THE UNIVERSITY OF ILLINOIS LIBRARY Digitized by the Internet Archive in 2013 http://archive.org/details/startingcurrentsOOyens STARTING CURRENTS OF TRANSFORMERS BY * TRYGVE D YENSEN M. S. University of Illinois, 1912 THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of ELECTRICAL ENGINEER IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS 1913 UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL 190 ') 1 HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY ENTITLED Z/ 7 BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE OF rT^Gfrar^e of Major Work ^fe-y — ^ R|*k3 of Department Recommendation concurred in: Committee on Final Examination 247478 UIUC university of illinois Engineering Experiment Station Bulletin No. 55 February. 1912 STARTING CURRENTS OF TRANSFORMERS WITH SPECIAL REFERENCE TO TRANSFORMERS WITH SILICON STEEL CORES By Trygve D Yensen, Assistant, Electrical Engineering Department, Engineering Experiment Station CONTENTS I. Introduction PAGE 1. Preliminary 3 2. Acknowledgments 3 3. Theory 3 4. Method of Investigation 7 II. (a) Actual Measurements of Phenomena by Means of Oscillograms =5. Connections 8 6. Transformers 8 7. Residual Magnetism 9 8. Oscillograms 10 II. (b) Theoretical Calculations from Transformer Data 9. Magnetization Curves and Hysteresis Loop 12 10. Calculations 15 11. Agreement between Oscillograms and Calculations 23 III. Calculations of Maximum Starting Current for Various Types 23 IV. Effect of Resistance and Inductance in Series with Transformer Primary 34 V. Summary and Conclusions 38 Appendix 41 STARTING CURRENTS OF TRANSFORMERS WITH SPECIAL REFERENCE TO TRANSFORMERS WITH SILICON STEEL CORES I. Introduction 1. Preliminary. — It is generally known that, in closing the primary circuit of a transformer, a transient effect may take place in the form of a momentary rush of current, due to the residual magnet- ism of the transformer iron. With the introduction of the new silicon steel for transformer cores, with the resulting increase in flux densities, this transient effect has been materially magnified, and may, in some cases, reach dangerous proportions. It is the object of this bulletin to present some facts with regard to this phenomenon, obtained by means of commercial apparatus, and to show how to protect the system from injury due to this cause. 2. Acknowledgments. — Valuable assistance in the preparation of the oscillograms has been rendered by Messrs. C. E. Bennett and A. C. Hobble, of the Electrical Engineering Department. 3. Theory. (a) Inductance without Iron. — If an alternating e. m. f. e = £ max sin 0, be impressed upon a circuit containing resistance and in- ductance without iron, in series, this impressed e. m. f . will be consumed by the counter e. m. f . of the inductance, and by the drop through the resistance, and this must be true at every instant, i. e., for every point of the impressed e. m. f. wave. We have, therefore, , = £ raax sin0 = L d ± +Ri (1) where Since and max dt is the phase angle of the impressed e. m. f. = 2tt ft. di di dO di , Jt = Jo dt = Je 2ir ' L — = 2 7T fL ~ = X where X = inductive reactance dt d6 L d0 di £ max sin d = X l di + Rid -£ max( f (cos0)=X L di + RidO 4 ILLINOIS ENGINEERING EXPERIMENT STATION di = (cos 6)—£- id 6 ( 2 ) If the circuit be closed at that point of the e. m. f. wave where < ?==£ max> i- e., when B = 90 = - , and if the resistance drop be assumed negligible, (2) becomes E di = d (cos 6) (3) L If the circuit be closed at different points of the e. m. f. wave, the current will rise to different values, and these values can now readily be investigated by means of the last equation. Suppose for instance, that we close the circuit at the 90 point of the e. m. f. wave, i. e., when the e. m. f. is a maximum. Integrating (3) from tt/2 to tt j di = — ^r*J d (cos 6) X which is the maximum current reached, since integrating from - to ir + a, where a is a constant, less than 2 w, results in a value less than ■^max showing that the current decreases from this point. Suppose, in the next case, that the circuit be closed at the o° point of the e. m. f . wave, i. e., when e = o and 6 = o. Integrating (3) from o to - gives P E P J.*=- :?J. d (cos 6) E max X. the same as before. Integrating from o to ir, however, i. e., the maximum current obtained in this case is twice that obtained when the circuit is closed at the 90 point of the e. m. f . wave. In a similar way it can be shown that by closing the circuit at any other point of the e. m. f. wave, the maximum current reached will lie d (cos 6) = + 2 X, YICNSKN — STARTINC ( I ' UKI'.NTS OF TKAN'Sl'OKM KKS 5 between and 2^i x In general, the current assumes its normal value only when the circuit is closed at that point of the impressed e. m. f. wave, where the permanent value of the current is zero. In the above case, where there is negligible resistance, this is the 90 point of the wave. The effect of the resistance is to move this point towards the zero point. (b) Inductance ivith Iron. — The above calculations assume a constant inductance, i. e., a straight line magnetization curve, obtained by using an inductance without magnetic material as core. If an iron core be employed, such as is the case with the ordinary induction coil or the transformer, the inductance is not constant. As the flux density increases, the inductance decreases, until the iron is perfectly saturated. After this point is reached, the inductance remains constant at a small value, depending only upon the flux passing between the coil and the core through the air or non-magnetic material. Since the flux is not any longer proportional to the current, the counter e. m. f. due to the inductance must be written A dB A de where B = flux density and A = constant, instead of , di di L-r or X -r- dt L dd and equation (1) becomes e=E m3X smd = A^- + Ri (4) — £ n „ x d (cos 9) = AdB + Rid dB = — ^d(cosO)— ^-idd (5) Under normal conditions, the resistance drop due to the magnetizing current of a transformer is negligible, and dB = ^ d (cos 6) The normal maximum value of B is then obtained by integrating dB IT from - to 7r. 2 J, dB = B =— E max max cos 1 ^ = £ m^x A 6 ILLINOIS ENGINEERING EXPERIMENT STATION .