(BQ) Part 2 book Electric machinery fundamentals has contents: DC machinery fundamentals, DC motors and generators, single phase and special purpose motors, the universal motor, other types of motors, introduction to DC motors, the equivalent circuit of a dc motor,... and other contents.
CHAPTER \ I DC MACHINERY FUNDAMENTALS ( LEARNING OBJECTIVES Understand how vo ltage is induced in a ro tating loop Understand how curved pole faces tribute to a constant flux, and thus more constant output voltages Understand and be able to use the equation fo r induced voltage and torque in a de machine Understand comm utation Understand problems with commu tation, including armature reaction and L ~~ effects Understand the power fl ow diagram for de machines DC machines are generators that convert mechanical energy to de electric energy and motors th at convert de electric energy to mechanical energy Most de machines are li ke ac machines in that Lhey have ac voltages and currents within them- de machines have a de output only because a mechanism exists that converts the internal ac voltages to dc voltages at thei r terminals Since tllis mechanism is cal led a commutator, de machinery is also known as commutating machinery The fund amental princi ples involved in the operation of dc mac hines are very simple Unfortunately, they are usually so mewhat obscured by the complicated construction of real macrunes This chapter wi ll first explain the principles of dc machine operation by us ing simple examples and then co nsider so me of the complications that occur in real dc machines 7.1 A SIMPLE ROTATING LOOP BETWEEN CURVED POLE FACES The linear machin e studied in Section 1.8 served as an introducti on to basic machine behavior Its response to loading and to changing magnetic fields closely 404 I I, DC MACHINERY FUNDAMENTALS 405 resembles the behav ior of the real de generators and motors that we will study in Chapter However, real generators and mo tors not move in a straight linethey rotate The next step toward understand ing real de machines is to study the simplest possible example of a rotating machine The simplest possible rotating de machine is shown in Figure 7- It consists of a single loop of wire rotating about a fixed axis The rotating part of this machine is called the rotor, and the stationary part is called the statOl: The magnetic field for the machjne is supplied by the magnetic north and south poles shown on the stator in Figure 7- J Notice that the loop of rotor wire lies in a slot carved in a ferromagnetic core The iron rotor, together with the curved shape of the pole faces, provides a constant-width air gap between the rotor and stator Remember from Chapter that the reluctan ce of air is much higher than the reluctance of the iron in the machine To minimize the reluctance of the flux path thro ugh the machin e, the mag netic flux must take the shortes t possible path through the alr between the pole face and the rotor surface Since the magnetic flu x must take the shortest path through the air, it is perpendicular to the rotor surface everywhere under the pole faces Also, sin ce the air gap is of uni fo rm width, the reluctance is the same everywhere under the pole faces The uni form rel uctance means that the magnetic flu x density is constant everywhere under the pole faces ( The Voltage Induced in a Rotating Loop If the rotor of thi s machine is rotated, a voltage will be ind uced in the wi re loop To determine the magnitude and shape of the voltage, exam ine Figu re 7-2 The loop of wire shown is rectangular, with sides ab and cd perpendicular to the plane of the page and w ith sides be and da parali el to the plane of the page The magnetic field is constant and perpendicular to the surface of the rotor everywhere under the pole faces and rapidly fall s to zero beyond the edges of the poles To determine the total voltage elm on the loop, examine each segment of the loop separately and sum all the resulti ng voltages The voltage o n each segment is given by Equation ( 1-45): e;" = (v x B) -I ( 1-45) Segment abo In thi s segment, the velocity of the wire is tangen ti al to the path of rotation The magnetic field B points out perpendicular to the rotor surface everywhere under the pole face and is zero beyond the edges of the pole face Under the pole face, velocity v is perpendicular to B, and the q uantity v x B points into the page Therefore, the induced voltage