Mregee LIBRARY Michigan State — University MSU LIBRARIES ay VE, RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES wil] be charged if book is returned after the date Stamped below. The Design and Construction of a Potential Regulator of the Induction Type A Thesis Submitted to The Faculty of MICHIGAN AGRICULTURAL COLLEGE By G. Me Glidden O. K. Henry Ve. C. MoColl Candidates for the Degree of Bachelor of Soience June, 1917 THESIS top. PREFACE Due to the fact that the fire of March 5, 1916, destroyed the Engineering Hall and much of the Electrical apparatus in it, the need of new apparatus was keenly felt. Among the foremost needs was that of a potential regulator giving a large range and great flexibility for altermating current and voltage control. Since a regulator of the induction type would satisfy this need, and as a search among the ruins of the fire disclosed the stator of an induction motor and armature punchings of suitable size, it was decided that the design and construction of such a regulator could be made the subject of a thesis. The authors felt that the development of this subject would be an excellent opportunity to further their knowledge in design and conetruction as well as to provide the Depart- ment Engineering with a piece of much needed apparatus; we therefore asked to be assigned this subject. The authors desire to acknowledge their appreci- ation for the suggestions and services of Professor J. A. Polson and Foremen of the various shops. The descriptive matter is intended to give a discussion of the principles of potential regulators of the induction type, and, if studied in conjunction with the references given, should enable the reader to understand 96445 the operation of this particular machine. G. M. G. O. K. H. Ve. C. Me SECTION f. GENERAL DISCUSSION OF THE THEORY OF INDUCTION REGULATORS ieee VA NAN ao WRRRRRD REEL 3 Commercially the voltage regulator is used in connection with the most economical size of wire to com- pensate any excessive voltage drop in transmitting power. It has been found that by installing a wire large enough to keep the voltage regulation at the service point with- in the limite, without the use of a regulator as men- tioned above, the cost of the line would be excessive and in some cases prohibitive. In the laboratory, however, conditions are much different, there the regulator will be used only in maintaining either a constant voltage or to obtain the variable voltages needed in performing ex- periments. There are two types of regulators, the compen- sating and the induction type. The former is shown in fig.1, where a transformer is used with its primary "PP" connected acrcss the feeder line thru the reversing switch "a", and taps brot out from various points along its low voltage secondary coil "SS* to contact blocks on a switch "b7b3", over which slides the contact arm:"c".. This arm 1s connected to the feeder in such a manner that the volt- age E,, induced in the secondary coil between the points "b)* and "c", is either added to or subtracted from the primary voltage, depending upon the position of the re- versing switch "a", Thus, if Eg be the maximum voltage that can be obtained from the secondary with "c" moved up to "bo", = = es ee ee _=— the limits of the voltage are, Ep + EJ, depending upon which way the switch "a" is thrown. The induction type of regulator insures a smooth variation in the secondary voltage as no contacts or definite tapping points are used to obtain the required voltage control. The operating principle ie shown in Fig. 3. A primary coil *PP*® is connected across the bus bars or the line as in the compensator type and produces alternating flux in the iron core "c*®. This flux induces an e.m.f. in a secondary coil "Ss" (which is placed at an angle of 90 degrees with "PP") provided the core "CC" does not happen to lie in the same plane with this secondary coil. In the latter event, no e.m.f. is induced in "SS" because the flux is parallel to the tums of "SS* and does not link with them. The secondary coil is in series with the transmission line or feeder. If the core "cc* is turned in one direction thru the secondary coil "8S", the e.m.f. induced therein is in the same direction as the primary e.m.f. and the voltage on the load side of the regulator is greater than the voltage on the generator side by an amount equal to the voltage E,, induced in the secondary coil. If the core "*cc* be turned slightly so: as to incline oppositely with respect to the plane "8S", while still ap- proximately perpendicular to "PP" as before, the e.m.f. E, induced in "8S" is in the opposite direstion, and the feeder voltage becomes (Ey - £,) With E, and primary Load Primary and Secondary Connections STi Phase Ye . 