\^ = £ max and^=!^ (6) max Substituting (6) in (5) dB B m d (cosd)— §®*Rid6 (7) max Since the relation between the magnetizing current and the resulting flux can not be expressed mathematically in any practical equation, the magnetizing current necessary to produce the required flux according to the above equation can be determined only analyt- ically, as follows : Fig. 1 Suppose Fig. 1 to represent the saturation curve of a transformer and the hysteresis loop for normal voltage and frequency. The hys- teresis loop shows what residual magnetism remains in the iron after the current has been removed, ob and od represent this residual magnetism, depending upon whether the current has died down from a positive or a negative value. Suppose the circuit is closed when the impressed e. m. f. passes through from negative to positive, i. e., 8 = 0, and that the residual magnetism is ob. It is evident then that the change of flux to pro- duce the counter e. m. f. must start from b. If equation (7) be re- written in the form *£ = -£ max A(cos0) - p^Ri^e ......(8) max and small intervals of 6, say io°, be taken, the actual conditions can very nearly be approached. Starting from b, the flux will follow a curve, such as the dashed curve between b and a, and will continue on the saturation curve. From equation (8), A B can be calculated for YENSEN — STARTING CURRENTS OF TRANSFORMERS 7 each increment of io°, starting from 0° in this case, and from Fig. i can be obtained the corresponding magnetizing current required to produce the total flux, B i -f AB, B i being the total flux at the beginning of the interval. After having determined the magnetizing current, the resistance drop effect is calculated, equal to jf* Ri A 6 (9) This will, however, reduce the value of A B, and a few trials will have to be made before the correct value of A B is found. Proceeding in this manner, the flux and the corresponding mag- netizing current may be determined for any number of cycles. For decreasing values of flux, the upper dashed curve in Fig. i has to be used. It will be found that the magnetizing current may reach for- midable values under unfavorable conditions, particularly for the first cycle. The amplitude of the peaks decreases rapidly, the more so the larger the amplitude of the first peak, on account of the more pro- nounced effect of the resistance in that case. 4. Method of Investigation. — In Part II (a) will be taken up the actual measurements of the magnetizing current of a transformer upon closing the primary circuit at a predetermined point of the e. m. f. wave, and with a known residual magnetism in the iron. These meas- urements were made by means of oscillograms, showing the impressed e. m. f., the primary magnetizing current, and the secondary induced e. m. f. Part II (b) takes up the calculations of the flux and magnetizing current for the conditions under which the oscillograms were taken. In order to do this, all the characteristics of the circuit and transformer having any bearing upon the magnetizing current were carefully ob- tained. The curves plotted show that there is very close agreement between the actual curves, as obtained by means of the oscillograms, and the calculated curves as obtained by means of the circuit and transformer characteristics. This agreement shows that it is possible to make calculations of these phenomena, that can be fully relied upon, and that it is unnecessary to resort to the oscillograph in order to obtain reliable results. It was therefore deemed sufficient for the investigation of the rest of the transformers, covered by this bulletin, to obtain the transformer data necessary to make the calculations as shown in Part III. These calculations cover the most critical condi- tion only, namely, the rush of current upon closing the circuit at the o° point of the e. m. f. wave with the residual magnetism in the same direction in which the increase of flux will take place upon closing the circuit. 8 ILLINOIS ENGINEERING EXPERIMENT STATION In I art IV, is given the result of placing a resistance or air core inductance in series with the transformer, and it is shown how to cal- culate a resistance or inductance sufficient to limit the rush of current to safe values. II. (a) Actual Measurements of Phenomena by Means of Oscillograms. 5. Connections.— Fig. 2 is a diagram of the connections used for obtaining the oscillograms. G is a 10 kw. 440-v. alternator, 60 cycles with taps, so as to give either 3-phase or 2-phase current, as shown in Fig. 2a Taps 1, 3 and 5 are used for 3-phase, taps 1-4, 2-6, for 2-phase. the closing switch was designed and built specially for the investiga- tion of these phenomena. 1 It was attached to the end of the generator C/osiny Smtch} i r /Cow Afon /nduct'w fes/stance- Transformer /v\tvw-@-T Fig. j Osci/oarapfj 4 Fig. 2a shaft, and can be set so as to close the circuit at any predetermined point of the e. m. f. wave. However, it would not operate satisfactorily at the normal speed of the generator, 1800 r. p. m. A speed of 650 r. p. m. was finally decided upon, which resulted in a frequency of 22 cycles. 6. Transformer.