**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.

**R****2new ****= (1/2) R****2**

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