Chapter 2 DC Machines

Transcription

1 Chpter 2 DC Mchines 3.1 Introduction Converters tht re used to continuously trnslte electricl input to mechnicl output or vice vers re clled electric mchines. The process of trnsltion is known s electromechnicl energy conversion. An electric mchine is therefore link between n electricl system nd mechnicl system. In these mchines the conversion is reversible. If the conversion is from mechnicl to electricl energy, the mchine is sid to ct s genertor. If the conversion is from electricl to mechnicl energy, the mchine is sid to ct s motor. These two effects re shown in Fig In these mchines, conversion of energy from electricl to mechnicl form or vice vers results from the following two electromgnetic phenomen: ١. When conductor moves in mgnetic field, voltge is induced in the conductor. (Genertor ction) ٢. When current crrying conductor is plced in mgnetic field, the conductor experiences mechnicl force. (Motor ction)

2 44 Chpter Two Mechnicl Energy Genertor Motor Electricl Energy Fig.3.1 The Energy directions in genertor nd motor ctions. These two effects occur simultneously whenever energy conversion tkes plce from electricl to mechnicl or vice vers. In motoring ction, the electricl system mkes current flow through conductors tht re plced in the mgnetic field. A force is produced on ech conductor. If the conductors re plced on structure free to rotte, n electromgnetic torque will be produced, tending to mke the rotting structure rotte t some speed. If the conductors rotte in mgnetic field, voltge will lso be induced in ech conductor. In generting ction, the process is reversed. In this cse, the rotting structure, the rotor, is driven by prime mover (such s stem turbine or diesel engine). A voltge will be induced in the conductors tht re rotting with the rotor. If n electricl lod is connected to the winding formed by these conductors, current i will flow, delivering electricl power to the lod. Moreover, the current flowing through the conductor will interct with the mgnetic field to produce rection torque, which will tend to oppose the torque pplied by the prime mover.

3 DC Mchines 45 Note tht in both motor nd genertor ctions, the coupling mgnetic field is involved in producing torque nd n induced voltge. 3.2 Induced Voltge An expression cn be derived for the voltge induced in conductor moving in mgnetic field. As shown in Fig.3.2, if conductor of length l moves t liner speed v in mgnetic field B, the induced voltge in the conductor cn be obtined with the help of frdy s lw s shown in the following eqution: e = Blv (3.1) where B, l, nd v re mutully perpendiculr. The polrity (Direction) of the induced voltge cn be determined from the so-clled Fleming's Right-Hnd Rule s explined in the previous chpter. The direction of this force is shown in Fig.3.2(b).

4 46 Chpter Two Fig.3.2 Motionl voltge, () Conductor moving in the mgnetic field. (b) Right hnd screw rule. Fleming's Right-Hnd Rule Hold out your right hnd with forefinger, second finger, nd thumb t right ngles to one nother. If the forefinger represents the direction of the field, nd the thumb represents the direction of the motion then, the second finger represents the direction of the induced emf in the coil. 3.3 Electromgnetic Force, f For the current-crrying conductor shown in Fig.3.3(), the force (known s Lorentz force) produced on the conductor cn be determined from the following eqution:

5 DC Mchines 47 f = Bli (3.2) where B, l, nd i re mutully perpendiculr. The direction of the force cn be determined by using the Fleming s Left Hnd Rule or right-hnd screw rule s explind in the previous chpter nd re stted in the following. The direction of the force is illustrted in Fig.3.3(b). Fleming s Left Hnd Rule: Hold out your left hnd with forefinger, second finger nd thumb t right ngles to one nother. If the forefinger represents the direction of the field, nd the second finger tht of the current, then thumb gives the direction of the motion or force. Right-Hnd Screw Rule: Turn the current vector i towrd the flux vector B. If screw is turned in the sme wy, the direction in which the screw will move represents the direction of the force f. Note tht in both cses (i.e., determining the polrity of the induced voltge nd determining the direction of the force) the moving quntities (v nd i ) re turned towrd B to obtin the screw movement.

6 48 Chpter Two Equtions (3.1) nd (3.2) cn be used to determine the induced voltge nd the electromgnetic force or torque in n electric mchine. There re, of course, other methods by which these quntities (e nd f) cn be determined. Fig.3.3 Electromgnetic force. () Current-crrying conductor moving in mgnetic field. (b) Force direction. 3.4 Simple Loop Genertor In Fig.3.4 is shown single turn rectngulr copper coil ABCD moving bout its own xis, mgnetic field provided by either permnent mgnets or electromgnets. The two ends of the coil re joined to two slip-rings or discs nd b which re insulted from ech other nd from the centrl shft. Two collecting brushes (of crbon or copper) press ginst the slip rings. Their function is to collect the current induced in the coil nd to convey it to the externl lod resistnce R.

7 DC Mchines 49 A D φ N B C S y x 1 Lod 2 b Fig.3.4 Simple loop genertor Working Theory: Imgine the coil to be rotting in clockwise direction (Fig:3.5). As the coil ssumes successive positions in the field, the flux linktd with it chnges. Hence, n EMF is induced in it which is dφ proportionl to the rte of chnge of flux linkges ( e = N ). dt When the plne of the coil is t right ngles to the lines of flux s shown in Fig.3.5 (), then, the direction of velocity of both sides of the coil is prllel to the direction of the field lines so, there is no cutting for the field lines. Then flux linkges with the coil is

8 50 Chpter Two minimum. Hence; there is no inducxd EMF in the coil. Let us tke this no emf on verticl position of the coil s the strting position. The ngle of rottion or time will be mesured from this position so we cn determine the first point (ngle 0 o ) of Fig.3.6. A D D A B C X 1 C b 2 Y B X 1 b 2 Y

9 DC Mchines 51 C B A D D A X 1 B b 2 Y C X 1 b 2 Y Fig.3.5

10 52 Chpter Two Fig.3.6 As the coil continues rotting further, the rte of chnge of flux linkges (nd hence induced EMF in it) increses, till position 2, Fig.3.5 (b) is reched t 90 degrees. Here the coil plne is horizontl i.e. prllel to the lines of flux. As seen, the rte of chnge of flux linkges is mximum. Hence, mximum EMF is induced in the coil s shown in Fig.3.6 t 90 degrees nd the direction of current flow is ABXYCD s shown in Fig.3.5 (b). In the next qurter revolution i.e. from o to 180 o 90, the rte of chnge of flux linkges decreses. Hence, the induced EMF decreses grdully till in position 4 Fig.3.5(c) of the coil, it is reduced to zero vlue nd the direction of current flow is ABXYCD s shown in Fig.3.5 (b). Note tht:

