PS3_MAE206_GPPA463_2024
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University of California, San Diego *
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Course
206
Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
Pages
5
Uploaded by trungnguyen010696
Problem Set #3
MAE 206/GPPA 463 W24
Professors Tynan & Victor
February 20, 2024
Due:
29
?ℎ
February, 2024 at 11:59 PM PST
Submission Instructions:
•
Turn in your assignment as a PDF through Canvas. Use your PID instead of your name in your
homework file as the filename (e.g.,
A12345678.pdf
)
•
Avoid written handwriting as much as possible and keep solutions concise
•
Highlight or box your final answers and reference any external values used in your calculations, as
well as reference sources
•
Discussion with peers is encouraged, however, the final solution should be your own
•
In case of any questions/clarifications please email Shiny and Zhenhua at
schoudhury@ucsd.edu
and
zhz121@ucsd.edu
1
1
All Class: Electricity Markets (30 pts)
Recall from the Electricity Markets lecture that in deregulated electricity markets, the market operator
has to clear the market by matching electricity supply and demand in real-time and determining the
equilibrium prices at each of the pricing nodes/zones. The equilibrium price is when the supply is equal
to the electricity demand, and then used to calculate the payment that goes to each generator.
The table below shows the available power generation capacity and marginal costs of generation in a
given hour (
?
) in a hypothetical market. In this problem, assume that the generators bid all their available
capacity with marginal costs into the electricity markets. Also, assume that we have a single pricing zone
where the price is universal across locations and ignore the transmission network.
Generator
Available Capacity (MW)
Marginal Cost of Generation ($/MWh)
Coal
2,400
50
Natural Gas
1,500
35
Solar
700
0
Wind
600
0
Nuclear
400
5
1. Calculate the equilibrium prices under each of the following demand scenarios.
(a) The electricity demand always stays at a level of 800 MW.
(b) The electricity demand always stays at a level of 4,000 MW.
(c) The electricity demand is highly inelastic and can be characterized by a function
?
(
?
)
=
−
10
?
+
4500, where
?
(
?
)
is the demand and
?
is the electricity price.
(d) The electricity demand is highly elastic and can be characterized by a function
?
(
?
)
=
−
60
?
+
4500, where
?
(
?
)
is the demand and
?
is the electricity price.
2. Calculate the total revenues and profits that can be obtained by each generator type in hour
?
,
assuming that the electricity demand is highly inelastic and always stays at a level of 4,000 MW.
3. Suppose the available wind and solar capacities increase by 80% in the next hour (
?
+
1). What
would be the resulting equilibrium prices and generator profits in hour
?
+
1?
Assume that the
electricity demand is the same as Part (1c).
2
All Class: Pro Forma (50 pts)
Imagine you are the project developer of a 400 MW wind power plant and are using a pro forma template
to model your key financial considerations. Alter the template (provided as an MS Excel file) to create a
simple pro forma for your 400 MW wind project. Use the “20-year annual w/ taxes” tab to help answer
the following questions.
1.
Basic understanding:
Before diving into the detailed calculations, let’s build a basic understanding
of the pro forma template. For each of the questions below, limit your answers to 1-2 sentences for
clarity and brevity.
(a) How would you characterize the costs relevant to the wind project?
2
(b) How would high interest rates affect some of the key financial metrics?
(c) Why might you want to increase the debt-to-equity ratio as much as possible?
(d) What types of government support have been considered in this template?
(e) Suppose you want to sell wind energy in the electricity market, why might you want to offer
a low price, even though that may sacrifice some amount of profit?
2.
Financial sensitivities:
As a project developer, you might want to see how sensitive the financial
results are to different inputs. For each of the scenarios listed below, report the
after-tax internal
rate of return
(IRR), assuming that you are an efficient taxpayer. Hold all the other variables the
same as the original pro forma while examining the impacts of the single affected variable. Note
that the default IRR in the template is 12.0%.
(a) The capital cost of wind turbines decreases by 20%
(b) Interest rate from debt increases to 9%
(c) The project developer has signed a Power Purchase Agreement (PPA) with a buyer, where the
wind energy will be sold to the buyer at a fixed energy purchase rate of $90
/
MWh
(d) The project developer receives direct government subsidies of $10 for each MWh of wind
generation from year 1 to year 5
(e) Production tax credit increases to $40
/
MWh
3.
Carbon tax for natural gas:
Suppose that you have a competitor in the same area that is planning
on developing a new combined-cycle gas turbine (CCGT) plant. The CCGT plant has a combustion
process that burns natural gas as fuel, and the combustion heat is used to generate electricity through
a turbine and a generator.
(a) Your competitor also plans to sign PPAs with potential buyers. What would be the minimum
energy purchase rate that the CCGT developer is willing to offer to the buyer? Assume that the
CCGT plant has a heat rate of 6900 BTU/kWh, and average fuel costs are estimated to be 8.0
$/MMBTU. The operational and maintenance (O&M) cost for the CCGT plant is 5 $/MWh.
