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AC Machine Fundamental

AC Machine Fundamental 2
AC Machine AC Machine F Fundamental ndamental 618 221 Basic Electric Machines Mr. Mr. Kittithuch Kittithuch Paponpen Paponpen Electronic and Computer System Engineering Department ofi f Electrical Engiineeriing Faculty of Engineering and Industrial Technology¾¾¾¾¾¾¾¾ Outline Outline A simple loop in a uniform magnetic field The Voltage Induced In A Simple Rotating Loop The Torque Induced In A Current The Torque Induced In A CurrentCarrying Loop Carrying Loop The Rotating Magnetic Filed The Relationship Between Electrical Frequency And The S Speed d Of M Of Magnet ti i F c Fil ild ed R Rot tat ti ion Mag gnetomotive Force And Flux Distribution On AC Machine¾¾¾¾¾¾¾¾¾¾ Outline Outline The Induced Voltage In Coil On A TwoPole Stator The Ind The Induced Voltage ced Voltage In A Three In A ThreePhase Set Of Coils Phase Set Of Coils The RMS Voltag ge In A ThreePhase Stator Induced Torque In An AC Machine AC Machine Power Flows And Losses The PowerFlow i Diagram Voltage Regulation And Speed Regulation Voltage Regulation And Speed RegulationOutline Outline AC M AC Machi hines Synchronous Machines Induction Machines Magnetic filed current, I , Filed current is supplied by F is supplied by a separate dc magnetic induction power source (transformer action) into their filed windings their filed windings. The filed circuits are located on their rotors.¾¾¾¾¾¾ A Simple Loop In A Uniform Magnetic Field A Simple Loop In A Uniform Magnetic Field A lA large statiionary magnet prod duci ing an essentil ialll y constant d and uniform magnetic filed Rotating loop of wire within that filed. The rotating part of the machine is called the “rotor” The rotating part of the machine is called the “rotor” The stationary part of the machine is called the “stator”¾¾¾¾¾¾¾¾¾ The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop The voltage The voltage on each segment on each segment is is e = vBוl ( ) ind Segment ab: Point into page ev = vBוl=Bl sinθ ( ( ) ) ba ab ee =× =× vB vB••ll== 0 0 ( ( ) ) Segment bc: Segment bc: cb vB × ⊥l e = vBוl= 0 Segment da: ( ) ad Point out of page Segment Segment cd: cd: ev =× vB•l=Bl sinθ ( ) dc cd ¾¾¾ The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop Total Total induced induced voltage voltage on on the the loop loop ee=+e+e+e =vBl sinθ +vBl sinθ ind ba cb dc ad ab cd and sinθ = sin 180 −θ θ = 180 −θ ( ( ) ) Note that ab ab ccdd ev =2sBlinθ ind If the loop is rotating at a constant ω, the angle θ of the θ = ωt. loop will increase with time, vr = ω The tangential velocity v of the edge of the loop: er =2s ωBlinωt ind Area of the loop: φ = AB eA = ωBsinωφt = ω sinωt A = 2rl max ind maxThe Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop The The voltage voltage generated generated i in n t the he loop loop is is a a s sinusoid inusoid. eA = ωBsinωφt = ω sinωt ind maxƒƒƒ ¾ The Voltage Induced In A Simple The Voltage Induced In A Simple Rotating Loop Rotating Loop eA = ωBsinωφt = ω sinωt ind max VVg oltage in anyy real machine will deppend on three factors: The flux in machine (B) The speed of rotation (ω) A constant representing the construction of the machine (the number of loopp, s, etc)¾¾ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop If a current flows in the loop, then a torque will