WLI | | mt | i oar es ok OW THESIS ORC eae R.M.HEASLEY = R. D. WYCKOFF 1920 “7? a f.¢ Alternating Current ‘ave Form. -hesis- Submitted to the Faculty of the ingineering Department of luichigan e same time would increase the frequency of the pulsations, both of which would be desirable. In the design of & machine both the shape of the pole fece and the number of clots must be considered with respect to the harmonics that will be introduced in the voltage wave form. Besides this pulsating of the flux due to varistions of the reluctance of the magnetic circuit there is a to and fro motion of the flux under the pole due to the action of the teeth as they come under the pole tip. This to and fro motion will be at a frequency of 45 and hence will induce an LHi® of 4S-l and 4541 times the fundimantal frequency. The amplitude of thie harmonic will 4n most cases be euch that it will not Q@ppear i: the terminal voltage wave. In the photographs taken these higher harmonic ripples together with the ripples due to pulsation were found only on the gonverters and it is very likely that the D.C. comutation had a pronounced influene. The third condition that may effect the presence of harmonics in the terminal voltage of an alternator is the distribution of the conductors on the armature which are connected in series. A full pitch concentrated winding will have generated in it an iii" wave of the seme shape as the field dicetribution and will be cymetricel. A fractional pitch or "chorded winding" will have the effect of smoothing out the wave to conform more nearly to a sine fori and while it is possible that the wave will not be symetrical during both halves of the cycle the probilit. of t'!.is distortion is ver; remote. Further, if there are a number of condtictore per pole which are spread over ea number of elots ag i: a "distributed winding" the effect will be much the same but more pronounced, the greater the distribution the more nearly will the ult wave approach a cine form regardles:: of the flux distribution. It is possible by proper selection of distribution and pitch of windings to suppress certain undersireable harmonics so that they do noe appear in the terminal voltage of the machine. This may be shown in the following illustration; Assume that the flux distribution of a particular machine is such that an undesBireable third harmonic is gen- erated in the windings. It is desired to é@liminate this harmonic from the terminal voltage. In figure 3 are shown two poles of an alternator and a full pitch windingsrepresented by the conductors AA. Under the assumption that the flux distribution of these poles is such as to generate a third harmonic we may consider that this third is generated by auxiliary poles &s shown ,instead of a distorted flux in the main poles. A full pitch winding under such an arrangement will have generated in it a third harmonic superimposed on the fundimental. Now if we replace the full pitch winding with one spanning only 120 fundimental degrees or 2/3 pitch as shown ,A,A, no triple frequency can 1 appear at the terminals of the winding for as far as the third harmonic is concerned the conductors ere passing under like poles at the same instant and the eem.fs. generated in each are neutralized. This is of course only = rough illustration but it is acceptable because of its simplicity. It might be said then that a winding of 2/3 pitch and distributed over 60 degrees can have no third harmonic apyrearing at the terminals. At the same time the ninth, fiftecnth, and other odd mult- iples of the third are eliminatea. In the same manner a winding could be designec to eliminate other harmonics ineteéd of the third and its multiplee, Or, if not entirely eliminated may be reduced to such a low value as to have little or no effect in distorting the terminal e.m.f. Dietribution of the windings will have this effect and may even elininate some of the harmonics entirely. In @ distributed winding the e.m.fs. generated in the several coils are out of phesce by an ampunt depending upon the number of slots included in 180 electrical degrees on the armature. The resultant of these ceverél e.m.fs. will then be lees than would ie the case where the e.m.fs. are in phase. The greater the distribution the greater will be thés reduction. Furthermore, the reduction factor is not the same for the fundimentul as for the higher harmonics but will be far greater for the letter. This may be illustrated by con- sigering a winding which is distributed ofer 60 degrees. fhis Winding will be distributed over 180 third harmonic degrees with a consequent greater reduction factor. Thus it is evident that the wave form of an alternator may be so regulated by proper design as to be almost entirely free of undesirable harmonics, especially théase of the lower orders, Zo show the ap»lication of the principles outliged above we have photographs of the terminal e.m.fs. of all the generators in the laboratory. These are shownin the following pages together with « brief explanation of the cause of the distortions where they appear. Fort ilayne Alternator ‘Types TRB orm ML 25 KW, 120 Volts, 120 Amps, 1800 RPM. This is a four pole revolving-armature type with 48 slots making 4 slots per pole per phase. sn examination of the wave shows @ good sine form but with e pronounced £3 harmonic. The amplitudesof these "tooth ripples" are & about 15/6 of th: fundimental. The source of the ripples is easily found from the formula given on page 6. The machine has 48 slots end four poles hence Ss 48/4 or 12 slots per pole. ‘The tooth ripples due to pulsations of the field would then be £5-1 or & twenty- third harmonic. An examination of the poles showed a design which would give e maximum of pulsation. The pole-face could have becn mad. slightly wider or narrower and the amplitude of th: ripples would probably be reduced considerably. Further- more, the narrow air-gap employed is most favorable to the production of flux pulsations. If & wider air-gap could be used it would also help in eliminating the rip:les. --- General Ulectric 10 Kw khotary Converter. Do Volts -220 Aups= 45.5 1800 Heli. ac Volts -147 amps-43 Ghis machine is also a four pole inachine with a 48 slot armature making four slots per pole per phase. The photograph shows & Slightly peaked wave ferm containing a twenty-third harmonic of about 9% amplitude. These ripples again follow the formule f= 28-1, 5 being equal to 12 as in the previous case. The peaked wave is due to a fifth harmonic in the flux distribution. The phase-belt of a converter is necescurily a span of 120 degrees which for the third harmonic corresponds to 560 degreé@s. Hence any third harmonic will be neutralized and cén not appear in the terminsl e.m.f. as is also the case of any odd multiple of the third. But even if at were possible for the third harmonic to appear at the terminals of the windings it could not appear in the terminal voltage of the machine due to the delta connection which would cuuse the thi#d and any multiple of it to be short-circu'ted in the closec delta. “3 Western Jlectric Converter SRK. This machine wes built from a 7% hp motor and hence has no special name-plate data. The wave form is very similiar to that obtained from the G.b. machine except that the tovth rivples sre not as prominent and are of a higher order coming perhaps from the to and fro motion of the flux which would give a 47th oy ggth in a 48 slot machine with four poles ae explained on page 7. Sparking at the commutator also se. med to contribute to this acticn. (These double frequency harmonics were also found to @pnvear in the e.m.f. of the Goi. converter during later runs and with too great @ consistency to be chargeable to @ resonant condition in the ribbons of the oscillograph.) wien Vrom a 1$K./ monverter built as « thesis experiment by one of the students. Thig is a 31 slot m&chine ani plainly shows st @ 351 harmonic due undoubtedly to the to and fro motion of the flux. =f= Port wayne Aiternator 417088 Type TRB Form BS 50 KW. 2300 Volts, 12.5 Amps 1200 Rei. (Star connected ) This machine #s a six pole revolving-field type with 2 slote . Again we have 12 slots per pole and from the formula e5tl we obtain a pth harmonic which is that present in the photograph. afm No-load voltage from line to neutrel of the above alternator. This wave is slightly flat topped due undoubtedly to a third harmonic in the flux distribution. This distortion cannot apvear in the line voltege of the machine because of the star connection which e4liminates the third. a 14 This shove the voltage from line to neutral of the Same machine when under approximately full-load. The very pronounced third hermonic precent is due to armature reaction and will be found in the neutral voltage of any alternator under load. Yhe magnitude of this third will depend not only on the load but upon the power-fector, a lagring current producing much greater distortion than the same current at unity power-fuctor. Of course it is élso fundimentally dependent on the design of the machine. Special design to eliminate this harmonic is poscible eni forms &n exception to the above statement. The presence of this thirc harmonic at the neutral of an elternator forms a most interesting problem in the interconnection of the neutrals of machines when operat- ing in parallel. YVhis will be taken up briefly in the following pages. =§< this photograph is of interest merely to show how the "tooth ripples" are eliminated on the line when several alternators are operated in parallel. ‘Thie mugt of course be accompanjed by an equelizing current in the connecting lines. 