Transcript Slide 1
Three-phase windings Rotor windings Threephase supply w Stator Air gap ws Rotor wm T The stator winding are supplied with balanced three-phase AC voltage, which produce induced voltage in the rotor windings. It is possible to arrange the distribution of stator winding so that there is an effect of multiple poles, producing several cycle of magnetomotive force (mmf) or field around the air gap. The speed of rotation of field is called the synchronous speed ws , which is defined by : ωs is syncronous speed [rad/sec] 2w Ns is syncronous speed [rpm] ws or p is numbers of poles p ω is the supply frequency [rad/sec] f is the supply frequency [Hz] 120 f Ns Nm is motor speed p The motor speed wm ws (1 S ) The rotor speed or motor speed is : Where S is slip, as defined as : Three-phase windings w wm S S wS Rotor windings Threephase supply w Stator Air gap ws Rotor wm T Or S NS Nm NS Equivalent Circuit Of Induction Motor Three-phase windings Where : Rotor windings Rs is resistance per-phase of stator winding Threephase supply Rr is resistance per-phase of rotor winding w Air gap Stator Rotor wm ws Is Xs Xs is leakage reactance per-phase of the winding stator Xs is leakage reactance per-phase of the winding rotor T Xr’ Rs Im Xm is magnetizing reactance Ir’ Rr’/s Vs Xm Stator Rm Air gap motor Rm is Core losses as a reactance Performance Characteristic of Induction Motor Is Xs Xr’ Rs Im Ir’ Rr’/s Vs Xm Stator Rm Air gap motor Stator copper loss : Ps cu 3 I s Rs Rotor copper loss : Pr cu 3 ( I r ) 2 Rr 2 ' 2 Core losses : 2 V V Pc 3 m 3 s Rm Rm ' Performance Characteristic of Induction Motor - Power developed on air gap (Power fropm stator to ' rotor through air gap) : ' 2 Rr Pg 3 ( I r ) S ' 2 - Power developed by motor : Pd Pg Pr cu 3 ( I r ) ' Pd Pg (1 S ) or - Torque of motor : or Td Pd wm Pd 60 Td 2 N m or Pg (1 S ) wS (1 S ) Pg ws Rr (1 S ) S Performance Characteristic of Induction Motor Input power of motor : Pi 3Vs I s cosm Pc Ps cu Pg Output power of motor : Po Pd Pno load Pd Pno load Po Efficiency : Pi Pc Ps cu Pg Performance Characteristic of Induction Motor If Pg (Pc Ps cu ) and Pd Pno load so, the efficiency can calculated as : Pd Pg (1 S ) 1 S Pg Pg Performance Characteristic of Induction Motor Generally, value of reactance magnetization Xm >> value Rm (core losses) and also X m 2 ( Rs 2 X s 2 ) So, the magnetizing voltage same with the input voltage : Vm Vs Therefore, the equivalent circuit is ; Is Xs Ii Im Xm Xr’ Rs Rr’/s Xm Vs Rm Po Pi Stator Air gap motor Is=Ir’ Ir’ Im Ir’ Rr’/s Vs Xs Xr’ Rs Stator Air gap rotor Performance Characteristic of Induction Motor Total Impedance of this circuit is : Ii Xs Xr’ Rs Is=Ir’ ' Ir’ Im Rr’/s Xm Vs Po Pi Stator Air gap rotor Ir ' The rotor current is : R X m ( X s X r ) jX m ( Rs r ) S Zi ' R ' Rs r j ( X m X s X r ) S ' Vs 2 Rr' ' Rs X s X r S 2 1 2 Ii Xs Xr’ Rs Is=Ir’ Ir’ Im Td Rr’/s Vs Po Pi Stator Air gap 3 Rr' Vs2 Rr' S ws Rs S 2 X s X r' rotor Tmax Td Tst TL Tm=TL Operating point S=1 Nm =0 Torque – speed Characteristic Smax S=Sm S=0 wm ws Nm Ns 2 Three region operation : 1. Motoring : 0 S 1 2. Regenerating : S 0 3. Plugging : 1 S 2 Torque Forward regeneration Forward motoring Reverse plugging Tmax wm ws wm ws wm ws Tst S=Sm -Smax ws S=-1 ws Smax S=0 Ns -Tmax ws =0 S=1 Nm =0 ws S=2 Performance Characteristic of Induction Motor Starting speed of motor is wm = 0 or S = 1, Starting torque of motor is : Tst 3 Rr' Vs2 ' 2 Rr ' 2 ws Rs X s X r S Slip for the maximum torque Smax can be found by setting : So, the slip on maximum torque is : S max d Td 0 dS Rr' R X X 2 s s 1 2 ' 2 r Performance Characteristic of Induction Motor Torque maximum is : Tmax 3 Vs2 2ws Rs Rs X s X r' 2 2 And the maximum regenerative torque can be found as : Tmax 3 Vs2 2ws Rs Rs X s X r' Where the slip of motor s = - Sm 2 2 Speed-Torque Characteristic : Td Rr' S ws Rs S X For the high Slip S. (starting) So, the torque of motor is : 3 Rr' Vs2 s Td And starting torque (slip S=1) is : X ' 2 r 2 X s X r' R Rs S ' r 3 Rr' Vs2 S ws X s X Tst 2 2 ' 2 r 3 Rr' Vs2 w s X s X ' 2 r For low slip S region, the motor speed near unity or synchronous speed, in this region the impedance motor is : R' ' 2 X So, the motor torque is : s Xr r S 3Vs2 S Td w s R 'r And the slip at maximum torque is : S max Rr' R X X 1 2 ' 2 r 2 s The maximum motor torque is : Rs Td s 3 Rr' Vs2 Rr' S ws Rs S 2 X s X r' 2 Stator Voltage Control AC Variable Voltage Sources Controlling Induction Motor Speed by Adjusting The Stator Voltage Td IM w Td Vs 3 Rr' Vs2 Rr' S ws Rs S 2 X s X r' 2 Td Vs > Vs1 > Vs2 Ii Xs Xr’ Rs Tmax Is=Ir’ Ir’ Im Rr’/s Vs Po Pi Stator air gap Tst Tst1 Tst2 TL rotor S=1 Nm =0 w2 w1 w S=0 ws Ns