11 DC Mchines 53 The direction of this induced EMF cn be found by pplying Fleming's Right hnd rule. So, the current through the lod resistnce R flows from X to Y during the first hlf revolution of the coil. In the next hlf revolution i.e. from 180 to 360 degrees, the vritions in the mgnitude of EMF re similr to those in the first hlf revolution but it will be found tht the direction of the induced current is from D to C nd B to A. Hence, the pth of current flow is long DCYXBA which is just the reverse of the previous direction of flow. Therefore, we find tht the current the resistive lod, R which we obtin from such simple genertor reverses its direction fter every hlf revolution s shown in Fig.3.5 nd Fig.3.6. Such current undergoing periodic reversls is known s lternting current. It is, obviously, different from direct current which continuously flows in one nd the sme direction which we need to generte from the DC genertor. So, we sould mke some modifiction to get unidirection current in the lod which will be explined soon. It should be noted tht lternting current not only reverses its direction, it does not even keep its mgnitude constnt while flowing in ny one direction. The two hlfcycles my be clled positive nd negtive hlf cycles respectively (Fig.3.6).

12 54 Chpter Two For mking the flow of current unidirectionl in the externl circuit, the slip rings re replced by split rings which shown in Fig.3.7. The splitrings re mde out of conducting cylinder which is cut into two hlves or segments insulted from ech other by thin sheet of mic or some other insulting mteril. As before, the coil ends re joined to these segments on which rest the crbon or copper brushes. In the prcticl genertor which hs more thn two poles nd more thn one coil the split rings hs not just two hlves but hs mny prts s shown in Fig.3.7 (b). Segments b Mic Bruches Fig.3.7 () Two segments split rings in simple genertor loop. (b) Mny segments split rings in Prcticl genertor loop.

13 DC Mchines 55 It is seen (Fig.3.8() to Fig.3.8 (b)) tht in the first hlf revolution current flows long ABXYCD i.e. the brush No. 1 in contct with segment cts s the positive end of the supply nd b s the negtive end. In the next hlf revolution (Fig.3.8 (c) to Fig.3.8 (d)), the direction of the induced current in the coil hs reversed. But t the sme time, the positions of segments nd b hve lso reversed with the result tht brush No. 1 comes in touch with tht segment which is positive i.e segment b in this cse. Hence, the current in the lod resistnce gin flows from X to Y. The wveform of the current through the externl circuit is s shown in Fig.3.9. This current is unidirectionl but not continuous like pure direct current. It should be noted tht the position of brushes is so rrnged tht the chngeover of segments nd b from one brush to the other tkes plce when the plne of the rotting coil is t right ngles to the plne of the flux lines. It is so becuse in tht position, the induced EMF in the coil is zero.

14 56 Chpter Two A D D A B C C B b 1 2 b 1 2 X Y X Y

15 DC Mchines 57 C A A D D B B C b 1 2 b 1 2 X Y X Y Fig.3.8

16 58 Chpter Two Fig.3.9 Commuttor The function of the commuttor is to fcilitte collection of current from the rmture conductors i.e. converts the lternting current induced in the rmture conductors into unidirectionl current in the externl lod circuit. It is of cylindricl structure nd is built up of wedge-shped:segments of high conductivity hrd-drwn or drop-forged 3.5 Prcticl Genertor The simple loop genertor hs been considered in detil merely to bring out the bsic principle underlying the construction nd working of s ctul genertor illustrted in Fig.3.10 which consists of the following essentil prts: (i) Mgnetic Frme or Yoke (ii) Pole-cores nd Pole-shoes (iii) Pole Coils or Field Coils (iv) Armture Core (v) Armture Windings or (vi) Commuttor (vii) Brushes nd Berings Of these, the yoke, the pole cores, the rmture core nd ir gps between the poles nd the rmture core form the mgnetic circuit wheres the rest form the electricl circuit.

17 DC Mchines 59 Fig.3.10 Prcticl DC mchine prts. Armture Windings Two types of windings mostly employed for the rmtures of DC mchines re known s Lp Winding nd Wve Winding. The difference between the two is merely due to the different rrngement of the end connections t the front or commuttor end of rmture. The following rules, however, pply to both types of the windings:

18 60 Chpter Two In lp winding, the number of prllel pths () is lwys equl to the number of poles (b) nd lso to the number of brushes. In wve windings, the number of prllel pths () is lwys two nd there my be two or more brush positions. The coils of rotor prt or rmture re rrnged in mny options which inflounce the performnce of DC mchines. Now, we will briefly discuss the winding of n ctul rmture. But before doing this, we hve to explin mny terms s shown in the following items. Pole-pitch The periphery of the rmture divided by the number of poles of the generte. i.e. the distnce between two djcent poles It is equl to the number of rmture conductors (or rmture slots) per pol. If there re 400 conductors nd 4 poles, then pole pitch is 400/4= 100 conductor. Coil spn or Coil pitch It is the distnce, mesured in terms of rmture slots (or rmture conductors), between two sides of coil. It is, in fct, the

19 DC Mchines 61 periphery of the rmture spnned by the two sides of the coil s shown in Fig End connections Coil sides Coil Spn Fig.3.11 One rmture coil. Bck Pitch The distnce, mesured in terms of the rmture conductors. which coil dvnces on the bck of the rmture is clled bck pitch nd is denoted by Y b. It is equl'to the number difference of the conductors connected to given segment of the commuttor.

20 62 Chpter Two Front Pitch The number of rmture conductors or elements spnned by coil on the front (or commuttor end of n rmture) is clled the front pitch nd is designted by Y f s shown in Fig Alterntively, the front pitch my be defined s the distnce (in terms of rmture conductors) between the second conductor of one coil nd the first conductor of the next coil which re connected together to commuttor end of the rmture. In other words, it is the number difference of the conductors connected together t the bck end of the rmture. Both front nd bck pitches for lp nd wve-winding re shown in Fig nd Fig.3.13 respectively.

