. RAO

FIG.3 Block diagram summerising the computer programfor Mode' operation of a VSI fed induction motor. GUESS­Formulation of EQ. [3J; RUNGE - Differential equations inrelation to the system; MATMUl and MATMPY - Matrixmultiplication; MATALG - Matrix inversion; RKLDEQ­Fourth order Runge-Kulle method.

given in F1g.3.the calculationtorques.

In addition provision is made in the program forof r.m.s. currents, instantaneous and average

The induction motor used for the purpose of compzisonwas a 12-pole machine with the parameters as given in Table 1.

TABLE 1

12-pole Induction Motor 2-phase equivalent Parameters

Base voltageBase speed

= 75= 500 RPMBase currant =

Base frequency15A50 Hz

Machine connection 'Y'Paramster Rp Xp Xm ~ XrP.U. Value 0.40* 2.23 1.67 0. 10 2.23*A self-cascaded induction motor built for operation at a speedcorresponding to 18 poles is reconnected as a 12-pole inductionmotor by a simple reconnection of the stator winding. Hence thep.u. parameters like the stator winding resistance and leakagereaotance are higher for this machine than in a conventional12-pole induction motor.

Fig.4 shows the analytical and experimental results when the motorwas operated at 25 Hz corresponding to a slip of 0.132, with thed ve , link voltage being e qual, to 0.684 p.u. Experimental resultscompare well with the computed ones. The slight inconsistenoy inthe predicted voltage to that of the experimental waveform couldbe attributed due to a small d.c. resistance inoluded in the d.c.link from the point of view of current protection, in the absenceof fast acting fuses. In addition the rotor of this motor devia­tes from a squirrel cage rotor in that it is a 9-phase rotor(which SUits to the establishment of fluxes of 0 and 12-poles in

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES 165

:' t:= ,.:o '0 'M 1<.

FIG.4 Comparison of analytical andexperimental results-Mode I connec­tion for a VSI fed induction motor.

the same magnetio oirouit) thusoontributing to inoreased rotor mmfharmonios

"".~:~~_'"......t.... _

'I'U'''~ _, U.'(1/1-.1/1

FIG.5 d-q Voltages for Mode II operation­VSI fed induction motor 120 o·mode inverter­connected passive load.

4.2 Mode II - Disoontinuous Current Conduction

Typioal phase voltage wave forms oorresponding to theinverter of 1200 gating logic feeding a passive R-L load underdisoontinuous ourrent mode of operation along with the two phaseeqUivalents are shown in Fig.5. For an aotive load suoh as a .~.

oonneoted induction motor, the phase-voltage wave-shape is modi­fied depending on the operating oonditions. It is generallyknown that two distinot periods have to be oonsidered while anal­ysing the system over 0 to 60-, aocordingly the forcing voltageshave to be identified during these periods.

Time Period 1: 0 ~c.;,t ~;,,(unknown)

During this region the phase current is zero and the d-qforCing voltages can be defined as

VdP = Back emf of. that phase (unknown)( 12a)Vqp = -E/1'3

Time Period 2: O-~ ',J t ~"'-/3

(12b)

nentThe phase current is non zero and the forcing d-q compo­

voltages applied to the machine during this region are

2= '3' E

= 0

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

166 V. V. SASTRY AND K. R. RAO

The steady state solution for this system depends on the accuratedetermination of the initial values of the currents,'~ and theback e.m.f. A computer program is written to caloulate theseaooording to the numerical approaoh described in the followingsteps:

Step 5

Step 3

Step 1

Step 4

Step 2

To start with suitable values of ~ and baok emf,together with 5 sets of initial guesses for thecurrents are assumed.Eqn (3) is integrated over 1/6 of a cyole With the sodefined forcing voltages given in eqn.(12). At eachpoint of integration upto and including ~ whether thederivative of that particular stator phase current iszero or not is verified. In case the derivative ofthe phase current is not zero, the assumed back e.m.f.at the prvious point is suitably modified and thecomputation is repeated from that point.The initial values of currents are determined accordingto the procedure outlined in eqn.(11).At the initial point during the O~: ,)..( ~whether themagnitude of the phase current is zero or not ischecked.If the phase current during this region is not zero,the value of ~ is updated and the computation is repeatedstarting from step II till the phase current is zero.

In the computer program developed, the flow chart forwhich is given in Fig.6, provision is also made for the calculation

FIG.6 Flow chart for the computer programrelating to Mode II operation of a VSI fedinduction motor.

