Influence of commutating reactance on the design of DC power supply converters DC railway systems have now crystallised into the three major categories of 750V, 1500V and 3000V, the latter being applied to main-line systems and the first two mainly to urban mass- transit or light-rail systems. This article reviews the significance of choice of transformer commutating reactance and highlights its importance in the design of DC substation convertors by L R. Denning Introduction Electrified railways are powered from either AC or DC supply systems, the choice being dependent on various factors, many purely historical. The ideal torque/speed characteristic of the simple DC series field motor for traction duty virtually dictated the use of DC trade supplies. Nevertheless, some early AC-fed railways were made to operate adequately, using locomotives driven by special commutator motors, the design difficulties of which limited the supply frequency to 16% or 25Hz, which, in turn, prescribed a relatively massive on-board transformer. These factors tended to negate the transmission advantages of high-voltage AC. However, AC-fed railways have become more attractive since the advent of reliable on- board static convertors, which now enable the advantage of high-voltage (25kV, 50kV) transmission at industrial frequency (50-60Hz) to be exploited, together with the highly desirable DC series motor. DC railway systems were fed at voltages ranging from 200V to more than 3000V, but the range has now crystallised into three major categories of 750V, 1500V and 3000V, the latter being applied almost entirely to main-line systems in order to maximise substation spacing. 750V or 1500V supplies are predominantly chosen for urban mass-transit or light-rail systems. This article expounds the 1 Four-car set on the Washington Metropolitan Area Transit Authority (WMATA) system in the USA. This system is supplied at 700V DC POWER ENGINEERING JOURNAL JULY 1987 181
Transcript
Influence of commutating reactanceon the design of DC power supplyconvertersDC railway systems have now crystallised into the three majorcategories of 750V, 1500V and 3000V, the latter being appliedto main-line systems and the first two mainly to urban mass-transit or light-rail systems. This article reviews the significanceof choice of transformer commutating reactance andhighlights its importance in the design of DC substationconvertors
by L R. Denning
IntroductionElectrified railways are powered from either ACor DC supply systems, the choice beingdependent on various factors, many purelyhistorical.
The ideal torque/speed characteristic of thesimple DC series field motor for traction dutyvirtually dictated the use of DC trade supplies.Nevertheless, some early AC-fed railways weremade to operate adequately, using locomotivesdriven by special commutator motors, thedesign difficulties of which limited the supplyfrequency to 16% or 25Hz, which, in turn,prescribed a relatively massive on-boardtransformer. These factors tended to negatethe transmission advantages of high-voltage
AC. However, AC-fed railways have becomemore attractive since the advent of reliable on-board static convertors, which now enable theadvantage of high-voltage (25kV, 50kV)transmission at industrial frequency (50-60Hz)to be exploited, together with the highlydesirable DC series motor.
DC railway systems were fed at voltagesranging from 200V to more than 3000V, butthe range has now crystallised into three majorcategories of 750V, 1500V and 3000V, thelatter being applied almost entirely to main-linesystems in order to maximise substationspacing. 750V or 1500V supplies arepredominantly chosen for urban mass-transitor light-rail systems. This article expounds the
1 Four-car set on theWashington MetropolitanArea Transit Authority(WMATA) system in theUSA. This system issupplied at 700V DC
POWER ENGINEERING JOURNAL JULY 1987 181
significance of the choice of transformercommutating reactance. While it is a key factorin the design of the vehicle-borne transformer,the main object of this article is to highlight itsimportance in the design of DC substationconverters using transformers and naturallycommutated diode rectifiers.
The article concentrates on converterswhich produce 12-pulse DC output voltage byutilising either transformers with threewindings, or combinations of pairs oftransformers, each with two windings: thescope is limited to full-wave rectification, andconsiders the arrangement of 3-phase bridgerectifiers in parallel or series combination.