21 DC Mchines 63 y b y f ` y r y r Fig.3.12 y b y r y f Fig.3.13

22 64 Chpter Two Resultnt Pitch It is the distnce between the beginning of one coil nd the beginning of the next coil to which it is connected s shown in Fig.3.12 nd Fig As mtter of precution, it should be kept in mind tht ll these pitches, though normlly stted in terms of rmture conductors, re lso sometimes given in terms of rmture slots or commuttor brs. Commuttor Pitch (Y c ) It is the distnce (mesured in commuttor brs or segments) between the segments to which the two ends of coil re connected s shown in Fig.3.12 nd Fig From these figures it is cler tht for lp winding, Y c is the difference of Y b nd Y f wheres for wvewinding it is the sum of Y b nd Y f. 21-2t, Single-lyer Winding It is tht winding in which one conductor or one coil side is plced in ech rmture slot s shown in Fig Such winding is not much used. 2t-2Z. Two-Lyer Winding In this type of winding,' there re two conductors or coil sides-per slot rrnged in two lyers. Usully, one side of every coil lies in the upper hlf of one slot nd other side lies in the lower

23 DC Mchines 65 hlf of some other slot t distnce of pproximtely one pitch wy (Fig.3.15). 1 he trnsfer of, the coil from one slot to nother is usully mde in rdil plne by mens of peculir bend or twist t the bck

24 66 Chpter Two Lp nd wve windings The winding types of the rmture of the DC mchines cn be devided to two min types, Lp nd Wve windings. The min difference between them is the method of connecting the terminls of coils to the commuttor segments. In cse of lp wound there re two kinds, the simplex lp winding nd multiple lp winding. For simple lp winding the two terminls of one coil is connected to djusent two commuttor segments s shown in Fig.3.12 nd Fig Generted EMF Eqution of Genertor. Let φ =flux/pole in weber.

25 DC Mchines 67 Z=totl number of rmture conductors = No. of slots*no. of conductors/slot. P=No. of poles. A= No. of prllel pths in rmture. N=rmture rottion in rpm E=EMF induced in ny prllel pth in rmture. Generted EMF=e.m.f. generted in one of the prllel pths. dφ Averge EMF generted/conductor= volt (3.3) dt Now, flux cut/conductor in one revolution, dφ = φ * P web. (3.4) Number of revolution per second =N/60; Then, time for one revolution, dt=60/n second Hence ccording to Frdy's lws of electromgnetic induction, dφ φpn EMF generted/conductor= = Volt (3.5) dt 60 For wve-wound genertor No. of prllel pths is 2 No. of conductors (in series) in one pth=z/2 φpn Z φzpn Then, EMF generted/pth= * = Volt (3.6) For lp-wound genertor No. of prllel pths =P No. of conductors (in series) in one pth=z/p

26 68 Chpter Two φpn Then, EMF generted/pth= * 60 Z P φpn Z In generl, generted EMF = * 60 A Where A=2 for wve-winding. And A= P for lp-winding. φzn = Volt (3.7) 60 Volt (3.8) 3.8 Clssifiction Of DC Mchines The field circuit nd the rmture circuit cn be interconnected in vrious wys to provide wide vriety of performnce chrcteristics n outstnding dvntge of DC mchines. Also, the field poles cn be excited by two field windings, shunt field winding nd series field winding s shown in Fig.3.9. The shunt winding hs lrge number of turns nd tkes only smll current (less thn 5% of the rted rmture current). This winding cn be connected cross the rmture (i.e., prllel with it), hence the nme shunt winding. The series winding hs fewer turns but crries lrge current. It is connected in series with the rmture, hence the nme series winding. If both shunt nd series windings re present, the series winding is wound on top of the shunt winding, s shown in Fig.3.9.

27 DC Mchines 69 Fig.3.9 Series nd shunt field winding DC genertors. The vrious connections of the field circuit nd rmture circuit re shown in Fig In the seprtely excited DC mchine (Fig.3.10 ), the field winding is excited from seprte source. In the self-excited DC mchine, the field winding cn be connected in three different wys. The field winding my be connected in series with the rmture (Fig.3.10b), resulting in series DC mchine; it my be connected cross the rmture (i.e., in shunt), resulting in shunt mchine (Fig.3.10c); or both shunt nd series windings my be used (Fig.3.10d ), resulting in compound mchine. If the shunt winding is connected cross the rmture, it is known s short-shunt mchine. In n lterntive connection, the shunt winding is connected cross the series connection of rmture nd series winding, nd the mchine is known s long-shunt mchine. There is no significnt difference between these two connections, which re shown in Fig.3.10d. In the compound mchine, the

28 70 Chpter Two series winding mmf my id or oppose the shunt winding mmf, resulting in different performnce chrcteristics. () (b) (c) (d) Fig.3.10 Different connections of DC mchines. () Seprtely excited DC mchine. (b) Series DC mchine. (c) Shunt DC mchine. (d) Compound DC mchine. A rheostt is normlly included in the circuit of the shunt winding to control the field current nd thereby to vry the field mmf.

29 DC Mchines 71 Field excittion my lso be provided by permnent mgnets. This my be considered s form of seprtely excited mchine, the permnent mgnet providing the seprte but constnt excittion. Exmple 3.1 A 4 pole, long-shunt, compound gtertor supplys 100 A t terminl voltge of 500 V. If rmture resistnce is 0.02Ω, series field resistnce it 0.04 Ω nd shunt field resistnce 100Ω, find the generted EMF. Tke drop per brush s 1 V, Neglect rmture rection. Solution: Genertor circuit is shown in Fig.3.11 Fig.3.11

30 72 Chpter Two 500 I sh = = 5 A 100 Current through rmture nd series field winding is: =100+5=105 A Voltge drop on series field windings=105*0.04=4.2v Armture voltge drop= 105 * 0.02=3.1 volt Drop t brushes= 2 * 1= 2 V Now, EMF = V + I R + series drop brush drop (3.9) + = = Volt Exmple 3.2 A 20 kw compound genertor works on full lod with terminl voltge of 250 V. The rmture, series nd shunt windings hve resistnces of 0.05Ω, 0.025Ω nd 100 Ω respectively. Clculte the totl EMF generted in the rmture when the mchine is connected s short shunt. Solution: Genertor voltge is shown in Fig Lod current =20000/250=80 A Voltge drop in the series windings =80*0.025=2V Voltge cross shunt winding=252 V.

