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Universidad Autónoma de San Luis Potosí

Dr. Ciro Alberto Núñez Gutiérrez Calidad de la Energía Eléctrica

ALGO DE HISTORIA DEL CONCEPTO

Presented at the 296th Meeting of the Ameri-can Institute of Electrical Engineers, Pittsfield,Mass., May 28, 1914.

Copyright 1914. By A. I. E. E.

HARMONIC VOLTAGES AND CURRENTS IN Y- ANDDELTA-CONNECTED TRANSFORMERS

BY R. C. CLINKER

ABSTRACT OF PAPERThe paper reviews the conditions under which triple harmonic

voltages and currents are produced in Y- and delta-connectedtransformers. These voltages are produced by hysteresis in thecore. In a single-phase transformer, increase of series resistancetends to suppress the current harmonic and produce the voltageharmonic. In three-phase transformers, a Y connection sup-presses the current harmonic and allows the full flux and voltageharmonics to appear. Delta connection provides a closed pathfor the current harmonic, and suppresses the triple voltage.A case is cited where a Y-oonnected auto-transfornier was used

to step up from 6600 to 12,000 volts at a substation. The neu-tral was not grounded, and trouble resulted due to partial res-onance at triple frequency between line capacity and trans-former reactance. The paper shows that, although not generallyrecognized, a triple component can exist in the line-to-line e.m.f.wave of a three-phase system. This is possible in a case wherea two-to-three-phase transformation is used, and when the e.m.f.wave of the two-phase generatQr contains a triple harmonic.Vector diagrams and curves are given illustrating this possibleeffect.

IN CONSIDERING the relative advantages and disad-vantages of Y and delta connections of transformer

windings, it is necessary to pay some attention.to the productionof harmonic voltages and currents occurring in such windingsdue to hysteresis in the core. This has been treated by severalsince the present writer first drew attention to the effect,' butit may not be out of place in the present discussion to reviewbriefly the conditions under which such harmonics becomcnoticeable, and to point out a further possible case which, so faras the writer is aware, has escaped notice.

If we take the case of a transformer winding connected to ana-c. source of supply, we find that though the e.m.f. wave maybe sine-shaped, the current wave necessary to produce the sineflux wave contains harmonics, notably a third and a fifth, whichare produced by hysteresis and by the variation of permeabilityof the iron. These current harmonics may be regarded as in-

1. See the Electrician for 10th November 1905 and 5th January 1906.723

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1914] CLINKER: HARMONIC VOLTAGES 727

impressed upon the primary, and this is transformed to a three-phase e.m.f. at triple frequency, which appears between the linesas a superposed harmonic on the fundamental three-phase e.m.f.It is a curious fact that this effect cannot be obtained by directthree-phase generation, but, apparently, only by transformationfrom a two-phase supply. The accompanying diagrams willmake clear the difference between the two cases, viz., (1) Tripleharmonic due to three-phase generator, or Y connection of trans-formers. Harmonic appears only between line and neutral, andnot between lines. Figs. 1 to 7 show the vectors at progressivelyvarying phases, during one-third of a cycle.

(2) Triple harmonic impressed on system by two- to three-phase transformation. Harmonic appears both between lines,

A

B,

C

30 60 5"

B~~~~~~~~~~~~ "B~~~~~~~~~~~~~~~~~~~~~~~~~

"A7

I20 150 At150'~~~~~~~~8FIGS. 9-15-VECTOR DIAGRAMS SHOwINt TRIPLE HARMONIC TRANS-FORMED INTO THREE-PHASE SYSTEM FROM TWO-PHASE SYSTEM.

(SEE FIG. 8 FOR WAVE SHAPES.)

and between each line and neutral. Fig. 8 shows the three-phasewaves produced between lines, assuming particular values forthe amplitude and phase of the triple harmonic in the two-phasee.m.f. Curves I and II are the assumed two-phase waves,having exaggerated harmonics. A, B, and C are the resultingthree-phase line voltages. Note that these waves are dissimilar.

Figs. 9 to 15 give the vector diagrams corresponding to Fig. 8.The dotted line A, representing one of the three-phase linevoltages, also represents by its projections on vertical and hori-zontal the two-phase voltages I and II respectively.The writer is not aware of any previous reference to this

possible effect, and it would be interesting to hear if such hasbeen observed on any line employing two- to three-phase trans-formation.





Presented at the 32d A nnual Convention ofthe American Institute of Electrical Engineers,Deer Park, Md., June 29, 1915.


I-FORM FACTOR AND ITS SIGNIFICANCE

BY FREDERICK BEDELL

ASSISTED BY R. BOWN AND H. A. PIDGEON

ABSTRACT OF PAPERForm factor is significant in the study of transformer losses;

as is well known, hysteresis loss is small when the form factoris large, and vice versa. Every wave shape has a definite valueof form factor; but the converse is not true, for a particularvalue of form factor does not indicate a particular wave shape.A wave may contain a third harmonic equal to seventy five percent of the fundamental and still have the same form factor asa true sine wave. Form factor, therefore, has no general signifi-cance as an indicator of wave form or wave distortion.A general expression for form factor is derived in terms of

the relative amplitudes and phase positions of its harmoniccomponents; curves are drawn showing the variation of formfactor with the amplitude and phase of the third harmonic.

Various wave forms are shown, very unlike in appearance,having the same form factor.

FRORM factor,f, is the ratio of the r.m.s. value to the averagevalue of an alternating quantity for half a period. The

quantity to which form factor refers is usually an alternatingelectromotive force, in which case f = E . Eav. Each particularwave shape has a definite form factor and so to a certain extentform factor indicates the shape of a wave and its departure froma true sine wave. Thus, a sine wave has a form factor 1.1107;a flat wave has a lesser form factor and a peaked wave a greater.If the converse were true and a particular value of form factorindicated one particular wave shape, the form of a wave couldbe accurately defined in terms of form factor, but, as will be seenlater, this is far from being the case.