— A 5-kw. 60 cycles 2200, 1100/220, no-volt transformer of the newest type was used in this test. It was connected for no volts primary, i. e., with the low tension coils in parallel. As the normal frequency is 60 cycles, and 22 cycles was used, the voltage J By O. B. Wooten, Research Fellow, Engineering Experiment Station. YENSEN — STARTING CURRENTS OF TRANSFORMERS 9 had to be reduced in proportion, i. e., the impressed voltage was 22 II0 ^6o = 4° v °l ts > to give normal magnetizing current. As it was desirable to use as stiff a field as possible in the gener- ator, in order to prevent too much of a voltage drop upon closing the transformer circuit, taps 2-3, (Fig. 2a), were used, giving 40 volts with about full field and 650 r. p. m. The oscillograms show that the voltage is kept up fairly well at the maximum rush of current. 7. Residual Magnetism. — The normal magnetizing current was ob- tained by impressing 110 volts at 60 cycles upon the transformer. The result is shown in the following table. Table i Volts Current Watts Freq. E 7 CX W F no .90 46.5 60 The maximum value of the exciting current = .90 X V 2 = 1.27 am- peres, and this is the current that produces the normal residual mag- netism. A series of experiments was made to ascertain the decrease of the residual magnetism after the removal of the e. m. f. These experiments are described in the Appendix. The following results were obtained : 1. There is no decrease in the residual magnetism of transform- ers under normal conditions. 2. The decrease of residual magnetism due to vibration or shock is very small, almost negligible. The oscillograms were taken with a residual magnetism in the iron that would remain after the removal of the normal voltage at normal frequency, which would be the case under normal operating con- ditions. This residual magnetism was produced by means of direct current from a storage battery, as shown in Fig. 2. The current used was that corresponding to the normal exciting current of the transformer, the maximum value of which is 1.27 amp. Hence 1.27 amp. D. C. was used. By means of a reversing switch, S 2 , the current could be reversed, producing a residual magnetism in the opposite direction. In order to be sure that the correct residual magnetism was produced, the iron was sent through the regular hysteresis loop a number of times, at least o S > s « S 10 ILLINOIS ENGINEERING EXPERIMENT STATION ten, by reversing the current by means of switch S.,. Let Fig. 3 rep- resent the normal hysteresis loop. Suppose the residual magnetism, at the beginning, is at 2'. Sending -j-/ m amperes through the transformer increases the magnetism to i' along the lower dashed curve. Opening the switch decreases the magnetism to 2'. Reversing the switch brings it near 3. Again opening the switch brings it near 4. Going through the same operations, the loop will approach 1-2-3-4 and, after a few reversals, practically coincide with it. so that when the switch is finally opened, the residual magnetism will be 0-2 or 0-4, according to whether the last current was -f- I m or — / m . Fig 3 8. The Oscillograms. — Out of a total number of eleven oscillo- grams taken, four are here reproduced, as follows: Oscil. 7. Circuit closed at o° point of e. m. f. wave. Residual magnetism, positive. Maximum rush of current =52.1 amp. Oscil. 9. Circuit closed at 90 point (more accurately 85 point) of e. m. f. wave. Residual magnetism, positive. Maximum rush of current = 18.0 amp. Oscil. 8 (a)* Circuit closed at o° point of e. m. f. wave. Residual magnetism, negative. Maximum rush of current = 3.78 amp. 12 ILLINOIS ENGINEERING EXPERIMENT STATION 8 (b)* Same conditions. Maximum rush of current, unknown. Oscil. 4. Circuit closed at o° point of e. m. f. wave. Residual magnetism, uncertain. Maximum rush of current = 32.0 amp. By positive residual magnetism is meant that the magnetism was in the same direction in which the flux would increase upon closing the circuit. II. (6) Theoretical Calculations from Transformer Data. 9. Magnetization Curves and Hysteresis Loop. — These were ob- tained in the following way. The transformer was connected as shown in Fig. 4. Direct current from a storage battery was supplied the high Fig. 4 tension side P of the transformer through a reversing switch, S, and a resistance R p . The low tension side was connected to a high resist- ance R, and a D'Arsonval galvanometer, connected across a small part of the resistance, with a very high resistance in series. A change of flux in the transformer would then produce a deflection of the galvano- meter coil, proportional to the total change of flux. R, R s and r were not changed during the experiment, so that the deflections obtained, mul- tiplied by a constant K, gave the flux density in the transformer core. In this investigation, the absolute flux density in gausses was not cal- culated, as it is only the relative flux values that are needed. The flux density is therefore, throughout this bulletin, expressed as a galvano- meter deflection multiplied by a constant, K, K u K 2 , etc. for different transformers. To obtain the curves, the desired current was sent through the transformer primary, reversed a number of times to be sure that the iron had entered the corresponding loop, and the current left on in the *Note. Two exposures were made on Oscil. 