<jupyter_start><jupyter_text>Excercises Electric Machinery Fundamentals Chapter 6  Problem 6-12<jupyter_code>%pylab notebook
%precision 4<jupyter_output>Populating the interactive namespace from numpy and matplotlib<jupyter_text>Description The power crossing the air gap of a 60 Hz, four-pole induction motor is 25 kW, and the power convertedfrom electrical to mechanical form in the motor is 23.2 kW. (a)* What is the slip of the motor at this time? (b)* What is the induced torque in this motor? (c)* Assuming that the mechanical losses are 300 W at this slip, what is the load torque of this motor?<jupyter_code>fse   = 60     # [Hz]
p     = 4          
Pag   = 25.0e3 # [W]
Pconv = 23.2e3 # [W]
Pm    = 300    # [W]<jupyter_output><empty_output><jupyter_text>SOLUTION  (a)The synchronous speed of this motor is:$$ n_\text{sync} = \frac{60 \cdot f_{se}}{p/2} $$<jupyter_code>n_sync = 60 * fse // (p//2)  # // is used for integer division in Python 3
n_sync<jupyter_output><empty_output><jupyter_text>The power converted forom the electrical to the mechanical form is:$$P_\text{conv} = (1-s)P_\text{AG}\quad \leadsto \quad s = 1 - \frac{P_\text{conv}}{P_\text{AG}} $$<jupyter_code>s = 1 - Pconv/Pag
s<jupyter_output><empty_output><jupyter_text>(b)The speed of the motor is:$$ n_m = (1-s) n_\text{sync} $$<jupyter_code>n_m = (1-s)*n_sync
n_m<jupyter_output><empty_output><jupyter_text>The induced torque of the motor is:$$\tau_\text{ind}  = \frac{P_\text{conv}}{\omega_m}$$<jupyter_code>Tind = Pconv/(2*pi/60 * n_m)
Tind # [Nm]<jupyter_output><empty_output><jupyter_text>Alternately, the induced torque can be found as:$$\tau_\text{ind}  = \frac{P_\text{AG}}{\omega_\text{sync}}$$<jupyter_code>Tind = Pag/(2*pi/60 * n_sync)
Tind # [Nm]<jupyter_output><empty_output><jupyter_text>(c)The output power of this motor is:$$ P_\text{out} = P_\text{conv} -P_\text{mech} $$<jupyter_code>Pout = Pconv-Pm
Pout # [W]<jupyter_output><empty_output><jupyter_text>And the output torque:$$\tau_\text{out}  = \frac{P_\text{out}}{\omega_m}$$<jupyter_code>Tout = Pout / (2*pi/60 * n_m)
Tout<jupyter_output><empty_output>
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