7 . - ie - = — Line, Primary and Secondary Connections Single Phase eee ee Line Loac Primary and SET cetat Connections TTA Me tea atm current growing in direction shown by the arrows, it is as if we thrust a north pole (shown by the arrows on "cc") up- ward thru "§8* in the first case, and downward in the second case. In either case Es is in phase with E> or at 180 electrical degrees to it, and the load voltage (E, + E,) is the arithmetical sum or difference of rE, and E. depend- ing upon the angular position of "oc". The value of E, will vary with this angle, as more or less of the primary flux is made to link with the secondary. The following theory of the induction potential regulator is given in order that one not familiar with its operation, but having some knowledge of alternating current phenomena, may be able to follow our design of this machine. The explanation of the regulator is that of a transformer having its secondary in series with some apparatus such as a motor (see fig. 4, 5, and 6), at which the voltage is to be held constant or is to be varied ae desired. The primary is connected across the line and is 80 constructed that it can be rotated thru 180 electrical degrees with respect to the secondary. The magnetic cir- cuite are so arranged that at an extreme position the voltage of the secondary is added to that of the line. At the other extreme, the secondary induced voltage is in the opposite direction thus reducing the service voltage (fig. 5). All possible values of voltage between these limits are obtainable by different positions of the primary. It should be wnderstood that in this type of single phase regulator the magnitude as well as the direction of the voltage is varied by the rotation of the primary. It will be noticed that at one position, the point of zero induced voltage, the secondary coil, being unaffected by the primary, would set up a field of its own, thus acting as & choke coil. This tendency is overcome by placing a short circuited coil on the primary core at right angles to the main winding. In the neutral position thie short circuited winding serves the purpose of the short circuit- ed secondary of a series transformer. The polyphase regulator differs from the single phase in that the induced voltage in the secondary winding is constant and the regulation is affected by shifting the phase relation between the line voltage and the regu- lator voltage. The primary of the regulator is wound with as many circuits as there are phases and produces a rotat- ing magnetic flux of practically constant value. The number of secondary circuits on the stationary core is the same as the primary and the voltage induced in them is of @ constant value, as the magnetizing flux generated by the primary windings is constant. The regulation of the line voltage is obtained as follows: When the regulator is in the position of maximum boost, the line "AB*® (fig. 6b represents the normal bus bar voltage, BC the reguiator voltage and *AC*® the resultant feeder voltage. When the LT Fig. 7 ST lied Fig. 8, core is moved 180 degrees from this position we have the condition of maximum buck and a minimum voltage on the out going feeder, the reguiator voltage is then represented by BD, and the resultant feeder voltage by AD. Inter- mediate compensating voltages may be obtained by rotating the moving element to any desired point. For example, by rotating the primary thru the angle "DBE", the resultant voltage may be made equal to *AE". The three phase regulator is much the same as the single phase regulator except that the e.m.f. added has a constant value, but since it is added vectorially the vector sum may be anything from E, + Ee to ED - E,- Where the induced e.m.f. is in phase with the original e.m.f. we have a 10% boost as in fig. 7. In the case where the rotor has moved thru 6& electrical degrees as in fig. 8, the resultant e.m.f. is thrown a little out of phase with the current. The exact angle is @. 