ECE 330 homework assignment #4, due in Mid-term examination
Problem 1
For the magnetic circuit in Fig. 1 below, the upper part with winding is fixed, and the lower part is
movable (up and down only). Take into account the effect of fringing in the air gap
ECE430
Spring 2011
Homework 9
Problem 5.5
(a)
Choosing the states to be
x=
x1
=
x2
,
the following second order nonlinear system results:
x2
24 sin x1 0.5x2
0.1
x=
.
Setting x = 0, and applying the restriction that = cfw_ R | 0 , provides the equilibrium
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 3 Solution
1. Problem 3.10
a. Assuming an ideal (lossless) transformer, the primary side current I1 may be
estimated to be
I1 =
N2 P2
120 4.8 kV A
N2
I2 =
=
= 20 A
N1
N1 V2
240 120 V
(1)
b.
ECE 330 homework assignment #2 (In class quiz Fri, Feb 7)
Text problem 2.16 (partial answer: I line = 1,255Amps, P+jQ tot = 600 +j450 MVA)
Text problem 2.17
Text problem 2.19
Text problem 2.20
Text problem 2.25
Special problem #1
A balanced, 3-phase, 3-wi
ECE 330 homework assignment #2 (In class quiz Fri, Sep 13)
Text problem 2.16 (partial answer: I line = 1,255Amps, P+jQ tot = 600 +j450 MVA)
Text problem 2.17
Text problem 2.19
Text problem 2.20
Text problem 2.25
Special problem #1
A balanced, 3-phase, 3-w
ECE330
Spring 2013
Homework 3
Problem 3.1
Amperes law may be applied to yield
J f nda
H dl =
s
C
2Hg lg + Hc lc = Ni
2lg
Ni
lc
+
,
=
0 Ag iron Ac
where the reluctances are as follows:
lg
0.3cm
At
=
= 3.145 106
0 Ag (4 107 )(3cm + 0.3cm)(2cm + 0.3cm)
Wb
lc
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 6 Solution
1. Problem 1
a. The co-energy function for this system is:
Wm0 (ias , ibs , ir , )
Z
Z ias
as (ias , 0, 0, )dias +
=
bs (ias , ibs , 0, )dibs +
Z
ir
bs (ias , ibs , ir , 0, )dibs
ECE 330 homework assignment #3 (In class quiz Fri, Feb 14)
Text problem 3.1 (and also find the magnetic flux density in the iron)
(partial answer: L = 6.1 mH)
Text problem 3.2 (part b only)
(partial answer: L11=3.125mH, L22=0.78125mH)
Text problem 3.3 (al
ECE330 Spring 2013
Problem 1
+ I1
V1
Req
Rc
I2/a
jXeq
V2
jXm
Load
_
10:1
Turns ratio a = 2200/220 = 10.
Rc' = a 2 Rc = 19500
'
X m = a 2 X m = 17000
Assume V2 = 2150 0 V,
Load current:
10000
I2 =
cos 1 (0.96 ) = 46.51 16.26 0 A
215
Primary voltage:
I
V
ECE330 Spring 2013
2.1
(
)
v(t ) = 100 cos 377t + 10 0 V => V =
(
)
i (t ) = cos 377t + 55 0 A => I =
1
2
100
2
10 0 V
55 0 A
Average power: P = VI cos( v i ) =
100 1
(
)
(
22
Power factor: PF = cos( v i ) = cos( 45 0 ) = 0.7071 leading
2.2
(
)
a) v(t ) =
ECE 330: Power Circuits and Electromechanics
Spring 2016
Homework 6 Solution
1. Problem 4.1
a. With the permeability of the core assumed to be infinite, the equivalent magnetic
circuit is as shown in Fig. 1, where the reluctances are defined to be
g
0 W 2
ECE 330 homework assignment #6 (In class quiz Mon, Mar 17)
Text problem 4.1 (c) and (d) only
Text problem 4.2 (b)
e
Text problem 4.4 but do not compute Wm (partial answer: f = -0*w*w*N*N*i*i/(2x*x) )
Text problem 4.6 but do not compute Wm
e
(partial answe
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 4 Solution
1. Problem 4.1
c. From homework 5, we note that (i, x) = 0 W 2 N 2 ( g1 +
2gx(i,x)
.
0 W 2 N 2 (g+2x)
1
)i,
2x
thus i(, x) =
We can compute the energy by:
Z
Wm (, x) =
0
x)d
=
i
ECE330
Power Circuits and Electromechanics
Dr. Nam Nguyen-Quang
Spring 2013
http:/www4.hcmut.edu.vn/~nqnam/lecture.php
Lecture 4
1
Electromechanical system Introduction
Magnetic circuits with one moving member will be studied.