15. Parellel Cperation of Three Phase Sererators, with Neutrale interconnected. The subject of neutral currents hes been discussed in considerable detail in the following wor: on transformers so &@ complete discussion will not be pleced here. It is generally understood that they ere of triple frecuency and are produced by those harmonics of e.m.f. which cérmnot exist in the lines of © three phase g:etem. je will take up the subject as related to the parallel operation of elternators. Consider e three phase star-connected generator in whose windings e.m.fs. are generated containing triple harmonics. The e.m.fs. in the coils differ by phase by 120 fundimental degrees, ti.e thitd harmonics differ by 5X 1<£0 or 360 derrees, the ninth harmonics by 9x1lZc0 or 1080 degrees, or, the trigle, ninth, fiftec.t?. and wil odd multiples of the third harmonic are in phage in all three coile. since the potential difference between the outer terminals of the two windings is equal to the potential difference between the the e.m.fs. generated in the coils- the triple harménics end its odd multiples will dis&éppear. Other harmonics will not be eliminated and will appear in the céme magnitudes &s in the coil voltage:. Thus in a 3 phase star _connecte: system no triple harmonic voltezge can exist between the lines. If this generator is con:ected to & balenced star- connected load currents will flow in the lines of Such wave- form and magnitud thet the potential dif erence betwecn the terminsls and neutral point (of the loud) will differ from the coil e.m.fs. of the generator only by conteining no triple 16 harmonics. “here cén te neo currents of these fre.uencies because they woulu be in phese in 611 three lines and hence could heve no return vath. It ig evident thet there will exist between the neutral of the generator cnd that of the load, a voltage meade up of the triple hernmonics generetec in the coils of the alternator. If theee points sere connected currente o- corresponding frequency will flow. whe current in thés interconiection will be three times the triple frequency in the lineg. If insteaa of e load another generator is connected to the first a difference of potentiel will exist Letween their neutrals equal to the vect.r difference between their coil emfs. with the neutrals interconnected & current »-ill flow Limited by the impeiences of the machines to trirle harmonics. These impedaiuces are in general muc!: cualler then the esynchro- nous impedinces. If the triple frequency e.m.fs. in the two machines are equal and in phese there cén be no neutral petential difference and hence no current in the neutral. This ideal condition can exist in general ouly when one or more of ti.c following cond- itions are obeerved; 1. equal instantaneous angular velocities, &e Similier weve forms, 5. suqual loads, 4. oxcitation corresponding to the loac, 5. Absence of all triple harmonics. 1) keciprocating machines whose angular velocities pulsates will produce curging betwecn the alternetors operated by them. It hac becn found by experience tc be wore tyaublesome in producing neutral currents than interchange between phases. liachinee thet will operate very estisfactorily without neutrel connections h:zve caused serious trouble when operatec with them. The obvious preventative for trouble of this kind is more unifori rotstion - the use of turbine crive. & ) ‘avhines frequently differ consicerably in wave formf ahey may be cimiliar ct no load but difver when loaded on account of armeture reactio n. attempts to operate eenerators thus differing have resultesx in emormous neutral cutfrents. The preventative in this cave is careful adjustmant of wave forms. 3) As stated above, generators m&é:; have the seme wave forms at no load or at equal loads yet the forms at any two different loads may be dissimilier. Lachines thue opprated at unequal icads wili show neutral voltage or currente. These load differencese are eatrily controlled except in the esse of Surging mentioned ubcve,efo no trouble should arise. at the instent of synchronizing however, the loxd difference is a maximum ani ceriout trouble mey ocezur. vifficulties o. ttle Kind has made the operation of eynel.ronizins impos: ible with several iechines o:: tie line. The obvious preventative is to close the neutral connection arter the loads sre edjuctec. In all the above c&ses th. interchange of triple harmonics may be reduced by using inpeduaces wt:ick are inserted in the neutral cormection. These impedances mey be object- ifonable on &cocunt of tieir size or the voltaze drop ix case of unbelénuced load. The neutral currents way be elicviinated by the connection of but & simgle generator to the neutral bus but this mathod has: its limitations. If more thin one genevator must be operated with neutral connection and if lmpedances are undesirable then the only remedy is to obtain machines generating no triple hermonic e.m.fs. It is unsafe to depend on satisfactory operaticn of alternators with interconnected neutrals unless triple harmonics are eliminated by proper design. uch mechines are practicable and ehould be specified whenever parall@ling of neutrals is required. Appendix. 1. Alternator Wave Form. The following oscillograms were obtained at the Ottowa Street station of Lansing Municipal Power Co. They are espacially interesting and valuable because they show what may be expected from large well designed turbo-generators. We had also hoped to study the current wave-forms in the various lines and tie-lines between neutrals of the machines. At the time the instruments were set up there was nothing of special interest to be obtained so we weve obliged to «bandon this idea. Unit #2 e -Name-plate Data.- Westinghouse Alternator Serial No. 702222 £500 K.de 4000 Volts, 361 Amps. 3 Phase,60 Uycle, 1200 H.P.ii. (Y-Connected. ) This machine had been in operation in the plant for a number of years but is of comparatively recent design. Phase Voltage of above Alternator. (lo load) This oscillogram shows a slight fifth harmonic which produces a flat-topped wave. It is undoubtedly due to a fifth harmonic in the field distribution. -39- Voltsge- Line to neutral. Westinghouse 2500Kv.A. (No load.) While the chording and distribution of the windings tend to reduce distortions produced by the non-sinusoidal flux distrib- ution there is still evidence of it in the terminal voltage as shown by the above photo. It would seem that since the wave isc peaked, that the the field must contain this same distortion. It is probably due to the rotor not beine slotted uniformly around the cir- cumference but having the iron left solid at the center of / each pole. 3 SPARE woton ula Jater é at: Sues Sas” par © C+ opens a5 We f heat ‘ ’ a eg WH Ore wi TS SA- Pas ao fa yt < = es . ji od eee --farge ii SQ OS ess ssh e J pene Dy OU MOY S tre Unit i73. -lName-plate Data- ee hole General slectric Alternator. Serial No. 889489. Type AvB-2-6250-8600 Form HT. 5600 R.P.ii. OOO K.W. P.F. 8 500 2300/4000 Volts. this machine was installed about 1917 and consequently represents < very recent design. =£0= Phase Voltage 5OOOK.i7. Gen. lect. App oer This shows a very good wave form with no visable harmonice. The tooth ripples are hardly discernable on the film and to all practical purposes, have been effectively eliminated. Voltage- Line to Neutral. (No load) 5000 K.i¥. Gen. Electric. As wes the case with the phase-voltage, this wave is free of harmonics and represents the results of good design. It would be very interesting to see the line-neutral volt- age under full load but this was impossible to obtain at the time. It is probable that very little if any third-harmonic would be precent . If this were the case one couhd be certain that several machines of this type could be operated in parallel and with neutrals interconnected without danger of excessive circulating currents. ~42= Phase-Voltage (Incoming Bus) This voltage wes taken from the buses that tie in with the machines at the Cedur St. station. At the time the oscillogpeph was taken there were three machines connected to the lines. These were a £500 KW and a 2000 K.i¥. machine at cedar Street station counected to a Delta-Delta step-up benk end transmission line to a step-down bank connected Delta-Star with the neutral grounded. (This secondary voltage is thereby made suiteble for connecting in with