It is true that, for certain purposes, the value of form factor issignificant, as for example in the determination of transformerlosses. Hysteresis loss in a transformer depends upon the maxi-mum value of the magnetic flux. But, inasmuch as the flux4p is determined by the relation q z fedt, the maximum value

1135


! = !!!"

!!Siendo E el valor eficaz del voltaje y Eav el promedio de medio ciclo de la onda

∅!"# = ! ÷ ! ×!!Flujo magnético en el núcleo




! =!!! + !!! +⋯1! !"#!

!

!

Un ejemplo: ! = !!!"#!"#$ + !!!"#!"# 3! − !!+ !!!"#!"# 5! − !! +⋯!

! = !"!

1136 BEDELL: FORM FA CTOR [June 29

of the flux is proportional to the average value of e and hence tothe r.m.s. value divided by form factor; that is,

4nmax = (E * f) X constant'.If a transformer is operated at a specified r.m.s. voltage fromsupply circuits having different voltage wave shapes, the maxi-mum flux and hence the hysteresis loss will, accordingly, havedifferent values for different form factors, becoming greater asthe form factor becomes less, and vice versa. It is well known

138

1 .36

1.16 | 1/ ! / /2 / ' 0l.\° <<-N&---0 l00<-l5X i20

1.34X /- t --

_ ~~~~~~~~~~~~PHASEANGLE,9

FIG. 1

that a tranzsformer operates lesG efficiently7 on a flat xx ve than ona peaked wave^.

If the r.mn.s. voltage, E, is increased or decreased in directproportion to form factor, so that the av7erage voltage, E/f,remains constant, the hysteresis loss in the transformer remainsunchanged and this fact is made ulse of in the determination oftransformer losses on a sine-wave basis. For this purpose, thevalue of form factor can be ascertained by meas;uring the r.m.s.

1.18-Z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

X cross section of iron in square centimneters X number of turns embrac-.n i

1.12 t.




ALGO DE HISTORIA DEL CONCEPTO Un ejemplo:




1942 !" = !!"#_!"!#$!!"#_!"#$%&'#(%)_

!

Factor de curva

!" = !!!"#!!!!

!!"#_!"#$%&'#(%)!

Factor armónico

Factor de desviación: Se ob5ene gráficamente comparando la forma de onda bajo estudio contra una sinusoidal del mismo valor eficaz

Factor de cresta: Es la división del valor pico de la señal entre el valor eficaz




Factor diferencial y Factor integral

! =!"(!)!" !"#

!"!(!)!" !"#

! ! = !(!)!" !"#!!(!)!" !"#

!




Presented at the 34th A nnual Convention ofthe American Institute of Electrical Engineers,Atlantic City, N. J., June 28, 1918.


METHOD OF SYMMETRICAL CO-ORDINATES APPLIEDTO THE SOLUTION OF POLYPHASE NETWORKS

BY C. L. FORTESCUE

ABSTRACT OF PAPERIn the introduction a general discussion of unsymmetrical

systems of co-planar vectors leads to the conclusion that theymay be represented by symmetrical systems of the same numberof vectors, the number of symmetrical systems required to definethe given system being equal to its degrees of freedom. A fewtrigonometrical theorems which are to be used in the paper arecalled to mind. The paper is subdivided into three parts, anabstract of which follows. It is recommended that only thatpart of Part I up to formula (33) and the portion dealing withstar-delta transformations be read before proceeding with Part II.

Part I deals with the resolution of unsymmetrical groups ofnumbers into symmetrical groups. These numbers may repre-sent rotating vectors of systems of operators. A new operatortermed the sequence operator is introduced which simplifies themanipulation. Formulas are derived for three-phase circuits.Star-delta transformations for symmetrical co-ordinates are givenand expressions for power deduced. A short discussion of har-monics in three-phase systems is given.

Part II deals with the practical application of this method tosymmetrical rotating machines operating on unsymmetricalcircuits. General formulas are derived and such special cases,as the single-phase induction motor, synchronous motor-genera-tor, phase converters of various types, are discussed.

INTRODUCTIONIN THE latter part of 1913 the writer had occasion to investi-

gate mathematically the operation of induction motors underunbalanced conditions. The work was first carried out, havingparticularly in mind the determination of the operating char-acteristics of phase converters which may be considered as aparticular case of unbalanced motor operation, but the scopeof the subject broadened out very quickly and the writer under-took this paper in the belief that the subject would be of interestto many.The most striking thing about the results obtained was their

symmetry; the solution always reduced to the sum of two ormore symmetrical solutions. The writer was then led to in-quire if there were no general principles by which the solutionof unbalanced polyphase systems could be reduced to the solu-

1027

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1034 FORTESCUE: SYMMETRICAL CO-ORDINA TES [June28

E2 E3 . ... En respectively, are taken separately they add up to ex-

pressions of the form ' (1+a+a2 +... al-) which are alln

equal to zero since (1 +a+a2. . . a - 1) is equal to zero. In likemanner in the expression for E2 E3.. . E,n respectively, all the termsof the components involving each of the quantities E1 E2 E3.. . etc.excepting the terms involving that one of which the components

are to be determined add up to expressions of the form ErAl ~~~~~~~~~~~n

(1 + a + a2 + ....an-') all of which are equal to zero, the re-maining terms add up to E2 E3.... E,, respectively. It willnow be apparent that (4), is true whatever may be the natureof El E2 etc., and therefore it is true of all numbers, real complexor imaginary, whatever they may represent and thereforesimilar relations may be obtained for current vectors and theymay be extended to include not only vectors but also the oper-ators.

In order to simplify the expressions which become unwieldywhen applied to the general n-phase system, let us consider athree-phase system of vectors Ea Eb EC. Then we have thefollowing identities:

Ea_E + Esb+ Ec +E, + a Eb + a2 E,Ea ~3 +3Ea + a2 Eb + a E,+ 3

Ea +Eb + Ec Ea + aEb + a2Ec

Ea+a2Eb+ a (5)3 3

~E_ Ea+ ±Eo+ C + Ea + a Eb + a2 Ec3

Ea + a2]Ab + a E13

(4) states the law that a system of n vectors or quantitiesmay be resolved when n is prime into n different symmetricalgroups or systems, one of which consists of n equal vectors andthe remaining (n - 1) systems consist of n equi-spaced vectorswhich with the first mentioned groups of equal vectors forms

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Se formula por primera vez la teoría de componentes simétricas o transformada de Fortescue




Two Reaction Theory of Synchronous MachinesGeneralized Method of Analysis-Part I

BY R. H. PARK*Associate, A. I. E. E.