8: 8 (a) in which the cur- rent only appeared; 8 (b) containing all quantities. The two exposures have been traced separately. VKNSEN — STARTING CURRENTS OF TRANSFORMERS 13 I Fig. 5. Magnetization Curve and Hysteresis Loop for Transformer A. ILLINOIS ENGINEERING EXPERIMENT STATION positive direction, corresponding to point i in Fig. 3. The galvano- meter was then connected. Opening the circuit, the resulting deflection corresponded to a change of flux 1-2, reversing the current produced a change 2-3 ; opening it produced a change 3-4 ; again reversing it pro- duced a change 4-1, completing the loop. Fig. 5 shows the hysteresis loop and magnetization curves for the transformer used for the oscillograms. It was obtained by the method explained above. As an example, is given the galvanometer deflec- tions for 1.22 amp. Table 2 Current 1 .22 Change Deflection = A X K 1-2 9-5 59-5 2-3 50.0 2 3-4 9-5 59-5 4-i 50.0 2 = 29.75 = 29.75 Resid. Mag. 29-75 — 9-5 = 20.25 The saturation curve was carried up to 119 amp. It is seen that at this point the curve has become a straight line, which means that the iron has become saturated, and the increase in flux is taking place only in the non-magnetic space between the iron and coil. Conse- quently, the curve can be extended indefinitely. O' 90' /80° 270' 760° -450° S40' 630' Fig. 6. Rush of Current on Closing the Primary Circuit of Transformer A. Circuit closed at o° point of e. m. f . wave. Residual magnetism = + 20 X K. YENSEN STARTING CURRENTS OF TRANSFORMERS 15 9. Calculations.— The data needed for the calculations of the magnetizing current are as follows : 1. Normal hysteresis loop; 2 Magnetization curve up to straight line relation ; 3. Total effective voltage impressed upon the transformer circuit; 4. Total resistance of circuit ; 5. Total inductance of circuit. Sine wave e. m. f. is assumed in these calculations. Equation (8), gives the relation : .(8) A S = -B max A(cos0)-|^/vtA0 assuming the circuit to have negligible inductance outside the trans- former. i80' eTO' 36 O' 45-0° S40° Fig. 7. Rush of Current on Closing the Primary Circuit of Transformer A. Circuit closed at 85° of e. m. f . wave. Residual magnetism equals +2oX£ l6 ILLINOIS ENGINEERING EXPERIMENT STATION B = flux, B mnx = max. flux of normal hysteresis loop ; £ m«x = » 1 'i^- impressed e. m. f. = y2£ eff ; R = total resistance of circuit ; t = instantaneous value of magnetizing current. In the present case, 5 ma X ( f rom Fig. 5) = 29.5 X K, where K = const. E ac = 40 volts. £ mix = yj 2 X 40 = 56.5 volts. R = .745 ohms. Substituting in (8), for increments of 8 of io°, i. e. A 6 = io c radians, A B = — 29.5 K A (cos 6) — .0685 K i. •175 14 so \ * X 8\4o — c l/CL Cut -re/ if / a/c j/a r. 'i/X « — / / \ / \ \ / / \ / 1 — \ / H— V \ 1 — / — V \ 1 \ ~r I \ -\- 1 r -V- \ h \ 1 \ \ -V- ~t -J- \ \ -v- x~~ / / / -\ v.. / 90° /So' 270' 360' 4S0° &4o' €SO' Fig. 8. Rush of Current on Closing the Primary Circuit of Transformer A. Circuit closed at 90° point of e. m. f. wave. Residual magnetism equals + 20 X if YEN SEN — STARTING ( URRENTS OF TRANSFORM ICRS IJ In Table 3 arc given the calculations for a number of different conditions, viz.. Conditions Closing Point on e. m. f. wave Residual Magnetism Impressed e. ra. f . , , ef 1 Frequency Resist, of Cycles/Sec Circuit Columns 4 to 7 Columns 8 to 11 Columns 12 to 15 Columns 16 to 19 Columns 20 to 23 0° 85° 90° 0° 90° + 20 K 4- 20 K + 20 K — 20 K — 20 K 40 volts 40 volts 40 volts 40 volts 40 volts 22 .745 22 .745 22 .745 22 .745 • 745 These conditions correspond to those under which the oscillograms were taken. Of 90' /80° 270' 360' 4S0' 540' €30' Fig. 9. Rush of Current on Closing the Primary Circuit of Transformer A. Circuit closed at 0° point of the e. m. f. wave. Residual magnetism equals — 20 X if. * [8 ILLINOIS LNGIN LICKING LXPERIMLNT STATION ^-/2 -60 90' /80' 630' e70° T60' 450' S40' Fig. io. Rush of Current on Closing the Primary Circuit of Transformer A. Circuit closed at go" point of the e. m. f. wave. Residual magnetism = — 20 X K. In Fig. 11 are plotted the calculated values of current, flux and impressed e. m. f. for the various conditions, to the same scale, in order to compare readily the effect of the closing point and the resi- dual magnetism. Fig. 11 is a summary of Fig. 6 to 10 inclusive and Table 3. 11a corresponds to Table 3, Columns 4-7, and Fig. 6. 11b corresponds to Table 3, Columns 12-15, an d Fig. 8. lie corresponds to Table 3, Columns 16-19, an d Fig. 9. ud corresponds to Table 3, Columns 20-23, an d Fig. 10. lie represents the condition in which the circuit is closed at the 90 point of the e. m. f. wave with no residual magnetism. This is the condition for normal closing, since the flux and current then will enter at once upon their normal path. The same result would be obtained under conditions of Fig. no. if the initial magnetism were negative maximum; under conditions in Fig. lib, if the initial magnetism were o; under conditions of Fig. 11c, if the initial magnetism were negative maximum, and under conditions of Fig. ud \i the initial magnetism were o. It is seen that the closer the conditions come to these normal 06 W I ,: O i to C Z -r < '> 06 II ^ H O 2 m o gg u S2 ^ cn w s «> Q H 2 < < g x 5 o g z> 51 Q 3 — < <5 O O o -i 2 2 ° IT; ?, ^ ^ ^ ,^ ^ -r 000000--(NiowqN(\jui l n o — uiO^Cv) — oooooooooooo o ~- o4 c4 ci fi f*i f*i po oj oj ^ _! o + 1 *5 3 u X + 1 1 + + 1 11 "?») m CQ OS O 00 + "OPj — . M O M Oi - - r-» C?N O ~ 00 C> O — I iO \ONOO\ I + + 0*°5;0'£>^^< v )OOOOCVlC'ir': in NO CO CJ\ 0\00vOio«m^OOOOMO^m\O!a On CO *0 in + + + + OM'tNK'tOi-NONtO'tN Tf CO O^OCOK^O^^-o-^ir-^OK CO 0> C?i OO'^KK'tO-trxOtsTfO 0\ CN 'X (N *0 — ' — > — (^r-Or-rrnr.OtsODCiON O On 0> 0Q t^*. + + + + o o o o o o o o o o o o o o o o o o oooo C\ O ^ M ^ T u-i C K X O O W T it, vO N&5 0\0 f o * d • n W + II E Cfl V M O • be u x .5 m n**£ rn Os O 00 «n i ^ Q o 6 . m W + o • - Ph 00 , -a § o i —
