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437
Subject
Electrical Engineering
Date
Apr 3, 2024
Type
Pages
6
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1
Lesson 1 Homework
Submission format: an unzipped, unencrypted, readable and appropriate .pdf file O
N
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Y
with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432
Problem 1
A 60 Hz source with an effective voltage of 240 volts supplies 4500 VA to a load with a power factor of 0.75 lagging. Determine the parallel capacitance required to improve the power factor to (a) 0.9 lagging and (b) 0.9 leading.
Problem 2
Determine the power tringles for each branch of the given parallel circuit and add them to obtain the power triangle for the entire circuit.
V = 20 60° V
30° Z
1
= 4
60° Z
2
= 5
I
1
I
2
Problem 3: In the circuit shown below, the voltage function is . Find and sketch the current , the instantaneous power , and the average power P
.
2
Problem 4:
A full wave rectified sine wave is clipped at 0.707 of its maximum value as shown in the figure below. Find the average and the rms values of the function. 1
Lesson 2 Homework
Submission format: an unzipped, unencrypted, readable and appropriate .pdf file ONLY with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432
Problem A Solar cell has the following specifications: Area: 1.6 Is: Ideality factor: 1.0 Current density: 0.40 Temperature: 300 K (27
°
)
1- Assume that the cell has a series resistance
parallel resistance is neglected.
a.
Calculate the characteristic resistance and new filling factor FF. b.
Calculate the maximum power Pmax. c.
Find the slope of the I-V curve near V
OC
. d.
How does the slope compare with the value of the series resistance? 2- Repeat the questions 1-a. and 1-b. by assuming a parallel resistance
series resistance is neglected.
a.
Find the slope of the I-V curve near I
SC
. b.
How does the slope compare with the value of the parallel resistance? 3- Assuming a parallel resistance
series resistance
a-
Find the .
b-
Find the ? 4- Draw the I-V curves of the cell as described in question 1 and 2 in the same graph or separately. Comment on the effect of series resistance and shunt resistance on the cell’s voltage and current.
5- Draw the P-V curves of the cell as described in question 1 and 2 in the same graph or separately. Comment on the effect of series resistance and shunt resistance on the P-V curves obtained.
Lesson 3 Homework
Submission format: an unzipped, unencrypted, readable and appropriate .pdf file O
N
L
Y
with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432
Problem 1
Find the optimal angle to orient a solar panel in your hometown to obtain the maximum power between the first day of spring and the first day of fall.
Problem 2
Find the optimal angle to generate power at 1pm (solar time) in Montreal on May 30.
Problem 3
Given the schematic diagram of an off-grid PV-connected house, which is located in Montreal in the figure below. a.
Use Homer simulation software to find a technical feasible solution considering the following conditions:
Location: Montreal – Eastern Time (UTC-05:00 US & Canada)
Location: Solar Global Horizontal Irradiance (GHI): download from internet
Components
:
PV panel:
-
Selecting/adding the CanadianSolar MaxPower CS6U-330P, or any other solar panel of a similar specification.
-
The capital cost of 1kW PV installation is $ 600
-
PV capacity 0, 0.330, 0.660, … 4.290 kW with DC electrical bus
-
No tracking System and the use of default panel slope.
2 Storage (battery): -
From Discover Energy storage type, choose Discover 12VRE-3000TF-L (12 V, 3.11 kWh) battery, or any other battery of a similar specification. -
choosing a capital cost of $ 410 -
selecting between 0, 1, … 10 sets Daily load profile: -
For the daily load profile, use the following table shown below to represent the load profile for all months of the year. Daily Hours Power
W 0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
16
17 18 19 20
21 22 23 Load Type hours
Kitchen light (l.)
24 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
Dining room l.
24 0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
5
Living room l.
24 0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
Bedroom l. 24 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
Bathroom l.
12 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
Fan
36 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
4
Refrigerator
100 0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
12
TV
42 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
5
Water pump
42 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
Emergency light
24 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
24
Total Power 352 24 24
24
24 24 24 124 172 124 24 124 24 124 124 24 124
124
166 250 328 262
150 48 24 Watt
b.
Study the most feasible solution when considering different sensitivity variables pertaining to the solar panel slope and azimuth values that are given below. What would be the least optimal configuration? Explain? A
-
0 1 Lesson 4 Homework Submission format: an unzipped, unencrypted, readable and appropriate .pdf file O
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with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432
Problem 1
An industrial freezer is designed to operate with an internal air temperature of -20
0 C when the external air temperature is 25
0
C and the internal and external heat transfer coefficients are 12 W/m
2
K and 8 W/m
2
K, respectively. The walls of the freezer are composite construction, comprising of an inner layer of plastic (k = 1 W/m K, and thickness of 3 mm), and an outer layer of stainless steel (k = 16 W/m K, and thickness of 1 mm). Sandwiched between these two layers is a layer of insulation material with k = 0.07 W/m K. Find the width of the insulation that is required to reduce the convective heat loss to 15 W/m
2
. 1
Practice Assignment 1 You have the option of doing the assignments on your own and reviewing the provided solutions, and/or attending the weekly tutorial session for assistance. Please see course agenda for tutorial information and dates. Submission format: an unzipped, unencrypted, readable and appropriate .pdf file ONLY with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432. Problem 1:
Given a circuit with an applied voltage of Volts and a resulting current of Amperes, determine the complete power triangle.