Synopsis.-Starting with the basic assumption of no saturation In addition, new and more accurate equivalent circuits areor hysteresis, and with distribution of armature phase m. m. f. developed for synchronous and asynchronous machines operatingeffectively sinusoidal as far as regards phenomena dependent upon in parallel, and the domain of validity of such circuits is established.rotor position, general formulas are developed for current, voltage, Throughout, the treatment has been generalized to include salientpower, and torque under steady and transient load conditions. poles and an arbitrary number of rotor circuits. The analy-Special detailed formulas are also developed which permit the sis is thus adapted to machines equipped with field pole collars,determination of current and torque on three-phase short circuit, or with amortisseur windings of any arbitrary construction.during starting, and when only small deviations from an average It is proposed to continue the analysis in a subsequent paper.operating angle are involved. * * * * *

T HIS paper presents a generalization and extension ia, ib, i, = per unit instantaneous phase currentsof the work of Blondel, Dreyfus, and Doherty eay eby e, = per unit instantaneous phase voltagesand Nickle, and establishes new and general *a, 'rb, V1 = per unit instantaneous phase linkages

methods of calculating current power and torque insalient and non-salient pole synchronous mac hines,under both transient and steady load conditions. d

Attention is restricted to symmetrical three-phaset P dtmachines with field structure symmetrical about Then there isthe axes of the field winding and interpolar space, ea=nthereribut salient poles and an arbitrary number of rotorl ea P 1a-rcircuits is considered. eb = P 4'b-r 'ib

Idealization is resorted to, to the extent that satura- e, = p Vlc - r i(1)tion and hysteresis in every magnetic circuit and eddy It has been shown previously' that

Axis of Phase a 21a Id COS 6- Iq sin 0X0~__ Xd +Xq [ ib___ 1

i

D \ \ - 3 ~~~~~~~~~~~~~~~[ia+ ib + icl - a-3 [3+b+c 2 J

Direction ofRotatiion Xf - Xq [ia cos 2 0+ ib Cos (2 6 - 120)

3

+ i, cos (2 6 + 120)]Quadrature Axis \1b Id cos (6- 120)- Iq sin (6- 120)

Axis of Phase b xis of Phase c ia + ib +ib 2Xd + xq ]i ic + ia_

FIG. 1 Xd- Xqd q[a COS (2 0 - 120) + ib COS (2 0 + 120)currents in the armature iron are neglected, and in 3the assumption that, as far as concerns effects depend- + i, cos 2 0] (2)ing on the position of the rotor, each armature winding I = Id cos (6 + 120)may be regarded as, in effect, sinusoidally distributed.3 ia + ib + icA. Fundamental Circuit Equations -Iq sin (6 + 120) -xo

Consider the ideal synchronous machine of Fig. 1,and let

Xd + X, - a+i

*General Engg. Dept., General Electric Company, Schenec- - 3 I C - 9 Jtady, N. Y.L

tSingle-phase machines may be regarded as three-phase xd - Xz o 26-- 2)±1 omachines with one phase open circuited. _ 3 [aCs( 2)+i O

tStator for a machine with stationary field structure.33For numbered references see Bibliography.Presented at the Winter Convention of the A. I. E. E., New York, + i.c os (2 6 - 120)]

N. Y., Jan. 28-Feb. i, 1929. where,716

29-33


1929

July 1929 PARK: SYNCHRONOUS MACHINES 717

Id = per-unit excitation in direct axis If there is one additional rotor circuit in the directI, = per-unit excitation in quadrature axis axis there is,Xd = direct synchronous reactance E-Ix, = quadraturesynchronousreactance I = I + XflId - (Xd -Xd) id To px0 = zero phase-sequence reactance

As shown in the Appendix, if normal linkages in -Ildthe field circuit are defined as those obtaining at no Fld = Xlld Ild + Xfld I -Xmi d id = Toload* there is in the case of no rotor circuits in thedirect axis in addition to the field, which gives,

4) = per-unit instantaneous field linkages [Xlld - Xfld] Told P + 1= I- (Xd - Xd') id G (p) A (p)

where,I = per-unit instantaneous field current To Told [Xlld (Xd - Xd') - Xfld Xmldl p2

2 + [(Xd X'd) Told + Xmld To] Pid = 3 Iia cos 0 + ib cos (O - 120) + i cos (f9 + 120)1 Xd (p) XXd A (p)

(3) where,On the other hand, if n additional rotor circuits A (p)=[XI1d-X.fXd21 To Told p2+[Xlld To+Told] P+I

exist in the direct axis there is, If there is more than one additional rotor circuit the4) = I + XfId Ild + Xf2d I2d operators G (p) and Xd (p) will be more complicated but

+ . . + Xfnd 'nd - (Xd - Xd') id may be found in the same way. The effects of externalwhere, field resistance may be found by changing the term I

Ild, I2d, etc., are the per-unit instantaneous cur- in the field voltage equation to R I. Open circuitedrents in circuits 1, 2, etc., of the direct axis, Xf1Id, Xf2d, field corresponds to R equal to infinity.