be induced on the wire loop p. Fl =i ×B ( ( ) ) Torque on the segment will then be τ =rF × τθ τθ== == Fr Fr sin sin rrFF s sin inθθ ( ( ) )( ( ) ) θ is the ang gle between the vector r and vector FÆ Æ Æ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop Fi = l×B ( ) Lefthand rule Index finger Field direction Middle fing ger Current direction thump Force direction¾¾ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop segment ab: ( (d d down di irect ti ion) ) Fl =ii ×=BlB ( ( ) ) ( (clockwise clockwise) ) τθ τθ== == Fr Fr sin sin rriillFF s sin inθθ ( ( ) )( ( ) ) ab ab ab segment bc: (into the page) Fl =×= i B ilB () τθ =Fr sin = 0 ( )( ) bc bc (b (both R th R and d F F it point i it nto ththe page) )¾¾ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop segment cd: Fl Fl =×ii ii ×BB =llBB ( (up) ) ( ( ) ) τ = F r sinθθ =rilF sin ( ( ) )( ( ) ) ( (co clocckw wise se) ) cd cd cd cd cd cd segment da: (out of the page) Fl =×= i B ilB ( ) τθ =Fr sin = 0 ( )( ) da da (Both R and F point out of the page)¾¾ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop T Tl otal i ind duced d torque on th he l loop τ =+ ττ +τ +τ =rilBsinθ +rilBsinθ ind ab bc cd da ab cd Note that: θ =θθ = ab cd τ =2s rilBinθ ind A = 2rl τθ τθ = = ABi ABi sin sin ind¾¾ The Torque Induced In A Current The Torque Induced In A Current Carrying Loop Carrying Loop If there is current in the loop, that current will generate a magnetic flux density B with the direction shown. loop µi BG loop B = i = loop G µ G is a factor that depends on the geometry of the loop µ is magnetic permeability of material Substitutinggq these into induced torque eq quation AG τ== BB sinθθ kB B sin ind loop s loop s µ µ τ =kBB × τ = ABi sinθ ind loop s ind¾¾¾¾¾¾ The Rotating Magnetic Filed The Rotating Magnetic Filed τ τ=× =× kkBB BB ind loop s If two magnetic fields are present in a machine, then a torque will If two magnetic fields are present in a machine, then a torque will B be created. S If one magnetic field is produced by the stator and the other one is B R produced by the rotor, then a torque will be induced in the rotor. τ =kBB × ind R S Thi i i s induced torque cause the rotor to turn and ali ign i itself f wi ith the stator magnetic filed. B R B S¾¾¾ The Rotating Magnetic Filed The Rotating Magnetic Filed If stator magnetic filed rotate, then the induced torque in the rotor would cause it to constantly “chase” the stator magnetic filed around in the cycle. B R B B S This is the basic principle of all AC motor operation.¾¾¾ The Rotating Magnetic Filed The Rotating Magnetic Filed How can the stator magnetic field be made to rotate “If a three phase set of current flows in a three If a three phase set of current flows in a three phase winding phase winding, then it will produce a rotating magnetic filed of constant magnitude” Æ Æ The Rotating Magnetic Filed The Rotating Magnetic Filed From magnetic filed principle: I mmf, F = Ni H = F/l H tH = sinωt∠0 Aiturns/m ( ( ) ) it =II siA in ωt A / ( ( ) ) M / aa M aa The Rotating Magnetic Filed The Rotating Magnetic Filed H H tH tH=∠ =∠ si sin nω ωtt 0 0 A Aiit turns/ urns/m m ( ( ) ) it it = =II sin sinω ωtt A A / ( ( ) ) M / aa M aa it=− I sin ωt 120 A ( ) / ( ) M bb it =I sin ωt − 240 A ( ) / ( ( ) ) M cc H tH=− sin ωt 120∠120 Aiturns/m () / () M bb H tH=− sin ωt 240∠240 Aiturns/m ( ) / ( ) M cc The Rotating