THESIS TE a Na Ly A, P. BOCK 19.20 THESIS er Te THESIS > : . l 1 ’ ros ° ' \ CG KI) \ ) 7 1 & 4 ed SF Ol AT, ; ' \ ( ¢ i l \ L~ cw ChE MOTHOD Or LUsINDAINING Tiles NLUTiAL —~ Of « DIhLOY CURpANT Gikna wilh OWSTEM SUPrPLIZD BY A KOTaAnY CONVENT AR A Thesis Submitted to The Faculty of liichigan Agricultural Collere By asP. Bock — candidate for the Degree of Bachelor of science June, 1920. TMESIS Contents Pare Tatroduction 1 Voltage nelations in hotary Converter O The Interconnected Star 7 Design of Transformers LO Results 17 94089 1. Introduction This thesis covers the design and construction and a study of the characteristics of interconnected star transformers to be used with a three phase inverted converter that ie to supply a three wire Edison system. The ordinary conditions under which.a converter supplies a three wire system ie with the converter feeding from the A.C. side. But in the electrical laboratory at ll.A.C., it was desiroe to have a continuous 110 volt D.C. voltage. Since £20 volts and an inverted converter were available, it was decided upon to design and construct interconnected star transformersfor maintaining a neutral that would be free from triple harmonic voltages, and that would allow the unbalanced D.c. through the transfppmer windings without magnetizing the cores. These transformers were not designed with the purpose of highest operating efficiency obtainable, but simply to get results with a reasonable amount of material and to make something for the Hlectrical ingineering vepartment to build up on in increasing the equipment. The core stampings used were previously cut, and while not the size to afford the highest economy in copper per turn for the capacity of the transformers constructed, they cerved their purpose very well. AS it was desirous to be able to get 110 or 220 volts A.C. from the converter, the design of the secondaries for those voltages is included in this thesia. Le Introduction Since this thesis covers the study of the interconnected etar for deriving a D.C. neutral, the secondaries for the transformers were not constructed. A brief discussion of rotary converters and the theory of voltage relations will be included as it is important to be familiar with them before dealing with the derivation of the D.C. neutral by interconnected csetar traneformers. The author is indebted to Profeesor hi.li. Cory for supervision and to Profeesor A.k. Sawyer for suggestions in the design of the traneformers. The author also wishes to acknowledge hie indebtedness to Mr, K.D. Wyckoff and Mr. Rolie Heasley in regards to the oscillograms furnished by them. Je Voltage telations in a xotary Converter The hotary Converter, used to change A.C. to D.c. or Dec. to A.C. combines the characteristics of both motor and generator in one armature winding. when used to change D.C. into A.C. it ie known as the inverted converter. This is the kind of converter dealt with in this thesis. Any synchronous converter can be operated inverted, the only difference being that the machine has the characteristics of a D.c. motor instead of the characteristics of a synchronous motor. The matter of voltage ratios between D.C. and a.C. and what affects them is one of importance in this thesis since it is required to get the specified A.C. voltages for parallel operation with other machines and to have the D.c. to neutral voltages balanced. First, the single phase converter, the value of the D.C. voltage is equal to the maximum value of the A.C. Chis is evident from the fact that the brushes in a D.C. machine are placed so that the D.C. voltage at all times is equal to the arithmetical sum of all the i.M.is of the armature coils that are in series. In th: case of an Aec, machine or the a.c. side of the converter, the a.C. voltage is equal to the arithmetical sum of the armature coil voltages in series at a time when both sides of the coils of each phase are directly under poles. This is the point of maximum voltage and is equal to the D.C. voltage. So for