. etc., are per-unit mutual coefficients between the Similarly, there will befield and circuits 1, 2, etc., of the direct axis. Iq = [Xq - Xq (p)] iq (5)

Similar relations exist for the linkages in each of the where,additional rotor circuits except Xd - Xd' is to be replaced 2by a term xm. However, since all of these additional i, =- ia sin 0 +ib sin(6- 120) +i, sin(6+120) } (3a)circuits are closed, it follows that there is an operationalresult Xq (o) = Xq, X ( ) =q

Id = I + Ild + I2d + . + Ind So far, 10 equations have been established relating= G (p) E + H (P) id (4) the 15 quantities ea, eb, e,, ta, ib ,I a4'ay tby ,t'c lid, iqy

where E is the per-unit value of the instantaneous field Id, I, E, 0 in a general way. It follows that whenvoltage, and G (p) and H (p) are operators such that any five of the quantities are known the remaining 10

G (o) = 1 G (co) = 0 may be determined. Their determination is veryH (o) = 0 H (co) = Xd-Xd" much facilitated, however, by the introduction ofXd' = the subtransient reactance2 certain auxiliary quantities ed, e, eoy i'o 'Pd, aqV 4/0'

It will be convenient to write H (p) = Xd Xd (p) Thus letand to rewrite (4) in the form,1

to lia+ ib + ic) (3b)Id = G (p) E + [Xd-Xd (P)] id (4a) i 3{ia+tb±%}If there are no additional rotor circuits, there is, as 2shown in Appendix I, ed= {eacos 0 + ebcos (o- 120) + e,cos (6 + 120)1

'I = I - (Xd - Xd') idE = TopT +I 2

where To is the open circuit time constant of the field e - f{ea sin 6+eb sin(0-120)+e, sin(0+120)1 (6)in radians.

There is then, 11 eO = 3j { ea + e?b + e~}

- G (p) T= -H2

XdTop +Xd )/d=3 {'{a COS 6+PbcOs (6-120)±+Pcc9s(0+ 120)}

*Thjs definition is somewhat different from that given in 'Pq =- { 'P sin O+'Ib sin(--120) +'Pc sin(60+1l20) } (7)reference 2.


July 1929 PARK: SYNCHRONOUS MACHINES 717

Id = per-unit excitation in direct axis If there is one additional rotor circuit in the directI, = per-unit excitation in quadrature axis axis there is,Xd = direct synchronous reactance E-Ix, = quadraturesynchronousreactance I = I + XflId - (Xd -Xd) id To px0 = zero phase-sequence reactance

As shown in the Appendix, if normal linkages in -Ildthe field circuit are defined as those obtaining at no Fld = Xlld Ild + Xfld I -Xmi d id = Toload* there is in the case of no rotor circuits in thedirect axis in addition to the field, which gives,

4) = per-unit instantaneous field linkages [Xlld - Xfld] Told P + 1= I- (Xd - Xd') id G (p) A (p)

where,I = per-unit instantaneous field current To Told [Xlld (Xd - Xd') - Xfld Xmldl p2

2 + [(Xd X'd) Told + Xmld To] Pid = 3 Iia cos 0 + ib cos (O - 120) + i cos (f9 + 120)1 Xd (p) XXd A (p)

(3) where,On the other hand, if n additional rotor circuits A (p)=[XI1d-X.fXd21 To Told p2+[Xlld To+Told] P+I

exist in the direct axis there is, If there is more than one additional rotor circuit the4) = I + XfId Ild + Xf2d I2d operators G (p) and Xd (p) will be more complicated but

+ . . + Xfnd 'nd - (Xd - Xd') id may be found in the same way. The effects of externalwhere, field resistance may be found by changing the term I

Ild, I2d, etc., are the per-unit instantaneous cur- in the field voltage equation to R I. Open circuitedrents in circuits 1, 2, etc., of the direct axis, Xf1Id, Xf2d, field corresponds to R equal to infinity.

. etc., are per-unit mutual coefficients between the Similarly, there will befield and circuits 1, 2, etc., of the direct axis. Iq = [Xq - Xq (p)] iq (5)

Similar relations exist for the linkages in each of the where,additional rotor circuits except Xd - Xd' is to be replaced 2by a term xm. However, since all of these additional i, =- ia sin 0 +ib sin(6- 120) +i, sin(6+120) } (3a)circuits are closed, it follows that there is an operationalresult Xq (o) = Xq, X ( ) =q

Id = I + Ild + I2d + . + Ind So far, 10 equations have been established relating= G (p) E + H (P) id (4) the 15 quantities ea, eb, e,, ta, ib ,I a4'ay tby ,t'c lid, iqy

where E is the per-unit value of the instantaneous field Id, I, E, 0 in a general way. It follows that whenvoltage, and G (p) and H (p) are operators such that any five of the quantities are known the remaining 10

G (o) = 1 G (co) = 0 may be determined. Their determination is veryH (o) = 0 H (co) = Xd-Xd" much facilitated, however, by the introduction ofXd' = the subtransient reactance2 certain auxiliary quantities ed, e, eoy i'o 'Pd, aqV 4/0'

It will be convenient to write H (p) = Xd Xd (p) Thus letand to rewrite (4) in the form,1

to lia+ ib + ic) (3b)Id = G (p) E + [Xd-Xd (P)] id (4a) i 3{ia+tb±%}If there are no additional rotor circuits, there is, as 2shown in Appendix I, ed= {eacos 0 + ebcos (o- 120) + e,cos (6 + 120)1

'I = I - (Xd - Xd') idE = TopT +I 2

where To is the open circuit time constant of the field e - f{ea sin 6+eb sin(0-120)+e, sin(0+120)1 (6)in radians.

There is then, 11 eO = 3j { ea + e?b + e~}

- G (p) T= -H2

XdTop +Xd )/d=3 {'{a COS 6+PbcOs (6-120)±+Pcc9s(0+ 120)}

*Thjs definition is somewhat different from that given in 'Pq =- { 'P sin O+'Ib sin(--120) +'Pc sin(60+1l20) } (7)reference 2.





Algunas anécdotas interesantes

Applications of Harmonic Commutation forThyratron Inverters and Rectifiers

BY C. H. WILLIS*Member, A.I.E.E.

