Starting of convertor-fed synchronousmachine drives

A.C. Williamson, Ph.D.. C.Eng.. M.I.E.E., and K.M.S. Al-Khalidi. M.Sc.

Indexing terms: Synchronous motors, Convenors

Abstract: The naturally commutated, convertor-fed synchronous machine is being used for drives of very highrating. At standstill and at very low speed, commutation is achieved by pulsing the current in the DC linkbetween the supply and the machine convertors, and this gives rise to significant low-frequency disturbances tothe supply system. The paper describes an alternative method, using a discontinuous current mode of operation,which gives smoother operation and less disturbance to the system. An analysis is given which shows that themethod can give an average torque as high as 1.0 per unit, and permits the rapid assessment of the potential ofthe method for a particular application.

List of symbols

L = inductance of link choke/ = effective inductance of machineR = resistance of link chokeIm = current in choke (assumed constant)i = current in linkE = average E M F of machine conver torV = peak value of supply line-line voltageco = angular frequency of supply ( = 2nf)v = supply conver tor ou tpu t voltagea = delay of firing angle of supply conver tor6 = cot angle of supply cycle from star t of conduct ion/? = value of 6 at which thyris tor blocks£ = value of 6 at which current begins to fallr\ = value of 9 at which link current becomes zero

at standstill and very low speeds, where winding resist-ances become significant in the commutation process.

,TL

a J

b = ? • - .

e = —

k =

3 col

E_

~V

average value of link current

/„., col

1 Introduction

The naturally commutated, convertor-fed synchronousmachine is now a well known form of variable-speed drive;although it is particularly favoured for applications of suchhigh rating and speed that there are only mechanical (i.e.turbine) alternatives, it is also being considered more fre-quently for lower rating applications. The main powercomponents of the drive in its simplest form are shown inFig. 1.

During normal operation, convertor CS and DC linkchoke L provide a controlled current source for the con-vertor CM, which absorbs the link power by operating inthe inversion mode, and is naturally commutated by themachine winding voltages at rotational frequency. Naturalcommutation is possible provided that the firing angle ofconvertor CM is suitably controlled and the winding volt-ages are adequate; however, such operation is not possible

Paper 3935B (PI, P6), first received 1st October 1984 and in revised form 18thMarch 1985

The authors are with the Department of Electrical Engineering and Electronics,UMIST, PO Box 88, Manchester, United Kingdom

IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985

CS CM

Fig. 1 Power components of circuitCM = machine convertorCS = supply convertor

The usual technique adopted for starting and very low-speed operation is to control convertor CS to bring thelink current down to zero, and hence reverse bias thedevices of convertor CM, whenever a commutation of CMis demanded by the rotor position. The current is thenbrought up to the required value, with the new firingpattern for convertor CM, and this pulsing occurs sixtimes per electrical machine cycle. To increase the rate atwhich the pulsing can be carried out, thyristor TL is fired atevery current reduction, allowing the energy in the choketo be maintained by free wheeling during the period of thelink current dip. This technique for commutating conver-tor CM can be used up to machine frequencies which arehigh enough to permit transition to natural commutation,with smooth link current.

It is important to note that, in this mode of operation,there is complete freedom with respect to the choice offiring angle of convertor CM, so that it can be adjusted togive an optimum relationship between stator and fieldMMFs in the machine with respect to torque production;this contrasts with the natural-commutation mode, wherethe firing angle is constrained by consideration of suc-cessful commutation in the inversion mode (and themachine must, effectively, work in the over-excited,leading-power-factor motoring condition).

The pulsed-link mode requires a control system which,in response to a change in the firing pattern of convertorCM (every 60 electrical degrees of rotation for the simplestform of drives), performs the following:

(i) applies firing pulse to thyristor TL(ii) takes convertor CS into the inversion regime to

reduce the link current to zero(iii) checks that current zero is obtained(iv) removes firing pulse from thyristor TL(v) brings convertor CS back into rectification to restore

the link current to its required value.

A consequence of this process which can be important for

209

large ratings is that the converter CS presents a dis-turbance to the supply system at intervals which vary asthe machine speed changes. The disturbance correspondsto noncharacteristic varying low frequencies, which canalso be unbalanced.

The control requirements and the disturbances to thesupply just described can be avoided for systems employ-ing six-pulse convertors, by operating in a discontinuous-link-current mode, as described in the following Section.

