MAE119_Intro_to_RE_HW_1_SP23
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Jan 9, 2024
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MAE 119 Introduction to Renewable Energy
Spring 2023
Prof.: Patricia Hidalgo-Gonzalez
TAs: Ka Man Chung, Rishabh Bhattacharya and Yeshvant Matey.
04/21/2023
Homework #1
Due on Tuesday, May 2nd before 11:59 P.M. PST. One submission per group through Grade-
scope. Groups of 1-2 students. Include all your work/code for full credit.
Exercise 1 (8 points)
Based on Masters 2013, Chapter 2, exercise 2.6.
A 63-gal electric
water heater is designed to deliver 5100 W to an electric resistance heating element in the
tank when it is supplied with 240 V (it does not matter if this is AC or DC).
a. What is the resistance of the heating element?
b. How many watts would be delivered if the element is supplied with 212V instead of 240V?
c. Neglecting any losses from the tank, how long would it take for 5100 W to heat the 63 gal
of water from 85
°
F to 125
°
F? The conversion between kilowatts of electricity and Btu/hr of
heat is given by 3412 Btu/h = 1 kW. Also, one Btu heats 1 lb of water by 1
°
F and 1 gal of
water weighs 8.34 lbs.
d.
If electricity costs USD 0.15/kWh, what is the cost of a 20-gal, 105
°
F shower if the
cold-water supply temperature is 45
°
F?
Exercise 2 (6 points)
Based on Masters 2013, Chapter 2, exercise 2.8.
A photovoltaic
(PV) system is delivering 20 a current through 14-gage wire to a battery 100 ft away.
a. Find the voltage drop in the wires.
b. What fraction of the power delivered by the PVs is lost in the connecting wires?
c. Using Table provided below as a guide, what wire size would be needed to keep wire losses
to less than 10 percentage of the PV power output? (Assume the PVs will continue to keep
the current at 20 A, which by the way, is realistic).
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Exercise 3 (8 points)
Based on Masters 2013, Chapter 2, exercise 2.12
Thevenin’s theorem says that the output of any circuit consisting of resistors and ideal
voltage sources can be modeled as a voltage source in series with a resistance. Suppose the
Thevenin equivalent of a circuit consists of a 24-V source in series with an 8
Ω
resistance.
(a) What is the output voltage with an infinite load so no current flows (called the open-
circuit voltage,
V
OC
?
(b) What is the output current when the terminals are shorted together (called the short-
circuit current,
I
SC
).
(c) Write an equation for the output current I as a function of the output voltage
V
out
. Draw
a graph of I versus
V out
(as the load changes).
(d) Using the equation found in (c), determine the location (I, V) on the graph at which the
maximum power will be delivered to a load. This is called the maximum power point and
you will see it a lot in the chapters on photovoltaics. Show that point on your
I
–
V
graph
from part (c)
(e) What load resistance will result in the circuit delivering maximum power to the load?
How much power would that be?
Exercise 4 (6 points)
Based on Masters 2013, Chapter 2, exercise 2.14
Suppose a photovoltaic (PV) module consists of 50 individual cells wired in series, (a). In
some circumstances, when all cells are exposed to the sun, it can be modeled as a series
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combination of fifty 0.4-V ideal batteries, (b). The resulting graph of current versus voltage
would be a straight, vertical 20-V line as shown in (c).
(a) When an individual cell is shaded, it looks like a 4-
Ω
resistor instead of a 0.4-V battery,
as shown in (d). Draw the I–V curve for the PV module with one cell shaded.
(b) With two cells shaded, as in (e), draw the I–V curve for the PV module on the same
axes as you have drawn the full-sun and 1-cell shaded I–V lines.
Exercise 5 (6 points)
Based on Masters 2013, Chapter 2, exercise 2.15
If the photovoltaic (PV) module in Problem 2.14 is connected to a 10-
Ω
load, find the current,
voltage, and power delivered to the load under the following circumstances. Comment on
the power lost due to shading.
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(a) Every cell in the PV module is in the sun.
(b) One cell is shaded.
(c) Two cells are shaded.
Exercise 6 (4 points)
Derive equation 5.9 and 5.11 from slide 28 in “Lecture 4 & 5. Solar
power.” Start the derivation from
I
=
I
SC
−
I
0
(
e
qV
kT
−
1).
Exercise 7 (24 points) Learning objective: Practical PV plant design.
Using PVWatts
Calculator from the National Renewable Energy Laboratory (click here to access it and here
for its documentation) design a 4kW solar fixed (open rack) array for the cases below. Use
default values provided for the other parameters, i.e. Resource Data Map: NREL Interna-
tional, standard module type, 14.08% system losses, DC to AC size ratio 1.2, 96% inverter
efficiency and 0.4 ground coverage ratio.
Case 1: Location: San Diego. Calculate and use the optimal Tilt angle for August 5th.
Case 2: Location: San Diego. Calculate and use the optimal Tilt angle for February
9th.
Case 3: Location: San Diego.
Calculate and use the optimal Tilt angle for August
5th, and West facing Azimuth.
Obtain the following:
1. (2 points) One plot for monthly solar radiation (kWh/m
2
/day) showing cases 1, 2 and
3
2. (2 points) One plot for monthly AC energy (kWh) showing cases 1, 2 and 3
3. (2 points) One plot for hourly AC System Output (W) for August 5th for the three
cases
4. (2 points) One plot for hourly AC System Output (W) for February 9th for the three
cases
Answer the following questions:
1. (2 points) What seasonal variation do you observe in the monthly solar radiation plot?
2. (2 points) What differences among the cases do you observe in the plot for monthly
AC energy? Why would you expect this?
4
3. (2 points) What differences among the cases do you observe in the plot for hourly AC
energy on August 5th? Why would you expect this?
4. (2 points) What differences among the cases do you observe in the plot for hourly AC
energy on February 9th? How do the shapes compare to the ones from Aug 5th? Why
could this be?
5. (6 points) Under which circumstances would you choose each case for your PV plant
design?
Exercise 8 (30 points) Professional objective:
Exploratory Renewable Energy
job search.
1. (5 points) Each team member has to find 5 job openings related to renewable energy
(i.e. 10 in total if it is a group of 2, and 5 if it is an individual submission). Openings
can be in industry, government and academia. For each posting include:
(a) Name of the company/agency
(b) position title,
(c) job description
(d) required qualifications
(e) desired qualifications
(f) seniority level
(g) employment type (full time, part time, internship)
2. (10 points) Write a 1-pager cover letter for your favorite posting (1 per student, 2 in
total for groups of 2 students). Highlight your skills and preparedness/experience for
the job, why you are a good for for the position and company, etc.
3. (15 points) Develop and list a set of questions you could be asked at the interview for
these two posting. Seven questions for each posting (i.e., 14 in total if it is a group of
2): there can be up to 2 questions in common, and the rest must be questions tailored
for the specific posting. Write answers for each question. Record a video (e.g. a Zoom
meeting) where you practice for the interview with your homework partner: Partner
1 asks all interview questions to partner 2, and then partner 2 interviews partner 1.
If you do not have a partner read the question out loud and practice answering them
in real time. Upload the video to a Google folder, include the link in your homework
solutions and please make sure to allow access for
“Anyone on the internet.”
If we
are unable to access it you won’t receive credit.
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