Problem 2:
The parallel RC circuit has an applied voltage of the waveform shown in the figure below. Sketch and determine the electric currents ,
, and .
400 µF
5
i
T
i
1
i
2
v
0
50
-50
2
4
6
8
v
(volts)
t
(ms)
Problem 3:
Given a circuit with an impedance
and an applied phasor voltage .
Correct the power factor to 0.9 lagging by addition of parallel capacitor. Find the after the correction is introduced, and the var of capacitors required to obtain such correction.
Problem 4:
Find the average and effective (rms) values of the sawtooth waveform shown below:
0
50
2
y
t
4
6
1
Practice Assignment 1 Solution Problem 1 (Problem 7.16 pp. 78):
Given a circuit with an applied voltage of Volts and a resulting current of Amperes, determine the complete power triangle.
Solution: Problem 2 (Problem 4.53 pp. 15):
The parallel RC circuit has an applied voltage of the waveform shown in the figure below. Sketch and determine the electric currents ,
, and .
400 µF
5
i
T
i
1
i
2
v
0
50
-50
2
4
6
8
v
(volts)
t
(ms)
Solution:
which is identical to the given voltage waveform. The resulting waveform of is shown in (a).
,
is determined as:
(1)
P = 2216.14 W
Q = 442.83 var
= 11.3
o
2
(2)
and (1)
(2)
is sketched as in (b).
Then, for every time span. It is sketched in (c)
Problem 3 (Example 2 pp. 72):
Given a circuit with an impedance
.
Correct the power factor to 0.9 lagging by addition of parallel capacitor. Find after the correction is introduced, and the var of capacitors required to obtain such correction.
Solution:
Lagging
OR so: or lagging
0
50
-50
2
4
6
8
v
(volts)
t
(ms)
0
10
-10
2
4
6
8
i
1
(A)
t
(ms)
0
10
-10
2
4
6
8
i
2
(A)
t
(ms)
0
10
-10
2
4
6
8
i
T
(A)
t
(ms)
20
-20
1
2
(a)
(b)
(c)
P = 1200 W
Q =
1600 var
Q
C
=
1018.86 var
Q’ =
581.14 var
3
and leading. To find C, Problem 4 (Problem 2.4 pp. 18):
Find the average and effective (rms) values of the sawtooth waveform shown below:
0
50
2
y
t
4
6
1
Practice Assignment 2
You have the option of doing the assignments on your own and reviewing the provided solutions, and/or attending the weekly tutorial session for assistance. Please see course agenda for tutorial information and dates. Submission format: an unzipped, unencrypted, readable and appropriate .pdf file ONLY with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432. Problem 1
A solar cell has the following specifications:
Area: 1.5 cm
2
Series resistance: Is: 1.0×10
-12
A/cm
2
Ideality factor: 1.0
Current density: 0.40 A/cm
2
Temperature: 300 K
i.
Draw the diode characteristic.
ii.
Draw I-V curve of the complete cell.
iii.
Calculate the characteristic resistance R
CH
and the new filling factor FF.
iv.
Calculate the maximum power P
max
.
Problem 2
Assume that the cell of problem 1 has a series resistance
i.
Draw the new I-V curve.
ii.
Calculate the new characteristic resistance and new filling factor FF
iii.
Find the slope of the I-V curve near V
oc
.
iv.
How does the slope compare with the value of the series resistance?
v.
Calculate the new maximum power P
max
.
Practice Assignment 2 Solution
Problem 1
i.
Draw the forward diode characteristics.
The diode characteristic is given by the following equation:
By plugging the given parameters in the above equation, we get:
By plugging different values
in the above equation, the corresponding values of can be obtained. From the obtained points, the diode characteristic can be drawn as follows:
ii.
Draw I-V curve of the complete cell.
The I-V characteristic of the cell is given by the following equation:
(2)
(1)
Fig. 1.
Forward diode characteristic
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By plugging different values
in the above equation, the corresponding values of can be obtained. From these points, the I-V characteristic of the cell can be drawn as follows:
iii.
Calculate the characteristic resistance and the fill factor FF.
To find the characteristic resistance R
CH
and the Fill Factor FF, four values are needed which are the open circuit voltage V
oc
, the short circuit current I
sc
, the voltage corresponding to the maximum power V
mp
, and the current corresponding to the maximum power I
mp
.
Eq.(2) will be used to find those values.
To find V
oc
, the load current should be set to zero in Eq.(2), which yields to Eq.(3)
(3)
By substituting the given parameters in Eq.(3), V
oc
= 0.6
V
To find I
sc
, the load voltage should be set to zero in Eq.(2). Therefore;
If,
Then,
Fig. 2.
I-V curve of the cell.