thc 4000 volt machines at the Ottowa street station.)A small water-power plant is stationec near this last bank of trensformers and e 7OORW. machine with grounded neutral wae connected here. Line to Neutral. (Incoming Bus.) Teken at the same time as No. 4£, we find the same wave shape as was obtained in the lxboratory for the delt: star connection,thet is, the wave is slightly flat-topped. whe Phase voltage (Incoming Bus) £000 K.W. achine operating alone at Cedar St. -45- Line to neutral voltage. (Incoming Bis.) 2000 K liechine operating alone et Cedar st. From « study of these curves it will te a. rerent thet they are not similiar and tht in parcllel operatior, circulatine current: are bound tc exist. This will be especislly true of the - neutral tie lines due to tre greater difference betwe nu the wave form of t-e neutrél voltzge in the different units and from the transformer bank. KEurthermore, when loaded,this difference in weve form wey be greatly increased beeause of the difference in Charucteristics betweent the alternators uni the trensformer, the latter huving the came through €11 ranges of loée while the neutral voltage of an elternator under lose will very cften contain a etrong third-harm nic due io armature reaction. At various times trouble has been experienced in t: is plant beséuse of the excessive circulating curre..t in the neutréel Wirée 19 Wave form in ‘lternating Ourrent Circuits. 7 Distortion of wave form will oceur whenever a Sine e.m.f. is impressed upon a circuit containing; 1) Pulsating inductance, 2) Pulsating Resistance, 5) Pulsating condensance. In many commercial circuits one or more of these conditions may be found with consequent distortion of either current or voltage waves. 1) Thus in any eircuit containing an iron-clad inductance the reactance varies while the current changes from its zero to its maximum values. Moreover the variation is not the same for the decreasing as for the increasing values of the current. 2) Likewise the resistance in the vapor of an arc lamp decreases with inorease of current and produces interesting distortions of the current or voltage waves. 3 ) Similarily under conditions where corona is produced at the crest of the voltage wave the condensance pulsates during the voltage cyclg. In a long high voltage transmission line this produces distortions in the charging current. It is evident that in the discussion of current wave Shapes we must divide them ihto two groups; a) Circuits with constant resistance, inductance and capacity. b) Circuits with pulsating resistance inductance and capacity. a) If the voltage applied to a circuit containing constant r, L and C is of sine form, the current will necessarily be of sine form of the same frequency but differing in magnitude and phase position. (Photo 9.) — J- But if a complex wave of e.m.f. be applied each harmonic will produce its own current independent of the fundimental or any other harmonic. However, the relative magnitude of the harmonics will not be the same as for the voltage wave for in each case the maximum current for each harmonic depends upon the impedance of the circuit to that harmonic. It is readily ween that the relative walues of r,L and C are of great import- ance in determining the current wave from a given impressed voltage wave. Thus & circuit containing resistance only will have a current which is in phase with the voltage wave and of the same form. In a circuit having both resistance and inductance the current wave differs from the impressed voltage. The higher the harmonic the less current flows for the same impressed voltage due to increase in reactance with increased frequency. For this reason the current hsrmonics are smaller than those in the voltage and the current wave more nearly approaches the Sine form. In a circuit having resistance and condensance the reverse is true because with an increase of frequency the impedance is lowered with a proportionate increase in current. Hence & complex voltage wave impressed upon such a circuit will give a current wave in which the relative values of the harmonics will be far greater than were found in the voltage wave. This is shown in photo 10 which is the impressed voltage and the line current of 6 transformer which has a small condens- er connected across the secondary. While this does not show @ sinusoidal current wave due to the presence of iron in the transformer it does show the amplifivation of the harmonics by the condense®. (Such would be the effect if this e.m.f. was applied t a long transmission line- the charging current would contain very pronounced hsrmonics.) If a circuit contains resistance, inductance and capacity, the wave form of the current with a given impressed voltage will be determined by the relative values of these quantities. Distorted current waves in circuits with pulsating inductance. The main sources of pulsation in inductive reactance in a cirouit are; 1) Variation of the reluctance around the armature conductors due to synchronous rotation. 2) Variation in permeability and the hysteresis with the flux density in iron-clad circuits. The pulsation of the generator field caused by the relative position of the armature slots as a primary source of voltage distortion is discussed in the previous work on alternators. It is evident that a similiar effect is produced by a synchronous motor or any other synchronous apparatus with slotted armature in the circuit. The harmonics introduced are obtained form the same formulae that are applied to generators. With a large air gap, large number of slots per pole, proper shaping and spacing of the armature slots and using fractional pitch wind- ings the distortions produced by pulsations in the synchronous reactance may be reduced to practically negligible values. The second factor producing pulsations of inductive reactance ig present in 811 iron-clad circuits. The value and nature of the distortion depending upon the hysteresis loop of the particular iron used. Consider an iron-clad circuit having an alternetizuge.mf. applied. The impressed voltage must at each instant be balanced by the induced or counter e.m.f. produced by the increasing or decreasing magnetic flux. Hence a magnetizing current will flow in the circuit just sufzicient to produce the flux required to balance the impressed voltage. With a given hysteresis loop and sine flux the magnetizing current corresponding to any point on the flux wave is found by drawing the horizontal line ac Fig.4, and taking the distance ab from the hysteresis curve. By laying off on ordinate dc the distance equal to ab one point on the current wave is found. The maximum of the current will come at the same time as the maximum of the flux wave but the current wave will not be of Sine form. It will consist principally of a third and & smaller fifth harmonic superimposed on the fundimental sine wave. In figure 5 are shown the impressed voltage, magnetizing current and flux in an iron-clad circuit. The equivalent sine wave of current is drawn to show that there is a power compon-= ent consumed by hysteresis. It is equal to the product of the current, voltage and cosine of the phase angle,(90°=), 24. Transformers. The single phase transformer is the simplest and most efficient of alternating -current apprratus. It consists of & magnetic circuit interlinked with two electric circuits,a primary and a secondary. At full load both the leakage flux and the power loss in the trangformer are small compared with the total flux and the power transmitted and in a preliminary discussion need not be considered. In an "ideal" transformer (one naving no losses) the veatae ratio is directly and the current ratio inversely proportional to the number of turns. The ratio between the number of turns on the primary and secondary may be any value and in commercial designs it varies within wide limits. The current and voltage relations in the primary and secofdary windings are clearly shown in the following oscill- ograms. -ll-e Here it is evident that the primery magnetizing current lags the impressed voltage by 90° as shown by the fact that the maximum of current occurs when the impressed voltage is pass- ing through the zero value. The distortion of the current wave due to the variation in permeability of the core, is also plainly shown. alee This shows the primary magnetizing current and the secondary e.m.f.4 comparison of 11 and 12 shows conclusively that the secondary e.m.f. is 180° out of phase with the primary impressed voltage. Voltage Wave at Alternator Terminals. -13- Voltage Wave at Secondary of Transformer. Photograph 14 shows the same voltage wave that is shown in 13 except that it has been through a transformer. It is merely to show that the secondary voltage is sn exact duplicate of the impressed voltage under ordinary conditions-when operated Single phase. 