SpecificationUrban-railway DC electrification can be
subdivided into two categories: light rail andmass transit. Usually light-rail systems will bepowered by substations with ratings between1MW and 2MW, while mass-transit systemscan have an installed substation capacity of8MW or even 12MW. It is usual for a DCsubstation to include more than one converterto provide the total substation rating. (Thisapproach provides a degree of redundancy,which permits normal service operation withone substation converter disconnected formaintenance or repair, provided the adjacentsubstations remain fully operational.) Bothnormal and abnormal power-supply feedingarrangements can be modelled at the designor planning stage using computer simulationtechniques.1-2 The results from suchsimulations provide optimum equipment ratingfor particular service conditions, and once therating of a substation is determined theindividual transformer-rectifier unit (theconverter) can be specified.
The value of the transformer commutatingreactance chosen will be demonstrated to beof fundamental importance to the supply-system performance.
To meet the electrical-performance criteriathe important aspects of a specification are:
(a) DC voltage regulation envelope(bj Initial DC fault current magnitude and
profile, as determined from the point-on-wave initiation and the final steady-statevalue
(c) Efficiency of the converter unit(d) Power factor of the converter unit(e) Amplitude and frequency of the harmonics
produced by the conversion process inboth the AC supply line currents and theDC output voltage.
With a normal substantial AC source of supply,the predominant influence on the performancecriteria identified above is the convertor-transformer.
Since the approach to achieving asatisfactory design is similar for each voltagecategory, as an example, to illustrate thediscussion, a converter specification isconsidered as follows:
Rated capacity: 3000kW; capable of delivering5000A at 600V DC
Overload capabilities: 150%, 300% and 450%of rated load, permitting demands for loadcurrent as follows:
7500A for 2h15000A for 1 min22500A for 15s
Voltage regulation: 6% is a typical value for DCvoltage regulation which applies over the linearportion of the regulation characteristic.3 It iscommon, for example, for mass-transit DCrailways, with train headways of the order of2min to 3min, to demand essentially linearvoltage regulation well into the convertor-overload region. This demanding requirementis necessary to support the high accelerationrates employed on such railway systems. Thespecification of voltage regulation therefore
2 Four-car set on theHong Kong Mass TransitRailway Corporation(MTRC) system. The1500V DC supplysubstation is included inthe station complex
182 POWER ENGINEERING JOURNAL JULY 1987
often takes the form of a table of voltage limitsfrom light load up to 450% of rated load (seeTable 1 and Fig. 4, which illustrates graphicallythe values in Table 1).
Table 1: Typical DC voltage-regulationspecification
Load(%)
1100150300450
DC current(A)
50500075001500022500
DC voltage(V)
min.
632594575518420
1 limits
max.
640606589538470
Short-circuit fault withstand: Specificationsoften concern themselves with defining thenumber of semiconductors to be included inthe rectifier to survive short circuits at the DCoutput terminals.3 Adequate bracing of thetransformer windings against stresses broughtabout by short-circuit forces is essential, as isthe capability of any DC circuit breaker in thetrack feeding circuits to successfully interruptany short circuit.
Efficiency: It is usual for a specification to statethat the efficiency of the convertor shall not beless than (typically) 94% when supplying ratedload. Occasionally minimum efficiency levels at50%, 100% and 150% rated load are stated.When comparing designs competitively, anadvantage may be given to the most efficientunit.
Power factor: It is usual for a specification tostate that the displacement power factor (i.e.including distortion factor)3 shall not be lessthan (typically) 0-95 per unit when supplyingrated load. Occasionally, as with efficiency,minimum power factors at 50%, 100% and150% rated load are stated.
Harmonics: If a specification is stringentenough to mention either AC line current orDC voltage harmonic amplitude levels it isusual to state compliance with the classicalvalues as determined by the type of circuitconnection.4 Also specifications can require acalculated statement of the levels of harmonicswhich can be expected as a result of using aparticular convertor system.
TransformerThe number and arrangement of windings in
the transformer are chosen, for a 3-phase ACsupply system, to provide either 6- or 12-pulseDC output voltage. Other output ripple levelsof amplitude and frequency, e.g. 24-pulse, areachievable with combinations of more thanone convertor unit.