31 DC Mchines I sh = = 2. 52A 100 I = = A IR = 82.52*0.05 = 4. 13V Then the generted EMF= =256.13V Fig.3.12 Exmple 3.3 The following informtion is given for 300 kw, 600 V, long-shunt compound genertor: Shunt field resistnce=75ω, rmture resistnce including brush resistnce= 0.03 Ω, commutting field winding resistnce=0.011ω, series field resistnce=0.012 Ω, divertor resistnce =0.036 Ω. When the mchine is delivering full lod, clculte the voltge nd power generted by the rmture.

32 74 Chpter Two Solution: Genertor voltge is shown in Fig Fig.3.13 Power output= 300,000 W Output current =300,000/600=500 A I sh I = = 600/75=8 A 500+8=508 A Since the series field resistnce nd divertor resistnce re in prllel (Fig.3.13) their combined resistnce is : * 0.036/0.048=0.009 Ω Totl rmture circuit resistnce = =0.05 Ω

33 DC Mchines 75 Voltge drop =508*0.05=25.4 V Voltge generted by rmture= =625.4 V Power generted= 625.4*508=317,700 W=317.7 kw Exmple 3.4 A 4 pole, lp;wound, DC shunt genertor hs useful flux per pole of 0.07 Wb. The rmture winding consists of 220 turns ech of Ω resistnce. Clculte the terminl voltge when running t 900 rpm if the rmture current is 50 A. Solution: Since ech turn hs two sides, Z=220 x 2 =440 ; N=900 rpm ; φ=0.07 Wb ; P=A=4 ZN P 0.07 * 440*900 4 E = φ * = * = 462Volt 60 A 60 4 Totl resistnce of 220 turns or 440 conductors=220*0.004=0.88ω Since, there re 4 prllel pths in rmture,. Resistnce of ech pth=0.88/4=0.22 Ω There re four such resistnces in prllel ech of vlue 0.22Ω Armture resistnce, R =0.22/4=0.055 Ω Armture drop = I R =50*0.055=2.75 volt Now, terminl voltge V = E I R,= = volt

34 76 Chpter Two Exmple 3.5 A 4 pole, DC shunt genertor with shunt field resistnce of 100 Ω nd n rmture resistnce of 1 Ω hs 378 wve-connected conductors in its rmture. The flux per pole is 0.01 Wb. If lod resistnce of 10 Ω is connected cross the rmture terminls nd the genertor is driven t 1000 rpm, clculte the power bsorbed by the lod. Solution: Induced EMF. in the genertor is: ZN P 0.02*378* E = φ * = * = 252Volt 60 A 60 2 Now let V be the terminl voltge i.e. the voltge vilble cross the lod s well s the shunt resistnce (Fig.3.14). Lod current= V/10 mpere nd shunt current= V/100 mpere Armture current= V V 11V + = Now, V=E rmture drop 11V Then, V = 252 1* = 227Volt 100 Lod current =227/10=22.7A;

35 DC Mchines 77 Power bsorbed by the lod is 227*22.7=5 153 W. 3.9 Armture Rection (AR) With no current flowing in the rmture, the flux in the mchine is estblished by the mmf produced by the field current (Fig.3.14). However, if the current flows in the rmture circuit it produces its own mmf (hence flux) cting long the q-xis. Therefore, the originl flux distribution in the mchine due to the field current is disturbed. The flux produced by the rmture mmf opposes flux in the pole under one hlf of the pole nd ids under the other hlf of the pole, s shown in Fig.3.14b. Consequently, flux density under the pole increses in one hlf of the pole nd decreses under the other hlf of the pole. If the incresed flux density cuses mgnetic sturtion, the net effect is reduction of flux per pole. This is illustrted in Fig.3.14c. At no lod ( I = 0) = t I the terminl voltge is the sme s the generted voltge ( E ) V =. As the lod current flows, if the t0 0 flux decreses becuse of rmture rection, the generted voltge will decrese (Eqution (3.6) nd (3.8) ). The terminl voltge will further decrese becuse of the I drop (Eqution (3.9)). R

36 78 Chpter Two

37 DC Mchines 79 Fig.3.14 Armture rection effects. In Fig.3.14d, the generted voltge for n ctul field current I f(ctul) is E 0. When the lod current I, flows the generted voltge is E = V + I R If E < E, the flux hs decresed (ssuming t o the speed remins unchnged) becuse of rmture rection, lthough the ctul field current I f(ctul) in the field winding remins unchnged. In Fig.3.14b, the generted voltge E is produced by n effective field current I f(eff). The net effect of rmture rection cn therefore be considered s reduction in the field current. The difference between the ctul field current nd effective field current cn be considered s rmture rection in equivlent field current. Hence,. I f ( eff ) = I f ( ctul ) I f ( AR) (3.10) where I f(ar) is the rmture rection in equivlent field current.

38 80 Chpter Two Fig. 3.14d Effect of rmture rection Demgnetizing AT per Pole, Since rmture demgnetising mpere-turns re neutrlized by dding extr mpereturs to the min field winding, it is essentil to clculte their number. But before proceeding further, it should be remembered tht the number of turns is equl to hlf the number of conductors becuse two conductors constitute one turn. Let Z= totl number of rmture conductors I = current in ech rmture conductor I I = for wve winding (3.11) 2 I I P = for lp winding (3.12) θ m forwrd led in mechnicl or geometricl or ngulr degrees. Totl number of conductors in these ngles= 4θ m * 360 z (3.13)

39 DC Mchines 81 Fig.3.15 As two conductors constitute one turn, Then totl number of turns in these ngels = Demgnetising mp-turns per pir of poles Demgnetising mp-turns/pole θ 360 2θ m * 360 2θ m ZI 360 Z (3.14) = (3.15) θ m = ZI (3.16) 360 m AT d per pole= ZI. (3.17) Cross-mgnetizing AT per Pole The conductors lying between ngles AOD nd BOC constitute wht re known s distorting or cross conductors. Their number is found s under: Totl rmture conductors/pole bth cross nd demgnetising =Z/P Demgnetising conductors/pole = 2θ m Z 360 Then, cross-mgnetising conductors/pole Z P 2θ m 1 2θ m Z = Z 360 P 360 = (found bove) Cross-mgnetising mp-condurtors/pole= ZI P (3.18) 2θ m