on the segme nt is f elx, = (v x B) - = { ~Bl positive in to page under the pole face beyond the pole edges (7-1) '1Ub E LI~C TR I C MAC H INERY i"UNUAM ENTALS o· ( (a) o· ' . + , , b ):00 d + o (1 11 (e) (b) -wm (~ v~~:i:~i: S e: F" N ( (d) FIGURE 7-1 A simple rotaLing loop between curved pole faces (a) Perspective view; (b) view of field lines; (c) lOp view; (d) front view 4U I UC MACHINERY FUN DAMENTALS B r ( FIGURE 7- Z Derivation of an equation for the voltages induced in {he loop Segment be In thi s segment, the quantity v X B is ei ther in to or alit of the page, while length I is in the plane of the page, so v x B is perpendicular to Therefore the voltage in segment be will be zero: (7-2) Segment cd In this segment, the velocity of the wire is tangential to the path of rotati on The magnetic field B points in perpendicular to the rotor surface everywhere under the pole face and is zero beyond the edges of the pole face Under the pole face, velocity v is perpendicular to B, and the quantity v x B points out of the page Therefore, the induced voltage on the segment is (v x B) • I { ~Bl positive out of page under the pole face beyond the pole edges Segment da Just as in segment be, V X (7- 3) B is perpendicular to I Therefore the voltage in this segment will be zero, too: (7-4) The total induced voltage on the loop 2VBl eind = { eind is given by under the pole faces beyond the pole edges (7- 5) 40H ELECrR1C MACl-lINERY FUNDAMENTALS 2vE! vBl - o~ ~ ~f -~ + vB! -2vBl ( FIGURE 7- The output voltage of the loop When the loop rotates througb 180°, segmen t ab is under the north pole face instead of tbe south pole face At th at time, the direction of tbe vo ltage on the segment reverses, but its magn itude remains constant The resulting voltage eta! is shown as a function of time in Figure 7-3 There is an altern ative way to express Equation (7- 5) which clearl y relates the behavior of the single loop to the behavior of larger, real de machines To w Pole surface are:, Af'~ rcrl v = rw Rotor surface area A=2rrrl FIGURE 7-4 Derivation of an alternative form of the induced voltage equation DC MA C HIN~RY FUNDAMENTALS 4U~ derive this alternative expression, examine Figure 7-4 Notice that the tangential velocity v of the edges of the loop can be expressed as where r is the radi us fro m the axis of rotation out to the edge of the loop and Will is the angular velocity of the loop Substituting this expression into Equation (7-5) gives _ {2rWmBI eind - eind ( = 2r1BWm { under the pole faces beyond the pole edges under the pole faces beyond the pole edges Notice al so from Figure that the rotor surface is a cylinder, so the area of the rotor surface A is just equal to 27frl Since there are two poles, the area of the rotor under each pole (ignoring the small gaps between poles) is Ap = 7frl Therefore, under the pole faces beyond the pole edges Since the flu x density B is constant everywhere in the air gap under the pole faces, the (ota.1 flu x under each pole is j ust the area of the pole times its flux density: Therefore, the final fo rm of the voltage equation is _{~¢wm eind - under the pole faces beyond the pole edges (7-6) Thus, the voLtage generated in the machine is equaL to the product of the flux inside the machine and the speed of rotation of the machi11e, multiplied by a constan t represen ting the mechankal construction of the machine In ge neral, the voltage in any real machine will depend on the same three factors: The fl ux in the machine The speed of rotation A constant representing the construction of the machine Getting DC Voltage Out of the Rotating Loop Figure 7-3 is a plot of the voltage etot generated by the rotating loo p As shown, the vo ltage out of the loop is alternately a constant positive val ue and a cons tant negative value How can this machine be made to produce a dc voltage instead of the ac vo ltage it now has? One way to cia this is shown in Figure 7- 5a Here two semicircular conducting segments are added to the end of the loop, and two fixed contacts are set up at 'HU ELb CTRIC M ACHIN ERY I" UN1)AMbNIAL~ ' N Commutator s ( (a) , ,- ¢w - , , - -¢w (b) FIGURE 7- Producing a dc output from the machine with a commutator and bmshes (a) Perspective view; (b) the resulting output voltage an angle such that at the instant when the voltage in the loop is zero, the contacts short-circuit the two segments In this fas hion, every time the voltage of the