Induction Machine Operation
For operation with rated L-L voltage of 230 V and rated frequency of 60 Hz, the performance of a particular 10 hp machine at its rated speed and power is:
Speed = 1750 rpm I1 = 24.5 A rms Pin = 7.93 Kw T = 40.7 Nm Pout = 7.46 Kw
S = 0.0277 Cos è = 0.811 Pg = 7.67 Kw I2
2R2 = 212w eff = 94.1 %
a) One important parameter change for efficiency improvement is to reduce the value of R2. Determine the new values of the quantities above for a second identical machine except that R2 is 1/2 as large and the machine is operated at 1/2 the slip (so R2/S = constant). This is a "thinking question", the answers can be obtained with only minimal calculation (many are unchanged) by reasoning guided by the equivalent circuit. Don't make it hard or long.
R2new = (1/2) R2
Slip = __0.01385___ Po = ___________ hp
Speed = ______ RPM cos è = _________
I1 = ___________ A Pg = ___________ w
Pin = ___________ w I2R2 = _________ w
T = ___________ Nm eff = ___________ %
b) The equivalent circuit parameters of the above10 hp, 230 V (rms L-L), 60 hz, 4 pole, three phase induction motor are:
r1 = 0.140Ù x1 =0.650Ù xm = 12.0Ù
r2 = 0.157Ù x2 = 0.650Ù Neglect core loss
Use the equivalent circuit to find the input current and developed torque at rated voltage and frequency and a slip of S = 0.01385 (1/2 rated slip). As a first approximation I1 and T were shown to be linear functions of slip. Compare your results with 50% of the rated slip values as listed below.
Equiv Ckt @ S= 0.5 SR 50% of Rated Values
I1 = _________ A I1 = __12.25__ A
T = _________ Nm T = ___20.35__ Nm
Induction Machine Operation
c) Evaluate the motor performance at 15 hz with constant volts/hz and at the same slip frequency as in part a (S = 4 x 0.0277 = 0.1108) neglecting R1). Recall that, without stator resistance, the current, torque and power factor are the same as the rated values given in part a, only the powers vary.
Optional: Include R1 This requires an equivalent circuit calculation.
R1 = 0 (25 points) R1 ≠ 0
I1 = ___________ A I1 = ___________ A
Pin = ___________ w Pin = ___________ w
T = ___________ Nm T = ___________ Nm
Po = ___________ hp Po = ___________ hp
cos è = _________ cos è = _________
Pg = ___________ w Pg = ___________ w
I2R2 = _________ w I2R2 = _________ w
d) Test s show the starting current and torque of a (different than in part a) motor to be
I = 6 x IR A T = 1.5 x TR Nm at rated voltage V = VR
Use this starting performance data to find the voltage ratio (Vo/Vin )of a transformer which when placed between the motor and the source Vin = VR will limit the transformer input side starting current to = 2 x IR A.
What is the torque and motor side current as multiples of rated values of when using this motor starting transformer? Hint: At starting, (S = 1) the motor is simply an impedance. (25 points)
Vo/VR = _________
I1 = ______ x IR
T = ______ x TR