I
sc
=
To find V
mp
and I
mp
, the maximum power P
max
should be found. The power of the cell can be calculated as follows:
(4)
By plugging different values
, the corresponding values of can be obtained. Form these points, the P-V curve can be drawn as follows:
From the P-V curve, the value of V
mp
is equal to 0.609 V as shown on the Fig.3.
The value of I
mp
can be calculated as follows:
=
And the characteristic resistance R
CH
can be calculated as follows:
The fill factor FF can be calculated as follows:
(5)
Fig. 3.
P-V curve
iv.
Calculate the maximum power.
The maximum power can be determined from the P-V curve of Fig.3 which shows a value of P
max
= 0.3499 W
Problem 2
i.
Draw the new I
V curve.
With the existence of R
s
, the equation used to calculate the output current (
I
) is as follows:
(4)
By plugging the given parameters in the above equation, we get:
By plugging different values
, the corresponding values of can be obtained. For example:
Point 1: Point 2: Point 3: ……..etc
Open circuit voltage
Point N:
Solving above equation by iterations,
0.
A
Therefore, the I-V characteristic of the cell is drawn bellow:
ii.
Calculate the new characteristic resistance and the new fill factor FF.
To find V
oc
, the load current should be set to zero in Eq. (6), so,
V
oc
=0.
V
To find I
sc
, the load voltage should be set to zero in Eq.(6)
Solving above equation by iterations,
0.
A
(short circuit current, )
=0.6912 V
Open
circuit voltage
(short circuit current, )
Fig. 4.
I-V curve
To find V
mp
and I
mp
, the maximum power P
max
should be found. The power of the cell can be calculated as follows:
(7)
Hint
: to draw P-V curve of the cell, just use P = V
d
* I
in Fig. 4.
From Fig. 5,
P
max
=
W
From the P-V curve, the value of V
mp
is equal to 0.346 V as shown on the figure.
The value of I
mp
can be calculated as follow:
=
Now, the characteristic resistance R
CH
will be found by using the following equation:
R
CH
=
V
mp
I
mp
Which leads to a value of R
CH
= 1.
.
The fill factor FF can be calculated according to the following equation:
FF=
V
mp
I
mp
V
oc
I
sc
Which leads to a value of FF
= 0.254
Fig. 5.
P-V curve
iii.
Find the slope of the I
V curve near V
OC
Two arbitrary points near
V
oc
on the I-V curve can be chosen. For example:
a (0.6912, 0.0289), b (0.6596, 0.0201)
By using the following equation:
The slope
m
found to be (-0.6471).
iv.
How does it compare with the value of the series resistance?
Increasing the series resistance would decrease the slope near
V
oc
.
v.
Calculate the new maximum power?
The maximum power can be determined from the P-V curve of Fig.5 which shows a value of P
max
=
W
1
Practice Assignment 3
You have the option of doing the assignments on your own and reviewing the provided solutions, and/or attending the weekly tutorial session for assistance. Please see course agenda for tutorial information and dates. Submission format: an unzipped, unencrypted, readable and appropriate .pdf file ONLY with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432. Problem 1 Find the optimal angle to orient a solar panel in Montreal to obtain the maximum power between the first day of spring and the first day of fall. Problem 2 Find the optimal angle to generate power at 2pm (solar time) in Montreal on the 13
th
of May.
Practice Assignment 3 Solution
Problem 1
Problem 2 1
Practice Assignment 4
You have the option of doing the assignments on your own and reviewing the provided solutions, and/or attending the weekly tutorial session for assistance. Please see course agenda for tutorial information and dates. Submission format: an unzipped, unencrypted, readable and appropriate .pdf file ONLY with a file size of maximum 10MB. File naming convention: Homework#_StudentName_StudentID. E.g. Homework4_JaneDoe_8765432. Problem 1
How many Joules of energy/second is conducted across a square body of 40 consisting of two materials in contact , the first is insulation with a thermal conductivity of 0.2, thickness 0.076m and the second is glass with a conductivity of 0.8 and thickness of 0.019. The temperature on the outside of the insulation is 25 degrees Celsius and the outside of the glass is 4 degrees Celsius. Table of Thermal Conductivities
Substance
Thermal Conductivity
k [J/(s-m-C)]
Substance
Thermal Conductivity
k [J/(s-m-C)]
Styrofoam
0.010
Glass
0.80
Air
0.026
Concrete
1.1
Wool
0.040
Iron
79
Wood
0.15
Aluminum
240
Body fat
0.20
Silver
420
Water
0.60
Diamond
2450
Practice Assignment 4 Solution
Problem 1 Table of Thermal Conductivities Substance Thermal Conductivity k [J/(s-m-C)] Substance Thermal Conductivity k [J/(s-m-C)] Styrofoam
0.010
Glass
0.80
Air
0.026
Concrete
1.1
Wool
0.040
Iron
79
Wood
0.15
Aluminum
240
Body fat
0.20
Silver
420
Water
0.60
Diamond
2450
To calculate the heat flow through the first insulation:
(1)
To calculate the heat flow through the glass:
(2)
Heat is like a fluid: whatever flows through the insulation must also flow through the glass. By knowing that Q
i
=Q
g
, solving equations (1) and (2) will yield to:
(3)
(4)
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