26 @1l5- Secondary e.m.f. of transformer and secondary amps. with a light load at unity power-factor. It is interesting to note the duplication of voltage harmonics in the current wave. Current Transformers. The above transformers are all of the constant potential type. In power measurement work transformers ere necessary to allow the measurement of heavy currents with small meter elements. It is common practice to use 5 amp. meter elements and depend upon current transformers to increase the range of the instrument. These transformers are usually built with ratios of 5/1, 10/1, 20/1, etc. The accuracy of the measurements is of course depend- ent upon the accuracy of the ratio. At full load this is less Subject to error than at lower loads. The cltief cause of error in ratio is the employment of an impedance in the secondary circuit higher than that for which the transformer was designed. For power measurements it is necessagy to know that not only the ratio of transformation is correct but that the phase relation of the pr&tmry and secondary currents are correct. In other words,the secondary current must be an exact image of the primary current. 27 aiGe To show this we have taken an oscillogrem showing the line voltage and the secondary amps. from a 5/1 current transformer. The load was about 20 amperes at unity power- factor. (Phato 16.) The current wave from the secondary of the transformer is not appreciably out of phase with the voltage and a comparison with the oscillogram 15 shows that it is an exact image of the line current. 28 Transformers in Three Phase Cirouits. The wave shape distortion in an iron-clad magnetic circuit has a very important bearing on transformer connections in three phase circuits. The e.m.f. and currents in a three phase system are dis- placed fwwm each other 120 degrees. Their third hermonics differ by 3x1Z0 or 360 degrees,or,are in phase with each other. That is, whatever third harmonic of e.m.f. or current may exist in @ three phase circuit must be inphase with each other in all three phases, or in other words, for the third harmonics the three phase system is single phase with no return circuit. 1) The sum of the three emfs. between the lines of a three phase system is zero. Since their third harmonics would be in phase and so add up, it follows; That the voltages cannot contain any third harmonic or overtones. (374, gth 15%h, 21°* eto.) 2) Since in a three wire three phase system the sum of the three currents is zero but the third harmonic current would be in phase and their sum therefore not zero, it follows; That the currents in the lines of a three wire three phase system or in other words the Y current cannot @mntain a third harmonic. Third harmonics however can exist in the Y voltage or the voltage between line and neutral of the system and since the third harmonics are in phase with each other, in this case @ potential difference of triple frequency exists between neutral of the system and all three phases as the other terminal, In other words, the whole system pulsates against the neatral &t triple frequency. 29 Third harmonics can also exist in currents between the lines or ,delta currents,since the two currents from one line to the other two lines are displaced 60 degrees from each other their third harmonics are in opposition and therefore neutralize. That is, the third harménic in the delta currents of a three phase system do not exist in the Y currents in the lines but exist only in the local closed éircuit or delta. Third harmonics can exist in the line currents in a four Wire three phase system or 2 system with grounded neutral. In this case the thirds of current return jointly over the fourth or neutral Wire, and even with balanced load on the three phases the neutral carries a current of triple frequencg. With a sine wave of impressed e.m.f. the current in an iron clad circuit such as the exciting current in a transformer, mst contain a strong third harmonic otherwise the e.m.f. cannot be a sine wave. Since in the lines of a three phase system the third harmonic cannot exist, interesting wave-shape distortions result in transformers when connected to a three phase system in such a manner that the third harmonic of exciting current is suppressed. For instance, connecting three reactors as the primary coils of three transformers- with secondaries open-circuited-= in atar or Y into a three phase system with a sine wave of e.m.f. impressed on the lines; normally the voltage across each trans- former should be a sine wave also and equal to Ey,n.//3- This however, would require that the current taken as exciting current 30 contain a third harmonic. £8 such & current cannot exist in a three phase ctreaht She wave of magnetism cannot be a sine wave b but must contain a third harmonic. The e.m.f. generated by this flux end therefore the transformer or Y voltage must contain a third harmonic an@ its overtones, and of an amplitude three times as great as that of the flux because of the triple frequency. With three transformers connected Y into a three phase system with open secondaries we have then, with a sine wave impressed on the lines, the conditions:- 1) The voltage at transformers or Y Yoltage cannot be a sine wave but must contain a third harmonic and its overtones, but can contain no others as the fifth, seventh etc. wouhd not eliminate by combining two Y voltages to the delta or line voltage and the latter was assumed to be a sine wave. 2) The exciting current in the transformers cannot contain any third harmonic or overtones but may contain all the others. 3) The magnetic flux is not & sine wave but contains a third harmonic and its overtones corresponding to those of the Y voltage but contains no other harmonics and is related to the exciting current by the hysteresis cycle. The practical importance of this is that by suppression of the third harmonic of exciting current in the three phase system the effective value of the véltage per transformer or between line and neutral, is inoreased by perhaps 10% while the maximum value inoreases to perhaps 50% higher than normal and the voltage wave is very peaked by @ pronounced third harmonic of about 40% of the effective value of the total wave. ol The very high peak of e.m.f. produced by this wave-shepe distortion is liable to be dangerous in high potential three phase systems by increasing the strain on the insulators between line and ground and leading also to resonance phen- omena with the third harmonic. Assuming now tyet—-@én such transformers connected primary in Y and the secondaries delta; The third harmonic of e.m.f. generated in the transformers secondaries are then in series in short-circuit and thus produce & local current in the closed secondary delta. This current is of triple frequency and hence supplies the third harmonic of excit- ing current which was suppressed in the primary. That is, by connecting the transformer secondaries in delta the wave-shape distortion disappears and the voltage and magnetism are again sine waves and the exciting current is that corresponding to a sine wave of magnetism except that it is divided between the primary and secondary; the third harmonic of exciting current does not exist in the primary but is produced by induction in the secondary. Obvaously in this case the magnetic flux and the voltage are not perfect sine waves but contain a slight third harmonic which produces the triple frequency exciting current. If the primary negtral of the transformers is connected to a fourth wire as in a four wire three phase system or a three phase system with grounded neutral, and this fourth wire leads back to the generator neutral or s neutral of a transformer in which 52 the triple frequency current can existe that is,in which the secondary is connected delta- the wave-shape distortion also disappears. It follows therefore, that in a three phase system attention must be paid to provide e pabh for the third harmonic of the t transformer exciting current either directly ob inductively, otherwise a serious distortion of the e.m.f. wave of the trans- former occurs. (Oscillograms were taken with different transformer connect- ions to show that the theory given above is true. These photograpgs will be shown as the garious methods of connecting are taken up. ) Three Phase Transformer Connections. Delta-Y, Connecting the primary in delta and the secondary Y becomes necessary in feeding four wire three phase systems. The Y connection of secondaries allows the bringing out of the neutral wire while the:.delta connection of the primaries maintains the voltage balance at unequal distribution of loads. The delta-Y connection of step-up transformers is frequently used in long distance transmission to allow grounding of the high potential neutral. ( Under certain conditions it is liable to induce excessive voltage by resonance with the line capacity.) Prim.-Delta, Sec.