9 = Tan-! .0866 E/E; = Tan7! .0866 = 4° 571 In this case Ez = E,/Cos 4° 571 + .5 x .1 Ey = E, (.9963 + .05 E,) = 1.005 E, + .05 E, = 1.055 F, ora 5.5% boost When the primary has been rotated thru 130 ee ee 1O electrical degrees from the neutral position making it add the e.m.f. to one which is 340 electrical degrees out of phase, it will buck or boost. In fig. 9, Eg = FE, - .05 E,/ Cos © 9 = Tan-! .0866/.95 = Tan “1 .0912 = 5° 10! E5 = .95/.995 Ey 955 FE, then we have 1 - .955 = .045 or 4.5% buck The e.m.f. has the greatest phase displacement when Eg = FE). Or when both cut the circle as in fig. 10. The third side of this triangle is then equal to .1 Ey): By the Cosine Law: (.01 E,)4 = rf + Eg ~ 2x E, x E, x Coe © but E, = E, then (,01 £,)* = 2 x He - 3 x EF x Cos @ and then 01 =23~ 2 Cos @ 68CosO@ = 1.99 Cos 9 = .995 © =5° 45: Which gives a power factor of .995 under the worst conditions, which is a very good performance. The core positions are not arbitrarily chosen, but gradually swing the vectors thru the complete angle and may be stopped at any point. As in fig. 11 suppose an i | | FA Ae 7 Tras 11 the primary is rotated thru 90 electrical degrees then two e.m.f.'s are added, one at 60 electrical degrees and one at 120 electrical degrees, and their resultant falls at 90 degrees to E) and is equal B= (e+ or ef)? and = (1.01 £)# and = 1.004 Ey and has very little effect in buck or boost, while the phase angle is 5° 45°, The stator of the induction regulator, which is the secondary in this case, is precisely like that of an induction motor and may have one or more pairs of poles per phase. In this case one pair is used making eix poles in all. Instead of having alternately, north and south poles as in the generator or synchronous machine, we have (1) a maximum north, (2) a decreasing north, (3) an increas- ing south, (4) a maximum south, (5) a decreasing south, and (6) an increasing north. The pole which is a maximum north one instant, becomes a decreasing north the next, and the one which at the first instant was a decreasing north passes thru zero and becomes an increasing south,and so on, (each flux revolves around the stator) making a revolving field. When the stator is wound for three phases the analysis of magnetic relations is shown in fig. 138, 135, and 14. When current flows in phase A only, in positive " é | hd 3 i ty oe y a 13 direction (A toward A'), the flux is in direction indicated by "Oa*® in fig. 18; similarly, positive direction of current in phases B and C produce flux in the direction "Ob" and "0Oc* respectively. At the instant t,> we see from fig. 15 that phases A, B and C produce fluxes respectively as follows (the ourrents or component fluxes A, B, C of fig. 13 veing 130° apart: a = @, (in positive direction, as indicated by "Oa" in fig. 12) b = g. gin 30° = .5 ¢ (in negative direction, or opposite to "Ob"® in fig. 132) c= g sin 30° = .5 g (in negative direction, or opposite to "Oc*® in fig. 132) In fig. 14 (t,), these three component fluxes "a", "pb", "c"® are combined in proper relative values and direds tions, producing the resultant total flux R = 1.5m, where g is the flux that would be produced by the maximum instane taneous value of the current in any one phase alone. At the inetant tg, 1/13 period or 30 electrical degrees later, the "a" component has decreased to the value @, Cos 30° or 879, but is still in ite positive direction (along "Oa" in fig. 12), the "b* component has reduced to zero; the "c" component has increased in value to g, sin 60° or .87 g., and still is negative, or in direction opposite to *Oc*" in fig. 18. The resultant total flux at this instant is shown as *R* in fig. 14 t , and is seen to have moved 30° from its 3° 13 previous position in fig. 14, t,, 1/12 period earlier, altho it has exactly the same numerical strength, namely, 1.5 O° Between the instants t, and t, the elapsed time is + period, and we see from fig. 14 that meanwhile the position of the resultant flux "R* has progressed steadily at uniform angular velocity thru 