Winding arrangements: A 2-windingtransformer connected to a 3-phase bridgerectifier circuit will produce a 6-pulse DCoutput voltage. A second transformer with a
3 An illustration of a69kV switchyard nearRecife in Brazil. Thesupply feeds into thesubstation through thethree convertortransformers which canbe seen outside thesubstation building, andthe 3000V DC feeds outto the railway which isbeyond the wall behindthe substation
4 Graphicalrepresentation of DCvoltage-regulationcharacteristic depictednumerically in Table 1:
nominal values;voltage envelope
limit values
700
> 600
tage
.vo
l
uo 500
Ann100 200
load.Vo300 A00
POWER ENGINEERING JOURNAL JULY 1987 183
5 Two 2MW, 700V DCsilicon diode rectifiersinside a WashingtonMetropolitan Area TransitAuthority (WMATA)substation in the USA
winding arrangement producing similarsecondary voltages, but which are displaced by30° from the first unit, will also produce a6-pulse DC output voltage when connectedthrough a 3-phase bridge rectifier circuit, butwith the 6-pulse ripple displaced by 30°. Byconnecting these two 6-pulse systems in seriesor parallel a 12-pulse DC output voltage can beproduced. A similar result can be obtained, forexample, by using a 3-winding transformerhaving a single primary winding and one starand one delta secondary winding to give thenecessary 30° phase displacement. The waythese windings are arranged during the designand construction of the transformerdetermines the parameters of short-circuitreactance, commutating reactance and loadloss. It is these parameters whichfundamentally determine: DC voltageregulation; DC fault-current magnitude andprofile; convertor efficiency; convertor powerfactor; and harmonic amplitudes.
Commutating reactance: When a rectifier isoperating, current flows through the diodebridge arms consecutively and transfers fromone group of diodes to another as thesecondary voltage of the rectifier transformerdictates. The reactance in the AC circuitdetermines the rate at which the currenttransfers. Also there is an associated loss of DCoutput voltage known as the reactive voltagedrop, which is the major component of the DCvoltage regulation. Since the technical term forthe transfer of current from one group ofdiodes to another is commutation, thereactance which governs the speed of transferis called the commutating reactance.
The reactive voltage drop can be calculatedfrom an expression of the form:
Reactive voltage drop £x
and 5)C Xc ld (References 4
where Xc = commutating reactance, Old = rated DC current, A, andC = constant for the particular rectifier
circuit (see Appendixes A and B)
Coupling factors: For transformers with onlytwo windings the percentage commutating
184
reactance and the percentage short-circuitreactance are equal when expressed to thesame base. For the 3-winding transformer orfor the combination of pairs of 2-windingtransformers in 12-pulse arrangements, thepercentage short-circuit reactance of thesystem can be as little as half the percentagecommutating reactance, or equal to thepercentage commutating reactance of thesystem. The ratio between these extremevalues depends on the degree of couplingbetween the leakage reactances of thetransformer secondary windings. Obviouslywith two separate transformers the degree ofcoupling is zero, and in this case the short-circuit reactance expressed as a percentage offull primary kVA base is half that of thecommutating reactance expressed to the samebase.
By definition short-circuit reactance isdetermined by circulating rated primary currentwith both secondary windings short-circuited.When commutation occurs there isinstantaneously an effective short circuit onthe windings of one secondary at a time owingto the 30° phase displacement between thesecondary windings.
When a transformer with three windings isutilised, the secondary windings can bedesigned so that the leakage reactances ofeach couple with one another to a greater orlesser degree, or are separate from one anotheras with the two individual transformers.6 Theperformance of a 3-winding transformer withuncoupled secondary windings is the same asthat with two separate transformers, each withtwo windings.
When the leakage reactances of thesecondary windings of a 3-winding transformerare designed to link with one another thewindings are said to be coupled. This meansthat, when current flows in one secondarywinding, the reactance of the other increasesowing to the effect of mutual coupling.Coupling factors K ranging from K = 0(uncoupled) to K = 1 (fully coupled) can beexpressed.7-8 The relationship between short-circuit reactance and commutating reactancehas been stated for the uncoupled case (K = 0).For the fully coupled case (K = 1) thepercentage short-circuit reactance is equal tothe commutating reactance when expressedon the same base (see Appendix C).