Magnetic Filed The Rotating Magnetic Filed BH = µ Magnetic flux density: Three phase set of magnetic flux density: B tB=∠ sinωt 0 T ( ) / M aa B tB = sin ωt−∠ 120 120 T ( ) / ( ( ) ) M bb B tB = sin ωt−∠ 240 240 T ( ( ) ) / ( ( ) ) M M cc cc B = µH Where M M The Rotating Magnetic Filed The Rotating Magnetic Filed ω ωtt = 0 0 at at 1 1 B B tt = 0 0 ( ( ) ) / aa B tB=− sin 120∠120 T ( ) / ( ) M bb B tB = sin−∠ 240 240 T ( ) / ( ( ) ) M cc     33 33 BB = ++= B B 0+−BB ∠120+ ∠240= 1.5B∠− 90 T // /    net M M M aa bb cc    22    1 The Rotating Magnetic Filed The Rotating Magnetic Filed at ωt = 90 ° 2 B tB=∠0 T ( ) / M aa B BtB tB ==∠ −0 0.5 5 ∠120 120 T T ( ( ) ) / / M bb BtB =−0.5 ∠240 T ( ) / M cc BB=+B+B=BB ∠0+−0.5 ∠120+−0.5B ∠240= 1.5B∠0 T ( ) ( ) // / net M M M M aa bb cc 2 ω ω,, counter counterclockwise clockwise 1The Rotating Magnetic Filed The Rotating Magnetic FiledThe Relationship Between Electrical Frequency And The Speed Of Magnetic Filed Rotation The e rotat otating g mag agnet etic c filed ed in a a stato stator rep eprese esented ted as as moving north and south stator poles.The Relationship Between Electrical Frequency And The Speed Of Magnetic Filed Rotation / ca ca−−bb (t (out f of page) ) Windings on the two Windings on the twopole pole stator occur in the order (taken counterclockwise) // // // ac−−ba− −c−b ff ff = = (t (two l poles) ) se sm (into page) // // ωω ωω = (t (two l poles) ) bb−−ac se sm and ω f are the mechanical speed of the stator fields in rps and rad/s sm sm f are the electrical frequency of the stator currents in hertz and rad/s and ω se seThe Relationship Between Electrical Frequency A And Th d The S Speed d Of M Of Magneti ic Fil Filed d R Rotati ion Electrical frequency 2 poles Mechanical rotor stator speed of magnetic fieldThe Relationship Between Electrical Frequency A And Th d The S Speed d Of M Of Magnet ti i F c Fil ild ed R Rot tat ti ion (in) Pattern of windings () (out) (ou (out) ) S (taken counterclockwise) // / / / / ac ac−−ba ba− −cc−bb−ac ac−−ba ba− −cc−bb N When I is applied to this stator, 3φ φ (in) 2 north poles and 2 south poles (in) (out) are produced in the stator are produced in the stator N winding. θ = 2θ (4 poles) em (out) S ff ff = 2 ( (4 4 poles poles) ) em em (in) ω = 2ω (4 poles) emThe Relationship Between Electrical Frequency A And Th d The S Speed d Of M Of Magneti ic Fil Filed d R Rotati ion Electrical freqqy uency 4 poles Mechanical rotor stator speed of Magnetic fieldThe Relationship Between Electrical Frequency A And Th d The S Speed d Of M Of Magnet ti i F c Fil ild ed R Rot tat ti ion Conclusion: P P θθ θθ = em 2 P ff = em 2 P ω = ω em 2 2 n m , we get when ff = m m 60 60 nP 120f m e ff = nn = ee m 120 PMagnetomotive Force And Flux Distribution On AC Machine Considering the small air gap between the rotor and the stator ( (a a) ) non nonsalient pole rotor (b) salient salient pole rotor (b) salientpole rotor pole rotor¾¾¾¾¾¾ Magnetomotive Force And Flux Distribution On AC Machine To produce a sinusoidal voltage in a machine: The magnitude of the flux density vector B must vary The magnitude of the flux density vector B must vary in a in a sinusoidal manner along the surface of air gap. B will vary sinusoidally only if the magnetizing intensity H (and magnetomotive force, F) varies in a sinusoidal manner along the surface of air gap. The number