loop switches direction, the contacts also switch connections, and the output of the con" tacts is always built up in the same way (Figure 7-5b), This connection-switching process is known as commutation The rotating semicircular segments are called commutator segments , and the fixed contacts are called brushes LJI , IVI AI , III I~e l{ Y I-< Ul~UI\IV l tl~ I J-\ L ;) L L 0' N Commutator s ( (a) ~ Current into c-d '" N F cd.ind page ~ \ ~-:.;w Current out of page F S ~,Z: (I-b (b) FIGURE 7-6 Derivation of an equation for the induced torque in the loop Note thaI the iron core is nOI shown in part b for clarity The Induced Torque in the Rotating Loop Suppose a battery is now connected to the machine in Figure 7- The resulting configuration is shown in Figure 7-6 How much torque will be produced in the loop when the switch is closed and a current is allowed to flow into it? To deter- mine the torque, look at the close-up of the loop shown in Figure 7-6b The approach to take in determining the torque on the loop is to look at one segment of the loop at a time and then sum the effects of all the individual segments The force on a segment of the loop is given by Equation ( 1-43) : 12 ELl:K.TRlC MACH INER Y I·' UNDAMENTA LS F = i(l X B) and the torque on the segment is given by '[ = rFsin8 (1 -6) where f) is the angle between r and F The torque is essentially zero whenever the loop is beyond the pole edges While the loop is under the pole faces, the torque is Segment ab oIn segment ab, the current from the battery is directed out of the page The magnetic field under the pole face is pointing radialIy out of the rotor, so the force on the wire is given by F oh i(1 X B ) itB tangent to direction of mo tion (7-7) ( The torque on the rotor caused by this force is Tah rF sin f) rUIB) sin 90" CCW rilB (7-8) Segment be In segment be, the current from the battery is flowing from the upper left to the lower right in the picture The force induced on the wire is given by F bc i(1 X B) o since is parallel to B (7-9) Therefore, (7- 10) Segment cd In segment cd, the current from the battery is directed into the page The magnetic field under the pole face is poi nting radially into the rotor, so the force on the wire is given by tangent to direction of motion ilB (7-11) The torq ue on the rotor caused by this force is Ted rF sin f) rUIB ) sin 90" rilB CCW (7-12): Segment da In segment da, the current from the battery is fJowing from the upper left to the lower right in the picture The force induced on the wire is given by DC MACI-IINERY FUNDAMEN 'IALS 413 i(1 x B) o since is parallel to B (7- 13) Therefore, 'Tda = (7-14) The resulting total induced torque on the loop is given by T md ( = By us ing the facts that Ap duced to {2rilB ~ under the pole faces (7-1 5) beyond the pole edges 7Trl and ", = ApB, the torque expressio n can be re- under the pole faces (7- 16) beyond the pole edges Th us, the torque produced in the machine is the product of the flux in the machine and the current in the machine, times some quantity representing the mechanical construction of the machine (the percentage of the rotor covered by pole faces) In general, the torque in any real machine will depend on th e same three fac tors: The flux in the machine The current in the machine A constant representing the construction of the machine Example 7-1 Figure 7-6 shows a simple rotatin g loop between curved pole faces connected to a battery and a resistor through a swi tch The resistor shown models the total resistance of the battery and the wire in the machine T he physical dimensions and characteristics of this machine are r = 0.5 m R o,3D VB 120 V 1.0 III B 0,25 T (a) What happens when the switch is closed? (b) What is the machine's maximum starling current? What is its steady-state angu- lar velocity at no load? (c) Suppose a load is attached to the loop, and the resulting load torque is 10 N· m What would the new steady-state speed be? How much power is supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or a generator? 