a single phage converter m Eag 7 E de or Egg = +70%Eao In @ quarter phase or two phase converter, the A.C. taps are taken out of the armature 90 electrical degrees apart while the D.C. brushes are 180 electrical degrees apart. The relation between the maximum A.C. voltage and the D.C. voltage in this case is the same as the ratio of the chord to the are of the circle ag shown in Fig. I. m = - Eac 0707 de or Eng = 0707 X.707 Sa. or .500 Eg, For 38 converter, the taps are taken out at 120 electrical degrees while the D.c. brushes are 180 degrees. m ~ o Eao 7 Sin 1/2:1£0° Ege or Eac - = Sin 60 X .707 Eqg or .612 Eag For a 6 ® converter, the taps are 60 degrees a. = Eae Sin 30 Eqe or Ego - Sin 30%.707 Eg, or .354 Egg For an n phase converter the formula would be “ac = sin a 707 Kaa The preceding ratios of bel. Ps apply only to generateé Leile®.S and under the assumption of a sine wave of A.C. If the a.0. voltage wave is peaked, the D.C. voltage will be higher, and if it is flat, the D.o. voltage will be lower. This fact is made use of in the split pole converter, a Awe ee f / | a ae ee”) y de i / Ae ey Tp 4a D.C. Vo/tage AC. Emax 29 Te F/6.£ VECTOR D/IHGRHM SHOWING VOLTAGE AELAT/ONS OF DC. TO ACMAXIMUM FOR 26,39.6¢ HND I2¢ CONVERTER 5. where the Aa.v0. Voltage wave can be made peaked or flat at will. (See "Llectrical Jngineering" by Uteinmetz) The variation of the ratio due to brush chift is important, especially in the smaller size machines. ijhen the D.c. brushes are in the neutral position, the voltare across the brushes ig equal to the maximum value of the aed. wave, but when not in the.neutral position, the voltere ic reduced accordingly, because they are not placed so that the coils have maximum voltage induced between the brushes. - ME ZK A E WITH BRUSHES OFF NEUTRAL when an inverteg@ converter operates singly, its Epeed may be seriously affected by a change in load or power factor on the Aa.c. side. The epeed change with change of power factor is so markea that ecafety devices are applied in some cases to prevent excessive speeds when a lagging power factor load is thrown on. In the cease of a lagging power factor load, the current component that is 9O degrees behind the voltage furnishesa m.m.f that opposes the field flux and reduces the number of lines of force cut by the inductors. This in turn reduces the 0..1.1..%. of the machine causing the speed to increase until the C.i.li.2. Is up to normal value again. In a converter feeding a threc wire system, the neutral can be derived by connection to the transformer neutral. for instance the neutral of a three phase star transformer connection can be used for the D.°. neutral with a three phace converter. The maximum voltage ("E) of the A.c. from any line to neutral is equal to one half the voliage across the D.C. brushes, or is half way between the D.C. voltage across the brushes. In the case of the converter Rw», the voltage across slip rings is 155. The voltage from any line to neutral is 135/43 or 78 volts. The maximum value of this voltage ("s) is 78/.707 or 110 volts, which is the D.C. voltage from either brush to the neutral of the star. Inverted converters are not af common ae synchronous converters, but are used to supply a small amount of A.C. from a D.c. supply. Converter Rp. is to be used for obtain- ing 110 volts D.c. from the £20 volt mains by the use of interconnected star transformers. The Interconnedted Star In a simple star connection, the voltage to neutral is distorted by a strong third harmonic. The reason for this is that since no third haswoniog can exist in the magnetizing currentof star connected transformers, the hysteresis of the iron distorts the flux and hence any HelieF. produced by the flux will have the same distortion as the flux. So the neutral of a simple etar is not a true neutral, but has a triple harmonic i.1!.F impressed upon it. when such a neutral is used for the neutral of a three wire system on D.C., these triple harmonic voltages at the neutral add themselves to the D.C. voltage to neutral and the resulting D.C. voltage will pulsate at a frequency of three times the frequency of the A.C. This ic very marked as shown by the accom- panying oscillogram which represents the D.C. voltage to neutral using a simple star for the neutral. 