Synopsis.-The problem of commutation in thyratron rectifiers inverter to produce a sinusoidal voltage and current, and permits aand inverters is discussed and a method of using a harmonic iircuit rectifier to draw a sinusoidal currentfrom the a-c system.of reduced kva to force commutation is described. The inverter is shown to differ from a synchronous converter onlyBy the aid of harmonic commutation, inverters can be operated to in that the sum of the a-c and d-c armature reactions of the inverter

supply lagging loads and rectifiers can be phase controlled in the must always be zero. By providing two sets of tubes in the inverter,leading quadrant. A rectifier which is phase controlled 90 degrees one on the unity power factor axis and the other on the zero powerleading becomes equivalent to a synchronous condenser and may be factor axis, a crossed axis inverter is developed which will furnishused for power factor correction. a sinusoidal current and voltage for all conditions of load.A duplex type of circuit is described which enables a polyphase * * * * *

INTRODUCTION applications of this type of commutation to invertersCOMMUTATION has not been one of the prob- and rectifiers.

lems to be solved in the development of the* . 1 ~~~~~~~HARMONIC COMMUTATIONmercury arc rectifier. The unidirectional conduc-tivity of the arc, in combination with the variation of One method of applying harmonic commutation isthe phase voltages, provides an inherent and entirely illustrated in Fig. 1, which represents the positive com-satisfactory means of commutation for purposes of mutating transformer T of a six-phase inverter withsimple rectification. This process may be designated by the thyratron tubes A to F inclusive. At some instantthe term phase commutation. the continuous current is entering through tube A andWhen the rectifier is provided with thyratron grids, the commutating voltage may be assumed as shown by

and operated as an inverter for supplying alternating the arrow e,. If now thyratron B is fired, the voltage e,current, phase commutation as used for rectification, will transfer the continuous current from tube A tomay still be employed, provided the load supplied bythe inverter has a leading power factor. Phase commu-tation in an inverter is, however, not so satisfactory as + D.C. TOLTHIR HROICin the case of a rectifier because it lacks inherent sta- Iobility, and because commercial loads seldom if ever have Ta leading power factor. 00The problem of commutation as presented by the ec

inverter is quite similar to the familiar problem of com-mutation in continuous-current motors, because of the A Cfact that the thyratron grids are not able to interrupt T vthe current through the arc, but are only able to main-tain an open circuit once the current has been stopped.' w[ E w.Early in the history of the d-c motor the commutating << < < < <z IC - r Irpole was developed as an aid to commutation and these a- a- a- a- a- a-have proved indispensible in modern machines. ° ° ° ° -.°A method of commutating thyratron equipment has

been developed which is closely analogous to interpolecommutation in continuous current machines. Thismethod of commutating thyratron apparatus employs tube B. After tube B has been conducting for 60 elec-a harmonic of the fundamental a-c frequency and has trical degrees the commutating voltage e, will have re-therefore been called "harmonic commutation." versed because it has triple frequency, and e, will thenA description of harmonic commutation may be found serve to commutate the current from tube B to tube C.

in the December issue of the General Electric Review.2 Thus the harmonic voltage of the commutating trans-Since this method of commutating inverters and recti- former may be used to commutate each tube in suc-fiers has been described only recently, its general fea- cession.tures will be briefly summarized before giving certain The only condition necessary for satisfactory com-

mutation is that the commutating voltage e0 shall*Asseiae Pof.Ele.Eg., Prneo Unvriy exceed any difference in phase voltage between the1. For references see bibliography.Presented at the Winter Convention of the A.I.E.E., New York, tubes under commutation for an interval sufficient to

Nf. Y., January 23-27, 1933. permit the current to transfer and the tubes to deionize.701

33-18


1933 Applications of Harmonic Commutation forThyratron Inverters and Rectifiers

BY C. H. WILLIS*Member, A.I.E.E.

Synopsis.-The problem of commutation in thyratron rectifiers inverter to produce a sinusoidal voltage and current, and permits aand inverters is discussed and a method of using a harmonic iircuit rectifier to draw a sinusoidal currentfrom the a-c system.of reduced kva to force commutation is described. The inverter is shown to differ from a synchronous converter onlyBy the aid of harmonic commutation, inverters can be operated to in that the sum of the a-c and d-c armature reactions of the inverter

supply lagging loads and rectifiers can be phase controlled in the must always be zero. By providing two sets of tubes in the inverter,leading quadrant. A rectifier which is phase controlled 90 degrees one on the unity power factor axis and the other on the zero powerleading becomes equivalent to a synchronous condenser and may be factor axis, a crossed axis inverter is developed which will furnishused for power factor correction. a sinusoidal current and voltage for all conditions of load.A duplex type of circuit is described which enables a polyphase * * * * *

INTRODUCTION applications of this type of commutation to invertersCOMMUTATION has not been one of the prob- and rectifiers.

lems to be solved in the development of the* . 1 ~~~~~~~HARMONIC COMMUTATIONmercury arc rectifier. The unidirectional conduc-tivity of the arc, in combination with the variation of One method of applying harmonic commutation isthe phase voltages, provides an inherent and entirely illustrated in Fig. 1, which represents the positive com-satisfactory means of commutation for purposes of mutating transformer T of a six-phase inverter withsimple rectification. This process may be designated by the thyratron tubes A to F inclusive. At some instantthe term phase commutation. the continuous current is entering through tube A andWhen the rectifier is provided with thyratron grids, the commutating voltage may be assumed as shown by

and operated as an inverter for supplying alternating the arrow e,. If now thyratron B is fired, the voltage e,current, phase commutation as used for rectification, will transfer the continuous current from tube A tomay still be employed, provided the load supplied bythe inverter has a leading power factor. Phase commu-tation in an inverter is, however, not so satisfactory as + D.C. TOLTHIR HROICin the case of a rectifier because it lacks inherent sta- Iobility, and because commercial loads seldom if ever have Ta leading power factor. 00The problem of commutation as presented by the ec

inverter is quite similar to the familiar problem of com-mutation in continuous-current motors, because of the A Cfact that the thyratron grids are not able to interrupt T vthe current through the arc, but are only able to main-tain an open circuit once the current has been stopped.' w[ E w.Early in the history of the d-c motor the commutating << < < < <z IC - r Irpole was developed as an aid to commutation and these a- a- a- a- a- a-have proved indispensible in modern machines. ° ° ° ° -.°A method of commutating thyratron equipment has

been developed which is closely analogous to interpolecommutation in continuous current machines. Thismethod of commutating thyratron apparatus employs tube B. After tube B has been conducting for 60 elec-a harmonic of the fundamental a-c frequency and has trical degrees the commutating voltage e, will have re-therefore been called "harmonic commutation." versed because it has triple frequency, and e, will thenA description of harmonic commutation may be found serve to commutate the current from tube B to tube C.