of conduction in each slot is given by the equation The number of conduction in each slot is given by the equation nN = cosα CC CC o N is the number of conductors at an angle of 0 CMagnetomotive Force And Flux Distribution On AC Machine The flux density as a function of angle α in the air gapMagnetomotive Force And Flux Distribution On AC Machine The magnetomotive force distribution resulting form the winding, compared to an ideal distribution.The Induced Voltage In Coil On A TwoPole Stator A rotating rotor magnetic field inside a stationary stator coil The Induced Voltage In Coil On A TwoPole Stator (b) (b) (b) The vector magnetic flux densities and velocities on the sides of the coil (c) The flux density distribution in the air gap ¾¾¾ The Induced Voltage In Coil On A TwoPole Stator Voltage Voltage induced in the coil induced in the coil e = vBוl ( ( ) ) ind segment ab: α =180 e = vB ×il ( ) ba (directed out (directed out of the page) of the page) = =vBl vBl   =−vB cos ωt−180 l ( ) Mm   =−vB l cos ω t−180 () Mm ( (Th The mi inus si ign comes f from th the f fact t th that th t the volt ltage i is b built ilt up with ith a polarity opposite to assumed polarity) ¾¾¾ The Induced Voltage In Coil On A TwoPole Stator segment bc: v×B B is perpendicular to l l e = vBוl= 0 ( ( ) ) ind ind segment cd: α = 0 e =× vBil ( ) ba (di (direct ted t d out of f ththe page)) =vBl vBl =vB  cos ωt l ( ( ) ) M m   =vB l cos ω t () Mm ¾¾ ¾ The Induced Voltage In Coil On A TwoPole Stator segment da: v×B l l is perpendicular to e = vBוl= 0 ( ( ) ) ind ind The total voltage on the coil will be ee=+=e −vBl cos ωt−180 +vBl cosωt ( ) ind ba dc M m M m cosθθ =− cos −180 Since ( ) e=+ vBl cosωt vBl cosωω t= 2vBl cos t ind M m M m M mThe Induced Voltage In Coil On A TwoPole Stator since the velocity of the end conductors is given byvr = ω m er = 222 ω Bl Bl cosωω tr = 2 lBlB cosω t ( ( ) ) ind m M m M m m ωω ωω = =ωω since since and and for for a a two twopole pole stator stator φ φ== BA BA BB 2 2rll ( ( ) ) me mm e = φ φωω cos tt ind If the coil in the stator has N turns of wire C FFi or singllephf hase of coi ill e =Nt Nt φ φωω cos ind CThe Induced Voltage In A ThreePhase Set Of Coils If three coils, each of N turns, are placed around the rotor magnetic c field, then the voltages field, then the voltages induced in each of them will be the same induced in each of them will be the same in in o magnitude but will differ in phase by 120 The Induced Voltage In A ThreePhase Set Of Coils et = N N φ φωω siiV n t V ( ( ) ) / C aa et et = =NN φω φω sin sin ω ωtt −120 120 V V ( ( ) ) / / ( ( ) ) C bb et=− N φω sin ωt 240 V ( ( ) ) / ( ( ) ) C C cc cc Conclusion: •• Rotor magnetic field inside the rotor by applying dc current into the rotor •rotate the rotor •rotor magnetic filed is rotated •Rotor magnetic field is rotate across the three phase stator winding •V is induce at the three phase stator winding ACÆ ÆÆ The RMS Voltage In A ThreePhase Stator fr from om eN eN = φω φω sin sinω ωtt / C aa EN = φω max C since ω = 2π f E = 2πNf φ ma max x C C The rms voltage of any phase of threephase stator 2 2π π EN = φ φ ff AC 2 EN EN = 2 2πφ φff AC VE VE = = 3 3 The stator is Y connected The stator is Y connected TA VE = The stator is ∆ connected TAInduced Torque In An AC Induced Torque In An AC Machine Machine The The stator stator f flux lux distribution