Asynchronous Machine Torque, Magnetic Fields, and Braking Analysis
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Asynchronous Machine Analysis: Torque, Fields, and Braking
Starting Torque and Stator Connection
Q: Demonstrate the relationship between the starting torque of an asynchronous machine with the stator connected in a triangle, being three times higher than the same machine with the star-connected stator.
Ta star = (1 / √3)2 Tb
Ta = 1 / 3 Ta
Ia star = 1 / 3 Ta
The starting current in star is 1/3 in a triangle, reducing starting torque to 1/3.
Magnetic Field and Rotor Speed
Q: Demonstrate that the magnetic field produced by the stator currents of an induction machine turns at the same speed as the magnetic field produced by currents induced in the engine.
The connection speed of the stator field created by the rotor is the sum of the speed but the torn trawl rotor on the stator.
S · W1 + W = (W1-W) + W = W1
W1 = S · W1 + W
This means that waves of magneto motive force created by the rotor and the stator rotate in synchrony.
Braking Torque Calculation
Q: A three-phase asynchronous motor with 4 poles and a wound rotor has the following equivalent circuit parameters per phase: Rest = 0.1 and Xeste R'rot = = = 0.5 turns X'rot rated at 1450 rpm. This is fed to 400 V, 50 Hz. Power is invested in two phases. Calculate the brake torque at the instant at which switching occurs.
n = 60 · f / p = 60 * 50 / 2 = 1500 rpm
S = (1500-1450)/1500 = 0.03
Feeding reverses two phases (countermarch) s' = 2-s = 1.97
I' 2 = U1 / √((R1 + R2 '/ s')2 + (XD1 + X'd2)2) = 404 then angle -90 º
Pm = m1 + R'2 · (1 / s'-1 )2 · I `2 2
T = Pm/(2π · n1/60) · (1-s) N * m
Plugging and Countermarch Braking
Q: Show that when feeding two phases of the stator, the machine changes.
This is one method of braking of induction motors, namely plugging for countermarch or (plugging): When an asynchronous motor reverses the connection of two phases, the motor becomes fed by a system of reverse sequence voltages, which is immediately translated into a reversal of direction of rotation of the field in the gap and thus, in a reversal of the synchronous speed of + ω1 a -ω1 and torque-speed curve.
Rotor Magnetic Field Speed
Q: We have an 8-pole motor and 50 Hz spinning to 735 rpm. Determine the speed of the rotor magnetic field.
2p = 8
f = 50
n = 735
n1 = 60f / p = 750
s = (n1-n)/n1 = 0.02
ω1-ωs = ω = s · ω1
ω = 15 RPM
If the requested frequency of rotating flows is needed, add to the end before the omegas:
Fcr = s · f1 = 50 * 0.02 = 1 Hz