40 82 Chpter Two Cross-mgnetising mp-turns/pole= ZI 2P θ m (remembering tht two conductors mke one turn) AT c /pole= ZI 2P θ m (3.19) Note. (i) For neutrlizing the demgnetising effect of rmture-rection, n extr number of turns my be put on ech pole. AT No. of extr turns/pole = I AT = I d sh for series genertor d for shunt genertor If the lekge coefficient is given, then multiply ech of the bove expression by it. (ii) If led ngle is given in electricl degrees, it should be converted into mechnicl degrees by the following reltion θ ( electricl) θ ( mechnicl) = or θ pir of pole m θ e 2θ e = = (3.20) P / 2 P Compensting Windings These re used for lrge direct current mchines which re subjected to lrge fluctutions in lod i.e. rolling mill motors nd turbo-genertors etc. Their function is to neutrlize the

41 DC Mchines 83 cross-mgnetizing effect of rmture rection. In the bsence of compensting windings, the flux will be suddenly shifting bckwrd nd forwrd with every chnge in lod. This shifting of flux will induce stticlly induced EMF. in the rmture coils. The mgnitude of this EMF will depend upon the rpidity of chnges in lod nd the mount of chnge. It my be so high s to strike n rc between the consecutive commuttor segments cross the top of the mic sheets seprting them. This my further develop into flsh-over round the whole commuttor thereby shortcircuiting the whole rmture. These windings re embedded in slots in the poleshoes nd re connected in series with rmture in such wy tht the current in them flows in opposite direction to tht flowing in rmture conductors directly below the poleshoes. An elementry scheme of compensting winding is shown in Fig Owing to their cost nd the room tken up by them, the compensting windings re used in the cse of lrge mchines which re subject to violent fluctutions in lod nd lso for genertors which hve to deliver their full-lod output t considerbly low induced voltges.

42 84 Chpter Two Fig No. of Compensting Windings No. of rmture conductors/pole Z = (3.21) P Z No. of rmture turns/pole = (3.22) 2P Then, No. of rmture-turns immeditely under one pole Z Pole rc Z = * 0.7 * (3.23) 2P Pole pitch 2P Then, No. of rmture mp-turns/pole for compensting winding ZI = 0.7 * = 0.7 * rmture mper Turn / pole (3.24) 2P

43 DC Mchines 85 Exmple 3.6 A 4 pole, DC shunt genertor hs simple weve-wound rmture with 35 slots nd 12 conductors per slot nd delivers 35 A on full-lod. If the brush led is 10 spce degrees, clculte the demgnetising nd cross-mgnetising mpere-turns per pole t full-lod. Solution. Z=35 * 12=420; θ m o θ =, = = = A m *17.5* 360 AT d / pole= ZI = = 204At 360 I 35 I AT c /pole 1 θ m 1 10 = ZI = 420*17.5* = 715 At 2P * Exmple 3.7 A 250 V, 500 kw, 8 pole DC genertor hs lp-wound rmture with 480 conductors. Clculte the demgnetising nd cross-mgnetising mpere-turns per pole t full-lod if the brushes re given forwrd led of 7.5 mechnicl. Solution:. Output current =500,000/250=2,000 A 2000 I = 2000 A, I = = 250A, Z = 480, θ m = θ m 7.5 AT d / pole= ZI = 480* 250 * = 2500.At o

44 86 Chpter Two 1 θ m AT c /pole= ZI = 480* 250* = 5000 At 2P 360 2*8 360 Exmple 3.8 A 4 pole, wve-wound motor rmture hs 880 conductors nd delivers 120 A. The brushes hve been displced through 3 ngulr degrees from the geometricl xis. Clculte () demgnetising mp-turns/pole (b) cross-mgnetising mp-turns/pole (c) the dditionl field current for neutrlizing the demgnetistion if the field winding hs 1100 turns/pole. Solution:. 120 Z=880 ; I= = 60A, θ = 3 2 θ m 3 () AT d / pole = ZI = 880* 60* = 440 At (b) AT c /pole= 880 * 60 * = Z I Or totl AT d /pole= * = * = 6600At P Hence AT c /pole=totl AT/pole -AT d /pole = =6160 (c) Additionl field current= 440/1100=0.4 A o Exmple 3.9 A 4 pole genertor supplies current of 143 A. It hs 492 rmture conductors () wve-wound (b) lp-connected. When delivering full lod, the brushes re given n ctul led of

45 DC Mchines 87 o 10. Clculte the demgnetising mp-turns/pole. This field winding is shunt connected nd tkes 10 A: Find the number of extr shunt field turns necessry to neutrlize this demgnetistion. Solution.: Z=492 ; o θ =10 ; AT d /pole= I = =153 A ; I=153/2...when wve wound I=153/4...when lp-wound () AT d / pole ZI * θ = 492 * * = At Extr shunt field turns =1046/10=105 pprox (b) AT d /pole= 492 * * = Extr shunt field turns =523/10=52 (pprox.) Exmple A 4 pole, 50-kW, 250-V wve-wound shunt genertor hs 400 rmture conductors. Brushes re given led of 4 commuttor segments. Clculte the demgnetistion mp-turns/pole if shunt field resistnce is 50 Ω. Also clculte extr shunt field turns/pole to neutrlize the demgnetistion. Solution.

46 88 Chpter Two Lod current supplied=50,000/250=200 A 250 I sh = = 5A 50 Then I = = 205A Current in ech conductor No. of commuttor segments Then, No. of segments θ m no. ofsegments *360 = = 200 AT d / pole I=205/2=102.5 A =Z/Awhere A=2.for wve winding =400/2=200 segments 4* = 400 * * = *360 = sh = 36 deg rees 5 ATd 820 Extr shunt turns/pole = = 164 turns I 5 At Exmple 3.11 A 30 h.p. (British) 440 V, 4 pole, wve-wound DC shunt motor hs 840 rmture conductors nd 140 commuttor segments. Its full lod efficiency is 88% nd the shunt field current is 1.8 A. If brushes re shifted bckwrds through 1.5 segment from the geometricl neutrl xis, find the demgnetising nd distorting mp-turns/pole.