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES 167

-~-

5. ANALYSIS OF AN INVERTER-FED VOLTAGE­FORCED CURRENT CONTROLLED DRIVE

of the r.m.s. value of phase curz-ent , phase voltage and averagetorque. The comparison between analytical res111ts and theexperimental data is made in Fig.7 for a 4-pole induction motoroperated at 15 Hz and a slip of 0.8with its p.u. parameters given in Table2. The discrepancy in the cllrrent wave­s~ape obtained experimentally is dl1eto a small resistance included in thed.c. link provided for protection. Thisproves clearly the generality as well asthe validity of this approach.

011.. _.- ••

So far athe analysis of a voltage­forced inverter fed induction motor drivesystem is considered which has referenceto 120o-mode inverters. In these systemsat low frequencies of operation the d.c.link voltage is varied as a function ofthe fre quency as well as that of the FIG.7 Compa",on of the experimental

stator resistance drop. Instead there and analytical results for Mode II operation

are applications where d vo , source voltage ot s VSI fed induction motor.

ie constant and the cllrrent through theinverter-induction motor system can be controlled only by switch­ing d s c , voltage Mlvel in_ an ON, OFF form such as in batterypowered vehicles L5,6,7,8J. The 120o-mode inverter is speciallysuited for this kind of operation. In other words, one couldoperate the inverter in a cl1rrent-controlled form for low frequeneyconstant-torque operation and as a voltage-forced inverter forconstant h.p. mode.

TABLE 2

4-pole induction motor 2-phase equivalent parameters

Base voltageBase speed

Parameterp .u, value

~0.042

20V Base Cl1rrent1500 RPM Base frequency

Machine connection 'Y'Xp Xm Rr Xr

0.60 0.532 0.078 0.60

- 20A- 50 Hz

The experimental resul!s relating to such schemes were pre­sented as early as in 1964 L5.1 , but till today no analyticalwork has been reported in the opinion of the authors except thatDuning [8J analysed this for a passive R-L load, and Heers ~61conaidered this for an induction motor load but assumed the phasevoltage to be of zero magnitude during the period of currentdiscontinUity. These limitations are now overcome in the appli­cation of the numerical approach for Sl1ch a system of an inverterfeeding an induction motor load with current-control •

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

168 V. V. SASTRY AND K. R. RAO

The analytical results shall be discussed with respect to a6-pole machine having the parameters given in Table 3 when

TABLE 3

6-pole induction motor 2-phaee equivalent parametersBase voltage aov Base current 100ABase speed 1000 HPM Base frequency - 50 Hz

parameterp.u. value

l\-0.0173

converted to a 2-phase system at 50 Hz. Extending the ideaspresented in the previous section, the forcing voltages in d-qform for such schemes over the 600 period needed from the steady­state analysis point of view will conform to Fig.a. Analyticalresults thus obtained are ehown in Fig.9 for a 6-pole motoroperated at 40 Hz and at a slip of 0.071 for half-a-cycle durat­ion. These compare well with the experimental results presentedby Abraham et. al [5] , Heumann &; Stumpfe C10j and Duning [a] •

11/.

FIG.8 d-o Components of tho forcing voltages for aninverter fcd induction motor with current controt-.120" -mode inverter.

FIG.9 Inverter fed induction motor with currentcontrol 120"·mode inverter. A connected inductionmotor,slip.Q71.

Finally it is worth stating at this stage in view of thespace limitations that the application of this approach to theanalysis of a current-fed induction motor reported in [19J resul­ted in identical results to those obtained according to state­variable technique [20] and boundary-value approach [21J •

6. CONCLUSIONS

An analysis haa been presented for 1200 and leO-square waveinverters according to an approach termed 'Numerical Approach' •The geneality of the approach has been validated with reference toan inverter-fed induction motor with current control. The ver­satality of the approach lies in that the solutions are obtaineddirectly in relation to time, with the added feature of the elementsof the matrix model of the machine remain unchanged irrespective

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

INVERTER-FED INDUCTION MOTOR SCHEMES 169

of the various states considered within the definite time periodof 0 to 600 necessary for the steady-state analysis.

7 REFERENCES

1. D.A. Bradley, C.D. Clark, R.M. Davis and D.A. Jones, "Adjust­able frequency inverters and their application to variable­speed drives", Proc. I.E.E., 1964, Vol.l11, (11), pp.1833-1846.

