A new connection for synchronous motor excitationA.C. Williamson, B.Sc, Ph.D., C.Eng., M.I.E.E.

Indexing terms: Synchronous motors, Induction Motors

Abstract: A new form of synchronous motor excitation is presented, which, by means of a simple connectionthrough a diode rectifier bridge, gives, effectively, series excitation in the synchronous mode. The steady-state behaviour of the scheme is explained by means of a simple analysis and illustrated by test results.

List of symbols

E_EI

r2

= voltage induced by flux across airgap7

= r.m.s. of fundamental component of statorcurrent

= stator equivalent of rotor (excitation) current= resultant magnetising current

=/ + /.= stator resistance= rotor resistance

Rb + jXb = equivalent impedance of rectifier bridgeRd = total resistance of rotor circuitRs+jXs = total effective series stator impedanceTr = effective rotor turns per phaseTs = effective stator turns per phaseV = supply voltageXm = magnetising reactance5 e = rotor angle with respect to supply voltage5,- = rotor angle with respect to line current

All quantities are 'per phase', and a bar indicates a phasor(complex) value.

1 Introduction

For fixed- and variable-frequency a.c. drives, a synchronousmotor is usually preferable, but in many cases inductionmotors are used because of their relatively low cost andsimplicity. This is especially true for smaller drives, wherethe cost of a separate excitation system would be pro-hibitive, and it has been the motivation behind recentresearch into reluctance motors, permanent magnetexcitation and other possibilities. This paper presents anovel, simple alternative, which, although demanding awound rotor with slip rings, requires only a diode rectifierbridge to give an a.c. motor with series excitation character-istics.

Fig. 1 shows the connections of the scheme investigated.The star point of the stator windings is replaced by the a.c.

rotor

stator

Fig. 1 Connection diagram

Paper 669B, first received 24th August 1979 and in revised form25th February 1980Dr. Williamson is with the Department of Electrical Engineering andElectronics, University of Manchester Institute of Science andTechnology, Manchester M60 1QD, England

IEE PROCEEDINGS, Vol. 127, Pt. B, No. 3, MA Y 1980

terminals of a rectifier bridge, the d.c. output of which issupplied, through slip rings, to the rotor winding. In thisway, the rotor, or excitation current, varies in sympathywith the stator current to give a synchronous motor with,effectively, series excitation. The system avoids therequirements of a separate excitation supply, transformersor additional machine windings. This paper is concernedwith the nature of, and, particularly, the calculation of,the steady-state characteristics of the proposed seriesmotor for the case of a cylindrical wound rotor.

2 Analysis of performance

An exact treatment of the circuit of Fig. 1 would becomplex, owing to the nonlinear nature of the rectifierbridge and the interactions between stator and rotorwindings during commutation of the bridge. An approximateanalysis is possible, with the following assumptions"

(a) Only the fundamental components of stator voltageand current need be considered when estimating machinetorque.

(b) The voltages at the a.c. terminals of the rectifierbridge are sinusoidal.

(c) The d.c. output of the bridge is smooth.Under these assumptions, the rectifier bridge can berepresented as an equivalent impedance (Rb + jXb) in eachstator phase. The excitation current If can be representedby a stator equivalent/,,, sothatthe induced airgap voltageper phase is given by E = j (I + Ie)Xm, where Tis the ^tatorphase current, Xm the magnetising reactance and/m = I + Ie

the resultant magnetising current. The machine represen-tation becomes conventional, with a resistance per phaseRs = rx + Rb and a reactance per phase X8 = Xb, allowingthe phasor diagram of Fig. 2 to be drawn.

In the phasor diagram, 5e is the conventional load angleand 6,- represents the angular displacement between the

Fig. 2 Phasor diagram

169

0143-^7038/80/030169 + 05. $01-50/0

distributions of stator and rotor m.m.f.s. If the values ofRb and Xb are determined, together with the relationshipbetween / and Ie, the performance can be calculated fromFig. 2. For the connection of Fig. 1, Ie = l/y/2'Tr/T8'Ifi

where Tr/Ts = rotor/stator turns ratio. Hence, if we writeIe = kl, then

k =-L.TL.!£.LLs/2 Ts Id I

0)

In the absence of any rotor-shunting circuits, If = Id andthe ratio Idjl can be obtained from analysis of the rectifierbridge.