8. By interconnecting the star windings go that two of the phases pass through each transformer, the voltage to neutral (A.C.) will be equal to the vector sum of the voltages across the coils or half primaries, which are (180+ 120) or 60 degrees out of phase with each other. The 180 degree shift is due to the connection of the two coils on each transformer in opposite directions as shown by Fig.II. The sign of 120 desrees depends upon the eequence of phases. The coils being 60 derrees out of phage with each other would indicate that 6 ® could be obtained. Thic is true and verifies the above reasoning. rig. III shows the instantaneous voltages in each coil, and the triple harmonic voltages which exist in each coil voltage. It can be readily seen from the fifure that the two fundementals will add up to a greater velue- 5 times one coil voltage- while the sum of the triple harmonic voltages is zero at all points. According to this, the D.C. voltage to neutral will be constant, using the interconnection, because the triple harmonic voltages are neutralized. Another very important reason for using the intercon- nected star with a converter supplying a three wire system iz the prevention of the saturation of the transformer co:es by the neutralization of the m.n.f.¢ set up b, the unbalanced =... which flows to the neutral. 4 tee | Re 7B 04-1 -d ea CM Le OE) ed ded YINYOLSNHYL INO SO AMHWIYd Ni SNOILYHTFIY APHLTOA iia) Pi | | Tos WILSAS FHIM ECE ol Pp Wa gen oe ek] oker ek At ee £2 OL Od A AL ked , TAYLNIN FA Cae a a _S SST —_> Ay yi ; 3 fe a 8) The effect of core caturation of the transformers is to increase the flux density of the transformer cores ¢€o0 that the mepnetizines a.o. will increase enough to materially reduce the power factor of the AeCe Circuit. The magnetizing or 90 depreec lag current becomes preat mnough in the armature of the converter to decrease the field flux and cuuse the speed of the converter to rise. £0 if a sudden ).c. load were thrown on the neutral, the converter would tend to race. 2y dividing each primary in two parts and con- necting then so that two on the came transformer oppose each other as shown in Fig. II, the m.m.f.'s set up by the D.o. are neutralized and the flux density in the trencsformer cores remains the came, regardless of the D.C. load to neutral. 10. Design of Transformers Symbols Used in Formulae Flux Density in lines per sq. inch. (max. value) Cross cectional area of Core frquency in cycles per second lumber of turns on primary (iuffective) lumber of turns on secondary (Actual) Number of turns on secondary Primary voltage for each transformer Secondary voltage (110) Resistance of primary in ohms Resistance of secondary in ohms (110) Primary current in amperes Secondary current in amperes Mean length of turn of primary ifean length of turn of secondary cemperature rise in Degrees Centiprade Coefficient of radiation (Average 180) surface of one coil unit in square inches ll. Design of Transformers 5 - 1.5 K.V.A. Transformers,primaries interconnected Star. Srequency 50 cycles per second. Punchings form a hollow rectangle whose area is 41.8 sq.in. ( See Blueprint of aseembly) Assumed i'fficiency 90%» Iron losveS----<--------= 75watts Copper logsses----- -- --- 75watts Total 150 watts Plux density used------ 60 OOO lines per eq. in. Loss per lb. of iron at 50 cycles for transformer iron 1.4 vatts . 85 = 204 cu. in. of iron 75 = 53 lbs. or 26 Le4 Lamination factor used----- 85 £04 = 41.8 X.85 5.7 inches high for the iron. Use 5.5 indhes. A = 5.5X1.75X.65 = 8.2 sq. in. Solving for effective number of turns in primary ABN) 27 f —o. VT 10~x V2 8 Z It ie interesting to note how this formula for counter L.lie®. corresponds to the formula for the voltage of a DeCQe machine E= BaxNyp , § corresponds to AB, p' 168 x p' corresponds to Ny, , and I! correspondsto wor 27 f. vesign of Transformers In the counter it.li.