In summary, let
X = percentage short-circuit reactanceXc(%) = percentage commutating reactanceK = coupling factor between the leakage
reactances of the transformersecondary windings.
then when K = 0, Xc(%) = 2XSC
and whenK=1,Xc(%) = Xsc
Fault current levels: As a direct consequence ofthis 2:1 ratio between Xsc and Xc(%) thesteady-state short-circuit current /sc (Fig. 6) canbe varied in the same 2:1 ratio for the sameinitial linear voltage regulation. In practice,when K — 1 voltage regulation can be
POWER ENGINEERING JOURNAL JULY 1987
maintained linear up to about 150% of ratedload, but if essentially linear regulation, up to450% of rated load, is required, it is usual toemploy transformers with K -* 0. It is essentialto recognise that this inherently means theshort-circuit fault current and associatedstresses will effectively double, and associatedequipment must be specified to suit.
The short-circuit current can be determinedusing expressions of the form:6
where a = 0°, 30°, 120°, 150°, 240° and 270°
0 = tan-1 ^LR
and the applied phase voltage Vm sin (cot + a)
Power factor: The inherent delay in the rise andfall of current during commutation, owing tocommutating reactance, causes a displacementof the fundamental current relative to thevoltage in the respective winding of thetransformer. Thus the commutating reactancedetermines the power factor of the convertor.The power factor (PF), which is strictly thedisplacement factor and the distortion factor,3-9
can be determined from expressions of theform
PF =I M2 Ed0)
where Ex is a function of commutatingreactance as already described.
HarmonicsThe commutation of the current from one
group of diodes to another gives rise toharmonics in both the AC line currents and theDC output voltage.
For 12-pulse output, AC line currentharmonics of the 11th, 13th, 23rd and 25thorder will predominate. In practice, smallamounts of 5th, 7th, 17th and 19th may alsooccur owing to minor inaccuracies in phasemultiplication or input waveshape distortion.
Harmonic voltages of 12th and 24th orderwill predominate in the DC output voltage. Inpractice, small amounts of 6th and 18th mayalso occur.4
Expressions for the amplitude of harmonicsin both AC and DC systems depend on thecommutating reactance for theirdetermination. For example, the expression forDC voltage harmonics is as follows:
E h . 1 cos[(h+1)u/2]
n r1 cos[(h-1)u/2]
where overlap angle u is a function ofcommutating reactance.9
From the foregoing the importance ofdesigning the commutating reactanceprudently is apparent if all the performance
light load voltage -
full load voltage -<Ed)
voltage regulation
voltage drop
•reactive voltage drop (Ex )
"resistive voltage drop (E r )
full-load current ( I d )
criteria required by a specification are to bemet.
Transformer load lossesThe load losses of the transformer
contribute a resistive voltage drop to the DCvoltage-regulation calculation. The magnitudeof the voltage drop at rated load can bedetermined5 using Er = PJ\& where Pr is therated load loss in watts and ld is the rated DCcurrent in amperes (see Appendixes A and B).
The transformer load losses, together withthe no-load losses, predominate in thecalculation of the convertor efficiency. With anallowance for the rectifier losses the convertorefficiency can be determined using:4
6 DC voltage regulationcharacteristic from no-load to short circuit forcoupling factors of K - 0andfC-1
ReconciliationTo clarify the earlier discussion consider only
the light-load/full-load DC voltage regulationmade up of a reactive-voltage-drop componentand a resistive-voltage-drop component, asshown in Fig. 7.
The proportions of the reactive componentand resistive component of the regulationvoltage must be assigned correctly.
For example, if the reactive proportion is toolarge the commutating reactance will be highand the power factor may be lower than the
POWER ENGINEERING JOURNAL JULY 1987 185
specification permits. Certain harmonicamplitudes will be higher than specified andthe voltage regulation will not stay linear as farinto the overload region as may be desired.
On the other hand, if the resistive proportionis too large it is likely that the load-loss levelswill make it difficult for the transformerdesigner to meet temperature-rise limits andfor the convertor to achieve specified efficiency.