2 Discontinuous link current

At very low machine speeds, the average link voltage isvery low, and, consequently, the converter CS outputvoltage contains a high ripple at six times supply fre-quency. With no link inductance, the voltage ripple wouldbe applied directly, line-line, across the machine windingthrough two triggered thyristors of convertor CM. Theeffective circuit inductance would be low (equal to twicethe subtransient inductance per phase) and the current dis-continuous for high average values.

If the link current is discontinuous, pulsating at sixtimes supply frequency, then all devices of convertor CMwill be reverse biased at the same frequency. Consequently,a change in firing pattern will result in an automaticchange in conduction pattern at the next ripple, withoutrequiring variation of the mode of operation of convertorCS or checking for current zero.

Such conditions can be approached if the thyristor TL istriggered continuously during the starting period, and thisis easily effected without great control complexity. In thisway the choke protects against rapid rate of rise of averagelink current, but has little effect upon current ripple ampli-tude for a steady average value. Although the windingcurrent will pulsate at high frequency, with a correspond-ing high-frequency torque pulsation, the average value willdetermine the average torque produced during one con-duction pattern. The pulsations in torque will be moreregular than those produced by the pulsed-link mode,which causes a reduction in torque to zero at every com-mutation of convertor CM, and also imposes a series oftransients upon the link current control.

There will be a limit to the average current possible inthe discontinuous current mode, depending upon machineparameters and operating conditions, and this is investi-gated in the following Sections.

3 Analysis of current ripple

The circuit of Fig. 1 can be approximated to the equivalentcircuit of Fig. 2 for the case where the machine windingfrequency is much less than the supply frequency. If thethyristor TL of Fig. 1 is triggered continuously during thestarting mode, it will behave as a diode across the choke(of inductance L and resistance R) as shown in Fig. 2. Theinductance / is that presented by the machine to currentvariations at six times supply frequency, flowing throughtwo phases, with the rotor at low speed; it will thus be

twice the subtransient inductance per phase. The machineconvertor will show a voltage E, which is assumed con-stant at this stage, although, in fact, it will vary through 60electrical degrees of rotor angle, since it is produced byrotational effects. The resistance r, equal to twice the effec-tive resistance per phase of the winding, will be assumed tobe smaller than the choke resistance R, and will beneglected.

The voltage v, the output of the supply convertor, willvary with convertor firing angle delay a. Assuming theoverlap in the supply convertor to be negligible, v will begiven by

v = V cos (cot + a — n/6) for 0 < cot < n/3

whereV = peak line-line supply voltage = y/2VLco =2n x supply frequency

and this repeats at six times per cycle.In a steady-state condition, therefore, the behaviour

shown by Fig. 3 can be expected, assuming current i to bediscontinuous.

Tt/3

Gzuut

Fig. 3 Expected variation of current in link

If 6 = cot then, at 9 = 0, i = 0 and the choke current isfree wheeling. The voltage v - E, being effectively appliedto inductance /, causes i to increase rapidly. At 9 = ft, ibecomes equal to the choke current, the thyristor blocks,and any further rise in current i is opposed by inductanceL. At 9 = s, the voltage across the thyristor reverses, itconducts, and i drops to zero at 9 = r\, with Y\ < n/3 fordiscontinuous current.

In most practical cases it can be expected that L > /,and the time constant L/R > 1/6/ Thus, the variation inchoke current will be small compared with the rippleamplitude, and it will be assumed that the choke currentmaintains a constant value Im.

Hence, for 0 ^ 9 ^ p,

V , d i , d i

v - E = I — = col —dt d9

giving, with i = 0 at 9 = 0,

VY E li = — sin (9 + a - n/6) - sin (a - n/6) - — 9 \

col\_ V J (1)

For p ^ 9 ^ e

For

Fig. 2 Equivalent circuit

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v , d i 1 d i

v-E = l — = col —dt d9IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985

giving, with i = Im at 9 = e,

i = /m + —|s in (0 + a -7 i /6)

- sin (e + a - n/6) - | (9 - e)l (2)

Given values of V, col, E and Im, further conditions necess-ary for the solution of eqns. 1 and 2 are obtained asfollows.

