MD Problem Set 5
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School
University of California, Berkeley *
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Course
100
Subject
English
Date
Feb 20, 2024
Type
Pages
7
Uploaded by LieutenantBookGoat28
ER100/PP184/ER200/PP284, Fall 2023
Problem Set #5
Total Points: 100 for ER110/PP184; 125 for ER200/PP284
1)
Electric Grid Voltage [25 points]:
a)
Some load requires 1.2kW of power. If it operates at a voltage of
7.5kV, then what is the current draw in amps? [5 points]
b)
Assume the transmission line connecting this load to a generator has a
resistance of 4000 ohms, what is the efficiency of the line, expressed as
power delivered to the load over power injected by the generator? [5
points]
c)
If the voltage were doubled, what would be the new line efficiency? [5
points]
d)
What is the motivation for differing voltages on the electric grid? [10
points]
Minimizing Energy Dissipation: The computations earlier demonstrated that
elevating voltage levels leads to a corresponding decrease in current when
transmitting the same amount of power. This effectively diminishes energy
wastage resulting from resistance in the transmission lines.
Enhanced Transmission Efficiency: Utilizing higher voltages enables power to
be conveyed across extensive distances with greater efficiency and through
thinner wires. This approach is economically beneficial and decreases the
quantity of metal required for wire production.
Adaptation to Usage Norms: Utilizing lower voltages is not only safer but also
more suitable for the everyday operation of household and commercial
devices, which are engineered to function at these conventional, lower voltage
levels.
2)
Natural Gas and Fracking [25 points]:
Answer the following questions with
a short paragraph each. Rely on course materials including lecture, section
notes, and readings. Cite your sources where appropriate. a)
Hydraulic fracturing has revolutionized the energy industry in the
United States, what are the consequences of this change, positive and
negative? Consider impacts to the environment, public health,
marginalized communities, land use, the economy, and politics.
[7
points]
Fracking has significantly influenced the U.S. energy scene, enhancing
oil and gas output, cutting energy prices, and decreasing reliance on
foreign oil, thus boosting the economy, job creation, and national
energy security (EIA). It's also substituted gas for coal in power
generation, reducing emissions since gas is cleaner (EIA). However, it
poses environmental risks, like potential groundwater pollution,
induced earthquakes, and methane emissions, a serious greenhouse gas
(Howarth et al., 2011). It's resource-intensive, impacting land and
water, and often burdens marginalized communities with its health and
environmental costs. Politically, it's a hot-button issue, intersecting
regulatory debates, energy independence, and climate policy.
b)
What are the benefits to using natural gas as an energy source and what
are the drawbacks? Think about its impact on the electric grid, carbon
emissions, energy access, and energy prices.
[8 points]
Natural gas is touted for its cleaner burn compared to coal, offering a
reliable energy supply that supports renewables and grid stability while
lowering energy costs. But it's not without downsides; fracking
impacts, greenhouse gas emissions, and potential methane leaks
challenge its environmental friendliness. Investments in gas
infrastructure may also delay the shift to greener technologies.
c)
Natural gas is sometimes called a “transition fuel.” What does this
mean and what are the implications for energy policy?
[10 points]
Dubbed a "transition fuel," natural gas is seen as a temporary step
towards a renewable energy-dominated future. It suggests a short-term
emission reduction as we scale up renewables and improve efficiency.
Energy policy must navigate the delicate balance between immediate
gains from natural gas and the ultimate decarbonization objective,
avoiding overinvestment in gas to prevent delaying renewable adoption
and ensuring alignment with climate goals.
3)
Nuclear Energy and Waste [25 points for undergrad, 50 points for grad]:
After the San Onofre Nuclear Generating Station (SONGS) closed in 2012, the
Diablo Canyon Power Plant is the last remaining nuclear power plant
operating in California. Located near San Luis Obispo, the Diablo Canyon
facility is operated by PG&E and is composed of 2 pressurized-water nuclear
reactors. Each reactor can produce electricity at a rate of 1,100 MW and the
plant typically operates at an average capacity factor of 0.83. Nuclear power
plants such as Diablo Canyon are important sources of baseload electricity
because of their high output capability and low variable operating costs. In
June 2016 due to a number of factors (including proximity to earthquake fault
lines), PG&E announced that it plans to close Diablo Canyon when the current
operating license expires in 2025. a)
Calculate the average annual electricity output of Diablo Canyon in
TWh.
[2 points]
Output per Reactor=1,100 MW×0.83×8,760 hours/year
Total Annual Output=2×Output per Reactor
Total Annual Output≈2×7.9718 TWh/year
Total Annual Output≈15.94 TWh/year
b)
The following chart shows California’s electricity generation mixes in
2011 (the last year the SONGS nuclear plant of southern California
operated) and 2016, respectively. Fill in your answer from part a in the
2016 column for nuclear, then calculate total CA generation for 2016.
Calculate the percent change (2 sigfigs) for each generation type
between 2011 and 2016. In 2016, what share of California’s electricity
supply was met by Diablo Canyon?