In addition, attention to the commutatingreactance in relation to short-circuit reactanceand coupling factor is essential in order tosatisfy specified regulation at overload levelswhile maintaining DC fault currents withinmanageable levels.
Practical restrictionsHaving considered any one specific case, for
which the parameters of commutatingreactance, short-circuit reactance and load losshave been optimised through an iterativeprocess, the design of the transformer can onlybe undertaken within the bounds of the limitsimposed by practical manufacturing tolerances.
For a 3-winding transformer it is reasonableto allow tolerances10 as follows:
± 0-5% on the nominal ratio± 10% on the specified impedance± 6% on the specified load loss
It is the application of tolerances which givesrise to the specification of maximum andminimum DC voltage limits as outlined inTable 1.
In the worst-case event of the parameters ofa tested transformer being measured attolerance limits, the resulting ratio could meanthat the secondary voltage is 0-5% low, so theno-load average DC voltage is 0-5% low. Thecommutating reactance could be 10% high, sothe reactive-voltage drop is 10% high. The loadloss could be 6% high, making the resistivevoltage drop 6% high. Starting with the lowestno-load average DC voltage and for a particularload condition, subtracting the maximumresistive and reactive DC voltage drops willachieve a point at the minimum-voltageextreme on the DC voltage-regulationenvelope. Similarly, on the other extreme of thetolerances, a point will be achieved on the DCvoltage-regulation envelope corresponding tothe maximum voltage specified for the loadcondition being analysed.
ConclusionThe article illustrates the importance of
assigning correct values of commutatingreactance, short-circuit reactance and loadlosses to the transformer parameters as well asthe more obvious ones of secondary voltage,turns ratio and rating. The reconciliationsection demonstrates that values cannot beassigned on the basis of, say, DC voltageregulation alone, and thus a process ofiteration is necessary. The whole calculationprocess lends itself to digital-computingtechniques. Appendix D shows the graphicaloutput results from such computation for the3000kW convertor example proposed.
The title of the article singles out the
commutating reactance because thispredominates in the calculations, and is themost significant parameter in thedetermination of all the quantities discussed,except the efficiency. A satisfactory convertordesign, which complies with all specifiedperformance criteria, relies on paying closeattention to the optimum assignment of allparameters.
AcknowledgmentsThe author would like to acknowledge the
help and advice given towards the preparationof this article by J. D. McColl (F), Director ofTechnical and Resource Development, GECTransmission and Distribution Projects Ltd; andThe General Electric Company Ltd. for givingpermission to publish.
References1 MELLITT, B., GOODMAN, C. J., and
ARTHURTON, R. I. M.: 'Simulator for studyingoperational and power supply conditions inrapid transit railways', Proc. IEE, 1978,125,pp. 298-303
2 MELLITT, B., MOUNEIMNE, Z. S., andGOODMAN, C. J.: 'Simulation study of DCtransit systems with inverting substations', Proc/EE, 1984,131, Pt. B, pp. 38-50
3 National Electrical Manufacturers AssociationStandards Publication (NEMA) Rl 9
4 British Standard BS44175 American National Standards Institute
Publication ANSI C34.26 DENNING, L. R.: 'Methods for predicting fault
levels'. Colloquium on 'DC Traction SubstationProtection', Feb. 1979
7 DORTORT, I. K.: 'Extended regulation curves for6-phase double-way and double-wye rectifiers'.AIEE Paper 53-36 1953
8 WITZKE, R. L, KRESSER, J. V. and DILLARD, J. K.:Voltage regulation of 12-phase double-wayrectifier; AIEE Paper 53-242 1953
9 READ, J. C: The calculation of rectifier andinverter performance characteristics', IEE Paper,Aug. 1945
10 American National Standards InstitutePublication ANSI C57.12
11 SCHAEFER, J.: 'Rectifier circuits: theory anddesign' (John Wiley)
L. R. Denning is Chief Engineer, Traction Systemswith GEC Transmission and Distribution ProjectsLtd., Stafford, UK. He is an IEE Member
Appendix A: Expressions(see Appendix B for definition of terms)
'a = -
5fe -
Pmr = — EdJd provided q > 2T0T Q tisin / _
(Reference 11)
186 POWER ENGINEERING JOURNAL JULY 1987
= Xc(%) n
100 2
3q sin (n/q) E,do
sin2(n/p) Lprovided q > 2
2nn
E, - i
C/rcu/t constants
ANSI C34.2circuit nos.