- Open. Primary line volts and amps. -17- Assuming a sine wave of cusffent, the current-voltage relations in a three phase star connected circuit would make the line current at unity power-factor lead the voltage by 30°. But since the magnetizing current of a transformer is nearly 90° lagging we Would expect to find the curreht in the above oscillogram leading the voltage wave by 30° - 90°. This would mean a lag of 60°. Apparently the lag is greater than this, but it must be remembere. that the theory assumes a sine wave and if we reduce the current wave in the above photo to equivalent sine wave it will be found to lag almost exactly 60°. a4 It is also apparent that the harmonic present is a prominent fifth which may be expected in the exciting current of « trans- former, but the third which is most prominent in single phase circuits is entirely absent in the three phase circuit. This is further support for ths theoretical explanation of the fact thet a third harmonic of current cannot exist in & three wire ‘three phase line. (See (2) Pp.28.) The suppressed third harmonic of current will flow, however, in the closed delta &8 explained on Pp.d1l, for it is immaterial whether the delta circuit be on the primary or secondary side. (See photo 20.) YSDelta. The Y-delta connection is, in general, not permissible Since it gives what has been called a floating neutral; the three primary Y voltages do noé remain even approximately constant at unbalanced loads on the secondary delta, but the primary voltage corresponding to the heavier loaded secondary and therefore also the corresponding secondary voltage collapses. Thereby, the common connection of the primary shifts towards One corner of the e.m.f. triangle or even outside of it. As a result the secondary triangle becomes very greatly distorted even at moderate unbalancing and the system loses all ability to maintain constant voltage at unequal distribution of the load and becomes inoperative. For instance, if only one phase of the secondary triangle is loaded, the other two unloaded, the primary current of the loaded phase must return over the other two transformers which at open secoydaries act as a very high reactances, thus limiting the current and consuming practically all the voltage, and the loaded primary, and thus its secondary, receives practically no voltage. Y-Delta is feasible only if the secondary losd is bélanhced or if primary neutral is connected with the generator neutral or the secondary neutral of a step up bank in which the primaries are connected delta,and the unbalanced current can return over the neutral. If with Y-Delta connection in addition to unbalanced load the secondary carries polyphase motors, the motors take different currents in the dif‘erent phases so that the total current in all three pheses is approximately the same. That is, the motors act as phase converters and so partly restore the balance of the system. Prim.-Y, Sec.-Open. (isolated neutral) Primary line volts and amps. -18- The fifth harmonic of magnetizing current 18 very pronounced just as in #17 and also the fact that no third can appear in the current in the lines is further substantiated. Prim.-¥, Sec.-Open. (isolated neutral) Line volts, Line-neutral volts. This shows the presence of a very pronounced third harmonic in the voltage across the transformer primaries. vv Due th this pexzked form the maximum velue of the e.n.f. im impressed on the transformers is considerably greater than would be expected from the given line voltage. Prim.-Y, Sec.-delte. (isolated neutral) Prim. line ee Current in clowped delta of sec. This photo clearly shows the triple frequency current that flows in the chosed delta when the third harmonic is suppressed in the primary. The variation in amplitude of the third harmonic wave is due to the slightly different operating cher- acteristics of the three transformers, working perhaps at slightly different flux densities. PrimeY, Sece Deltas. (isolated neutral) Prim. line volts, Prim. line to neutral volts. w21- By comparison with photo no. 19, the effect of th closed delta is apparent. The third harmonic component of magnetizing current being supplied by the triple frequency current in the da delta, the flux and hence the secondary voltage is no longer distorted, As explained on page 31 there is @ slight distortion from true sine form, for it is this distortion which produces the triple frequency current by induction. The oscillogram shows this as a slightly flat-topped wave on the secondary. Prim- Y, Sec= Delta. (isolated neutral) Prim.line curgent, Prim.line voltage. This wave shows & slight fifth in the line current but not @s pronounced as when the delta in the secondary is opened. Y -Y Connection. In this cease if the neutral is not fixed by connection with a fixed neutral either directly or by grounding it, the neutral is also"floating” and so abnormal voltages may be produced between the lines and neutral without appearing in the voltage between lines, and may lead to disruptive effects or to over- heating of the transformers. Hence it is not safe to use this connection without fixing the neutral. To show how interconnection of the neutral eliminates the undesirable harmonics, we have taken the following oscill- ograms. Due to the fact that all of the generators in the lab- oratory were without neutral connections, the neutral obtained to tie in with was from a Delta-Star bank of step-down transfore- mers. Prim- Y, Sec- Open (isolated neutral) Prim.line volts, Prim.line to neutral volts. This photo(no.23) shows the same distortion of the neutral voltage @s we would expect to obtain with isolated neutral and open secondaries. Prime Y, Sec- open. (interconnected neutral) Prim.line eee Current in neutral connection. A triple frequency current is found to exist in the neutral wire. This current is the triple frequency component of magnetizing current and we would expect no distortion of the inealen teal voltage with this connection in. This is shown in the next photo (no.25). Prim-Y, Sec- open. (Interconnected neutral) Prim-line volts, Prim-line to neutral wits. -25- Where in transformer connections in polyphase systems a neutral or com on connection exists, care must be taken to have this neutral a fixed voltage point irrespective of the variation of the load or its distribhtion, otherwise harmful phenomena may result from a "floating" or unstable neutral. 29% Open- Delta Connection. The operation of the open-delta or V-V connection on @ three phase system is slightly different from that of the three transformer method in that the third harmonic is not suppressed in the lines. This is due to the fact that only two transformers are used, one phase being transformed by two transformers: in series. Hence the third harmonic of exciting curreht may be supplied by two of the phase wires and the third wire will act as a returm, and because the third harmonics are in phase in all three phases there will be no distortion of the voltage in that phase which is transfor ed by the t-0 transformers in series or in either of the other two, elta. Prim-line volts, Prim- outside line amps. This shows plainly that the outside line ic carrying a third harmonic of exciting current exactly as in a singl phase transformer. pe elta. Prim-Line volts, Prim- common or middle line amps. -27e- Thé current in thie middle ,or common wire from the V is apparently a resultant of two waves showvm in 26, and shows that this wire acts as a return for the othrent in the other two lines. Titerconnected-star or Zig-Zag. This connection is especially useful in eonnect ion with & converter in deriving a neutral for operation Of 6: Ds. three wire cystem. shen the load is placed on the D.C. side even tho it is unbalanéed the current from the neutral through the transformer windings flow in opposite directions in each transformer and the magnetic effects on the core are neutralized and hence cause no saturation of the cores as iu the case of the plain Y comnecticn. Furthermore there is no third harmonic present in the voltage to neutral although it is present in the voltage across each coil or a single secondary coil placed on the core. This is because of the fact that the E.li.Fs. in the coils connected in series are 60 degrees out of phase, hence the third harmonics are 3 X 60 or 180 degrees out of phase and therefore neutralize and cannot eppear at the terminals. This relation is clearly chown in the accompanying figure. To show the «,plication of the interconnected-star to the three wire D.C. system we have taken the following oscillograms. Prim- Plain Y, Sec-open. brim- A.c.volts, Voltse-neutrel to D.C.line. -£6—- Showing the D.C. voltage pulsating at triple frewuency due to the triple harmonic e.m.f. at the neutral of s plain Y connection. Interconnected star or Zig-Zag. (secondery open) Prim-a.C.volts, Volts- héutral to D.C.line. 2Oo5m Showing almost entire absence of pulsation in the D.C. voltage. The slight pulsation is due to a slightly unbalénced Operation of the three transformers, probably because of the presence of slightly different emounts oi iron in the cores. Interconnected star. Prim-applied volts, Prim- line