in the December issue of the General Electric Review.2 Thus the harmonic voltage of the commutating trans-Since this method of commutating inverters and recti- former may be used to commutate each tube in suc-fiers has been described only recently, its general fea- cession.tures will be briefly summarized before giving certain The only condition necessary for satisfactory com-

mutation is that the commutating voltage e0 shall*Asseiae Pof.Ele.Eg., Prneo Unvriy exceed any difference in phase voltage between the1. For references see bibliography.Presented at the Winter Convention of the A.I.E.E., New York, tubes under commutation for an interval sufficient to

Nf. Y., January 23-27, 1933. permit the current to transfer and the tubes to deionize.701

33-18





Algunas anécdotas interesantes

ooo- Figure 14. (I1T)k In fact, it may be shown that the theo-factor for a six-phase retical method discussed in an earlier

_l - - l |l | rectifier plotted as a part of this paper for the grid-controlledfunction of IX/Eo for rectifier, may be applied to the inverter.

800 - _ [ several ratios of grid In order to do this it is merely necessaryv~ ^sc to define angles for the inverter which

can be used in the Fourier analysis as_ _ _ _ carried out for the rectifier. For both

c600 t the re,.ifier and the inverter the angle uu %Al _ _

: represents the angle of overlap. In theo . g:id-controlled rectifier a represents the

\400 L <°| l ew <l0angle of retardation, while in the inverterthe angle (u + a') represents the angle of

X__ ___ "[ " \- - |grid advance. The angle a' for the in-verter is in itself of significance since it is a

200_ L___ I I ' L 2 | A | tmeasure of the time available for de-200e- 4 ~ ~~-~_ ionizing. The notation using angles a'

l__ l__ | 1 --and u for the inverter is of particular ad-vantage in the study of the harmonic

o problem, since its adoption permits the0 0.05 0.10 0.15 0.20 0.25 use of the exact formulas derived for the

ixEo grid-controlled rectifier by the mere sub-

stitution of these values for a and umethod gives very satisfactory compari- figure 15 for the 12-phase rectifier are ob- respectively. The general curves ofsons with tests for a wide range of loads tained from harmonic currents for the 6- figures 4 to 15 inclusive may also be ap-and grid control ratios. The compari- phase rectifier plotted in figures 4 to 15 plied to the inverter by the substitutionsons in table II are better than those of inclusive, but with the 5th, 7th, 17th of the corresponding quantities for thetable III because in the former tabula- 19th, 29th, and 31st harmonics reduced inverter, being careful to use cosA, intion the tests were made on a system to 25 per cent of their 6-phase magni- place of cos a, the constant A, for thewhose supply-circuit reactance varied tudes. This factor of 25 per cent, as rectifier.linearly from 60 to 2,000 cycles, and in mentioned previously, is empirical butthis respect conformed more closely to is based on the recommendations of the Supply Circuits of Nonlinearone of the basic assumptions of the theo- EEI report on "Rectifier Wave Shape."7 Frequency-Reactanceretical method. It should be pointed out that these curves Characteristics

It will be noted that the harmonic dis- can be used only where the impedance oftortions for grid-controlled rectifiers may the supply circuit is linear with fre- The theoretical method, including thebe appreciably greater than those for quency. formulas and curves, has been derived onrectifiers without control grids. This the assumption that the supply-circuitratio for certain values of grid control Application of Theoretical reactances vary linearly with frequency.and load may be as great as four to one. Method to Inverters The question naturally arises as to how

this method should be modified in order toI T Product Curves The voltage and current wave forms apply it to circuits whose reactances at

in the inverter, as shown in figure 16, harmonic frequencies do not conform toIn detailed inductive co-ordination are closely related to those of the grid- this assumption. An empirical modifica-

studies it is generally necessary to con- controlled rectifier shown in figure 2. tion of the theoretical method of doingsider the influence of the individual har-monics. However, in preliminary esti-maties.iifeqently adequatesto - Table 11. Harmonic Currents for Grid-Controlled Rectifiersider only the I-T product; a quantity 3,125 Kw, 625 Volts, 5,000 Amperes; A-C Supply, 12,000 Volts, Three-Phaseequal to the a-c supply current multi-plied by its telephone influence factor.8 A-C Harmonic Current in AmperesAccordingly, figure 14 for the 6-phase Ide = 1,000 Idc = 2,500 Ide = 4,000 Ide = 4,000

Amperes Amperes Amperes Amperesrectifier and figure 15 for the 12-phase A = 0.96 A = 0.96 A = 0.96 A = 1rectifier have been prepared to show the a = 16.5° a = 16.50 a = 16.5° a = 0°I. T product factor, (I T)k, for given IX/Eo = 0.0106 IX/Eo = 0.0266 IX/Eo = 0.0425 IX/Eo = 0.0425

conditionsofoutput curret, commutat- Frequency Test Theoret. Test Theoret. Test Theoret. Test Theoret. Empirical

ing reactance, secondary voltage, and' . , ' ~~~~300. .4.5...5.94......13.7 .....14.8....23 ...23.4 ...20.8 .......22.3..16.6grid control ratios. The expression for 420.2.7.. 4.24.. 9. O 10.4 ...15.2 .. .16.4 .. 14.2 14.6.10.7the I.T product, considering trans- 66.24. .2.68.... 6.3 ...6.42.. 9.8 ...9.85.. 7.8 ..7.4. 5.46formerratio,isgivenbyequation 17. 1,020..1.4.1.70.... 3.35.. 3.91.. 4.6 .. 5.50.. 2.6 .. 3.05.2.57