90 mechanical degrees, maintaining meanwhile a constant strength represented by 1.5 ga SECTION II DESIGN 14 15 DIVISIONS OF SECTION II Part A Part B Part C Part D Part E --— General Conditions --- Calculations -—~ Construction --- Testing --— Conclusions 16 PART A GENERAL CONDITIONS Thie regulator is to be of a three phase induc- tion type and will in all probability be used for labora- tory experiments. The primary voltage is to be 320 volts alternating current of 6 cycles. The secondary voltage is taken as a plus or minus one-tenth of the primary voltage, or + 83 volts. The dimensions of the stator frame and rotor laminations reduced the possibilities of design by limiting the number of turne of wire that may be used. The data concerning the given parts, that of the stator and of the rotor laminations, is given as follows: STATOR Number Of Blots ..cccccccssceceees eees 62 Minimum width of slots .........eee. eo. 05185 inches Depth of SlOt cccccccscccrscsccsscecs . 1.0 inches Width of slot Slit wcrc ccccccenaae . 094 inches Length of Blot ..ccccccccccccues cee aee 6.5138 inches Minimum width of teeth ..........eeee0. e319 inches Cross section area of one tooth ...... 1.38 sq. in. Cross section area of frame ..........13.%4 eq. in. (Magnetic conditions per pole) Length of path ...ccccccccceccesceses.80000 inches Cross-sectional area of path......... 13.40 eq. in. 17 Length of path in the stator teeth .... 3.00 inches Cross-sectional area of teeth per pole 15.80 sq. in. *Length of path in air gap (assumed).... .031 inches Area of air gap per pole .......-...-+-. 30.00 sq. :in. Humber of slots per pole .......e.ees » 10.00 ROTOR Number Of BLOTS cece rccccccecseceece . 45.0 Width of the slots ............. cece -406 inches Depth of the slots ..... ccc cece cceces 828 inches Length of the slot ....csccccscccesees 66318 inches Cross-sectional area of the frame .... 11.66 inches’ Minimum width of the teeth .....creoee .2665 inches Cross-sectional area per tooth ....... 1.675 sq. in. (Rotor Magnetic Conditions per pole) Length of path in the rotor teeth .... 1.656 inches Cross-sectional area of teeth per pole 13.56 sq. in. Length of path in frame ............-- 18.55 inches Crose-sectional area of path in frame 11.66 eq. in. *I.C.S. Book 45B, Section 30, Page 40. 18 PART B CALCULATIONS Notation Used in the Calculations 9, = Maximum flux Ey = Primary voltage oH cw te sp Qt fo a yp + p Number of Primary turns 6x3.14xf Frequency, cycles per eecond = Secondary voltage 3.14 Number of Secondary turns Sectional area of the Rotor Frame Magnetic Flux Magnetic Permeability Ampere turns Length of magnetic circuit with the proper subscript to the certain magnetic circuit. Current in amperes Eddy current loss Hysteresis current loss Thickness of one lamina in inches Resistance in ohms 19 ML = Mean length of tum AT = Ampere turns per inch of length Q ii Coefficient for leakage @. = Phase angle CALCULATIONS From the conditions given in Part A, the primary voltage is 220 volts. The secondary voltage is assumed as 22 volts or E, = 880 + 33 volts. The frequency is 60 cycles. The cross-sectional area of the stator frame is given as 13.40 square inches, and let it be A: The flux density in the stator frame was assumed as 50,000 lines per square inch. Then in this case @ is equal to A,B and is equal to 30,000 x 15.40 = 462,000 lines in the stator frame. From Sheldon, Mason and Hausman G, = 10° xk mn xwW 20 When substituting n 8 for Dy, 8 lo" 2 EF, _. 108 3 £, 10° x E "a ow x Om Bvt x gf (oat o 8 10° £, Therefore ng = (art ¢ mn 100,000,000 x 328 Substituting the above values ne WB x 3.14 x 60 x 403,000 = 20.04 turme Dy 220 = ; orn, = 800 turns Ne rey From "Dynamo Electric Machines* by Weiner (page 339), also from I.C.8., Book 45B (page 40) ATaiy = AT ap per inch of length, and ATi ron = at rotor ¥ Stotator + Btrotor teeth + Aatyr tor teeth The flux density assumed for the stator frame is 30,000 lines per square inch, then atetator = 5.5 ampere turns per inch of length. 50,000 x 13.4 = 403,000 lines or total flux in the stator frame. 