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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Excercises Electric Machinery Fundamentals
Chapter 9
Problem 9-1
Step1:  Description
A 120-V 1/4-hp 60-Hz four-pole split-phase induction motor has the following impedances
Step2:  If the slip is 0.05, find the following quantities for this motor
Step3:  $$Z_B = \frac{(R_2/(2-s) + jX_2)(jX_M)}{R_2/(2-s) + jX_2 + jX_M}$$
Step4:  (a)
The input current is
Step5:  (b)
The air-gap power is
Step6:  (c)
The power converted from electrical to mechanical form is
Step7:  (d)
The output power is
Step8:  (e)
The induced torque is
$$\tau_\text{ind} = \frac{P_\text{AG}}{\omega_\text{sync}}$$
Step9:  (f)
The load torque is
Step10:  (g)
The overall efficiency is
Step11:  (h)
The stator power factor is
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Python Code:
%pylab notebook
%precision %.4g
Explanation: Excercises Electric Machinery Fundamentals
Chapter 9
Problem 9-1
End of explanation
V  = 120    # [V]
p  =   4
R1 =   2.0  # [Ohm]
R2 =   2.8  # [Ohm]
X1 =   2.56 # [Ohm]
X2 =   2.56 # [Ohm]
Xm =  60.5  # [Ohm]
s  =   0.05
Prot = 51   # [W]
Explanation: Description
A 120-V 1/4-hp 60-Hz four-pole split-phase induction motor has the following impedances:
$$R_1 = 2.00\,\Omega \qquad X_1 = 2.56\,\Omega \qquad X_M = 60.5\,\Omega$$
$$R_2 = 2.80\,\Omega \qquad X_2 = 2.56\,\Omega$$
At a slip of 0.05, the motor's rotational losses are 51 W. The rotational losses may be assumed constant over the normal operating range of the motor.
End of explanation
Zf = ((R2/s + X2*1j)*(Xm*1j)) / (R2/s + X2*1j + Xm*1j)
Zf
Explanation: If the slip is 0.05, find the following quantities for this motor:
(a)
Input power
(b)
Air-gap power
(c)
$P_\text{inv}$
(d)
$P_\text{out}$
(e)
$\tau_\text{ind}$
(f)
$\tau_\text{load}$
(g)
Overall motor efficiency
(h)
Stator power factor
SOLUTION
The equivalent circuit of the motor is shown below:
<img src="figs/FigC_9-28.jpg" width="70%">
The impedances $Z_F$ and $Z_B$ are:
$$Z_F = \frac{(R_2/s + jX_2)(jX_M)}{R_2/s + jX_2 + jX_M}$$
End of explanation
Zb = ((R2/(2-s) + X2*1j)*(Xm*1j)) / (R2/(2-s) + X2*1j + Xm*1j)
Zb
Explanation: $$Z_B = \frac{(R_2/(2-s) + jX_2)(jX_M)}{R_2/(2-s) + jX_2 + jX_M}$$
End of explanation
I1 = V / (R1 +X1*1j + 0.5*Zf + 0.5*Zb)
I1_angle = arctan(I1.imag/I1.real)
print('I1 = {:.3f} V ∠{:.1f}°'.format(abs(I1), I1_angle/pi*180))
Pin = V*abs(I1)*cos(I1_angle)
print('''
Pin = {:.1f} W
============='''.format(Pin))
Explanation: (a)
The input current is:
$$\vec{I}_1 = \frac{\vec{V}}{R_1 + jX_1 + 0.5Z_F + 0.5Z_B}$$
End of explanation
Pag_f = abs(I1)**2*0.5*Zf.real
Pag_f
Pag_b = abs(I1)**2*0.5*Zb.real
Pag_b
Pag = Pag_f - Pag_b
print('''
Pag = {:.0f} W
==========='''.format(Pag))
Explanation: (b)
The air-gap power is:
End of explanation
Pconv_f = (1-s)*Pag_f
Pconv_f
Pconv_b = (1-s)*Pag_b
Pconv_b
Pconv = Pconv_f - Pconv_b
print('''
Pconv = {:.0f} W
============='''.format(Pconv))
Explanation: (c)
The power converted from electrical to mechanical form is:
End of explanation
Pout = Pconv - Prot
print('''
Pout = {:.0f} W
============'''.format(Pout))
Explanation: (d)
The output power is:
End of explanation
n_sync = 1800.0 # [r/min]
w_sync = n_sync * (2.0*pi/1.0) * (1.0/60.0)
tau_ind = Pag / w_sync
print('''
τ_ind = {:.2f} Nm
==============='''.format(tau_ind))
Explanation: (e)
The induced torque is
$$\tau_\text{ind} = \frac{P_\text{AG}}{\omega_\text{sync}}$$
End of explanation
w_m = (1-s)*w_sync
tau_load = Pout / w_m
print('''
τ_load = {:.2f} Nm
================'''.format(tau_load))
Explanation: (f)
The load torque is:
$$\tau_\text{load} = \frac{P_\text{out}}{\omega_m}$$
End of explanation
eta = Pout/Pin
print('''
η = {:.1f} %
=========='''.format(eta*100))
Explanation: (g)
The overall efficiency is:
$$\eta = \frac{P_\text{out}}{P_\text{in}} \cdot 100\%$$
End of explanation
PF = cos(I1_angle)
print('''
PF = {:.3f} lagging
=================='''.format(PF))
Explanation: (h)
The stator power factor is:
End of explanation
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