(I.T)kI1,140.1.0... .1.51..... 3.15..... 3.40..... 4.6 ..... 4.52.... 1.9 ... 2.12. .2.14)IT = ,,7 1,380 . .1.0.. .1.25..... 2.55..... 2.75..... 3.4 ..... 3.37.... 1.05.... 1.23. .1.50R l1,500 ..91.14 ...2.30..... 2.42..... 3.0 ..... 2.77 .. 9 1.09 .1.291,740.8 9..1.90..... 1.90..... 2.1 ..... 1.96 .95..8..97

1,860 4 88...1.42..... 1.73..... 1.85..... 1.66..7 7. 85where factor (I. T)1 iS obtained from Root-mean-figures 14 and 15. The curves given in square. .40 . 100 . 160 . 142

866 Evans, Muller-Harmonics in Rectifier Circuits AJIEE TRANSACTIONS


Harmonics in the ,A-C Circuits .r Grid- hIarmonics on the d-c side of a rectifierarmonics in the %-t wircuits or ~Wri are commonly determined on the basis ofan "internal harmonic voltage" whose

Controlled Rectiriers adInverterstinfhopucre,agoov-ontroe ecti iersand nv resmagnitnde may be expressed as a func-tion of the output current, angle of over-lap, and amount of grid control. Theharmonic currents in the d-c load circuit

R. D. EVANS H. N. MULLER, JR. may then be computed from the harmonicvoltages and the d-c load circuit con-stants including the "internal induct-

Synopsis: This paper summarizes the re- put circuits. Several investigators have ance" of the rectifier. The internalsults of an investigation of the harmonic made contributions to the problem of de- harmonic voltages are estimated by acurrents and voltages in the a-c circuits of termining these harmonic voltages and theoretical method assuming an infinitelygrid-controlled rectifiers and inverters.The principal part of the paper presents the cuiTents under various conditions of recti- high inductance in the d-c load circuit.development of a theoretical method for fier operation. There are four distinct The formulas for the case of a rectifierpredetermining the magnitude of the har- steps in this development which are: without control grids have been givenmonics in terms of the d-c load current, the by several authors foi example, Princecommutating reactance, the rectifier trans- 1. D-c harmonics without grid control. bformer secondary voltage, and the amount 2. D-c harmonics with grid control. and Vogdes,l and Marti and Winograd.2of grid control. Harmonic voltages in the 3. A-c harmonics without grid control. Recently the corresponding case for grid-supply circuit may then be calculated from 4. A-c harmonics with grid control. controlled rectifiers has been analyzedthe harmonic currents and the supply- by Stebbins and Frick,3 who have ex-circuit reactances at the various harmonic These will be reviewed briefly in order to t tfrequencies. show the relation of the present investiga- toncve the praev tofreidcontrol

General curves are given to facilitate the tion to that of previous work. to cover the range of grid control.calculation of the harmonic currents for the Harmonics on the a-c side of rectifiersrange of conditions usually encountered. without control grids may be estimatedIn addition, curves are included for the A-C SUPPLY either by empirical or by theoreticaleasy determination of the product of thesupply-circuit current and its own telephone methods In tre empirical method de-influence factor, the I- T product, which veloped by Blye and Kent,4 the har-quantity is useful in inductive co-ordination monic currents are considered as beingstudies. Comparisons are given between caused by internal harmonic voltagesthe results of tests and the results of calcu- I

lations by the theoretical method presented acting on the harmonic impedances of thein this paper. These and other comparisons supply system and a fictitious resistanceshow very satisfactory checks so that the varying with the load. The theoreticalmethod may be considered to be established. method for rectifiers without controlThe case of the inverter is treated in a grids, presented by Brown and Smith,'

manner similar to that used for the grid- ,controlled rectifier. The general curves assumes (1) an inductive supply circuitfor the rectifier may also be applied to the through which commutation takes place,inverter by appropriate choice of the defin- LOAD and (2) a constant output current due toing angles. infinitely high inductance in the loadThe case of a-c circuits with nonlinear 0,, 1> o,

frequency-reactance characteristics is brieflyA M M AA M circuit. Using these assumptions, ana-

considered, and an empirical modification lytical expressions are derived foi theof the theoretical method is suggested. anode currents which have a "flat top"This modification may be applied to the wave form except during the commutat-case of a rectifier provided with a-c filtering _.equipment. The wave forms of current Figure 1. Schematic diagram of six-phase ing perod when the current is trans-and voltage in one such supply circuit were star grid-controlled rectifier ferred from the outgoing anode toobtained from oscillograms. A comparison the incoming anode in accordance withof these oscillograms shows the great im- the voltage available for circulating theprovement in wave form which may be ac- 6ce through the inductanc the

complishe by th diinffles 2 3 curtent through the Inductance of thecomplished by the addition of filters. ~ commutating circuit. The harmonic volt-

|// ,'it i| P I Xages in the supply system may then be

AWELL-KNOWN property of all E0 / y/ I E computed on the basis of the voltageA4 rectifier- and inverter-type appara- X drops due to the harmonic currents flow-

* , , * ....................... Z / X IX, \ \ ing through the various ciicuit elements,tus is that they produce harmonic dis- / i t t v c ,tortions in both the current and voltage considering the rectifier as the source of

these harmonic currents.wave shapes on both the SUpply and out-_________________________________u The fourth step is given in this paper

Paper number 39-38, recommended by the AIEE which presents a theoretical method forcommittees on communication and power trans- estimating harmonic currents and volt-mission and distribution, and presented at the AIEE i intheiwinter convention, New York, N. Y., January 23- 6 1 2 3 agesintesplcrutsogid27, 1939. Manuscript submitted October 4, 1938; T \ 1\ /controlled rectifiers. It may be viewedmade available for preprinting December 16, 1938. IDC as a of th hoeiaR. D. EVANS iS consulting transmission engineer generalizationtand H. N. MULLER, JR., is central-station engineer, E.. IwI method for rectifiers without controlWestinghouse Electric and Manufacturing f2om- Fiur 2.Vlaeadcretwv hps gispany, East Pittsburgh, Pa. gue2 Votgancretwvesps rd1. For all numbered references, see list at end of of a six-phase star grid-controlled rectifier The determination of harmonic cur-paper. under load rents and vroltages in the a-c and d-c

1939, VOL. 58 Evans, Muller-Harmonics in Rectifier Circuits 861


1939



ALGO DE HISTORIA DEL CONCEPTO ¿Cuando empieza a tomar mayor relevancia?