666 ELECTR IC MACH INERY FUNDAM ENTA LS and the magnitude of the quadrature-axis component of current is f, = f A cos ( e + 8) = (693 A) cos (36.87 + 4.65) = 519 A Combining magnitudes and angles yields Id = 459 L -85.35° A Iq = 519 L 4.65° A The resulting internal generated vol tage is EA = VrP + RAIA + jXdId + jXqIq = 480 L 0° V + V + )(0.1 0)(459 L = 524 L 4.65° V -85.35° A) + )(0.0750)(519 L 4.65° A) Notice that the magnitude olEA is not much affected by the salient poles, but the angle ofEA is considerably different with salient poles than it is without salient poles ( I C.2 TORQUE AND POWER EQUATIONS OF A SALIENT-POLE MACHINES The power output of a synchronous generator with a cylindrical rotor as a function of the torque angle was given in Chapter as p = 3V", EA sin Ks (4- 20) Thi s eq uation ass umed that the armature resistance was negligible Making the same assumption, what is the output power of a salient-pole generator as a function of torque angle? To find out, refer to Figure C- The power out of a synchronous generator is the sum of the po wer due to the direct-axis current and the power due to the quadrature-axis current: ~ \\ FIGUREC- Determining the power output of a salient-pole synchronous generator Both 1(/ and Iq contribute to the output power, us shown o /) 2'7\', - ,-,-]1 l.Y 'I' G0°,\\ A~\t'fl L S A LJI:: cos Xd 0) sino + 3Vq,(VI> Xqsin 0) cos ° 3VpEA sin + V' (- I - -1 ) sin cos Xd q, Xq Xd Since sin cos = Yz sin 28, this expression reduces to _ 3Vp EA P - X d sm + 3VJ (Xd - Xq) X X d q sm 28 (C-12) The first term of this expression is the same as the power in a cylindrical rotor machine, and the second telm is the additional power due to the reluctance torque in the machine Since the induced torque in the generator is given by 'Tind = Peony/will' the induced torque in the motor can be expressed as (C- 13) The induced torque out of a salient-pole generator as a function of the torque angle Ii is plotted in Figure C- PROBLEMS ( C-l A 2300-V, 1000-kVA, 0.8-PF-lagging, 60-Hz, four-pole, Y-connected synchronous generator has a direct-axis reactance of 1.1 Q, a quadrature-axis reactance of 0.8 Q, and an annature resistance of 0.15 n Friction, windage, and stray losses may be assumed negligible The generator 's open-circuit characteristic is given by Figure P4- l (a) How much field current is required to make VT equal to 2300 V when the generator is running at no load? (b) What is the il1temal generated voltage of this machine when it is operating at rated conditions? How does this value of EA compare to that of Problem4-2b? 668 ELECTRIC MACH INERY FUNDAMENTALS 'find N 'm Total torque Electrical -'-: -',, :IF -',, -~> angle " , degrees I F IGUREC-7 Plot of torque versus torque angle for a salient-pole synchronous generator Note the component of torque due to rotor reluctance ( (e) What fraction of this generator's fu ll-load power is due to the reluctance torque of the rotor? C-2 A 14-pole, V-connected three-phase, water-tu rbi ne-driven generator is rated at 120 MVA, 13.2 kY, 0.8 PF lagging, and 60 Hz Its direct-ax is reactance is 0.62 n and its quadrature-axis reactance is OAO Q All rotational losses may be neglected (a) What internal generated voltage would be required for this generawr LO opera£e at the rated conditions? (b) What is the voltage regulation of this generator at the rated conditions? (c) Sketch the power~vers u s- torque-an gle curve for this generator At what angle is the power of the generator maximum? (ei) How does the maximum power out of this generator compare to the maximum power avail abl e if it were of cylindrical rotor construction? C-3 Suppose that a salient-pole machine is to be Llsed as a motor (aJ Sketch the phasor diagram of a salient-pol e synchronous machine used as a motor (b) Write the equations describing the voltages and currents in this motor (c) Prove that the torque angle obetween EA and V all this motor is given by C-4 If the machine in Problem C- l is running as a motor at the rated conditions, what is the maxi mum torque that can be drawn from its shaft wi lhout it slipping poles when the field current is zero ? I I ! I APPENDIX D TABLES OF CONSTANTS AND CONVERSION FACTORS ( Constants Charge of the electron e = - 1.6 X 1O - 19 C Permeability of free space IlD = Permittivity of free space Eo = 8.854 X 10- 12 F/m 411" X 10- HIm Conversion factors Length meter (m) ~ 3.281 ft = 39.37 in Mass Force kilogram (kg) newton (N) = 0.0685 slug = 2.205 Ib mass (Ibm) = = 0.2248 Ib force (lb · f) 7.233 poundals = 0.102 kg (force) Torque newton-meter (N • m ) = ,738 pound-feet (lb • ft) Energy joule (1) = 0.738 foot -pounds (ft o lb) = 3.725 X 10-7 horsepowe r-hour (hp • h) = 2.778 X 10-7 kilowatt-hour (kWh) watt (W) = 1.341 X 10-3 hp ~ 0.7376 ft · Ibf I s horsepower ~ 746W Magnetic flux weber (Wb) = 108 