MAE119_Intro_to_RE_HW_2_SP23
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Subject
Aerospace Engineering
Date
Jan 9, 2024
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7
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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.
05/03/2023
Homework #2
Due on Friday, May 12th before 11:59 P.M. PST. One submission per group through Grade-
scope. Groups of 1-2 students. Include all your work/code for partial credit.
Exercise 1 (32 points) Learning objectives: 1) Develop an understanding on how
different generation technologies supplement generation from renewable energy.
2) Learn about regional differences between California and Texas (the largest
Independent System Operators in the U.S.). 3) Practice basics of data science.
In this assignment we will explore and work with data provided by the U.S. Energy In-
formation Administration (EIA). We will analyze how the total demand of electricity con-
sumption and generation by source change over time in California and Texas. The first step
is to download two worksheets (California.csv and Texas.csv) from Canvas. In both work-
sheets, you will see the hourly energy production (MWh) by source (wind, solar, natural gas,
coal, hydro, nuclear, other, petroleum) and the hourly demand (MWh) for certain years.
Once you have the data downloaded in your computer, select the data of January 2019 and
July 2019. Your task is to provide insights into the following questions based on the subset
of data specified.
Plot the hourly (0.00 A.M. to 11.00 P.M.) average of:
the generation by energy source,
the total generation, and the hourly demand in GWh for January 2019 and July 2019 for
California and Texas. This will be a total of 4 plots (2 months/state
×
2 states). Answer
the following questions:
1. How do the profiles of solar, wind and natural gas generation look throughout the day
for each state?
2. What technologies complement each other to meet the demand depending on the time
of the day?
(e.g.
when solar output decreases in the evening, which technologies
increase their generation?)
3. How different are the hourly generation mixes by technology in California versus Texas?
4. Do you observe yearly seasonality (variability between summer and winter) depending
on the resource and the state?
1
5. What are three main differences between California and Texas?
6. Comment on any trends or seasonality effects you observe in hourly demands.
7. California and Texas had their peak demand in August in 2019. What is the hourly
peak (highest) demand in August 2019 for both states? At what time and date did
these peaks take place?
8. Comment on the total demand and in-state generation for both states. Do you notice
any discrepancies? Which state is importing energy? Which state is neither importing
nor exporting (approximately)? Discuss.
Hint: Which states are a part of the WECC or other large interconnections?
How
would interconnections affect how the demand is met?
In your answer, you should
consider the following expression and assume transmission network losses to be zero:
Total generation + Imports = Demand + Transmission network losses + Exports
Include your code as part of your PDF submission.
2
Exercise 2 (6 points)
Based on Masters 2013, Chapter 5.
For the simple equivalent circuit of a 0
.
022 m
2
PV cell shown below, the reverse saturation
current is
I
0
= 5
×
10
−
11
A and at an insolation of 1-sun the short-circuit current is
I
SC
=
6
.
6 A. At 25
◦
C, find the following:
1. The open-circuit voltage.
2. The load current and output power when the output voltage is
V
= 0
.
59 V.
3. The efficiency of the cell at
V
= 0
.
59 V.
3
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Exercise 3 (4 points)
Based on Masters 2013, Chapter 5.
A 4-module array has two south-facing modules in series exposed to 1000 W
/
m
2
of insolation,
and two west-facing modules exposed to 500 W
/
m
2
.
The 1-sun
I
−
V
curve for a single
module with its MPP at 4 A
,
40 V is shown below.
Draw the
I
−
V
curve for the 4-module array under these conditions. What is the output
power (W) at the array’s MPP?
4
Exercise 4 (6 points)
Based on Masters 2013, Chapter 5.
A 175
−
W c-Si PV module
has NOCT = 47
◦
C and a temperature coefficient for rated power of
−
0
.
5%
/
◦
C.
1. At 1-sun of irradiation while the ambient is 25
◦
C, estimate the cell temperature and
output power.
2. Suppose the module is rigged with a heat exchanger that can cool the module while
simultaneously providing solar water heating. How much power would be delivered if
the module temperature is now 37
◦
C ? What percentage improvement is that?
3. Suppose ambient is the same temperature, but now insolation drops to 0
.
7 kW
/
m
2
.
What percentage improvement in power output would the heat exchanger provide if it
still maintains the cell temperature at 37
◦
C ?
Exercise 5 (6 points)
Based on Masters 2013, Chapter 7.
An anemometer mounted 15 m above a surface with high crops, hedges, and shrubs, shows
a wind speed of 8 m/s. Assuming 15
°
C and 1 atm pressure, determine the following for a
wind turbine with hub height 100 m and rotor diameter of 100 m:
a. Estimate the wind speed and the specific power in the wind (
W/m
2
) at the highest point
that the rotor blade reaches. Assume no air density change over these heights.
b. Repeat (a) at the lowest point at which the blade falls.
c.
Compare the ratio of wind power at the two elevations using results of (a) and (b)
and compare that with the ratio obtained using Equation 7.20. (Masters 2013, Chapter 7,
Equation 7.20)
Exercise 6 (4 points)
Based on Masters 2013, Chapter 7.
The analysis of a tidal power facility is similar to that for a normal wind turbine. That is,
we can still write
P
= 1
/
2
ρAv
3
but now
ρ
= 1000
kg/m
3
and
v
is the speed of water rushing
5
toward the turbine.
The following graphs assume sinusoidally varying water speed, with
amplitude
V
max
.
We assume the turbine can accept flows in either direction (as the tide
ebbs and floods) so it is only the magnitude of the tidal current that matters.
For a sinusoidal tidal flow with
V
max
= 3
m/s
a
. What is the average power density (
W/m
2
)in the tidal current? A bit of calculus gives
us the following helpful start:
(
v
3
)
avg
=
avg
(
V
max
sin
(
v
))
3
= (
V
max
)
3
R
π/
2
0
sin
3
(
v
)
dv
π/
2
=
4(
V
max
)
3
3
π
b
. If a 800-kW turbine with 12-m diameter blades has a system efficiency of 33%, how
many kWh would it deliver per year in these tides?
Exercise 7 (3 points)
Based on Masters 2013, Chapter 7.
An early prototype 5-kW Makani Windpower system consisted of two 2.5-kW wind turbines
mounted on a wing that flies in somewhat vertical circles (like a kite) several hundred meters
above ground. A tether attached to the “kite” carries power from the turbines down to the
ground. Since the speed of the kite-turbines moving through the air is much faster than the
6
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wind speed, much smaller turbine blades can be used than those on conventional ground-
mounted wind turbines.
Also with no need for a tower, the cost of materials is far lower
than for a conventional system.
Suppose each wing/turbine is moving through the air at 60 m/s and suppose the overall
efficiency is half that of the Betz limit, what blade diameter would be required to deliver 2.5
kW of power per turbine. Do not bother to correct air density for this altitude.
Exercise 8 (8 points)
Solve exercise 7.7 from Masters 2013, Chapter 7.
7