47 DC Mchines 89 Solution: Fig.3.17 The shunt motor is shown digrmmticlly in Fig.3.17 Motor output=30 * 746 W, - η = 0. 88% 30*746 Motor input = = 0.88 Motor input current= 25432W = 57.8A 440 I sh = 1.8A, I = = 56A Current in ech conductor = 56/2=28 A θ m = 1.5*360 /140 = 27 / 7 deg rees 27 AT d / pole = 840 * 28* = 252 At 7 * AT c /pole= 840 * 28* = 2688 At 8 7 *360

48 90 Chpter Two 3.10 Shifting The Brushes To Improve Commuttion Due to the shift in the neutrl zone (Fig.3.18) when the genertor is under lod, we could move the brushes to reduce the sprking. For genertors, the brushes re shifted to the new neutrl zone by moving them in the direction of rottion. For motors, the brushes re shifted ginst the direction of rottion. As soon s the brushes re moved, the commuttion improves, mening there is less sprking. However, if the lod fluctutes, the rmture mmf rises nd flls nd so the neutrl zone shifts bck nd forth between the no lod nd full lod positions. We would therefore hve to move the brushes bck nd forth to obtin sprk-

49 DC Mchines 91 less commuttion. This procedure is not prcticl nd other mens re used to resolve the problem. For smll DC mchines, however, the brushes re set in n intermedite position to ensure resonbly good commuttion t ll lods. Fig.3.18 () Mgnetic field produced by the current flowing in the rmture conductors.

50 92 Chpter Two Fig.3.18 (b) Armture rection distorts the field produced by the N, S poles Commutting Poles (Interpoles Windings) To counter the effect of rmture rection in medium nd lrge-power DC mchines, we lwys plce set of commutting poles (Sometimes clled interpoles windings) between the min poles (Fig.3.19). These nrrow poles crry windings tht re connected in series with the rmture. The number of turns on the windings is designed so tht the poles develop mgnetomotive force mmf c equl nd opposite to the mgnetomotive force mmf of the rmture. As the lod current vries, the two mgnetomotive forces rise nd fll together, exctly bucking ech other t ll

51 DC Mchines 93 times. By nullifying the rmture mmf in this wy, the flux in the spce between the min poles is lwys zero nd so we no longer hve to shift the brushes. In prctice, the mmf of the commutting poles is mde slightly greter thn the rmture mmf. This cretes smll flux in the neutrl zone, which ids the commuttion process. Fig.3.19 shows how the commutting poles of 2-pole mchine re connected. Clerly, the direction of the current flowing through the windings indictes tht the mmf of the commutting poles cts opposite to the mmf of the rmture nd, therefore, neutrlizes its effect. However, the neutrliztion is restricted to the nrrow brush zone where commuttion tkes plce. The distorted flux distribution under the min poles, unfortuntely, remins the sme.

52 94 Chpter Two Fig.3.19 Commutting poles produce n mmf c tht opposes the mmf of the rmture Seprtely Excited Genertor Now tht we hve lerned some bsic fcts bout DC genertors, we cn study the vrious types nd their properties. Thus, insted of using permnent mgnets to crete the mgnetic field, we cn use pir of electromgnets, clled field poles, s shown in Fig When the DC field current in such genertor is supplied by n independent source (such s storge bttery or nother genertor, clled n exciter), the genertor is sid to be seprtely excited. Thus, in Fig.3.20 the DC source connected to terminls nd b cuses n exciting current I X to flow. If the rmture is driven by motor or diesel engine, voltge E o ppers between brush terminls x nd y.

53 DC Mchines 95 Fig.3.20 Seprtely excited 2-pole genertor. The N, S field poles re creted by the current flowing in the field windings. 3.1 No-Lod Opertion And Sturtion Curve When seprtely excited DC genertor runs t no lod (rmture circuit open), chnge in the exciting current cuses corresponding chnge in the induced voltge. We now exmine the reltionship between the two Field flux vs. exciting current. Let us grdully rise the exciting current I X, so tht the mmf of the field increses, which increses the flux (φ per pole). If we plot φ s function of I X, we obtin the sturtion curve of Fig This curve is obtined whether or not the genertor is turning.

54 96 Chpter Two When the exciting current is reltively smll, the flux is smll nd the iron in the mchine is unsturted. Very little mmf is needed to estblish the flux through the iron, with the result tht the mmf developed by the field coils is lmost entirely vilble to drive the flux through the ir gp. Becuse the permebility of ir is constnt, the flux increses in direct proportion to the exciting current, s shown by the liner portion 0 of the sturtion curve. However, s we continue to rise the exciting current, the iron in the field nd the rmture begins to sturte. A lrge increse in the mmf is now required to produce smll increse in flux, s shown by portion bc of the curve. The mchine is now sid to be sturted. Sturtion of the iron begins to be importnt when we rech the so-clled "knee" b of the sturtion curve. Fig.3.21 Flux per pole versus exciting current.

55 DC Mchines 97 The output voltge vries to the field current for seprtely excited DC genertor is shown in Fig.3.21b. Fig.3.21b Sturtion curve of DC genertor Shunt Genertor A shunt-excited genertor is mchine whose shunt field winding is connected in prllel with the rmture terminls, so tht the genertor cn be self-excited (Fig.3.22). The principl dvntge of this connection is tht it elimintes the need for n externl source of excittion. How is self-excittion chieved? When shunt genertor is strted up, smll voltge is induced in the rmture, due to the remining flux in the poles. This voltge produces smll exciting current I X in the shunt field. The resulting smll mmf cts in the sme direction s the remining flux, cusing the flux per pole to increse. The incresed flux increses E 0 which increses I X, which

56 98 Chpter Two increses the flux still more, which increses E 0 even more, nd so forth. This progressive buildup continues until E 0 reches mximum vlue determined by the field resistnce nd the degree of sturtion. See next section. Fig Self-excited shunt genertor.

57 DC Mchines 99 b. Schemtic digrm of shunt genertor. A shunt field is one designed to be connected in shunt (lternte term for prllel) with the rmture winding Controlling The Voltge Of A Shunt Genertor It is esy to control the induced voltge of shunt-excited genertor. We simply vry the exciting current by mens of rheostt connected in series with the shunt field (Fig.3.23). Fig.3.23 Controlling the genertor voltge with field rheostt. A rheostt is resistor with n djustble sliding contct. To understnd how the output voltge vries, suppose tht E 0 is 120 V when the movble contct p is in the center of the rheostt.