Systematic derivation of mat
ECE330
Fall 2013
Homework 3
Problem 3.1
Amperes law may be applied to yield
l
H d =
C
n
J f da
s
2Hg lg + Hc lc = Ni
2lg
Ni
lc
=
+
,
0 Ag iron Ac
where the reluctances are as follows:
lg
0.3cm
At
=
= 3.145 106
0 Ag (4 107 )(3cm + 0.3cm)(2cm + 0.3cm)
Wb
ECE 330 homework assignment #2, due on Monday, February 18, 2013
Problem 1
A coil of 180 turns is wound uniformly over a wooden ring having a mean circumference of 700
mm, and a uniform cross sectional area of 400 mm2. If the current through the coil is 6
ECE330
Fall 2013
Homework 2
Problem 2.16
(a)
Assuming a balanced 3- conguration, the complex power per phase is
S 1 =
S 3 750
=
= 250 MV A.
3
3
Taking the line voltage to be the reference angle, the complex impedance per phase is
2
S 1 =
V
Z
=
(345 kV)2
Z
ECE 330 homework assignment #11 (No class quiz)
Text problem 7.3
Text problem 7.4
Text problem 7.11
Text problem 7.14
Special problem #1 (see solution Spring 2005 final)
A 460 Volt (line to line), 60 Hz, 3-phase, Y-connected, 4 pole Induction motor is run
ECE 330 homework assignment #4 (In class quiz Thu/Fri, Sep 24/25)
Text problem 3.2
Text problem 3.10 a) and b) only
(answers: 20A, 12 Ohms)
Text problem 3.12
Text problem 3.14
Text problem 3.17
Special problem
A 480/240 V, 4.8 kVA, 60 Hz, single-phase tra
ECE 330 homework assignment #5 (In class quiz Fri, Oct 10)
Text problem 4.1 (a) and (b) only
Text problem 4.2 (a) only (partial solution: L1= (1/4)*(0N*N*(Ag0/g0)+(Ag1/g1)
Special problem #1 (see Exam 2 Spring 2004 for solution)
For the structure drawn in
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 5 Solution
1. Problem 4.14
The dynamics of a translational electromechanical system are described by
d2 x
dx
+ 0.1 i + x3 x = 0
2
dt
dt
dx
di
2 i+x +i5=0
dt
dt
a. Defining the states to be
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 2 Solution
1. Problem 3.1
Let Rg and Rr to be the reluctances of each air gap and the iron coil, respectively.
Figure 1: Magnetic circuit for Problem 3.1
Neglecting the fringing effects, th
ECE 330: Power Circuits and Electromechanics
Summer 2016
Homework 1 Solution
1. Problem 2.1
Converting both the voltage and current waveforms from their time-domain representation to phasors, we get
100
v(t) = 100 cos(377t + 10 ) V V = 10 V,
2
1
i(t) = co
ECE 330 homework assignment #4
(In class quiz Fri, Sep 23)
Text problem 3.2
Text problem 3.10 a) and b) only
(answers: 20A, 12 Ohms)
Text problem 3.12
Text problem 3.14
Text problem 3.17
Special problem
A 480/240 V, 4.8 kVA, 60 Hz, single-phase transforme
ECE 330 homework assignment #3
(In class quiz Thu/Fri, Sep 17/18)
Text problem 3.1 (and also find the magnetic flux density in the iron)
(partial answer: L = 6.1 mH)
Text problem 3.2b (part b only)
(partial answer: L11=3.125mH, L22=0.78125mH)
Text problem
ECE 330 homework assignment #5
(In class quiz Thu/Fri, Oct 8/9)
Text problem 4.1 (a) and (b) only
Text problem 4.2 (a) only (partial solution: L1= (1/4)*(0N*N*(Ag0/g0)+(Ag1/g1)
Special problem #1 (see Exam 2 Spring 2004 for solution)
For the structure dra
ECE 330 homework assignment #11 (In class quiz Monday Dec 5)
Text problem 7.3
Text problem 7.4
Text problem 7.11
Text problem 7.14
Special problem #1 (see solution Spring 2005 final)
A 460 Volt (line to line), 60 Hz, 3-phase, Y-connected, 4 pole Induction
ECE 330 homework assignment #9 (In class quiz Fri, Nov 11)
Text problem 5.1
Text problem 5.4 (a and b only)
Text problem 5.5
Special problem #1 (see solution Spring 2004 final)
A dynamic system is modeled as:
x1 3x1 2 x2
x2 x12 2 x2 2
a) Find all equilibr
ECE 330 homework assignment #10 (In class quiz Mon Nov 28)
Text problem 6.3 (the angle solution should be 43.2 degrees)
Text problem 6.4
Text problem 6.11 (The machine is also loaded to rated current)
Text problem 6.15