At 9 = e, the diode (thyristor) voltage is such that block-ing ceases, and since i = Im = constant, this corresponds tov — E < 0. Hence

V cos (e + a - n/6) - E = 0 (3)

The energy consumed by the choke resistance in one rippleperiod, equal to /2 R(n/3co), must be supplied during theinterval /? < 9 < e when the diode (thyristor) is blocking.Thus

(u - E)Im dt = I2mR —

3OJ

giving

siiV | sin (e + a - rc/6) - sin (0 + a - n/6) - — (e - /?)

= ImR-n/3 (4)

Using eqn. 1 for i = Im at 0 = e and eqn. 2 for i = 0 at9 = i], these equations can be rearranged and written innormalised form as

e = cos"* (e) — cc + n/6

ee = 7(1 - e2) - a{\ + b) - sin (a - n/6)

e/? = sin (/? + a — n/6) — sin (a — n/6) — a

e>7 = sin (rj + a — 7r/6) — sin (a — n/6) — ab

wherecol n R E

(5)

(6)

(7)

(8)

For given values of the dimensionless parameters a, b ande, eqns. 1 and 2 must be solved simultaneously for a and s;this is done with an iterative procedure, and a convenientstarting point is with a = n/2 as an initial value. With aknown, eqns. 7 and 8 can then each be solved iterativelyfor (3 and rj, respectively. The average value of i can beobtained from integration of the waveform of Fig. 3 and isgiven by

V

where

n\_k = -\a(ri-b)-- (P2 + (ri- e)2) + e + cos (a - n/6)

— cos {fi + a — n/6) — cos (rj + a — n/6)

— fi sin (a — n/6) — (rj — e) sin (e -I- a — n/6)

4 Experimental verification

A drive with the basic configuration of Fig. 1 was operatedin the mode discussed. The relevant parameters of thesystem are

V = J2 x 415 V

IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985

1 = 2 x 1.223 mH (x" = 0.112 per unit)

R = 0.45 Q (giving b = 0.613)

Machine rating 415 V, 70 A at 50 Hz

L = 43 mH

Fig. 4 shows the current waveform measured with themachine at standstill in the discontinuous mode with an

Fig. 4 Measured and calculated waveforms of link current at standstill

average link current of 50 A. The waveform is similar tothat shown in Fig. 3, the three regions of current conduc-tion being clearly discernible. A noteworthy feature is thealmost flat top, indicating that the choke current variesvery little compared with the link current ripple, andremains close to 70 A, in this case, throughout the cycle.

Also shown in Fig. 4 is the waveform calculated bythe analysis of Section 3 for a value of a = 0.0918(corresponding to Im = 70 A). Agreement between themeasured and the calculated waveform is good, and thecalculated average value is also close to that measured.

Fig. 5 Measured and calculated waveforms at machine frequencyof 8.5 Hz

Fig. 5 shows the current waveform measured at a lowercurrent, but with the machine motoring at a frequency of8.5 Hz and producing an average link voltage at convertorCM of 125 V. The waveform of this voltage is also shown.During the two periods when the choke thyristor is con-ducting, the voltage waveform is that produced by thesupply convertor, whereas, in the flat-top period duringwhich the thyristor blocks, the voltage waveform is that ofthe machine convertor.

The ripple of the supply convertor voltage, superim-posed upon an average value, is obvious; the ripple of themachine convertor voltage is less obvious, but detectable,going through one cycle of its variation in approximatelysix link ripples at this machine speed. Owing to the firingangle chosen for the machine convertor, its voltage rippleis small, the maximum of £ being only 5% greater than theaverage value, and Fig. 5 indicates that, under these condi-tions, the assumption of constant E is valid.

211

Also shown in Fig. 5 is the variation in current calcu-lated for values of a = 0.0654 (corresponding to Im = 50 A)and e = 0.213 (corresponding to E = 125 V). Agreement isagain very close.

Fig. 6 gives a comparison between measured and calcu-

50.5A max34 A mean

Fig. 617.3 Hz

Measured and calculated waveforms at machine frequency of

lated currents for an average link current similar to that ofFig. 5, but with the machine motoring at a frequency of17.3 Hz, and producing an average link voltage of 310 V.Conditions for this test were limiting, in that this was themaximum current possible for this voltage. The ripple inthe convertor voltage is more obvious than in Fig. 5, goingthrough its cycle in approximately three link currentripples, and a modulation of the ripple current waveformat this frequency can be observed. Agreement betweenmeasured and calculated current variations is, however,very close, and it can be assumed that the method ofanalysis is satisfactory.

