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AC Machine Fundamental

AC Machine Fundamental 2
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HelenBoyle,Greece,Researcher
Published Date:14-07-2017
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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 Current-Carrying 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 Two-Pole Stator The Ind The Induced Voltage ced Voltage In A Three In A Three-Phase Set Of Coils Phase Set Of Coils The RMS Voltag ge In A Three-Phase Stator Induced Torque In An AC Machine AC Machine Power Flows And Losses The Power-Flow 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 ( ) Left-hand 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