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ECE349F 2018 INTRODUCTIONTOENERGYSYSTEMS E.pdf
ECE349F_2018_INTRODUCTIONTOENERGYSYSTEMS_E.pdf
Showing 5-9 out of 11
ECE349F 2018 INTRODUCTIONTOENERGYSYSTEMS E.pdf-UNI...
ECE349F_2018_INTRODUCTIONTOENERGYSYSTEMS_E.pdf-UNIVERSITY OF TORONTO DEPARTMENT OF ELECTRICAL
ECE349F 2018 INTRODUCTIONTOENERGYSY...
ECE349F_2018_INTRODUCTIONTOENERGYSYSTEMS_E.pdf-UNIVERSITY OF TORONTO DEPARTMENT OF ELECTRICAL
Page 5
[20 Marks]
3.
Shown below is a 60Hz, 240 Vrrns synchronous generator, modeled by its back emf and stator self
inductance, which supplies a 120Vrrns residential load through an ideal transformer. To minimize
fuel consumption of the generator you install a solar PV inverter, which connects to the 240V side of
the transformer. The desired load voltage is
v, (t)
=
h
120 cos(27r60t)
.
The self inductance of the
generator is Lss =20mH, the filter inductance of the PV inverter is Ll0mH. The voltage of the solar
array is Vd=50OV. The load parameters are R= 4 ohms, L=10 mH.
IIIIIIIIEIIE
1 0
II'
L
V
dc.
Find the complex power drawn by the load, S
If the Solar PV inverter is "off" and drawing/supplying no current, i.e. 1(t)0, find the
required back emf, ei(t).
c.
The solar PV inverter is now "on" and it is injecting 1kW of power at unity displacement
factor. (Note that unity power is measured after the internal filter inductance of the inverter,
meaning that vs(t) have is(t), as shown, have the same phase angle.) Find the new generator
current,
ig,
in RMS phasor form.
Page
5
of 11
Page 6
d. For the conditions in part (c), find the modulation index, m(t), needed for the solar PV
inverter.
Page 6 of 11
Page 7
[20 Marks]
4. Shown below is a toroidal core with square cross-section. Dimensions are rl=0. im, r2=0.08m, and
its cross-section is 0.02m x 0.02m (in other words it is 0.02m deep). The B-H curve of the material is
shown. The material has a relative permeability of 1000 below the knee point and a relative
permeability of 1 above the knee point, with a knee point at B=1.0 Tesla (recall:
t
o
=
4t
x l0). There
is no hysteresis or eddy current loss to be considered.
104
H
a. We want to build a DC inductor using this core. We place 10 turns on the core. What
inductance value will result, assuming you do not saturate the material?
b. What is the "saturation current" of this 10 turn inductor? In other words, how much current
will be flowing when the flux density is at 1 Tesla?
c.
How much energy is stored in the coil under the conditions of part (b)?
Page 7 of 11
Page 8
d.
In a linear core if I increase the current by 10 times, I have 100 times the stored energy, but
not so if you enter saturation. If you increase the current 10 times higher than in part (b), how
much total energy will be stored?
Page 8 of 11
Page 9
[20 Marks]
5
You wish to build a mag-lev tram using only the concepts of reluctance force for propulsion. Another
team builds the levitation system that ensures the tram is always exactly
5cm above
the track (gap not
to scale). You are tasked with building the propulsion system that produces force along the x-
direction. The "track" is shown below. The track is kilometers long, but exactly 1 meter wide (into
the page). The track is made of magnetic material, but has no windings and no source of power.
Inside your tram you will have a "C-core" with N-turns. The winding has a peak current carrying
capacity
Of
'max• The cross-section of the C-core is im x im, and its position and other dimensions are
shown below. All magnetic material has infinite relative permeability.
.t
I
5
CW\
30-P
I
k
1
t
ii
You are free to make reasonable engineering assumptions in your solution, provided that you
explicitly state them. Make sure you a are aware of assumptions an explicitly identify any that
you make!
a. Determine a symbolic expression for the mutual inductance Lm(x) and plot it in the top plot
on the next page. Label its peak value.
On the axes on the next page, plot the current you will chose to run in the C-core winding as a
function of position x, such that the average force in the x-direction is maximized, in the
positive x-direction. [Note spare plots at bottom of page if you wish to make intermediary
plots.]
Plot the instantaneous propulsion force as a function of x and give symbolic expressions for
(i) the maximum peak force and (ii) the "average" propulsion force.
If Imax200A and N=1000, how much average propulsion force is produced?
Page 9 of 11
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