58 100 Chpter Two If we move the contct towrd extremity m, the resistnce R t between points p nd b decreses, which cuses the exciting current to increse. This increses the flux nd, consequently, the induced voltge E 0. On the other hnd, if we move the contct towrd extremity n, R t increses, the exciting current decreses, the flux decreses, nd so E 0 will fll. We cn determine the no-lod vlue of E 0 if we know the sturtion curve of the genertor nd the totl resistnce R t of the shunt field circuit between points p nd b. We drw stright line corresponding to the slope of R t nd superimpose it on the sturtion curve (Fig. 4.24). This dotted line psses through the origin, nd the point where it intersects the curve yields the induced voltge. For exmple, if the shunt field hs resistnce of 50 Ω nd the rheostt is set t extremity m, then R t = 50 Ω. The line corresponding to R t must pss through the coordinte point E = 50 V, I = 1 A. This line intersects the sturtion curve where the voltge is 150 V (Fig.3.24). Tht is the mximum voltge the shunt genertor cn produce.

59 DC Mchines 101 By chnging the setting of the rheostt, the totl resistnce of the field circuit increses, cusing E 0 to decrese progressively. For exmple, if R t is incresed to 120 Ω, the resistnce line cuts the sturtion curve t voltge E 0 of 120 V Fig3.24 The no-lod voltge depends upon the resistnce of the shunt-field circuit.

60 102 Chpter Two If we continue to rise R t, criticl vlue will be reched where the slope of the resistnce line is equl to tht of the sturtion curve in its unsturted region. When this resistnce is ttined, the induced voltge suddenly drops to zero nd will remin so for ny R t greter thn this criticl vlue. In Fig.3.24 the criticl resistnce corresponds to 200Ω. We hve seen tht the rmture winding contins set of identicl coils, ll of which possess certin resistnce. The totl rmture resistnce R is tht which exists between the rmture terminls when the mchine is sttionry. It is mesured on the commuttor surfce between those segments tht lie under the (+) nd (-) brushes. The resistnce is usully very smll, often less thn one hundredth of n ohm. Its vlue depends minly upon the power nd voltge of the genertor. To simplify the genertor circuit, we cn represent R s if it were in series with one of the brushes. If the mchine hs interpoles, the resistnce of these windings is included in R. The equivlent circuit of genertor is thus composed of resistnce R in series with voltge E 0 (Fig.3.25). The ltter is the voltge induced in the revolving conductors. Terminls 1, 2 re the externl rmture terminls of the mchine, nd F 1, F 2 re the field winding terminls. Using this circuit, we will now study the more common types of direct-current genertors nd their behvior under lod.

61 DC Mchines 103 Fig.3.25 Equivlent circuit of DC genertor Seprtely Excited Genertor Under Lod Let us consider seprtely excited genertor tht is driven t constnt speed nd whose field is excited by bttery (Fig.3.26). The exciting current is constnt nd so is the resultnt flux. The induced voltge E o is therefore fixed. When the mchine opertes t no lod, terminl voltge E 12 is equl to the induced voltge E o becuse the voltge drop in the rmture resistnce is zero. However, if we connect lod cross the rmture (Fig.3.26), the resulting lod current I produces voltge drop cross resistnce R. Terminl voltge E 12 is now less thn the induced voltge E o. As we increse the lod, the terminl voltge decreses progressively, s shown in Fig The grph of terminl voltge s function of lod current is clled the lod curve of the genertor. In prctice, the induced voltge E o lso decreses slightly with incresing lod, becuse pole-tip sturtion tends to decrese the field flux. Consequently, the terminl voltge E 12 flls off more rpidly thn cn be ttributed to rmture resistnce lone.

62 104 Chpter Two Fig.3.26 Seprtely excited genertor under lod. Fig.3.27 Lod chrcteristic of seprtely excited genertor 3.15 Shunt genertor under lod The terminl voltge of self-excited shunt genertor flls off more shrply with incresing lod thn tht of seprtely excited

63 DC Mchines 105 genertor (Fig.3.27). The reson is tht the field current in seprtely excited mchine remins constnt, wheres in self-excited genertor the exciting current flls s the terminl voltge drops. For self-excited genertor, the drop in voltge from no lod to full lod is bout 15 percent of the full-lod voltge, wheres for seprtely excited genertor it is usully less thn 10 percent. The voltge regultion is sid to be 15% nd 10%, respectively Compound Genertor The compound genertor ws developed to prevent the terminl voltge of DC genertor from decresing with incresing lod. Thus, lthough we cn usully tolerte resonble drop in terminl voltge s the lod increses, this hs serious effect on lighting circuits. For exmple, the distribution system of ship supplies power to both DC mchinery nd incndescent lmps. The current delivered by the genertor fluctutes continully, in response to the vrying lods. These current vritions produce corresponding chnges in the genertor terminl voltge, cusing the lights to flicker. Compound genertors eliminte this problem. A compound genertor (Fig.3.28) is similr to shunt genertor, except tht it hs dditionl field coils connected in series with the rmture. These series field coils re composed of few turns of hevy wire, big enough to crry the rmture current.

64 106 Chpter Two The totl resistnce of the series coils is, therefore, smll. Fig.3.28b is schemtic digrm showing the shunt nd series field connections.

65 DC Mchines 107 Fig.3.28 (). Compound genertor under lod. (b). Schemtic digrm. (c) V-I chrcteristics. When the genertor runs t no-lod, the current in the series coils is zero. The shunt coils, however, crry exciting current I X which produces the field flux, just s in stndrd self-excited shunt genertor. As the genertor is loded, the terminl voltge tends to drop, but lod current I c now flows through the series field coils. The mmf developed by these coils cts in the sme direction s the mmf of the shunt field. Consequently, the field flux under lod rises bove its originl no-lod vlue, which rises the vlue of E o. If the series coils re properly designed, the terminl voltge remins prcticlly constnt from no-lod to full-lod. The rise in the induced voltge compenstes for the rmture drop.