distribution i in n t this his machine: machine: BB α = sinα ( ) SS A simplified ac machine A simplified ac machine with a sin ith a sinusoidal stator fl soidal stator flux distrib distribution and tion and a single coil of wire mounted in the rotorInduced Torque In An AC Induced Torque In An AC Machine Machine The induced force on conductor 1 is: Fl Fl = =ii××BB = =ilB ilB sin sinα α ( ( ) ) S (lefthand rule: with direction as shown) 1 Torque on the conductor is Torque on the conductor is τ = r×F =rilB sinα ( ) ind ,1 S (counter clockwise)Induced Torque In An AC Induced Torque In An AC Machine Machine The induced force on conductor 2 is: Fl Fl =ii ×BB =ilB ilB si inα ( ( ) ) S (lefthand rule: with direction as shown) 2 Torque on the conductor is τ = r×F ( ( ) ) =rilB sinα ind,2 S (counter clockwise) (counter clockwise) Torque on the rotor loop is τ =2s rilBinα ind S (counter clockwise)Induced Torque In An AC Induced Torque In An AC Machine Machine Torque can be expresses ii n a more conventi ional fform: 1. The current I flowing in the rotor coil produces a magnetic filed of its own, H that is directly proportional to the current flowing in the R rotor: H = Ci (1) R 2 2. The angle between the peak of the stator flux density BS and the peak The angle between the peak of the stator flux density BS and the peak of the rotor magnetizing intensity HR is γInduced Torq que In An AC Machine ° sinγ=− sin 180αα= sin …(2) ( ) Combining these two observations: τ =2s rilBinα ind ind SS (counter clockwise) τ =KH B sinα ind R S (counter clockwise) (counter clockwise) τ =KH×B τ =kkBBB ×B ind RS ind RSInduced Torque In An AC Induced Torque In An AC Machine Machine since and B=B +B τ =kB×B net R S ind RS B=B −B But,, ,, so Sn Sneett RR 0 τ==kk B× B B B×B−k B×B ( ( ) ) ( ( ) ) ( ( ) ) ind Rnet R R net R R τ=× kBB τ =kB B sinδ ( ( ) ) in indd Rn Rneett ind ind R R ne nettInduced Torque In An AC Induced Torque In An AC Machine Machine Cl Conclusiion: •• Supply Supply a three phase set of current in to the three a three phase set of current in to the threephase stator coils phase stator coils • Occur the rotating stator magnetic field, B S • The rotating stator magnetic field rotate across the rotor • Supply DC current into the rotor winding and rotor magnetic field is produced, B R • Two maggp netic fields are present in a machine,, then a torq que will be created •• Torque causes the Torque causes the appearing of rotation of ac machine appearing of rotation of ac machineAC Machine Power Flows And Losses AC Machine Power Flows And Losses P P out out η=×100 η η=×100 PP PP + + P P out loss in Losses that occur in ac machine can be divided into four basic categories: 2 2 PI PI =RR 1 1. Electrical or copper losses (stator: Electrical or copper losses (stator: rotor: ) rotor: ) PI PI = = 3 3RR RC RCL L F F F F SCL A A 2. Core loss (only in synchronous machine) 3. Mechanical loss 4. Stray load lossesThe Power The Power Flow Diagram Flow Diagram P = τ ω conv ind Power flow diagram of a threephase ac generatorThe Power The Power Flow Diagram Flow Diagram P =τ ω conv ind Power flow diagram of a threephase ac motorVoltage Regulation And Speed Regulation Voltage Regulation And Speed Regulation VV − nl fl AC generator VR = ×100 V V fl nn − nl fl AC motor SR = ×100 n fl ω −ω nl fl SR=×100 ω fl
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