current. -3 Showing the absence of the third harmonic of magnetizing current as in all three-transformer connections an7 ‘eading to a belicf that there mist be @ distorted voltage across a primary coil. Interconnected star. Prim-applied volts, fFrim- volts across a cingle coil re showing the expected third harmonic in the voltage ccross One coil or across a4 single coil which would be used as a secondary. The resultant of two such waves 60 degrees out of phase would eliminate the third harmonic. This ig done in the interconnection. To further point out the importance of us&hg the inter- connected star transformers for derivine the D.C% neutral we have taken ths following oscillosrams; Prim=- ¥, Sec- open. Prim- A.C.volts, Current in D.C.circuit to neutral, This photo was taken to choy that the pulsations of the D.C. voltage is carried thru into the current wave with very slight if any decrease in aaplitude with increxuse of load. Prim-Y, Sec-open . Prim-A.C.volts, Prim-A.C.line amps,(loac on @.C. to neutral) -33- Showing the very pronounced cecond harmonic in the line current due to saturation of the core of the transformers by the direct current. This conditionis eleminated in the inter- connected transformers. In this connection it may be interesting to mantion the fact that practically the only source of even harmonics in commercial lines is due to saturation of the cores in a trans- former bank by direct current. Since it takes but a slight current to produce saturation it is possible when the transformers have a& grounded neutral in the vicinity of a grounded D.C. system and stray currents from this system flow thru the transformers and into the transmission lines. B40 Three-Two phase Transforimation. Balanced T or Scott Connection. This connection is in common use in changing from three to two phase or visa versa. It requires two transformers one of which carries « 50% tap and one an 87% tap on the three phase side. As was the case with the open-delte connection where only two transformers were used, this connection reduces the capacity of the units to 86.6 per cent of the combined K.V.A. capacit;. Because of the fact that exciting current is furnished by all three lines with a neutral point within the windings which is not "fixed", the third harmonic of exciting current is suppres:ed and an interesting distortion occurs in the voltage on the two phase side. One phase comes through without distortion but the other has a flat-topped e.m.f. wave. This may be explained by the accompanying figures. A,B,and C are the three terminals and N the neutral point within the windings. Because of the suppression of the third harmonic of exciting current, this neuttal will Suiwats with triple frequency just as in the case of the Y connection with isolated neutral and open secondary. The chifting of this neutr@l may be represented by the point n revolving ebout the emall circle as shown= or by the revolution of the points a, b, and c about their respestive centers with triple frequency. ‘Since all three points revolve Ste in synchronism the e.m.f. between the points a, b, and ¢@ remain the same but since the point d is fixed with respect to A_ the e.m.f. between a and ad will contain a triple harmonic, as will be obvious by carrying the figure through a complete revolution of the points about their centers . This distortion appears in the line voltage on the two phase side in the form ef a flat- topped wave, the other phase having a wave which is not distorted. This is clearly shown in the oscillogram shown below. (iNo.34.) Three -Two phase, scott Transformation. Secondary voltages on Two Phase side. aes It is obvious that a distortion must also occur when changing from two to three phase with this connection. It is possible to eliminate this distortion by bringing out the neutral and grounding it or by direct connection with generator neutral thus providing «& path for the third harmonic of exciting current and as in the case of the Y connection eliminating the flux distortion and hence the voltage distortion across the transformer. Spezial Uses of Trensrorm rs. Jtatic Frequency Converters. It is possible by maans of special design and ccnnecticn of transformers, to use them as frequency converters. By this means the freque:cy may be doublea with two transformers. The efféaciency of the set is low however, end for ordinary commerciul work is impractical. Cne valueble apvlication of the method is found in redio work where the production of hign frequency current of the order of ecV,000 to 560,0C0 cycles is necessary. ‘'o do this bi means cf arenerator glone ig very difficult bec&use of the excee ive speeds at whiern the generator must be rua. Lut by buildings «4 10,002 cyele mé&criine and ctep ine up the frecuency by wean: cr t treneformers, quite suetisfactory results sre obiasined. The principle of operation for aoublins ti« frequency is as follows; a get of trancformers as shown in the accompany ing fi,ure is uede and virect current is apslied to the vJindings so as to saturate the ccrece If an ulter.veatinge current is then apoliec t- the primary windings a very distortea e.n.f. weve will aspear ut the sesonasry teruingls. It wil be we vave containing @ very pronounced second harmonic. Low if the secondaries ere connect ec in geries and witn the fundijsentele 160 cevsrees out of phase they will neutralize. The cecond harmonics will be € K 180 or o60 decrees out of phese or in other words trey are in phase ena will ac@ up, aprearins at the term’nals as a double frequency GeMele The following oscillograms enslyse the operation ii sc clear MEernnere 60 cycle volts,=- e.m.f. at seéondary of transformer fl. ’ -35- This shows a very pronounced second harmonic. 60 cycle,volte,-e.m.f.at secondary of transformer ;2. Jah e 5 2) The same pronounced second harmonic as obtained in No. 3: -37- 60 cygle applied voltage and the double frequency obtained at the secondary terménals. Cbtained by combining Cscillogra:jus 55 and 36 with a phase displacement of 180 deprees. Triple Frequency Trensformation. in obtaining triple frequency by means of two transformers the principle is somewhat the same. Two special tran8formers are designed so that when their primary windings are connect: d in series and an alternating current applied, the flux density of one transformer is much greater than that of the other. The secondary e.m.f. wave of the trensformer working at high density will be flat-topped while that of the other will be peaked. Both of these waves contain & pronounced third harmonic and the hase relatioasof these harmonics are such that if the secondary windings of the two traneformers are connected in series with the fundimentals 160 degrees out of phase, the fundimental e.u.f. waves will neutralize while the third harmonics will carry through and appear as a triple frequency e.m.f. at the terminals. (Due to the special design of treneformers recuired, oscillogremse were not teken to illustrate this .ethod.) APPenLIS ke Characteristics of »oome Poljphase Trancformer Jonnectious. (General Llectric Jo.) Three phase transformer connections. 1. Delta-Delta Connection. Advantages; 1. any three similiar single-phese trausformers can be connected in delta at their rated voltage, whereas it would not always be poscible to connect them Y. Re The bank can operate in open-delta when one #f the unite is disabled,delivering 86.6 per cent of the rated X.V.a. capacity of the remeining units. Shell-type three-phase units must heve their disabled phase dis- connected from the others and short circuited. cCore-typge three- phace units must have their disabled phase disconnected enc open circuited, which however, is not slays practicable. 3. This connectioi is free from all third harmonic voltage trouble. The primary and secojudary deltas carry all the thira-harmonic magnetizing current which cannot appear on the lines. 4. For relatively low voltages and high currents the delta conn- ection gives a@ more economical design then the Y connection. Disadvantages s 1. The neutral cannot be derived. be Differences in the voltege ratios of the units cause a circulating current in both primary sani secondary windings lim- ited only by their impedance. Se Differences in the impedances cause unequal load division among the units. 4. Hor very high voltages the delta connection co:ts somewhat more than the Y connectiom, 5 II. Y-Y Connection. adventages; le. ‘The neutral can be brought opt for grounding. &. The differences in retio and imped- ance of the units do not c&éuse_any cir- culéting currents or appreciatle unecual load cistribution. 