  • n o O cm flfl *o Nlm^o 00 00 ^ <*) so ON win O c*5 CM — • + ^mNNCM cm o o\ Moocooomnt^M-'OOOOooa'-^ cc Jf;^ o >£• © CTi 00 M" <^ M ~rr>\n CM OfOOO-^M"N^tN^^ , f c ^^ cv i ro 00 rjo V° MMnro m* t •'T Tj-^Tj-fofOoiCNj — — • + 1 inWOW^ O CO O O N T O CC C in ^] C> K a K O O C - ft ) ^. O\Cvv0 r*3 — CM Oj\O^OCi'HKOOC\t> 1 >0'-CCO;0'-| ^•tTt^iri CM --^ " " ^^CMc^rOrr^Tf^Tr^^TtcoCMCNj^ + + + + HNOOO^O m VO CO ' CO CO O^'OO^OO^) CO^OrN. r>. OVOOSVOODW r- M n rt Tr -f JONOQ O O O ^- *-< <^ O ^---ih O OOloCM^hOOOOOOOOOOOOO O OOOO + >— i CM T O ^i-t>.r^lm -i CO t W . + ^ K Q O >n % c,rniO VO "sf^OOO\OCCMO'-"*l l ^MNts\OinrsO ^t" CMCMtJ-On o t i - ^ m 35 cct^t^ cm :»^^\o^^^cr\o>c^ONr^oqvor^r^o\ ^ co «o in in o03KcvivDon in o Trroot^r^o>r^r^cvjr^c^'^ioONCM'*in *o io^-cmon ++ r^l -T T c*~j — + + ooooooooooooooo ooo o ooooooooooooooooo o oooo wcm n-tm^K oocNO^cviron- m m3k co ONOr-Mro^mOfsooONO -"MfnTj-v; o nco ao r~, ^ r-t _ ( i—\ «— ( ^ CM CM CM CM CMCMCM CM CM CM CO C} CO CO CO CI CO ro co CO ft -J o W i o ■ Oh ° 5b £ « n! _ — . rt ^ -o <^ O ^ bib «j s <3 + — — f^^O^^ "M O lt. <"■"/ CM X -5M 3 u u , 1 "? m 00=0 I < I —* (VJ r*5 ' ■ T T rt rn CM — 00 o O O O O O O O O O O O O O O *H ~->*-«~h * — ' ~* — < o oo ooo o o o o o o o o o o oooo u ■ u >— < CM CM CM I CM i— i r— i ++ ,2 M fa I OOOO •O'-'CMCMroi-TI-Tt-f- -r f <-o cm -h — •h H TT ■ ■^•i-'i-'i-Tr'i-rccMCNj^ + I + ooooooooooooooo ooo o ooooo ooo ooooooooo o oooo "CM TO-^-LOVOC^.COC^O'— 'CMfOrf i/) VOK 00 OvO-iC^rO XT lo MD r» CO C?\ O •— ' CM f"i TT LO NO t>» CO C\ O ^ ' i— < t-( .— i — i r-« i— • »-hCMCMCMCM CMCMCM CM CM CM CO nfironro fO nco f^T YENSEN — STARTING CURRENTS 0E TRANSFORMERS 23 conditions, the less rush of current takes place. Fig. 11c comes very close to these normal conditions, while Fig. lia is farthest away. Fig. 11b and d are practically identical, with the exception that in Fig. 11& the rush of current is positive, while in Fig. lid it is negative. 10. Agreement between Oscillograms and Calculated Curves. — The values of flux and current from Table 3 have been plotted in Fig. 6 to 10 inclusive, together with the actual currents, as given by the oscillograms. The full lines give the calculated currents. The dashed lines give the calculated flux. The dotted lines give the actual currents. From these plates it may be seen that the agreement between the actual curves and the calculated curves is very close. Indeed, for the first case, corresponding to Oscil. 7 and Table 3, Columns 4-7, the two current curves practically coincide. For the second case, cor- responding to Oscil. 9 and Table 3, Columns 12-15, the maximum dis- agreement is only 4.5 per cent, while in the third case, corresponding to Oscil. 8a and Table 3, Columns 16-19, the disagreement is 25 per cent. The closer agreement in the first case was to be expected, con- sidering that a small variation in the residual magnetism in Oscil. 8 would have a greater effect than in Oscil. 7, on account of the dampen- ing effect of the resistance in 7, while the resistance has practically no effect in 8. While the attempt was made to have the residual magnetism constant in all cases, it is possible that it may have varied a small amount. Assume, for instance, that the residual magnetism for Oscil. 8 was — 18.0 K instead of — 20 K, the maximum positive flux would be approximately 37.8 -f 2.0 = 39.8 K corresponding to a current of 3.75 amp. (instead of 2.8 amp.) which is the current shown by the oscillogram. However, the agreement between the oscillograms and the calcula- tions is such as to warrant the conclusion that reliable results of the starting current of transformers can be obtained by calculations, if the complete data of the transformer and circuits are at hand, as tabulated on p. 15. III. Calculation of Maximum Starting Current of Trans- formers of Various Types and Makes. In the preceding section, have been given the starting currents of a no-volt 60-cycles transformer by impressing upon it 40 volts at 22 cycles. While this resulted in normal magnetizing currents under normal operating conditions, the percentage of resistance drop in 24 ILLINOIS KNOINKKKINC KXPKRI M I'.NT STATION terms of total impressed e. m. f. is much greater for the same current than if 1 10 volts were impressed. For no volts, 60 cycles, equation (8) takes the following form: (the resistance of the circuit remaining .745 ohms) 29. e K A B = — 29.5 K A (cos 6) — — ~— Ri A 6 IIO ^2 A B = — 29.5 K A (cos 6) — .025 Ki which shows that the effect of the resistance in decreasing A B, and consequently the current, is decreased by 1 10/40, or in proportion to the voltage. In this section, calculations are given for the case in which the transformers are connected directly to constant potential busbars with sufficient power behind to maintain the voltage constant in spite of large starting currents. The potential in this case is the normal voltage of the transformers, and the resistance of the leads is assumed negligible. The following transformers have been treated: Capacity VOLTS Year of Designation K.V.A. Primary Secondary Freq. Make Mfg. Remarks Transformer A 5 2200/ 1 100 220/110 60 X 1910 Same transfor- mer as was used in obtain- ing oscil- Transformer B lograms. 5 2080/1040 460/230 60 X Old Transformer C Type 50 ?200/lI00 440/220 60 Y 1910 Transformer D 440 no 60 Y Old Transformer E Type IS 440/220 220/110 60 Z 1911 The transformers will now be taken up in order, and the current calculated for the case where the circuit is closed at the o° point of the e. m. f. wave, with the residual magnetism positive, i. e., for the conditions of Oscil. 