66 108 Chpter Two In some cses we hve to compenste not only for the rmture voltge drop, but lso for the I R drop in the feeder line between the genertor nd the lod. The genertor mnufcturer then dds one or two extr turns on the series winding so tht the terminl voltge increses s the lod current rises. Such mchines re clled over compound genertors. If the compounding is too strong, low resistnce cn be plced in prllel with the series field (The nme of this resistnce is diverter resistnce). This reduces the current in the series field nd hs the sme effect s reducing the number of turns. For exmple, if the vlue of the diverter resistnce is equl to tht of the series field, the current in the ltter is reduced by hlf Differentil Compound Genertor In differentil compound genertor the mmf of the series field cts opposite to the shunt field. As result, the terminl voltge flls drsticlly with incresing lod s shown in Fig.3.28c. We cn mke such genertor by simply reversing the series field of stndrd compound genertor. Differentil compound genertors were formerly used in DC rc welders, becuse they tended to limit the short-circuit current nd to stbilize the rc during the welding process DC Motor

67 DC Mchines 109 The DC mchine cn operte both s genertor nd s motor. This is illustrted in Fig When it opertes s genertor, the input to the mchine is mechnicl power nd the output is electricl power. A prime mover rottes the rmture of the DC mchine, nd DC power is generted in the mchine. The prime mover cn be gs turbine, diesel engine, or n electricl motor. When the DC mchine opertes s motor, the input to the mchine is electricl power nd the output is mechnicl power. If the rmture is connected to DC supply, the motor will develop mechnicl torque nd power. In fct, the DC mchine is used more s motor thn s genertor. DC motors cn provide wide rnge of ccurte speed nd torque control. Fig.3.29 Reversibility of DC mchine. () Genertor. (b) Motor. In both modes of opertion (genertor nd motor) the rmture winding rottes in the mgnetic field nd crries current. Therefore, the sme bsic equtions (3.5), (3.6) nd (3.8) hold good for both genertor nd motor ction.

68 110 Chpter Two Shunt Motor A schemtic digrm of shunt field DC motor is shown in Fig The rmture circuit nd the shunt field circuit re connected cross DC source of fixed voltge V t. An externl field rheostt (R fc ) is used in the field circuit to control the speed of the motor. The motor tkes power from the DC source, nd therefore the current I t flows into the mchine from the positive terminl of the DC source. As both field circuit nd rmture circuit re connected to DC source of fixed voltge, the connections for seprte nd shunt excittion re the sme. The behvior of the field circuit is independent of the rmture circuit. The governing equtions for stedy-stte opertion of the DC motor re s follows: V = I R + E (3.25) t t f I = I + I (3.25b) E E φzn p = K φ ω m = (3.25c) 60 A * where = V I R (3.25d) t K is the mchine constnt. The rmture current I nd the motor speed mechnicl lod connected to the motor shft. ωm depend on the

69 DC Mchines 111 Fig.3.30 Shunt DC motor equiv lent circuit Power Flow nd Efficiency The power flow in DC mchine is shown in Fig The vrious losses in the mchine re identified nd their mgnitudes s percentges of input power re shown. A short-shunt compound DC mchine is considered s n exmple (Fig.3.31). With the mchine operting s genertor (Fig.3.31b), the input power is the mechnicl power derived from prime mover. Prt of this input power is lost s rottionl losses required to rotte the mchine ginst windge nd friction (rotor core loss is lso included in the rottionl loss). The rest of the power is converted

70 112 Chpter Two into electricl power E I. Prt of this developed power is lost in R (which includes brush contct loss), prt is lost in R = R + R, nd prt is lost in R sr. The remining power is f fc fw vilble s the output electricl power. Vrious powers nd losses in motoring opertion re shown in Fig.3.31c. The percentge losses depend on the size of the DC mchine. The rnge of percentge losses shown in Fig.3.31 is for DC mchines in the rnge 1 to 100 kw or 1 to 100 hp. Smller mchines hve lrger percentge of losses, wheres lrger mchines hve smller percentge of losses. The efficiency of the mchine is: Poutput efficiency = (3.26) P input

71 DC Mchines 113 Fig.3.31 Power losses in DC mchine Condition for Mximum Power The mechnicl power developed by motor is:

72 114 Chpter Two P m = V * I I R (3.27) t 2 Differentiting both sides with respect to I we get: dp di V 2 I R = 0 m = t (3.28) Then, I R = V / 2 (3.29) t As V = E + I R nd I R = V / 2 t Then / 2 V t * t E = (3.30) Thus mechnicl power developed by motor is mximum when bck EMF is equl to hlf the pplied voltge. This condition is, however, not relized in prctice, becuse in tht cse current would be much beyond the norml current of the motor. Moreover, hlf the input would be wsted in the form of het nd tking other losses (mechnicl nd mgnetic) into considertion, the motor efficiency will be well below 50 percent Torque By the term torque is ment the turning or twisting moment of force bout n xis. It is mesured by the product of the force nd the rdius t which this force cts. Consider pulley of rdius r meters cted upon by circum ferentil force of F Newton which cuses it to rotte t N rps

73 DC Mchines 115 Then, torque T F * r = Newton meter (N-m) Work done by this force in one revolution =Force * distnce = F * 2π r Power developed = F * 2π r * N joule/second = ( F r) * 2πN * joule/second Now 2πN = ngulr velocity ω in rd/second power developed = T * ω joule/second or wtt (3.31) Series-wound DC motor In series DC motor field & rmture circuits re connected in series, s shown in the Figure below; so I = I. Assuming liner dependence of flux on the field current (pproximtely), we hve: f

74 116 Chpter Two Note, there is no voltge drop cross the inductnce in stedy-stte regime (becuse I=const in time) 3.22 Armture Torque of Motor Let T be the torque developed by the rmture of motor running t N rps If T is in N-m, then power developed, P dev = T * 2πN wtt (3.32)

75 DC Mchines 117 We lso know tht electricl power converted into mechnicl power in the rmture is E * I (3.33) Equting (3.32) nd (3.33), we get T * 2πN = E Since P E = φzn volt, we hve: A P T * 2π N = φzn * I (3.34) A Then, or T T 1 φzi 2π P A = N-m (3.35) P = 0.159φZI N.m (3.36) A Note. From the bove eqution for the torque, we find tht T α φ I () 1n the cse of series motor, φ is directly proportionl to I (before sturtion) becuse field windings crry full rmture 2 current. T α. I I (b) For shunt motors, φ is prcticlly constnt, hence T α I It is lso seen from (3.34) bove tht, T 1 EI = N m (3.37) 2π N.