Three Phase Induction Motors

Lecture 3 3 Induction Motor Equivalent Circuit Rotor Frequency Rotor Emf, Current, Impedance Rotor Equivalent circuit Load Representation Power Stages Lecture 3 Exercise Summary Dept of E & E, MIT Manipal L3 – 01

Equivalent Circuit Ic V1 Rc Xm R2 Xr=sX2 I1 E1 Er= s E2 Im Rotor Dept of E & E, MIT Manipal L3 – 02 Rc Xm V1 R2 Xr=sX2 I1 E1 Er= s E2 Ic Im Rotor Air Gap Stator R1 X1 Stator V1 = Supply voltage R1 = Stator Winding Resistance X1 = Stator Leakage Reactance I1 = Stator Winding Current Rc = Core Loss Resistance Xm = Magnetising Reactance E1 = Stator Self Induced Emf Rotor Er = Rotor Induced Emf under Running Conditions s = Operating Slip E2 = Standstill Rotor Induced Emf R2 = Rotor Winding X2 = Rotor Leakage Reactance at Standstill Xr = Rotor Leakage Reactance under Running Condition

Rotor Frequency For rotor speed N, relative speed = NS - N f = Frequency of ac supply, Hz P = No. of poles NS = Speed of RMF, rpm s = fractional slip fr =frequency of rotor, Hz Note At instant of starting, N = 0, s = 1, fr = f Dept of E & E, MIT Manipal L3 – 03

Rotor Emf At standstill, s = 1, max relative speed, max rotor induced emf If E2 = per phase rotor induced emf at standstill, E2  NS If E2r = per phase rotor induced emf under running conditions, E2r  (NS - N) Thus for any slip, Dept of E & E, MIT Manipal L3 – 04

Rotor Equivalent circuit Dept of E & E, MIT Manipal L3 – 05 Rotor windings offer resistance, represented by R2 Presence of leakage flux, represented by X2 Standstill Operating Emf E2 E2r = s E2 Resistance R2 Reactance X2 X2r = s X2 Impedance Z2= R2 + j X2 Z2r= R2 + j ( s X2 ) Current I2 I2r R2 X2r E2r I2r

Rotor Equivalent circuit cont’d … Dept of E & E, MIT Manipal L3 – 06 R2 X2r E2r I2r E2r = per phase rotor induced emf = s E2 R2 = per phase rotor resistance X2r = per phase rotor leakage reactance = s X2 I2r = per phase rotor current s = operating slip X2 E2 I2r

Load Representation X2 X2 R2 E2 E2 I2r I2r Dept of E & E, MIT Manipal L3 – 07 X2 E2 I2r R2 X2 E2 I2r Variable Rotor resistance can be split into two parts : Resistor R2 to represent the rotor side copper loss Resistor RL to represent the electrical equivalent of mechanical load Mechanical load on the motor is represented by

PNet = PGross – PFriction & Windage Loss Power Output Dept of E & E, MIT Manipal L3 – 08 R2 X2 E2 I2r Gross Power Output (Rotor Output) Net Power output (actual Power output or Shaft output) PNet = PGross – PFriction & Windage Loss

Torque Dept of E & E, MIT Manipal L3 – 09 R2 X2 E2 I2r TSh = Tg – TFw

Torque Slip Characteristics – Squirrel Cage Dept of E & E, MIT Manipal L3 – 10 Torque, Nm Tmax Low to medium slip region High slip region Tst sM s = 1 Slip, % s = 0

R2 < (R2 + y) < (R2 + 2y) < (R2 + 3y) Torque Slip Characteristics – Slip Ring Dept of E & E, MIT Manipal L3 – 11 R2 < (R2 + y) < (R2 + 2y) < (R2 + 3y) Torque, Nm Slip, % sM sM = 1 R2 R2 + y R2 + 2y Tmax Tst R2 + 3y

Lecture 3 Exercise [1] A 3, 50 Hz, 6 pole induction motor has a no load slip of 1 % and a full load slip of 3 %. Determine (a) synchronous speed (b) no load speed (c) full load speed (d) frequency of rotor current at standstill (d) frequency of rotor current at full load 1000rpm,990 rpm,970 rpm,50Hz,1.5Hz [2] A 3, 50 Hz, 4 pole induction motor has a star connected rotor. The per phase rotor resistance is 0.1  and per phase standstill reactance is 2 . If the induced emf between the slip rings is 100 V, full load speed is 1460 rpm, determine (a) slip (b) rotor induced emf (c) per phase rotor reactance (d) rotor current. Assume the slip rings are short circuited. 2.67%,1.50,0.052 ,13.3A [3] A 3, induction motor has a star connected rotor. The rotor emf between the slip rings at standstill is 50 V. The rotor resistance and standstill rotor reactance are 0.5  and 3  respectively. Determine (a) per phase rotor current at starting if a star connected rheostat of 6  per phase is connected across the slip rings (b) full load rotor current and for a full load slip of 4 % (c) per phase rotor emf under full load condition Dept of E & E, MIT Manipal L3 – 12

Lecture 3 Summary Induction Motor as a generalized Transformer Rotor Equivalent circuit Electrical equivalent of mechanical load Power Output Gross Power Output, Friction & Windage Loss, Shaft Output Torque Gross Torque, Shaft Torque, Friction Torque Torque slip characteristics Dept of E & E, MIT Manipal L3 – 13