%. formula for trensformers it is necessary to divide by the J2 since B represents the maximum value of the flux density. The formula can be put into the form £xNp* AB = P Ey Ty: « 4,44 Since the transformers are star connected, the voltage across one primary will be equal to ae = 78 volts. This is the same as the voltage to neutral. The slip rime voltarse of the converter is 155. 78 2 50”Np* 8 -£*60000*%4 44 108 - 78000 = N ~ e Pp 5X8 -BxX6X 4,44 71 Effective Turns Actual number of turns required for the interconnected star 2 « 75" x - 82. (see Fig. VI) For convenience in winding use 80 turns and solve for the new value of flux density. The new value of flux density will then be E. x108 78 x.10° =61500 B- PU - 4,44 X 50 * 69.5 X 862 4244 x TxN, xa Fe OL Le) 40 TURNS 9 e's ie INTERCONNECTED STHA PRIMARY STHR SECONDARY Pai VA) a 120° | PETORh 135 AES cw a VECTOR DIAGRAM OF INTERCONNECTED STAR VOLTAGES F/iICV VECTOR DIAGRAM SHOW/NG VOLTAGE 70 NEUTRAL ON FF THREE PHASE CONVERTER DR, ae "A AGE Pry 34 13. Design of Transformers Since the effective turns produce the flux, the secondary voltage is proportional to the ratio of secondary turns to effective primary turns and not the actual number that is put on the primary. The new value for effective turns when 80 uctual are used is 80 x 3 - 69.5 . Shy 5 if N. 7 ee xy = 110 x 69.5 = 57 Turns for 110 volts 8 Ep Pp 135 2X57 = 114 total turns for 220 vplts Current Densities Current in the primary is equal to the line current for the star connection. Primary power input Output+ losees Primary pover input = [2500X3) + 450 = 4950 watts. .~ 4950 = | I, = 135s 21.15 amperes. 1. 4500 - | 8 110x73 ~ £506 anperes. Use a current density of about 1500 amperes per sq.in. 21.15 = .0141 sq.in. Use 2 No. 10's = .01631sq.in. 1500 £1.15 one | Current density will then be ~ 01651 1295 avip.e per sqein. 14. vesioen of Transformers. Current in Secondary £526 amperes. £3.6 = 1500 eO1572 sq. in. Use £ no. 10's eO1l631 sq.in. c5e6 | Current density will then be (01631 1450 amp. /sqein. Khesistances of rrimary and Secondary p 18 inches or 1.5 ft. ( ze inches or 1.83 ft. }~ a see Fig. VII) _ #8 ___ 80 ¥ 1,5 X 558 Rp = 1000 .067 Uhms. 57X 1.83 X.556 R, = 1000 = 0583 Chms. 0558 = hesistance per 1000 ft. of 2 No. 10's. Copper Losses Primary = ESx Rk, * 21.152 x .067 = 30 watts. p Secondary= I2xR, = £3.6° X .0583= 32.5 watts. Total Copper lossses 62.5 watts. Iron losses Loss per 1b. at 50 cycles when B = 61500 1.42 watts. 53.5X1.42 = 76 watts. Total losses at 1.5 k.V.aA. 156.5 watts, DRAWING OF WINDINGS SHOWING /CTUAL MERN LENGTH OF TURN ae © PRIMARY SECONDARY ae . N accencaine Aina a Son a oes) a 15. Design of Vrensformers Temperature nice calculations The temperature rice was figured se one coil consisting of one primary unit aud one secondary uuit slipped Over it. Vhe currents in the two are neurly the same so the average of the two was used. £1e15 + £3.6 ow £2.37. 2 Average current = 2 " « x 2 R R= Kp + Ke = .045 Ohms. S 4 2 . £2.37" X .645 _ tT = 180X = 6525 ~ 47 Degrees Cent. Each unit consists of 1/4 of the primary and 1/2 of the 110 volt cecondary. 16. Data on Transformers Primary-- 4 coils of 20 turns each of &€ No. 10 BES gage Deceve wires. in parallel. ap --- 80 Ny--- 69.5 effective turns osecondaryee 2 coils of 29 turns each of 2 No. 10 B.S gare D.O.c.e wires in parallel. £ coils of £8 turns exch of single Ry --- eO67 Chms. Rycc-- ©0583 Chms. 1,--- 1.5 ft. ls--- 1289 ft. Lbe. of copper recuired for primaries (3 traneformers) £3 Lbs. of copser required for secondaries " " 31 54 Size of form for winding secondary vross section---- Zz 7/8 ine x 7 ine 17. nesults The transformers were connected to the slip rings of the converter Ko as chown in Pig. II and D.c. at 20 vOlis wes fed in ot the brushes. Jpon measuring the voltage across the slip rings, it was found to be 1