maxwells (lines) Magnetic flux density I tesla (T) Power ( = l Wb / m2 = 10,000 gauss (G) = 64.5 kilolines/in Magnetizing intensity ampere · turn/m = = 0.0254 A · turns/in 0.0126 oersted COe) 669 INDEX A Acceleration, 4, Acceleration/deceleration circuits, 524 Acceleration ramps, 378 ac circuits, power in, 46-52 ac current, 2, 26-28, 67 ac machines distributed windings, 648- 56 effects of coil pitch, 639 4-8 induced torque, 160 69, 178- 81 induced voltage, 172- 78 magnetomotive force and flux distribution, 169- 72 modeli ng with simple wire loop, 153-60 overview, 152- 53 power flows and losses, 182-86 winding insulation, 182, 183 Across-the-line starting, 357, 359- 61 Air-gap flux density distribntion, 639 Air-gap line, 209 Air-gap power, 321, 324, 333, 593-94 Air gaps, 14, 449 Alternators, 191 See also Synchronous generators Amortisseur windings, 293-97 Ampere 's law, 8-9 Angular acceleration, 4, Angular position, Angular velocity, 3-4 Apparent impedance, 72- 73 S" also Impedance Apparent power autotransformers, 112- 15 in ideal transformer, 72 open-delta transformer connection, 127- 29 in single-phase ac circuits, 49-50,52 synchronous generators, 252- 53,255 in three-phase circuits, 625 transformer ratings, 138- 39 670 Approximate transformer models, 89 Arc welding generators, 542 Armature reaction cylindrical rotor synchronous generators, 198, 199-201 de machines, 433-36, 439 permanent-magnet de motors, 492 salient-pole synchronous generators, 660, 663 64 shunt de motors, 47 1-72, 476 Armatures See Rotors Armature voltage controls bas ic principles, 483- 84 use with field resistance controls, 485-86 Ward-Lenard system, 514-17, 519 Armamre windings coils and, 42 1- 23 connection to commutator segments, 423- 24 copper losses, 455 defined, 192,451 maximum acceptable current, 252- 53,260 Autotransformers apparent power rating advantage, 112-15 basic features, 109-11 internal impedance, 115- 16 speed control with, 588 voltage and current relationships, 111-12 Auxilimy winding, 578-80 Average flnx per turn, 78 B Base speed, 367 , 368- 69, 370 Belt harmonics, 646 B locked-rotor condition, 317 Boldface type, Breadth factor, 650-52 Breakdown torque, 336 See also Pullout torque Brush drop losses, 525 Brush drop voltage, 467 Brushes basic fea lures, 193~94, 41O, 420 effects of commutation problems, 435, 438, 454 in real de machines, 421 , 452- 54 voltage at, 18 Brushless de motors, 606- Brushless exciters, 194-95, 196, 292 Brush losses, 456 Bmsh shifting, 439 ( C Cage rotors basic features, 308, 309- 10 effects of design on induction motor characteristics, 345-48 starting codes, 357, 358 Capability diagrams, 254-59 Capacitive loads, 1, 52 Capacitors synchronous motors as, 289, 290 voltage versus curre nt in, 389, 390 Capacitor-start, capacitor-m n motors, 582- 83 Capacitor-start mo tors, 58 1, 582, 583 Chamfered pole faces , 45 Chorded windings, 422, 64 Classification See also Ratings insulation, 182,261,454-55 rotor construction, 345-50 Clock motors, 600 Code letters, 357, 358 Coercive magnetizing intensity, 492,494 Coercive magnetomotive force, 27 Coils See also Windings construction in de machine rotors, 421-23 harmonics and, 639, 644-48 pitch, 640-41 (See also Fractional-pitch coils) I I I I I IN DEX Common current, 109 Common voltage, 109 Common windings, 109 Commutating poles, 439-42 Commutation frog- leg windings, 432, 433 lap windings, 424-27 problem remedies, 439-44 proble ms in real de machines, 433-38 ( ( in rolating wire loop, 410 rotor coi ls, 42 1-23 simple fou r-loop dc machine, 416-21 wave windings, 427-3 winding connection type~ , 423-24 Commutator construction 452 Commutator pitch, 423 427 Commutator segments, 41 O, 420-21 Compensating windings 443-44 Complex power, 50 51 Compounded de motors, 500-505 Condensers , synchronous motors as, 289, 290 Conductors, 34-35, 421 Consequent-poles method, 363-64 Constant-horsepower connections, 366 Constants 669 Constant-torque connections, 366 Conversion faclors, 669 Copper losses ac machines, 184 de machines, 455-56, 524 impact on transformer efficiency, 102 induction motors, 32 1, 322, 324, 325- 26, 594 in no-load test, 380 in real transformer behavior, 86 Core-form transformers, 67, 68 Core-loss current, 83, 87 Core losses ac machines, 184 basic principles, 26-28, de machines, 456, 525 induction motors, 322, 324 synchronous generators, 205, 206 Countervoltage-sensing relays, 513 Critical resistance, 537 Cross-field