3. For relatively high voltages and small currents the Y-connect- ion is genertlly more sconomical than the dclta connecti.n. “v oy Th rT ' on ie . ” apg ait « - © 4. A chort cireuit iu or on one Vhese does not ciuse a pover 4 crort circuit;exncept & very lerse mpiuctisins current gue 10 the over excitatio. cP tt. reusiciuysy unite et 1.75 tines the rated v.ltage. bisasdvuntepes 1. the neutrel ig unsteble. ee The mashines cunncot be loaded cin. unless: the neutrél of the prinsery is cenerator. cle-phase Line to neutrgl connectec to thet of the 5. There is « thir¢ harmonic voltire from line te neutral (althe it doet not &p ear between lineé) Smountine to as mach es 50 per cent in Single-phase units @nu :heli type threce-phese wiits, anc cw Oo or 4 per cent in core type u::its. 4. If the neutral is ~rourdea this third harmonic vcltage imu; be aggravatec by the capecitance chérsings current cof tre lines, uni may a@lco cause telephone i:.terference. 5. the Y-Y ban c mnot operate temporarily with to units when cne uit ic diesbled. Ge a Short circuit ou cne unit reices the voltage or the other uiits to 1.7c tines normel value. ,ecormneniations pue to the thirc harucnic voltese troubles, the Y-Y connection of hivh-voltsce cinrle-phuse units or chell-type threc-phase units is aot te be recommended except under the follovins condit- fons in whieh « Loweimpedance path is offered to the flo of the third-harinionice excitetion current and thereby the third-haracnic voltage is fupcressed. Thus: 1. when the neutral of the primary Y is permaneatly connected to the neutral of the genorator. If this counectiou is opened for ‘ .. a reason the third-harmonic voltage reapsearc. &e If tre neutral of the secondar; Y of a sten-u benk is grounded and is aleo permanently ‘connected to a erounded Y-pri:nerzy, delte- secondary translormer. The third-harmconie excitins current then circul:.tes between the two banks. In this gage, however; a) Teleshotie interference should be tuken into couvideratiou. b) If the Y-deita transformer is disconnected fro: the lines or the grouié on ite neutral agisconvectec, or its delte opened, the third-heriuculie voltarse re&ppexers on the former with the acecupsuyiis dengers of reronance. 5. If the secondery Y ie permanentl, connected to & synchronous converter in diauetric fesnion.[T ce sec. xx1V,Y-diumetrie Conn.) 4. If the neutrél of one Y is permenently; coniected to the neutral Of a tie-zas uuto-trensformer (‘ireetly or thru eround) on the same linec. 5. If auxildary windings (tertiary wiudings) are proveded connected in delta. The Y-Y connection of core-typr three-phase uuits is always safe whether the neutral is grounded or isolated, so fer as the third-harmonic voltage stresses are concerned. However, when such a unit is grounded with & low@impedance return path such as mentioned ebove, the third-harmonic current in the neutral will be apprecieble and telephone interference may heed consideration. Ill. Y-dZig-cag Connection. Advantares: 1. The neutral of the zig-zag can be grounded without any third-harmonic voltage trouble. « third-harm:nic volt- age appears in ea:h coil but not from line to neutral on the zig-zeg side. - The mechine can be lraded with a cingle phase load froii line to neutral of the Zig-zac. _— Disadvantages. 1. The connection requires 15 perccent more copper for the zig-zag than for the ecuivalent Y. 2. The regulation and efficiency are liakly to be comewhat poorer than those of the equivulent delta-Y. Kecommendations: As a standard con..ection delta-Y is preferable to the Ye zig-zag connecticn. The latter, however, may be advigable in some exceptional cases as, for instance, when a change in system voltage is comtemplated and the transformers may be temporarily operated delta-zig-zag to be changed later on th the Y-zigzag. IV. Delta =-Y Connection. Generally considered to be the best three- phase connection. Advantages: - The neutral can be brought out both for grounding and for loacing. £e The neutral is stable, being locked by the delta. 3. The connection is practieally free from third-harmonic voltares. The delta circulates the necessary third-harmonic exciting current. 4. Difrterences of mugnetizing cuprent, voktage ratio, and impedénce in the different units are adjusted Ly a small megnetizing current circulating i. the delta. 5. A short circuit tm one leg of the Y does not effectnthe voltares on th: secondary lines. 6. A Single-phase chort circuit on the secondary lines sauss a smaller short-circuit strees on a delta-Y bank than on a delta- delta con-ected one. Disadventagess 1. The delta- Y bank cannot operate pemporarily with two units when one of the units is disebled. Se A short-circuit in one unit is extended to &11 three units. 3. If the delta on the primary side should accidently become Opened the unemzcited leg on the Y cide may resonate with the line capacitance and cause damare. V. Cpen=-Delta or V-V Connection. Advantages: This connectioi requires only two units and is, therefore, useful as an emergency connection. Distdvantages: da The internal power-factor being only 86.6 per cent (assuming unity power-factor load) it can deliver only 86.6 per cent o* the rated K.V.A. capacity of the units. Hence it is not very desirable for continuous operation. «- Load voltages become unbalanced under load, even with balenced three-phase load, the magnitude of the uhbalancing depending on the impedance of the units and the power-factor of the load. 5. Being electrostatically unbalenced, the Y-V connection is not recommended for very high voltage systeme. VI. T-7 Connection. Advaataces: 1. This connection is similisr to the V-V in that it requires only two units. &. The voltage across the teaser being only 86.6 per cent of that of the main, the core loss in this conrection is less than in the v-V connection, assuming similier or inter- Changeable unite. 3. ‘the neutrel point cen be derived and brought out for ground- ing, although not for loading unless the tvo halves of the main are interlaced. visedvantares;: 1. Both prinary end secondary sides reculre 50 fer cent teps Whier ere not reqiired by the V-V connection. ee afte correspoudinues helvesc of tl) riuery and ceecncdar, of tle maid muct te interlaced, althouct tt. twe halves of one tan tas need not be interleced with each other unless the heutrel is t brougnt out con thet side anc it is desirec to te cble to losd te neutral. oe olimilier to tle w-V connection, the ratio of output te U.V.a. zs is only 66.6 per cent end the revulation is: poor. Three-whase suto-Treneforuer CJonzectious. General Jnaracteristics. advangares: le For « given output, auto-trancfcrmere ure much cheaper t)en transformers. Yunis ecouomy is gmeater the nearer the high aud low line voltézves &prroach e&cl. other. Re auto-transformers gfhve better efficiency and remuletion then transformers. This adva.fage elso inereasces as the ratio of tre nigh end low tine voltares Gpproacies unit; Disadve:tarces: 1. The high and low-voltage windings being continuous the low- voltage circuit and connected apraratuc ure liablt to be eub- jected to abnormal voltuzes due to disturbsices and frounds ox the hish-voltege circuit. This ic particularily objecticna’le when there is « large difference of potential between thre high at + id the low sides, ee whort-circuit curreats at normal excitation of the unit ere larger with auto-trancformers than with transformer: and the more so tie nesrer the high aud low voltages sere alike. It is often luprecticeble to decien cutottransformere to withstand thc ther- mal gud machanical effects cf short circuits. since as the ratio of Llow-voitere line potenti:1l to high- voltare line poteitial decreases anu insuletioi ducers inereage, eautc-trensformers are usually couri@erec only when the lew volt- age is as much as 8U to SO per cent of th high veltere. a Low volteze not less than 50 percent of high voltase may be consider- ed & good engineering lisit for the use of auto-treneformer: under very favoreavle co:.ditions. Recommendations: auto-transformers may be recommendec. for isolated systems provided that th. low-voltage circuit and tue connected ap: aretus are desiened to etund the high-voltage test potenticl. They mey : appe Ce be recommended for grounded systeme provided that th: neutral of the auto-transformer is &lso grounded. VII. Y-Connection. advantages: - This is the most economical and there- fore the most common auto-transformer connection. The retio of rating to out- put is Ey-Ep/Ey , where ii, ie the high- voltege line potential andEs is the low- voltage line potential. 2. The neutral may be derived and ground- ed for the protection of the low-voltage circuit if the generator neutral is also grounded. Disadvantages: 1. Similiar to the Y-Y connectio.. of transformers (see Sect. Il) there is a third harmonic voltage from line to neutral. Single phase and shell type units are not recommended, espec- jally if the neutral is to be grounded. ucre-type units (three phase) may safely be used either grounded or ungrounded. &. The machin:s cannot be Loaded single-phase from line to neutral. This is especially true for single-phase units and for shell-type threc-phase units. Core-type three-phace units may give tolerably good results. The best results ere obteined by the zigzag connection. VIII. V or Open-Delte Connection. 