408,000 x .66 = 268,000 lines or total flux in the stator teeth. Bl In three phase work the flux (total) in the frame is 1.5 times that in single phase magnetic paths as discussed in Section I. This condition is also discussed in Timbie and Higbie, Second Course, page 443. aS 000 = 19,400 lines per square inch in stator ° teeth. at stator teeth = 3.5 ampere turns per inch of length. From "*Dynamo-Electric Machines*® by §.P.Thompson, page 6832. C Coefficient of leakage =o x g/t where © i A conetant depending upon the ratio of pole pitch to core length. g = Length of the air gap in inches. t Pole pitch in inches. c = 17 (From tables page 683) g = .051 t = 17.7 ae 3% of the flux is lost by leakage. 100 = 3.5 = 97% of the rotor flux is used in the stator. 288,009 x 100_ = 376,000 lines or total flux in . rotor teeth and the air gap. BE 276,000. = 15,800 lines per square inch in the air Gap. at = 15,800 x .3133 = 4330 ampere turns per inch air gap of length. 8752000 = 63,000 lines per square inch in the rotor ° teeth. at = 3.9 ampere turns per inch of length. rotor teeth 876,000 x 1.5 = 414,000 lines or total flux in rotor frame. 408,000 = 55,500 lines per square inch in the rotor frame. at = 6.6 ampere turns per inch of length. rotor frame Total AT ~ atetator frame * 11 + Stetator teeth * 13 + atiotor teeth * 13 + Strotor frame * 14° + ateir x 15° Total ampere turns stator frame 5.5 x 23.6 = 129.8 Total ampere turns stator teeth 3.5 x 3.0 = 7.0 Total ampere turns air gap 4330.0 x .051 = 134.0 Total ampere turns rotor teeth 3.9 x 1.65 = 6.4 Total ampere turns rotor frame 6.6 x 18.5 = 88.5 Grand Total Ampere turns ........ 559.7 559.7 = 1.8 amperes at full feeder load not 800 including leakage and losses. From "Dynamo Electric Machinery" by 8. P. Thompson page 685, the Magnetizing Current is: In = 83 x Bi, xg (1 + 4) x® w here Bmax = Maximum lines of flux per square inch. g = Width of the air gap. i = Iron reluctance allowance P = Number of pairs of poles per phase. z = Turns per pole. I, = .23 x 13,600 x .031 x 1.15 x ton = 1.16 amperes From “Dynamo Electric Machinery* bg 8. P. Thompson (page 685), the Hysteresis Current is: Ih = In where SE) E) = 220 volte I, = 1.16 = h 52550 -0017 amperes. The no load current from the above reference is: I, = \r3 + 1? = 1.17 amperes. The total primary current equals 1.8 + 1.17 = 2.97 amps. B4 The size of wires selected are based upon a carrying capacity of 1000 amperes per square inch cross- sectional area. From a B and 8 wire table a $14 wire was selected as the correct seize to use for the primary circuit. Assuming a maximum feeder load, as a 10 h.p. motor three phase, the current per phase thru the secondary is: 10 x 746 198 x 3 = 21.5 amperes. From a B and § wire table a $6 wire was selected as the correct size to use for the secondary circuit. The length of an average turn of the stator wind- ing (around one tooth) is 15.5 inches, then 620 x 15.5 = 310 inches 210. = 25.9 feet of wire used per phase and 325.9 x 3 = 78 feet of wtre needed for the three phases. The length of an average turn of the rotor wind- ing (around one tooth) is 15.0 inches, then 200 x 15 = 3000 inches Sogo = 350 feet of wire used per phase and 350 x 3 = 750 feet of wire needed for the three phases. 25 The following table is a list of the Specifica~ tions recommended by the authors: Size of Ampe res No. Lbs. Wire Used Wire Primary 14 B97 10 Circuit Secondary 6 21.50 8 Circuit For the primary wiring use distributed windings. This will require 15 form wound coils of 36 wires each and 30 cails of 37 wires each. In wiring a 7 slot pole, use 8 coils of 26 wires each and 5 coils of 37 wires each. Winding an 8 slot pole, use 3 coils of 26 wires each and 5 coils of 37 wires each. For the secondary wiring use a distributed wind- ing. This will require 60 coils of 1 wire each. Wiring diagrams will be found in the pocket in the back cover of this book. 26 PART C CONSTRUCTION Drawings of the mechanical details may be found in the pocket on the back cover of this book. B7 PART D TESTING The authors had hoped to complete the con- struction of the regulator and run the following tests to ascertain the correctness of their designs I. No load test to determine - a. Hysteresis current. be. Magnetizing current. GC. Copper losses. d. Other losses. II. Full load heat test. III. Efficiency test. PART E CONCLUSIONS B88 WINS \HVINSWS Idd Ns — x <== 2 > ‘Witsivin pone AEN oe | 774 il 3 1293 0 WN