theory, 575- 77 Cumulative compounding, 500 671 C umulatively compounded de generators, 543-47 Cumulatively compounded de motors, 501-2 lap windings in 424-28 magnetization curve, 468-69 modeling with simple wire loop, 404-13 Current as motors, 39-41 in delta connections, 620-2 induction motor limits, 394 induction motor starting codes, 357-59 production of magnetic flux , 11 in single-phase ac circuits, 48 starting problems, 42-43 three-phase genemtion, 613- 16 in wye (Y) connections 617-20 Current inrush 139-40 Current-limiting ci rcuits 524 Current-limiting fuses 52 Current paths in rotor windings, 424-27 Current ratio 83-86 C urrent transformers, 69, 141-42 D Damper windings, 248, 293-97 de current behavior in ferromag netic materials, 21-24 early power systems based on, 66-67 starting problems 42-43 dc generators basic features, 527 cumulatively compounded, 543-47 differentially compounded, 547- 51 equivalent circui ts, 528 main types, 526 separately excited, 528-34 series, 540-42 shunt, 534-40 Ward-Lenard system, 16-17 de machines basic linear modeJ, 36-37 commutation in simple fourloop machine, 41 21 commutation problem remedie~, 439-44 commutation problems, 433-38 construction 449-55 defined,404 frog-leg windings, 432, 433 as generators, 1-42 induced torque, 4() 447-48 internal generated voltage, 445-47 JXlwer flows and losses, 455-57 rotor coils, 421 -23 st31ting, 37-39, 42-43 wave windings in, 428-3 1,432 de motors ac power supply for, 566 basic principles 40, 465-66 brushless, 606-9 common applications, 465 compounded, 500-505 efficiency, 524-26 equivalent circuits, 467-68 permanent-magnet, 491 - 93 separately excited, 469, 470 series, 493-99, 500, 566 shunt motor nonlinear analysis 475 76 shunt motor open field circuits, 490-9 shunt motor terminal characteristics, 470-72 shunt type defined, 470 speed control , 479-90, 514-24 starting, 505-14 de test, 382-83 Deceleration ramps, 378 Deep-bar rOIOrs, 347-48 Delta-delta connections, 123 Delta-wye connections, 121-22 Delta connections, 620-21, 624 Demagneti zation, 492 Derating 135 ,367 Design classes See Classification Developed mechanical power, 324 Developed torque, 325 Differentially compounded dc generators, 547-51 Differentially compounded dc motors, 502-3 Direct synchronous reactance, 663 Distributed windings, 648-56 Distribmion factor, 650-52 Distribmion fransformers, 69 Diverter resistors, 545, 546 Domains in ferromagnetic materials, 27-28 Dot convention, 70-71, 83-84 85,500 Double-cage rotors, 348 672 INDEX Double-layer windings, 650 Double-revolving-field theory, cumulatively compounded dc generator, 543 de generators, 527,528 dc motors, 467- 68 differentiall y compounded dc generators, 548 induction motors, 315- 21, 570-73, 590 Drooping frequency-power characteristics, 229, 242-44 Duplex windings, 423 Dynamic stability limit, 245 46 380- 87 E Eccentric pole faces, 451 Eddy current losses ac machines, 184 defined, 28 impact on transformer efficiency, 102 ind uction motors, 321 in real transformer behavior, 86 reducing, 31 - 32 Edison, Thomas, 66 Efficiency ac machines, 184 de motors, 524-26 induction motors, 354-57 relation to power factor in synchronous motors, 288 transformers, 102- Electrical losses, 184,455-56 See also Copper losses Electrical machines, 1-2 Electric clocks, 600 Electric power grid, generator behavior in, 233- 37 Energy conversion factors, 669 Energy losses ac machines, 182- 85 compensati ng for, 83 dc machines, 455-58 , 524 26 in early power generating systems, 66 in ferromagnetic cores, 26- 28, 31 induction motors, 32 1- 22, 324- 26, 380 major types in real transformers, 86, 102 reducing, 1-32, 354- 55 sing le-phase induction motors, 592, 594 synchronous generators, 194, 205, 206, 253 synchronous motors , 288 transformer functions and, 67 Energy recovery, 391-92 English units, 2-3, 669 Equalizers, 425- 27 Equivalent circuits compounded de motors, 501 real transfo rmers, 86-94 salient-pole synchronous generator, 660- 66 separately excited dc generators, 528, 529 series de generator, 541 series dc motor, 495 shunt dc generators , 535 single-phase induction motors, 590-97 synchronous generators, 198- 202,203 synchro nous motors, 272- 73 Equivalent field currents, 476, 531 Excitation current modeling for transformers, 87 as percentage of full load , 89 real single-phase transformers, 83,84 Exciters, brushless, 194- 95, 196, 292 F Fan torque connections, 366 Fan torque patterns, 379 F