2. / Idealised treatment

An indication of motor behaviour can be readily obtained ifall machine impedances except the magnetising reactanceXm are neglected. In this case, the bridge behaves as a shortcircuit, with Id = y/2I and k = Tr/Ts, a constant. Moreover,on a constant voltage supply, the current Im is constant,since E — V, and the phasor diagram simplifies to that ofFig. 3.

k=3/2 I

k=2

k=3

k=2/3

k=1/2

Fig. 3 Loci of I for ideal machine

1-5r

10

3 E

05

k=2/3

0 30 60 906e .electrical degrees

Fig. 4 Torque-angle curves for ideal machine

• steady-state stability limit

170

120

Letting V be real, and / = Ip ~jlq, it is easily shownthat •

(2)(k2 - 1) -1)

Since k and Im are constant in this case, eqn. 2 gives thelocus of / as a circle, and the loci for various values of k aredrawn in Fig. 3 as chain dotted lines.

The torque is given, in this case, by

T =1

(3)

The ratio fp/Im is plotted against 5e , for various values ofk, to give the torque-angle curves of Fig. 4. These curvesshow that peak torque can occur at angles other than 90°,with some unusual features for values of k > 1.

Fig. 3 suggests that values of k > 1 would give a betterpower factor than k < 1 for a given torque; however, Fig. 4,which also indicates steady-state stability limits, shows thatpeak torque cannot be realised for k > 1 before stability islost (this occurring at unity power factor), and a value ofk < 1 is to be preferred in respect of peak torque capability.For the ideal conditions assumed, a value of k = 1 givesinfinite torque capability, but this obviously will not be thecase in practice because of stator series impedance.However, for k close to 1, the no-load current is approxi-mately halved, compared with the induction motor case, sothat an improvement in power factor when on-load cantherefore be expected.

2.2 Represen ta tion o f rec tifier bridge

If harmonics are ignored, the voltage at the a.c^terminals ofthe bridge is the phasor difference between V and E. Thissinusoidal voltage is rectified to produce the d.c. outputwith a corresponding fundamental component of current/ displaced in phase by an angle related to the overlap angleof the bridge. The overlap angle will be a function of thea.c. voltage, the d.c. load resistance Rd and the com-mutating reactance per phase Xc. The effects uponcommutation of a.c. circuit resistance will be neglected.

The analysis of the rectifier bridge is well known, andmuch information is available with respect to inputimpedance, power factor and waveforms. However, the caseconsidered here is unusual in the sense that, for typicalmachine parameter values, the bridge will be almost short-circuited on the d.c. side (Rd will be comparable with Xc

in ohmic value). Consequently, it has been necessary toanalyse the bridge for these conditions throughout thecomplete range of modes of operation, including that ofnear-short-circuit with four devices conducting simul-taneously.

It is found that, if the bridge impedance to thefundamental component of current is Rb +jXb, thenRb/Xc, Xb/Xc and Id/I are functions only of Rd/Xc; theseare plotted in Fig. 5. If the commutating reactance is takenas equal to the stator leakage reactance (Xc=x1) then,with a knowledge of Rd, Fig. 5 enables Rb +jXb to bedetermined, together with Idllx and, hence, k, fromeqn.1.

2.3 Machine performance equations

The previous Section showed that the values of k, Rs =rx + Rb and Xs=Xb can be calculated from machine

IEE PROCEEDINGS, Vol. 127, Pt. B, No. 3, MA Y1980

parameters; the performance can therefore be calculatedfrom the phasor diagram of Fig. 2. In order to take accountof the nonlinear nature of the machine magnetic circuit it isconvenient, in analysis, to take the angle 5,- as an in-dependent variable.

Choosing /, the input current, as real, we have

Ie = kl (cos 5; — / sin 5,)

and

Tm = T+Te = / ( I + k cos 5/ — jk sin 5,)

with

Im = I[\+k2 + 2k cos 5,]1/2

(4)

(5)

(6)

The relationship between E and Im is the magnetisationcharacteristic, easily obtained from the no-load or open-circuit test on the machine, so that E is a known, nonlinearfunction of Im. Eleads Im by 90°, so that

E [k sin 5f + / (1 + k cos 5,)][1 +k2 + 2A:cos5;]

1/2

The terminal voltage is given by

V= Vr+jVi = I{rx +Rb)+jIXb+E

which, in turn, gives

Ek sin 5 ,-Vr = +Rb)

V: = IX h +

Ll +k2 +2k

E{\ +kcos8j)+ k2 + 2k cos 8 {]1/2

with

V = [V2+VJ]

(7)

(8)

(9)

(10)

00For fixed voltage operation, the above equations can besolved iteratively for a series of values of 5,-, to determinethe value of / which satisfies eqn. 11 for the terminalvoltage V, E being taken from the magnetisation curve forthe values of Im given by eqn. 6.