7, which give the maximum rush of current. Transformer A 5-kw., 2200, 1100/220, no volts, 60 cycles, new type, no-volt winding used as primary. YKNSKN — START I NT. C I'RRKNTS OF TRANSFORM I'.KS 25 Data Hysteresis loop and magnetization curve are given in F'g- 5- Normal effective voltage = no volts. Resistance of circuit = resistance of transformer = .0253 ohms. Maximum value of normal exciting current =1.27 amp. Hence equation (8) becomes A B = — 29.5 K A (cos 6) — .00084 Ki. Table 4 gives the calculations for this and the following cases from o to 200 . For transformer A. it gives a maximum current of 390 amp., while the maximum value of the full load current is only J 2 X45 = 64.3 amp., i. e., the maximum rush of current is 6.1 times normal full load. Transformer B 5-kw. 2080, 1040/460, 230 V., 60 cycles, old type, 2080- volt winding used as primary. Data Hysteresis loop and magnetization curve are given in Fig. 12. Normal eft', e. m. f . = 2080 volts. Resistance of transf. (2080-volt winding) = 9.35 ohms. Maximum value of normal exciting current = 0.1 amp. From Fig. 12 # max = 26.25 Normal residual magnetism = 20.0 X K 4 . £ ms = y]* X 2080 = 2940. Equation (8) becomes A B = — 26.25 X KiA (cos 0) — .0146 KJ. From Table 4, Columns 8-1 r, the maximum current is 13.5 amp. or about 4 times the maximum value of the full load current, viz., V 2 X 2.4 = 3.4 amp. Transformer C 50 kw. 2200, 1 100/440, 220 volts, 60 cycles, new type, 2200-volt side used as primary. JO ILLINOIS ENGINEERING EXPERIMENT STATION -0/ 0./ 02 03 0.4 0.5 Fig 12. Magnetization Curve and Hysteresis Loop of Transformer B. YENSEN — STARTING CURRENTS OF TRANSFORMERS 2 7 Data From Fig. 13 Hysteresis loop and magnetization curve are given in Fig. 13- Normal eff. e. m. f. = 2200 volts. Resistance of transformer (2200-volt winding) = .446 ohms. Maximum value of normal exciting current = .5 amp. / / / / s * / too 200 s J00 —- — — es 60 80 *^ s / // 1 rf 1 1 1 1 //Of? 0O/=> / 1 \ -as Fig. 13. Magnetization Curve and Hysteresis Loop for Transformer C. ILLINOIS ENGINEERING EXPERIMENT STATION fi m ,x = 2075 Normal residual magnetism = 15.25 A'., ^max = yj? X 2200 = 31 10 VOltS Equation (8) becomes A B = — 20.75 ^2 A ( cos ^) — -00052 K„ i From Table 4, Columns 12-15, the maximum current is 235 amp. or about 7.3 times the maximum value of the normal full load current, viz., J2X 22.7 = 32.1 amp. -/ / 2 j 4 s Fig. 14. Magnetization Curve and Hysteresis Loop for Transformer D. <<<+ & a II § a I 06 os r o . o « o _ rt o t-,H . c ho . In tv. in oo o m m i«) pi o oo o ~-.x -tONO »Ov o i-i o o\ x in o qqqinqvONq in c ^ pi rn'i-'^-in'^f^t-^t T i'< v: JP : >Pi ™ + + + O PI cofJmOOC On OnOO O IS m 00 Q q - in lO h «' pi pi ^ in in in in 'i- -rt- po pi pi" ^- w On 00 NO lO ^ ^ M O O m -i O ©n00 - Is O O O00 N N O -tKO In t O tKN *t00 O 00 "t O On OnX In no iOi^h o i- (nino KW On On O On On + + oooooooooooooooocoo oo m Cj t ir/O 1^00 O O .S 8 O M Ph n „ c o ° « bo *j o u P4 8 8S 8 8 8 8 8 8 SS? , g < 5£ = 222 S u 5 pq 8 'o IT 1 f; t- I?; 8> 8 8 8 8 8 8 8 8 8 8 8 — Ix O — O O O "I 'O io o >o P) TOO W >OOC O PI 1*5 KJ H H M P| « (I « 00 3 5 : O O O O O C > *q o\o qi t t 'hx N ,,: > o\ pi i *c o\ m to in uS "S *f 0) pi f> n T -J - T mmuiui mm iC CCOCOOOOOO i-;. >o □ 5 i^o c> -t o\ f a fi J" « VP s *T I/5O0 o O PI <*5 N >- OWO PI Q tx C5 PI O -T m x to iXoNPommmTPioqvq qn^rspp "? q + .q too -r T< + + pq '-U M (SI <• < W o s z in < 00 en «: o o> .S- — nu-i O\oo <*5 <*s r^oo ml OS o w io t< di col pi oi o io\o t o — ^oo pooo p) fo o n f> ^^q q> t> PI M N M 01 M ^ n "j- >t m^OOiOVO tN.txt^ Ix (~0\O •^-< V 00 "11 P) T ifl OWO "T^O PI TTJ-Tt-T'-; 1/5PI -*\D 00 n N N i-i i-i PI rCP0T'rf^J-Tf T l" T 3"P0P0PI w + + I COVO -"T^PIOO PIOOOOOOOO P100 PI 'tvO in ooco -To pi TT^ftNvq -to oq q 'MHf|P5tO'T't"t4^4l , 5^fiMM' + + I u ^ II £ £ a O 5 23 in 2 ^ H O < O < 3£ 5 3 £ 2 Oh * °o 3 " be £ > ■M '5 in u ooooooooQO°Q v S v S + + 11 On " in io ft io m q\00 O ml> N« + ++ I I u >< O 00 w > 3 o> •li Ph c o O o °^ 4-. O ■ s o oooooooooooS5°2 0(v,,;, '2' l/ " > 3"fi 9 O O O O O O O O Q o o Q o "i hH . ""J 'I Q + . c bo v 5 ffl , s i o <*3^o o\ moo Tj-o\oo)Tj-o\>-f9"?t>^ 1 lodd^'>-Tc^^d\uS«vdc4K«v3d\«2i'j ji rr VOVO t^.00 00 00 Ol 0\ Ol ON MDMOOOOOOOOOOOOOOO + "ONOOOOOOOOOOOOOOMVOMDJJ, + + 32 ILLINOIS ENGINEERING EXPERIM KNT STATION Transformer D 7^2-kw. 440/110 volts, 60 cycles, old type, 440-volt side used as primary. Data Hysteresis loop and magnetization curve are given in Fig. 14. Normal eff. e. m. f. = 440 volts. Resistance of transformer (440 volt-winding) = .26 ohms. Maximum value of normal exciting current = .655 amp. From Fig. 14 5 max — 33-0 X A\ Normal residual magnetism = 28.0 K 1 £ max = -y/2 X 440 = 622.5 VoltS. Equation (8) becomes A B = — 33 K l A (cos B) — .0024 K r i From Table 4, Columns 16-19, tne maximum current is 62 amp. or about 2.6 times normal full load current, viz., -yj 2 X 17 = 24.1 amp. Transformer E 440, 220/220, 1 10 volts, 60 cycles, new type, 440-volt side used as primary. Data Hysteresis loop and magnetization curve are given in F'g- IS- Normal eff. e. m. f . = 440 volts. Resistance of transformer (440-volt winding) = .195 ohms. Maximum value of normal exciting current = .87 amp. From Fig. 15 5 max =38.0^3 Normal residual magnetism = 25.0 K 3 £ ma x =tJz X 440 = 622.5 volts YK.NSK.N — starting itkrknts ok transform i:ks 33 Equation (8) becomes A B = — 38.0 Kj A (cos 6) — .002 1 KJ From Table 4, Columns 20-23, the maximum current is 255 amp. or 5.3 times the maximum value of the normal full load current, viz., -^2 X 34- 1 = 48-2 amp. 34 ILLINOIS ENGINEERING EXPERIMENT STATION IV. Effect of Resistance and Inductance in Series with Transformer Primary. In the preceding section, have been presented the results of con- necting some transformers directly to the busbars with negligible resistance in the leads. It was shown that with the old type of trans- formers, the initial rush of current may amount to two to four times normal full load current, while with the new type, with silicon steel cores, the initial rush may exceed