5 Limiting criteria

It is important to establish the maximum average linkcurrent possible in the discontinuous mode for any parti-cular equipment and operating condition. The limit isreached when current conducts for an angle approaching7r/3, and the equations of Section 3 can therefore be solved

0.1 oor

0.07 5

0.050

0.025

0.25 0.5

Fig. 7 Variation of maximum average current In

ance and machine convertor voltage

n R E Ira/b = e = — K^ =

3o)/ V max V

0.75

with choke resist-

for r\ = n/3 to determine kmax, the maximum possible valueof k. Fig. 7 gives the variation of kmax with e for variousvalues of b, and therefore affords a rapid method of assess-ing capability.

Some useful generalisations can be made from Fig. 7 forthe case where the machine has a rated voltage, at supplysystem frequency, which is equal to the supply systemvoltage at the supply convertor CS. If the subtransientreactance per phase of the machine at supply frequency isx" per unit based upon machine rating, then col is given by

where IR = rated machine current, and Iav = kV/col isgiven by

When the machine rotates, currents in the damping cir-cuits oppose all airgap flux pulsations, so that the averageof the torque is determined by the fundamental com-ponents of the stator winding currents. The phase currentwill be substantially of the form of a quasisquare wave, ofamplitude Iav, with the ripple superimposed. Consequentlythe RMS value of the fundamental component will begiven by

Substituting for Iav, and taking a per unit value, gives

r 3 k

I = per unitn x

Fig. 7 shows that the choke resistance R, represented bythe parameter b = (n/3)(R/col), can have a significant effect.The loss in the choke is continuous, and for rated funda-mental current in the machine, with Im = (n/yj6)(IR), willbe (TC2/6)(/^ R). If this loss is p of the machine rated VA atsystem frequency, then it can be shown that

n xIn order to achieve a high drive efficiency, the choke lossmust be kept low, and a value of 5% of machine nominalrating (at system frequency) is a reasonable limit, givingp = 0.05. The capability of this type of drive is criticallydependent upon commutating inductance and a low valueof subtransient reactance is desirable. However, it isunlikely that a value for x" lower than about 0.1 per unitcan be achieved without greater derating, so that the par-ameter b is unlikely to exceed about 0.5.

Fig. 7 shows that, for e = 0 (i.e. very low-speedoperation), a value of b = 0.5 gives a value of kmax = 0.08.Taking a value of x" = 0.1 per unit gives a value of/ = 0.765 per unit, as the likely maximum possible value ofeffective, torque-producing stator current. For a machineoperating at rated flux, and with the machine convertorfiring angle chosen to give maximum torque production,the torque produced would therefore be 0.765 per unit.However, it is usually possible to substantially increase theairgap flux at low speeds, by excitation control, and anincrease above the rated value of only 30% would beneeded to develop a torque of 1 per unit. It should bepointed out that, if the supply convertor voltage is higherthan the machine rated value at system frequency, then theestimates just described will be improved.

212 IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985

As the machine speed increases, the average link voltageincreases, and the amplitude of the voltage rippledecreases. This reduces the average value of link currentpossible in the discontinuous mode, as shown by the effectsof the parameter e in Fig. 7. If the machine convertor oper-ates for optimum torque production, the voltage it pre-sents to the link will have a low amplitude ripple, with amaximum of y/2Vm and an average value of (3/n){y/2Vm), sothat little error, and a pessimistic estimate will be given byassuming E = y/2Vm, where Vm is the RMS machine linevoltage at rotational frequency. If the ratio machine-frequency/supply-frequency is n, and the machine operatesat c times rated flux, then

K =

Hence

ncV

72

nised to any supply event, occur at varying intervals andaffect individual phase of the supply in a variable manner.This is illustrated by Fig. 9 which shows the waveforms oftwo of the supply-system line currents for the two alterna-

r "\ J * \

e = - = nc

Taking a value of c = 1.3, Fig. 7 shows that capability isnot affected for n < 0.08 (or a machine frequency of 4 Hzin the case of 50 Hz supply frequency), and falls by only10% for e = 0.4, or n approximately one third. It is appar-ent, therefore, that the capability will not decrease signifi-cantly over the speed range for which this form ofcommutation of the machine convertor is likely to berequired (typically to n = 0.1).