The torque can be calculated as

T = 3/(Kr -/(#•. +Rb)) (12)

15r

Fig. 5 Impedance to fundamental a.c. of rectifier bridge

IEE PROCEEDINGS, Vol. 127, Pt. B, No. 3, MA Y1980

the input power as

P = 3VJ

the input power factor angle as

0 = tan"1 -*" r

and the load angle as

§ e = 0 + S . - 1

3 Experimental results

03)

(14)

05)

A wound-rotor induction motor, rated at 150W, 200 V,50 Hz and 1 -55 A, was tested as shown in Fig. 1. Couplingtorque was measured by a coupled dynamometer machine,and rotor angle by stroboscope and calibrated disc. Theparameters of the machine are given in the Appendix

A straight connection between the rectifier bridge androtor windings gave a value of k = 0-894, representing thehighest value obtainable with the given windings. Lowervalues of k = 0*74 and k = 0-622 were obtained, however,by shunting the rotor windings by resistors, therebyreducing the ratio If 1^ in eqn. 1.

Figs. 6, 7 and 8 give the measured variations with rotorangle of coupling torque, input current and input power,respectively, for the three values of k. The behaviourobserved is in line with that expected from the idealisedtreatment of Section 2.1. Applying the analysis described inSection 2.3 gave the calculated performance which is alsoplotted in Figs. 6, 7 and 8. In deriving the coupling torque,30 W was subtracted from the calculated airgap torque toallow for rotational losses, and 40 W was added to thecalculated input power to allow for stator core loss.The very good agreement shown between the calculatedand measured performances justifies the assumptions andapproximations made in tRe analysis with respect toharmonics, representation of the rectifier bridge, com-mutating reactance and magnetic saturation.

500

30 60 906 e j electrical degrees

120

Fig. 6 Measured and calculated torque-angle curves

171

In order to assess the performance obtained from themachine in the synchronous motor mode, it was testedas a conventional induction motor with the slip rings short-circuited. In Fig. 9, the measured variation of input currentwith coupling torque for the induction mode is comparedwith that for the synchronous mode with the inherentvalue of k = 0-894. An ideal machine, working at unitpower factor and 100% efficiency, would give the straightline shown. It is evident that the synchronous modedemands less current than the induction mode for torquesup to about 1-5 times the rated value of 250 W. At ratedtorque there is a reduction of nearly 25% in line current,and this is as expected from Section 2.1.

25r

20

§ 1-5

0 5

0 30 60 906e , electrical degrees

Fig. 7 Measured and calculated variations of input currentk

120

600r0 894

400

200

0-622

Fig. 8

172

30 60 906C,electrical degrees

Measured and calculated variations of input power

120

The machine tested was also more efficient in thesynchronous mode as shown by Fig. 10, where the variationsof input power with torque are compared. The reduction intotal loss is a result of a reduction in stator ohmic lossassociated with the improvement in power factor, andindicates that no significant additional losses are caused byharmonics.

4 Conclusions

A simple method of achieving synchronous operation of awound-rotor induction motor has been described, whichrequires the provision of only an uncontrolled rectifierbridge; there is no requirement for additional machinewindings or transformers. For some applications, wherebrushes and slip rings can be tolerated, the new connection

induction

20rsynchronous

400coupling torque, synchronous W

Fig. 9 Measured variations of input current with output forinduction and synchronous modes (k = 0-894)

600r

.400-

200

induction synchronous

100 200 300coupling torque, synchronous W

400

Fig. 10 Measured variations of input power with output forinduction and synchronous modes (k = 0-894)

IEE PROCEEDINGS, Vol. 127, Pt. B, No. 3, MAY 1980

may prove to be a more economical way of obtainingsynchronous operation than the use of a separate excitationsystem or permanent magnet excitation, and could besuperior to a reluctance motor in terms of machine size,>utilisation and power factor.

A method of analysis has been presented, which,although extremely simple, has been shown to accountsatisfactorily for the behaviour of the machine semi-conductor combination. This analysis can be used todetermine optimum design parameters for any particularapplication.

The representation of the rectifier bridge for the rangeof parameters given by Fig. 5. may be useful in thetreatment of other systems, and a significant feature of thepaper is justification of the assumptions made with respectto harmonics produced by the nonlinear devices.

5 Acknowledgments

The author is grateful for the facilities provided by theUniversity of Manchester Institute of Science andTechnology.

6 Appendix

The motor used in the investigation had the followingparameters obtained by test

Nominal ratingRated currentStator resistance r\Rotor resistance r2

Stator leakage reactance xTurns ratio Ts: Tr

Magnetising reactance Xm

= 250 W output at 200 V= 1-55A= 3-63 ft= 12-1 ft= 9-5 ft= 106= 104ft (unsaturated)or 89-7 ft (at rated volts)

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