IEC146circuit nos. q m n s p d description
23, 24, 25and 26
31—
1011a13a
61212
112
121
222
3 13 13 1
3-phase bridgeparallel bridgesseries bridges
Appendix B: Definition of terms
q = pulse numberm = number of simple rectifiers in seriesn = number of simple rectifiers in parallelp = number of phases per simple rectifiers = 1 for single way (half wave), 2 for
double way (full wave)d = number of simultaneous
commutations per primaryEs = transformer-secondary no-load RMS
secondary line current, A= transformer rated primary apparent
power, VA= angle of overlap= angular frequency
Appendix C: Additional data for rectifiertransformers
3-winding transformers with one wye andone delta secondary can be constructed withthe leakage reactance common to bothsecondary windings (coupled secondaries) orthe leakage reactance of each secondarywinding wholly independent of the othersecondary winding (uncoupled secondaries).Partial coupling results when the leakagereactance of each secondary winding is notwholly independent or completely common tothe other secondary winding.
With rectifier transformers the degree ofcoupling between secondary windings greatlyinfluences both the voltage regulation atoverload levels in excess of 200% and themagnitude of the fault current the equipmentcan produce when subjected to short circuit.
To ensure that specified voltage regulation iscomplied with it is necessary to specify boththe commutating reactance and the short-circuit reactance, since this determines thedegree of coupling between secondarywindings.
Notes:(i) Percentage commutating reactance is the
value which would be determined if it werepossible to short-circuit either secondarywinding independently of the other. It isexpressed as a percentage based on fullprimary kVA.
(ii) Percentage short-circuit reactance is thevalue determined when both secondarywindings are short-circuited together. It isexpressed as a percentage based on fullprimary kVA.
If the transformer reactance is symbolicallyrepresented as follows:
X,
where X = primary reactanceXs = secondary reactanceK = coupling factor
then the commutating reactance Xc = Xp + Xs
the short-circuit reactance Xsc = Xp +XJ2the degree of coupling K = Xp/Xc
Hence, when Xp = 0, K = 0, the secondaries arewholly uncoupledwhen Xs = 0, K = 1, the secondaries arefully coupledwhen Xp and Xs are such that K isbetween 0 and 1, the secondaries arepartially coupled.
In order to ensure good load sharing betweenthe rectifiers connected to each secondary it isessential to have good equality of the leakagereactance to both the wye and deltasecondaries, and to achieve this it may bepreferable that very close coupling is notattempted. A coupling factor of 0-85-0-9 willgenerally be satisfactory. A short-circuit test onthe transformer, with both secondaries short-circuited, should result in secondary currentswhich are within 10% of each other. For thesame reason it is essential to have goodequality of secondary voltages, i.e. a turns ratiobetween secondaries which gives an accuratevalue of V 3 (e.g. 15:26 or 11:19).
POWER ENGINEERING JOURNAL JULY 1987 187
PERFORMANCE OF SUBSTATION TRANSFORMER S RECTIFIER UNITSYSTEM : EXAMPLESUBSTATION : SUB. NO. 1
Efficiency at full loadPower factor at full loadMagnetising current
0.978 (Per Unit)0.959 (Per Unit)0.8 (X)
I
I5-
DATAAC Harmonic Currents DC Harmonic Voltages
(X of fundamentalline current)
(X of no loadvolts )
8.00^
6.00 J
4.00.:
2.00J
4.00 _
3.00 J
2.00.:
l.oo.:
o.oo200 300
12th
24th
Rated power :Rated DC current :Full load voltage .Light load voltage :Primary line voltage :Fault level :X/R ratio .Supply frequency :Primary rating :Secondary line voltageTransformer reactance .Copper losses :No load loss .Coupling factor :Overload class .Connection type .