APAGÓN DE NUEVA YORK DE 1965



ALGO DE HISTORIA DEL CONCEPTO IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, VOL. PAS-87, NO. 5, MAY 1968

Static Inverter Standby AC Power for Generating

Station ControlsJACK D. FARBER, SENIOR MEMBER, IEEE, DAVID C. GRIFFITH, SENIOR MEMBER, IEEE, AND

ALTON B. PFLIEGER, SENIOR MEMBER, IEEE

Abstract-The reverse transfer static inverter and static ac bustransfer switch system, as applied to power generating stations, areintroduced. Equipment for which such protection is required andthe power quality necessary are discussed. The proper protectionmethods for branch circuit coordination with static systems is de-scribed, using a particular power plant as an example.

INTRODUCTIONTHE DEMAND for a continual increase of operating effi-

ciency in new and existing electric generating stations isresulting in an ever increasing use of electronic instrumentation,controls, data loggers, and process control computers. Thisequipment is often necessary not only for optimization but fordirect control as well as providing the "eyes" for the plant op-erating personnel. Since this equipment is completely dependentupon the integrity of its power supplies, it is evident that highlyreliable power must be provided for these loads.

Recognizing this need, further reinforced by the experiences inthe recent Northest blackout, a trend has developed in the powerindustry to provide static standby ac power systems to insurecontinuity of power to these critical loads. Because of the sensi-tivity of many of these loads (such as flame scanners and com-puters) to even momentary power disturbances as well as to arequirement for precise frequency and well regulated voltage,essentially no break static standby ac power systems are beingapplied in increasing numbers. This paper describes an applica-tion in a modern efficient power station where a unique staticstandby power system has been installed and operated for over ayear.

INVERTER SYSTEMS

The basic concept employed in this application is termed the"reverse transfer" system, which has four main componentsas shown in Fig. 1. Two of the components are a solid-statebattery charger and a lead acid storage battery which can serveas the station "control bus" battery as well. The other two partsof the system are a static inverter and a static automatic ac bustransfer switch.

This system has the combined major features of several othersystems which are as follows.

1) It provides regulated sinusoidal voltage and frequency tocritical loads during normal and emergency operations.

Paper 31 TP 67-15, recommended and approved by the PowerGeneration Committee of the IEEE Power Group for presentationat the IEEE Winter Power Meeting, New York, N. Y., January 29-February 3, 1967. Manuscript received October 31, 1966; madeavailable for printing August 15, 1967.

J. D. Farber is with Burns and McDonnell Engineering Company,Kansas City, Mo.D. C. Griffith is with TRW Inc., Cleveland, Ohio 44117.A. B. Pflieger is with Exide, a division of Electric Storage Battery

Company, Philadelphia, Pa.

2) It provides isolation for critical loads against transients onthe power line.

3) It provides an alternate source of power to critical loads inthe event of failure of the prime source without disturbance of theload.

NORMAL OPERATIONDuring normal operation, ac power from the station energizes

the battery charger which in turn maintains charge in the storagebattery as well as powering the static inverter. The inverter isconnected to the critical load through the static switch, and it issynchronized and in phase with an ac power line connected to thealternate pole of the static switch. The regulated battery chargermaintains a constant potential at the battery and inverter inputterminals regardless of normal power line variations. The inverterwith its built-in closed-loop voltage regulation therefore main-tains constant output voltage at all times and at any load withinits rating. Operation of the inverter itself is described else-where.t'1 In fact, transient disturbances on the ac power line dueto effects such as starting of large motors and remote lightningstrikes are isolated from the critical load by the filtering actionof the storage battery and the inverter filters.

If the battery is also used for "control bus" service, transientsmay occur due to actuation of dc loads on the bus in conjunctionwith line reactance. This effect is shielded from the inverter byits input filter.The load frequency is maintained in exact synchronism with

the ac line even during sudden load changes, an important factorfor many computer loads. By the addition of frequency relaysthe synchronizing circuit can be disconnected if the line frequencydeviates outside of tolerable limits. In this case the inverter willoperate from its own internal frequency reference and maintainthe load frequency within an acceptable band.

POWER FAILUREIf the normal ac power line should fail or drop below the op-

erating range of the battery charger at any time, the battery willmaintain power into the inverter during the outage withoutinterruption or disturbance. Fig. 2 is an oscillogram of a powerfailure for such a system. During this period, the battery voltagewill continue to drop due to discharge, requiring operation of the

ACPOWLR

C& JiCALAC LOAD

Fig. 1. Reverse transfer system.

1270




ALGO DE HISTORIA DEL CONCEPTO En los años 80’s se crea el

IEEE Working Group on Monitoring Electrical Quality

Outage Outage Outage

Minutes

Surge, impulse

Swell, Surge

Impulse



ALGO DE HISTORIA DEL CONCEPTO ¿Dónde estamos actualmente?

EQUIPOS ANALIZADORES DE LA CALIDAD DE LA ENERGÍA ELÉCTRICA



ALGO DE HISTORIA DEL CONCEPTO ¿Dónde estamos actualmente?

EXISTEN MÚLTIPLES SOLUCIONES CON DIFERENTES GRADOS DE

COMPLEJIDAD Y COSTO

REGULADORES

VARISTORES

FILTROS DE ARMÓNICAS

FILTROS ACTIVOS

RESTAURADORES DINÁMICOS DE VOLTAJE

STATCOMS Y DSTATCOMS

SISTEMAS DE ALIMENTACIÓN ININTERRUMPIBLES

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