[3 points]
California Electricity Generation (GWh)
Source
2011
2016
%
Change
Hydroelectric
42,731 28,977
-32.21%
Nuclear
36,666 15,940
-56.55%
In-State Coal
2,096
324
-84.54%
Oil
36
37
2.78%
Natural Gas
91,021 98,846
8.60%
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Geothermal
12,685 11,582
-8.69%
Biomass
6,051
5,868
-3.02%
Wind
7,598 13,500
77.68%
Solar
1,115 19,786 1674.35%
Direct Coal Imports
13,032
8,768
-32.75%
Other Imports
79,525 83,572
5.09%
Total Electricity Generation
(CA Generation plus Net
Imports)
292,55
6
287,20
0
-1.8%
c)
Assuming total electricity generation in 2012 remained the same as in
2011, and all of the lost capacity from shutting down SONGS was
made up by increased output from California’s natural gas-fired power
plants, how much additional CO
2
, in pounds, was released in
2012? Assume that when SONGS was operational (prior to 2012) its
electricity generation emitted no CO
2
, Diablo Canyon generated as
much electricity in 2012 as it did in 2016, and that California natural
gas-fired power plants emit 375 lbs of CO
2
per MWh.
[5 points]
15.94TWh=15.94×10^3 MWh
15.94TWh=15,940MWh
The natural gas CO2 emission rate of 375 lbs CO2/MWh to find the additional CO2
emissions:
Additional CO2 (lbs) = Power generated by SONGS (MWh) × CO2 emissions rate
(lbs CO2/MWh)
Additional CO2 (lbs)=15,940MWh×375 lbs/MWh
Additional CO2 (lbs)=5,977,500 lbs
Therefore, an additional 5,977,500 pounds of CO2 would have been released in 2012
due to the shutdown of SONGS and the subsequent increase in natural gas-fired
power plant output to make up for the lost capacity.
d)
Diablo Canyon stores 95% of its spent nuclear fuel onsite.
i)
In what year will the Plutonium-240 (Pu-240) expended by
Diablo Canyon in the year 2016 have decayed to one-third of
its 2016 quantity? [8 points]
ii)
How many metric tons of Pu-240 in the spent fuel will still be
onsite in that year? [7 points]
Assume the following: ●
In a light water reactor, approximately 1.0kg of spent nuclear fuel is produced
for every 50. megawatt-days (MWd) of thermal energy input.
●
For the purposes of this analysis, assume the spent nuclear fuel produced is
1.8% Pu-240 by mass. Pu-240 has a half-life of 6,430 years.
●
The thermal efficiency of the power plant is 38%
●
Use equation for radioactive decay: Q
t
= Q
0
e
-kt
where: ●
Q
t
= quantity of radioactive material at time t
●
Q
0
= original quantity of radioactive material
●
k = the decay constant ●
t = time interval in years
●
The decay constant k is defined by the relation: Half-life = ln(2)/k
e)
Yucca Mountain in Nevada is a site that has been considered for
indefinite underground storage of spent nuclear fuel. The legislative
limit on the capacity of Yucca Mountain is 77,000 tons of spent fuel.
At the current installed nuclear capacity for the United States, 99,000
MWe, how many years of spent fuel from the U.S. could a Yucca
Mountain-style repository store? Assume that the rest of the nuclear
power plant fleet in the US has the same capacity factor, thermal
efficiency, and rate of spent fuel production as Diablo Canyon.
[10
points GRAD ONLY]
f)
How many kilograms of uranium fuel (U-238) – 3% of which is
enriched to U-235 by mol (not by mass) – are used to generate the
amount of electricity from nuclear energy calculated in part a? Assume
that each fission of U-235 produces 200 MeV(mega electron volts).
HINT: calculate the number of atoms of U-235 that need to be
fissioned to generate the energy, and then calculate the kg of U-238
you would need to start with to have that many U-235 atoms present in
the enriched fuel. (1 MeV = 1.602 x 10
-13
J)
[15 points GRAD ONLY]
4) Policy Memo [25 points]:
It is time to start thinking about the policy memo. A
policy memo is a recommendation that you are making to a real government official
(or other relevant audience) on a topic you have chosen to analyze. Read the
assignment information and sample policy memo that is posted on the class website to
get an idea of what your final product should look like. You should then brainstorm
and write down the following information, which will begin to form the initial outline
of your memo:
●
What is the policy problem that this action is addressing? (10 points)
●
What could be a proposed action? This should be a concise,
sentence-length version of your recommendation. (10 points)
●
To whom are you addressing your memo? (Which institution or authority
figure is able to take this particular action?) (5 points)
Note: you do not have to commit to the policy you choose here for your policy memo.
We just want you to get started on thinking about what you might want to write about.
Policy Problem: The policy problem is the underutilization of artificial intelligence
(AI) and big data analytics in enhancing the resilience of urban infrastructure against
the growing threats posed by climate change. While AI has the potential to optimize
energy consumption, reduce emissions, and improve disaster response mechanisms,
there is currently no comprehensive policy framework to harness these technologies
effectively within city planning and emergency management systems.
Proposed Action: The proposed action is to create a 'Smart Resilience Framework' for
cities that mandates the integration of AI and big data analytics into urban planning,
energy systems, and emergency response protocols. This framework would guide
investments in smart technologies that can predict and mitigate the effects of extreme
weather events, optimize energy grids for reduced carbon output, and ensure rapid,
data-driven responses to natural disasters.
Addressee for the Memo: This memo would be addressed to the Administrator of the
Federal Emergency Management Agency (FEMA) within the U.S. Department of
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Homeland Security. The Administrator is poised to influence national disaster
preparedness and response strategies, collaborate with state and local governments on
resilience planning, and can leverage federal resources to pioneer the integration of
smart technologies in mitigating climate-induced risks.