seven times full load current. The only remedy for reducing these abnormal currents, where the transformer is to be connected to constant potential busbars, is the introduction of resistance or inductance in series with the primary winding, i. e., that side of the transformer which is to be connected to 1 rWA/WVV T Transformer Fig. i 6. the power station. This inductance or resistance will take care of a part of the impressed e. m. f., leaving only a fraction of it to be taken care of by the counter e. m. f. of the transformer. This is shown diagrammatically in Fig. 16. The general equation then is - . . . dB ,_ di , E ™ Sm6 = A d6 +X ,d8 +Rl ( I0 > which, if solved for A B in the same way as in Part I, gives A£ = -l? max A(cos0)-^ X (At)-^^(A(9) (ii) This reduces to (8) if X h is negligible. R is the total resistance of the circuit, including the transformer pri- mary, and Z L is the inductive reactance outside the transformer. In the following, will be calculated the maximum rush of current with either resistance or inductance in series with the transformer primary for two of the silicon steel transformers, transformer A and transformer C. Transformer A. Case i. — For negligible inductance outside the transformer equa- tion (n) becomes Y K X S !■'. X — ST A RT IXC. (IRK K N TS O I' IRA X SIORM !•: RS 35 B nvxx A (cos 6) — ^ x Ri (A 6) urn Suppose now that A' = 1.21 1 ohms, i. e., that the outside resistance is 1.21 — .025=1.185 ohms, since the resistance of the transformer primary is .025 ohms. For io° intervals of 0, A = .175. 5 max = 2 9 . 5 K ^m,x = 155 VOltS R = 1. 2 1 ohms A B = — 29.5 K A (cos 0) — .0403 K i. Case 2. — For negligihle resistance in the leads, the total resistance of the circuit may be neglected, and (n) becomes A5 = -5 max A(cos0)-|^ X t (A i) max Assume X L =1.21 ohms A B = — 29.5 K A (cos 6) — .23 K (At) Table 5 gives the calculations for these and the following cases. It is seen from this table that the maximum rush of current for Case 1 is 78.0 amp., and for the second case 86.0 amp. or less than twice full load current. Transformer C. Case 1 — Negligible inductance outside transformer. „ _ V 2 normal voltage 11 00 For R = ' — 5_ _ = 43 c ohms full load current 24 or 43.5 — .5 = 43 ohms in series with the 2200-volt winding, equation (11) reduces to A B = — 20.75 Kz A ( cos #) — -°5 l K 2 i. Case 2. — Negligible resistance outside transformer. For X h =43.5 ohms in series with the 2200 volt-winding, equation (11) becomes, neglecting resistance : A5 = — 20.75 K 2 A (cos 6) — .29 K 2 (At). From Table 5, Columns 12-14, it may be seen that the maximum rush of current for Case 1 is 50.0 amp., and for Case 2, 55 amp., i. e., in both cases less than twice full load current. From the above calculations, it may be seen that the initial rush of current upon closing the primary circuit of a transformer can be lim- ited to safe values by inserting either a resistance or an air core in- ductance in series with the primary circuit. In the particular cases above, the current was limited to less than twice full load current by J This resistance multiplied by full load current, 45.5, gives a drop equal to half normal voltage: 1.21X45.5 = 55 volts. ■fPllNOipOO'O'O '000 H 0\ K H ir, ir, (vj fi N N N fi -I M + OOOO'l'OiO i q -rvq ©\ pi oc pi mo in in i in w in o o O >n >- -i n IMO Tf invd VC vO tO -fvd -4 H N <0 Tf invC I^OO 00 CO 00 q vq oq oxiflmooN o >noo % ~ ^g g g> vtS2SP92.2 SL.S oocoioiflMTfo o + iJX i-O mo Q O O O OO q q m Troq tqio S>- « oq i-l oi pi pi nqqeoio5o 5ooo w PO O 1-1 VO O "O Pi 00 I VO d - pi po »nvo K. q vq cq q\q\r-;.rNcoo\ovovo t^.o in. moo o o 2 2 S SSNS 2. d\ food m *fvd oo cd od k ° o — OmOOOOOOO O N h 0,00 O VO w O O « pi pi p^ ^ tj- *f («i j o c o o o o o M PO I> P) In o o + O\00 VO"">r*}POvo od d ci "Sod « ro ■* \d i^-oc d\ d d d d do mm ~p-cP4P)p)Pimmrococomco *t T -I" T -t t PI -T iOC0 O O O in O O in in o O O >o »o to »r, TT00 *t o I^CO O m fl ts in to O\00 in m ►» m m m P4 0) PI C5 PI 01 i-i m i-. + + S 3" u to « d < ^ 5 o J3 ° 12 o ~ a 1-4 04 CI Ui 3 & <" v -uooag VA'S 00 o o o S3 ■a O ooooooooo S M Tf« tN "I » OOOOOOOOO o ooo to 5 tts N « O O n l -" t t 0) N w « m M « < « U QW bo _c ■a e re "o > 40 ILLINOIS K NO IN KICK INC L'XI'KUI M KNT STATION If each set of transformers be connected to one generator, the problem will consist simply in bringing the voltage up slowly with the transformers connected, but in cases where it becomes necessary to connect transformers to busbars of full potential, it becomes necessary, for safe operation, to insert in the primary circuit a resistance or in- ductance to limit the transient current to safe values. It has been shown that a resistance or inductive reactance amounting to l / 2 normal voltage full load current will limit the current to less than twice full load current under the most critical conditions. This resistance or inductance needs to be in the circuit for only a very short time, since the current will fall down to below full load Transformer Fig. 17 current after a few cycles. The resistance or inductance may be con- nected as shown diagramatically in Fig. 17, where an extra contact, A, is provided on the switch, in such a way that, in closing the switch the contact A is reached before the main contact B is reached. It might be possible to provide such a contact even on oil switches. As the in- terval between the time the switch touches A until it touches B, need be only a fraction of one second, no change in the operating mechanism of the switch would be necessary. Usually, it takes an oil switch about 0.5 second to close, i. e., from the time it starts until the switch is closed. If the contact A is located 1/3 of the way from the closed