6 Discussion

It is apparent from the foregoing that an alternative tocontinuous triggering of link thyristor TL is a single triggerpulse of duration £ of a supply cycle, at each demand for acommutation from the rotor position sensing circuit. If thelink current and the machine voltage are inside the limit-ing criteria discussed in the preceding Section, such a pulsewill result in the machine convertor current being taken tozero and a new conduction pattern being establishedwithin one supple ripple.

Such a process appears at first sight to be preferred tocontinuous triggering, since it gives less high-frequencyripple in machine and supply currents. However, eachpulse of the link thyristor subjects the link current controlloop to an impulse which, if occurring at six times machinefrequency, will be sensed by a fast-acting loop, resulting inan overshoot of link current when the commutation iscomplete. Continuous triggering of the link thyristor givesimpulses to the current control loop at six times supplyfrequency and this will be outside the bandwidth of atypical loop, resulting in an undisturbed behaviour of linkcurrent.

Fig. 8 shows link current waveforms measured at differ-ent times for identical conditions (machine motoring at6.6 Hz and developing a torque of 29 Nm) during oper-ation with the link thyristor pulsed only for 3.3 ms at eachmachine commutation request. The erratic behaviour ofthe current produced by the impulses upon the controlloop is obvious and should be compared with the steadybehaviour shown by Figs. 4, 5 and 6 for continuouspulsing.

It must be stressed that, with continuous pulsing, thelink current waveform remains almost constant in itswaveshape throughout the acceleration period from stand-still to the transition to natural commutation. In contrast,the alternative of pulsing only at commutation requestresults in link current transients which are not synchro-

Fig. 8 Link current waveforms for single-pulse mode

Fig. 9 Supply system currents for alternative modes

tive modes all to the same scale and with the machinemotoring at 6.3 Hz and developing a torque of 74 Nm. Fig.9a is for the single-pulse mode and covers less than onemachine conduction period; consequently the full natureof the disturbance is not demonstrated, but it is clear thatlow-frequency components of current are produced in anunbalanced manner. Fig. 9b shows that, for continuoustriggering, although the harmonic content is increased, it iscomposed of characteristic components which are bal-anced and constant during the acceleration, or low-speedrunning period.

The true pulsed-link mode can be expected to produceeven larger variations in link current and disturbance tothe supply system since it operates upon the currentcontrol directly, requesting zero current at each com-mutation. The result will vary with the instant in thesupply cycle at which the request occurs, giving spasmodicovershoots and variable periods of zero link current. Thiswill reflect not only in the supply system, but also in theresulting conduction period of the machine convertor, inmachine electrical degrees. It should be pointed out thatany method used for commutating the machine convertor

IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985 213

which uses the supply convertor to switch the link currentcannot result in balanced machine conducting periods of120 electrical machine degrees. The continuous pulsingtechnique proposed and analysed in this paper, of all theother alternatives discussed, will produce the closest tosuch balanced conditions. The high-frequency torque pul-sation (at 300 Hz) has not been noticed during operation,whereas the low-frequency pulsation (at 6 x machinefrequency) has noticeably been exacerbated by the single-pulse technique.

7 Conclusions

For those applications where a very large starting torque isrequired, the naturally commutated, convertor-fed syn-chronous machine must be started by cyclic phasing of thesupply convertor, from rectification to inversion and viceversa, to pulse the link current down to zero at machine

convertor commutation frequency. However, for applica-tions which require a starting torque of the order of ratedtorque or less and/or the power-conditioning units havelimited overload capability, then operation in the discon-tinuous link current ripple mode described in this papermay be possible. The advantages are that the drive controlis simpler, low-speed operation is smoother and the supplysystem suffers less disturbance. The characteristic harmo-nics (e.g. 5th and 7th) will be increased, but will beunvarying during the starting and low-speed period, andthis is probably to be preferred to the varying, unbalanced,low-frequency effects produced by the alternative startingtechnique.

The paper has given an analysis of current in the dis-continuous ripple mode and demonstrated its validity. Theanalysis has been used to derive the maximum averagecurrent possible in this mode, and this has been presentedin the form of normalised curves which can readily be usedto establish the capability of a particular system.

214 IEE PROCEEDINGS, Vol. 132, Pt. B, No. 4, JULY 1985