2. K.Y.G. Li, "New 3-phase inverter circuit", ibid, 1968, Vol.115,(11), pp 1677-1683.

3. E.D. Ward, "Inverter suitable for operation over a range offrequencies", ibid, vol.lll, No.8, 1964.

4.• B.L. Jones and B.J. Cory, "Polyphase thyristor invertors", IEEConference publication No.10, 1965, pp 241-252.

5. r,. Abraham, K. Heumann and F. Koppelman, "Wechselrichter ZurDrehzahlsteuerung von Kafiglaufermotoren" (Inverter for speedcontrol of induction motors). A.E.G. Vol.54 (1964), Hl/2,pp.89-106.

6. P.D. Aggarwal, "The G."-. high performance induction motor drivesystem". IEEE PAS, Vol.PAS-88, No.2, 1969, pp.86-93.

7. K. Steimel and K. Heumann, "Kommutatorloser Bahnmotor mit pulswechselrichter fur Akkumulatortriebwagen "(commulatorlesstraction motor with pulae-width controlled inverter for batterydriven locomotives), AEG MVol.55, 1965, pp.220-226.

8. G. Duning. "Zum Antrieb Von Strabenfahrzeugen durch wechselrich­tergespeiste Asynchronmotoren" (Inverter fed asynchronousinduction motor as a drive for street cars) Dr. lng.Dissertation.Technical University, Braunschweig, (F.R.G), 1972.

9. S.B. Dewan and A. Straughen, Power Semi-conductor Circuits,(Book) John Wiley & Sons, 1975, pp.418-426.

10. K. Heumann and A.C. Stumpe. T ristoren-Ei en schaften UndAnwendllngen (Thyristors,-properties and Applications, Book),B.G. Teubner, Stuttgart, 1970.

11. K.Y.G. Li, "Analysis and operating an inverter fed variablespeed induction motor", Pz-oc , IEE, Vol.116, 1969, No.9, pp.1571­1580.

12. P.C. Krause and J.R. Hake, "Method of multiple reference framesapplied to the analysis of a rectifier-inverter induction motordrive", IEEE Trans. Power App.Syst., Vol.PAS-88, 1969, pp.1635­1645.

13. F. Harasimha and K. Uchida. "Analysis of inverter-fed inductionmotor system by state transition matrix", Electrical Engineering(Japan) Vol.89. No.12, 1969, pp.27-34.

14. E.M. Sabiae; and VI. Shewan, "Characteristics of an adjustableopeed Poly-phase induction machine", IEEE Trans. on PAS, Vol.PAS-87, 2968, pp.613-624.

15. T.A. Lipo and F.G. Turnbull, "Analysis and Comparison of two

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014

170 V. V. SASTRY AND K. R. RAO

types of square-wave inverter drives", IEEE Trana. on lA,VOl.IA-11, No.2, 1975, pp.137-147.

16. E. Heera, "Berechnung des Betriebsverhaltens wechselrichter­gespeister Asynchronmaschinen mit KurzachluBlaufer unterBerucksichtigung der sattigung (Investigations relating tothe performance of an inverter fed asynchronous machinetaking saturation into account). Dr. Ing. Dissertation,Technical University, Braunschweig, (F.R.G.), 1973.

17. L. Fox, Numerical solution of ordinar and Partial Differen­tial Equations, Book, ddison ealey, 9 , pp. 4-

18. S.J. Khane, "Note on two-point boundary-value problems",Vol.AC-8, No.3, July 1963, pp.253-254.

19. K. Ranganathan Rao, "Analysis of inverter :Eed asynchronuouamachine drives", Ph.D. Thesis, Indian Institute of Technology,Madras-Deoember 77, Chapter 5.

20. T.A. Lipo and E.P. Cornell, "State-Variable Steady-Stateanalysis of a controlled-current induction motor drive", IEEBTrans. lA, Vol.IA-ll, 1975, PP.704-7 12.

21. K.R. Rao and V.V. Sastry, "Current-fed induction motor anal­ysis using boundary value approach", IEEE Trans. on IEOI,Vol.IECI-24, May 1977, pp.178-183.

Manuscript received in the final form, July 26, 1978

Dow

nloa

ded

by [

Uni

vers

ity o

f A

uckl

and

Lib

rary

] at

14:

43 1

8 D

ecem

ber

2014