position, it may take the contact 0.1 second to travel from A to B, and this time will be sufficient even for 25 cycle systems. \ ENSEN — START I. \(, l" I' RUE NTS OF TRANSFORM ICRS 41 Appendix Residual Magnetism. — It has been generally believed that residual magnetism is of a transient nature, i. e., that the magnetism that re- mains in the iron, after removing the magnetizing force, gradually decreases. As this point is very important in connection with the starting current of transformers, an experiment was undertaken to ascertain whether the residual magnetism is a permanent quantity or not. Con- nections were made as shown in Fig. 18. Fu;. i 8 Referring to the hysteresis loop of Fig. 3, it may be seen that, starting at 1, opening the circuit produces a change of flux correspond- ing to 1-2; reversing the current produces a change 2-3, etc. However, if the residual magnetism at 2 decreases before the current is reversed, the change of flux will be less than 2-3. Consequently, the problem consists in determining whether this change varies with the time elaps- ing between opening the circuit and closing it again in the opposite direction. The time interval was controlled by means of a pendulum and four contacts, A, B, C and D. By tracing out the connections in Fig. 18, it will be seen that with all the levers in the upright position, the current flows through the circuit in the direction of the arrows, while the galvanometer G is shortcircuited by means of contact B. If now the pendulum is started from the position shov/n, lever A is first knocked down opening the primary circuit. The change of flux 1-2 does not produce any deflection of the galvanometer, because it is shortcircuited until lever B is knocked down. Finally, C and D are knocked down, 4-' ILLINOIS KMILM-KKIM, I'.X l'l'.K I M I'.N T STATION reversing the current, producing a change of flux 2-3, and since the galvanometer is no longer shortcircuited, this change produces a de- flection of the galvanometer, proportional to the change of flux. The shortest distance between A and D corresponded to about .1 second, and it could be increased to about y 2 second. The transformer used was the 5-kw. 2080, 1040/460, 230 volt, 60-cycle transformer, designated as transformer B. A resistance R v , of 400 ohms, was inserted in the primary to decrease the time constant, and the current was maintained at the maximum value of the normal magnetizing current, namely, .1 amp. 1. The deflection corresponding to change 2-3 and .1 second interval between A and D was 48.0 cm. The interval was then in turn increased to Yz second, and by hand operation to 1 min., 5 min., 90 min., 12 hrs., and 24 hrs. The deflection corresponding to the change 2-3 was in every case the same. 2. To ascertain whether there was any decrease of flux during the .1 second period, the resistance R g amounting to more than 1 megohm was cut out. The sensitiveness of the galvanometer is such that io~ 8 amp. corresponds to 1 mm. deflection. The transformer core has a cross-section of about 4 sq. in. and the number of turns of the 230-volt winding is 80. The normal flux density is about 50 000 lines per sq. in., and the resistance of the galvanometer circuit was less than 1000 ohms. Hence to produce a deflection of one cm. required iO' T amp, or io -7 X io 3 = io -4 volts. IO 8 IO~ 4 IO 8 IO 4 = — = - — = 12s lines per sec. 80 80 That is, it requires a change of flux of 125 lines per sec. to produce a large deflection of the galvanometer. As the total normal flux is 50000 X 4 = 200000 lines, this is less than 1/10 per cent, so that any material change of flux occurring within the first 1/10 sec. after open- ing A would be recorded. The time elapsing between A and B was less than .01 sec. The pendulum was stopped after knocking down B,. so that any deflection occurring after the change 1-2 would be due to the decrease of the residual magnetism. As a result of the several trials, not the slightest deflection could be detected. 3. It was finally attempted to determine the effect of vibration and blows upon the permanency of the residual magnetism. With the same connections as in 2, A and B were knocked down. The trans- V KNSKN — STARTING ITKRKNTS ()!•' TRANSKORM ICRS 43 former core was then given a series of blows with a hammer. The first blow produced a deflection of about 50 cm., and the successive blows produced deflections decreasing very rapidly. This deflection corresponds to about 50/1000 = .05 cm. with the resistance R g in circuit. Change 1-2 produced a deflection of 8.5 cm. Change 2-3 produced a deflection of 48.0 cm. Total change = 5 6 -5 cm - This means that the maximum value of the normal flux corresponds to 28.3 centimeters deflection, and the residual magnetism to 28.3 — 8.5 = 19.8 cm. deflection. Consequently, a deflection of .05 cm. corresponds to a decrease of residual magnetism due to severe blows of 5/20 per cent =1/4 per cent. The transformer was finally given continuous hard blows for 5 minutes (one blow every other second) after point 2 had been reached. With the resistance R g cut out, the effect of the last blows could hardly be noticed. R g was then replaced in the circuit and the deflection cor- responding to the change 2-3 was observed. The result showed that the effect of the above severe treatment was to decrease the residual magnetism by 4 per cent. Conclusion. — From the above, the conclusion seems justified that there is no decrease in the residual magnetism of a transformer under normal conditions, and that the decrease due to vibration and ordinary shocks is negligible. ^^^^^^^^^^^^^^^^ arc* -V ./r^-jr* /■ 538 aw . <5frf "T i^itf? ^^*** <^4tc7 UNIVERSITY OF ILLINOIS-URBAN A 3 0112 086829667