(b) The local government wants to implement a carbon tax for carbon-emitting power generation
sources. What would be the required carbon tax, in units of $/tonne of CO2, for the natural
gas plant to reach price parity with the wind project? Assume that natural gas has a carbon
intensity of 0.071 tonnes/MMBTU, and wind energy has zero carbon emissions. Note in the
original pro format template, the wind project developer has a 68.5 $/MWh PPA rate.
4.
Impacts of financial incentives:
Knowing that carbon tax is politically challenging to implement,
President Biden and Secretary of Energy Jennifer Granholm are considering other policy instruments
to make wind energy more competitive to encourage further deployment. In this question, assume
that the policy instruments are applied in addition to the existing production tax credits of $25
/
MWh
in the original pro format template.
(a) Depreciation is a way to account for the value that is lost as equipment wears out over time,
but policymakers often accelerate allowable depreciation since that creates incentives for
investment.
Since the costs of depreciation (like other costs) are deductible from taxable
income, accounting for depreciation in a given year functions as a tax credit in that year.
Furthermore, since money earned today is worth more than money earned in the future,
3
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the earlier a project can account for depreciation, the greater the overall boost in economic
performance. In the ”20 year annual w/ taxes” sheet of the pro forma, Rows 60-62 show the
entire wind project
(
100%
)
depreciating in chunks over the first 6 years of the project life
(
Cells E61-J61
). To see the effect of an even more rapid depreciation policy incentive, change
these values so that all depreciation occurs in year 1. What happens to the after-tax IRR in the
efficient taxpayer scenario?
(b) Suppose now there are federal grant programs that are established to diversify the funding
sources and reduce the need for debt and equity. If the project developer manages to secure
a lump-sum grant of $8 million before the construction starts, what happens to the after-tax
IRR in the efficient taxpayer scenario?
5.
Optimal financing strategy:
The wind project developer wants to figure out the optimal energy
purchase rate that they should charge the buyer and specify in the PPA. A higher rate is likely to
make it more challenging to find a buyer, while a lower rate won’t the developer meet their debt and
equity obligations.
(a) What would then be the minimum price per MWh of wind generation that the developer should
charge the buyer, and at what debt-to-equity ratio?
Assume that the developer must maintain the minimum debt coverage ratio listed on the ”Debt
Assumptions” tab and a minimum IRR of 12%. Also, assume that the developer is an efficient
taxpayer. Note: power prices can be found to the nearest $0
.
50, and debt ratios to the nearest
whole percent.
(b) How does changing the debt-to-equity ratio impact returns? How does the debt-to-equity ratio
impact the price you must offer to meet your debt and equity obligations? Limit your answers
to 3-4 sentences.
3
MAE Only: Solar Potential (20 pts)
By mid-century, the large majority
(
>
60%
)
or so of humanity is expected to live in urban areas. Many
decarbonization policies in the OECD are focused on the use of distributed renewable energy sources to
meet much of their energy demand. If a city of one million inhabitants occupies a land area of 100 km
2
and these occupants use electrical energy at the same rate as used in Western Europe, estimate the average
demand for electrical power per unit land area that will result. Could this demand be met by deploying
renewable solar power on the rooftops throughout the city if the panels are 20% efficient and the solar
insolation (i.e. the power per unit area from the sun) is 1000 W
/
m
2
for 8 hours per day.
(
Note
: Assume that sufficient storage is available to meet energy demand when the PV system is not
producing electricity (e.g. at night, and late afternoon/early morning))
4
4
GPPA Only: EV Charging Demand (20 pts)
The Biden-Harris Administration has announced the plans to build a national network of 500,000 electric
vehicle (EV) chargers along the U.S. highways and in the communities and have EVs make up at least
50% of new car sales by 2030 (
White House, 2023
). It is estimated that the total EV charging demand
will increase by over 30% annually in the next decade.
1. We learned from the earlier lectures that the Kaya Identity is one way to decompose the total carbon
emission level. How would you adapt this method to calculate the annual EV charging demand in
the U.S.? Decompose the annual demand (in GWh) into at least 3 factors.
2. The chart on the following page shows the aggregate charging load profile for a typical weekday
for projected years 2036 and 2050 in the U.S. according to a recent study. Notice the mismatch
between peak charging demand and peak solar generation that usually occurs from 11 am - 1 pm.
What would be the implications of this mismatch?
3. Discuss at least two policies that you think could be effective in getting consumers to shift their
charging from the nighttime to the daytime.
For each policy program, 2-3 sentences will be
sufficient.
4. Identify at least two organized interest groups that might be opposed to a
shift in charging
policy
and describe the underlying reasons. What do you think they would do to prevent such a policy?
For this part, 3-5 sentences will be sufficient.
5