1. This connection is frec from third- harmonic voltége, ££. The ratio of rating to output is 15 per cent more than in the Y-connection. This counection has characteristics similier to those of celta-delta connected transformer: 1. It is free from third-harmonic voltage. Le he ratio of reting to output is ” 6 m . (EY-ES) /1.732,49 3. For « given load, the ratio of the K.V.a. rating of this connection to that of the Y-connection is equal to:- (0.577%0.57%:,/s5 ) Thus, id the low-voltage line potential is 50 per cent of the high voltage, the delta connection requires 1.75 times the kvea. rating of the Y-connection. ApDpe Tes Therefore, when the Y-connection i: undesirable on account of third harmonic voltuge, the V or extended-delta connections figure out more economical than the delta connection. XxX. kExtended-Delta Connection. The ratio of rating to output is; & , 1.73E,/27, where u, is the voltage of the extended portion and 4, is the high-voltage line potential. Recommendation; when the low-voltage ig lesc than 92 per cent of the high voltege, the extended-delta connection requires a smaller rating than either the straight-delta or V connections. hen this ratio is greater than 92 per cent, the V-connecticn requires the least rating of the three. alg 4igzacz Connection. l. ‘This connection is used to derive a fourth wire for four-w ire three-phase distribution systems, cuck as £300/4000 ¥Y distrivution systems, when this wire ie not available at the generator or step-down transformer. e. i/ith balenced three-phase load, heither the neutral wier nor the coils carry any current. 3. An unbalenced load flows in the neutrel and is distributec equelly in all three phases. 4. The neutral may be grounded. 5. The neutral can also be used to derive the neutral of conv- erters for the return of the unbalance’ direct current in a three-wispe direct current distribution system. aA straight ¥ could not be used for this purpose (excepting three-phase core- type unite), it being necesgary to preve..t the saturaticn of the trancformer core by direct current. 6. with the neutral grounded, :: ground on one of the lines extends the short circuit to all three phases. ADP. “Bs SLi axtended sligzag Connectious. When it is desired to tréneform a given line voltege to some other value for four-wiwe distritution the extended uigzer may be used. fhe JIxtension shown in the figure is better tha n ae etraight extension for it distributeésthe neutral current ecually in all three phases and maintains better repuletion thereby. The etraeige::t extention ie easier to build but does not completely elimin:.te the third har- monic voltase from line to neutral and in addition hae a focrer repulation for uabalanced lcads. three-fhase Two-Phase Trensformer Connections. XIII. Belanced 7 or Scott Connecticn. advantages; 1. This connection requires only two single-phase units or one two-phese 1iit. ws. It ic edeptable to either three-wire or four-wire two- phase service. 3. soth two and three-phise voltages can be obtained on the primary using only four line vires if the 86.6 per cent tap of the teaser ie connected to the middle of the main. Lisadvanteges: 1. The two halves of the main winding on the three-phas: side must be interlaced. £. with interchangetble units, there must be provided one 50 per cent tep and one 86.6 per cent tep in each unit. 3. The three-phase side carries 15 per cent more current then thatcorresponding to the two-phase side, and, therefcre,requires 15 per cent more copper. 4. If the interlacing of the halves of the three-phase side of the main is efrected by using two coils iu multiple on the two- phase side, then the latter :lso carries 15 per cent more current and therefore requires 15 per cent more copper. 5. Combining the features of the above items 3 and 4, two Single-phase units in Scott connection can deliver only 86. = per cent of their combived single-phase rating. AIV. VYoodbridge Connection. Advantages: 1. This connection has an internal ) power-factor of 100 per cent and will OF rl ae 20 therefore, deliver two-phase three- * eee phase power equal to ite single-phase rating. 3 PHAs& Side. wiimern,! ©, The three-phase side can be cone nected delta or Y, making it ppssible to change the system voltege without discarding the traneformers. Disadventages: is This connection is not adaptable for three-wire two-phase service, end has, therefore, not become popular. Be Taps are impracticable except on the three-phase side. 3. The multiplicity of windings required generally more than offset th advantages in econmy of materiel and ior this reason is seldom used. 4. This connection requires three single-phase units or one three-phase unit. XV. Combined Two and Three-Phase. Of the connection shown in Fig. 15, the straight three-phase side may be Y or delta. On the other side, both two and three- phase power may be obteined from four wires. It is suitable when the three-phase load is predominant. The déménsions of the smaller delta are 15 per cent of those of the larger delta, and the windings whose voltages are parallel are wound on the same core leg. Oe iD4S 3 PHASE SiD ae Peery ae This connection is similiar to that of fig.15 except thet it requires five wires instead of Tour's a AT ee Ve eta kT eh fall A) App. 20. XVII. Taylor Connection. This connection is similiar to those of Fig.15 end 16, except that the two-phase threepphase side recuires six wires. Three-Phase Two-Phase Auto-Transformer Connections. scott Connected Auto-Trancformers. XVIII. Three-wire three-phase to four-wire two-phase. XIX. Three-wire three-phase to three-wire two-phase. This connection is the same ac that of Sec. XVIII, except that the ratio of voltages is 1 to l. The maftn earries only the teas- 3 £ er current which divides ecual- sae 7 ly in the two halves of the main. This connection is the came as that of Sec.XVIII except that the ratio of voltages is 100fer cent three-phase to 70,7 per cent two-phase. A eel Te ee oT eo nae Le) fe) dE a Fré.g/ APpe Ite This connection is the same as that of Sec. AIX, except that the ratio of voltages is 100 per cent three-phase to 86.6 per cent two-phase. The teaser then becomes unnec- essary and can be left out, the bank oper- ating with only one single-phase unit. One phase of the two-phase load takes the place of the teaser. Three-Phase to Six-Phase Connection. XXIV. Y-Diametric Connection. Advantages: 1. The delta connection of one side eliminates third-harmonic voltage troubles. 2. The diamatric connection of the six-phase side requires only three coils as against six require’ by the double delta connection and hence is more economical. Oe The diametr&é connection lends itself more conviently for starting-taps and switchgear. 4. The neutral of the diametric connection can be brought out to derive the neutral of the converter for three-wire d-c. ser- vice except in ine case of split-pole converters. Disadvantages: The bank cannot operate with two units when one breaks down. XXIV. Y-Diametric Connection. This connection has the advantages of the diametric secondary, and is free from third-harmonic voltage trouble when oper- ating converters, except eplit-pole con- verters. In the first case, the third harmonic excitation current circulates through.the diametric coils and converter in the latter cese, the third-harmonic voltage is made use of in regulating the voltege of the converter and is then a desirable feature. Recommendations: Delta-diametric and Y-diametric are the most common three- phase to six-phase connections. whether primary should be Y or delta is getormined by either the convéahence of design or the users preferences. Appe ste Sa a XXV. Delta~Double-Delta. Advantages: 1. The bank can temporarily operate with two units when one breaks down. &. The secordary side can be operated three-phase withput change of voltxge and will deliver one half rated load operat- ing only one of the deltas. If the dia- matric is connected in delte for three- phase service the voltage is increased 15 per cent but it will deliver full rated load. Disadvantages: 1. The multiplicity of coils in the secondary tends to make the cost somewhat higher than that of the diametric connection. 2. The double-delta secondary is illeddapted for starting taps or for deriving the neutral of converters for three-wire é@-c. service. XXVI. Y-Double-Delta. | This is a possible connection that is seldom used. It may have an advantage in design and cost if the three-phase voltage is very high and the cix-phase voltage very low. XXVIII. T=Double-7T Connection. This connection is not much used for three- phase to six-phase transformation on account of its low ratio of output to rating,which, similiar to the T-7T connection is only 86.6 per cent; and it is not well adapted for starting taps. Two-Phase to Six-Phase Connections. AXVIII. This connection is the one commonly used for two-phase to six-phase trans- formation. ee a eee cette. T621.2 H436 101174 Heasley — * : - = ee _ MICHIGAN STATE UNIVERSITY LIBRARIES iia