Solved by a verified expert :April
11, 2016
ESP 167
Energy Policy
Spring
2016
Problem Set 1: Energy Conversion and Energy Economics
Due April 25
1.
A person in the US uses an
average of 300 Gigajoules of primary energy per year. On a continuous basis,
day and night, how many kilowatts of primary energy does the person use?
The following list gives the energy content
of some primary energy sources:
Coal
28 GJ/tonne
Natural gas 1 GJ/1000 cubic feet
Biomass 18 GJ/ dry tonne; one hectare of land produces 15 dry tonnes
Oil 6 GJ per barrel (42 gallons per barrel)
Solar energy maximum = 1 kW/m2;
US average = 200 watts/m2
Also, for gasoline 1 gallon = 0.12 GJ
These sources can be converted to
electricity, heat and transportation fuels with the following energy conversion
efficiencies.
Coal can be converted to electricity at 40%
efficiency
Biomass can be converted to electricity at
40% efficiency
Natural gas can be converted to electricity
at 50% efficiency, and heat at 80% efficiency.
Oil can be converted to gasoline at 90%
efficiency
Solar energy can be converted to
electricity at 12% efficiency.
Biomass can be used to make liquid
transportation fuels at 60% efficiency.
A person uses 300 gallons of gasoline, and
10,000 kWh of electricity per year.
How much coal, natural gas or biomass would
be needed each year to make electricity for this person? For biomass or solar
how much land would be needed?
How many barrels of oil would be used per
year to make gasoline? If biofuels were used instead, how much land would be
required to grow the biomass?
2.
An engine operates at 1000
degrees C and rejects heat to the environment at 50 degrees C. The company
brochure claims that the engine is 80% efficient at producing mechanical work
from heat. Is this a reasonable claim? Why or why not?
3.
Calculate the present value of
the following expenses, assuming a discount rate of 8%.
a)
$100 spent 10 years from now
b)
$30 spent 2 years from now
c)
a sum of expenses:
$100 in year 1
$300
in year 2
$200
in year 3
$150
in year 4
$50
in year 5
4.
If you have $1000 now, and
invest it at 10% rate of return, how much will it be worth in 10 years, in 30
years?
5.
The “PowerGen”
company is building an 100 Megawatt (1 MW =106 watt) natural
gas-fueled electric power plant. PowerGen obtains a loan at 6% interest to finance
building the plant over three years. PowerGen spends the following total
amounts each year (for equipment, engineering, construction).
Year 1:
$50 million
Year 2: $25 million
Year 3:
$100 million
The plant starts producing electricity in
year 4.
a) What is the present value
in year 4 of the total capital
investment in building the plant, counting interest during construction?
The power plant operates at an average
annual capacity factor of 80%.
b) How many hours per year
does the plant operate on average? How many kilowatt hours (kWh) of electricity
are produced per year?
The energy conversion efficiency of natural
gas to electricity in the plant is 40%. (40% of the energy in natural gas is
converted to electricity). Natural gas
costs $4 per Gigajoule (GJ). (1 GJ = 277.8 kWh)
c) How much natural gas is
used per year to produce electricity?
d)
What is the total cost each
year for natural gas for the power plant?
The plant operates for 20 years after
opening. PowerGen’s investors expect a
12% rate of return on their investment.
e) What is the capital
recovery factor CRF, assuming a plant lifetime of 20 years?
Fixed operation and maintenance costs for
the plant (labor) are 3% of the total capital investment cost of the plant.
Find the present value of:
f)
the total capital investment in building the plant
g) the natural gas input to
the plant
h) the fixed operation and
maintenance costs
i)
Find the lifecycle cost of the plant ($)
j)
What is the annualized lifecycle cost of the plant ($/yr)?
k) Estimate the levelized cost
of electric power from this plant ($/kWh).
l)
What is the levelized cost of electricity if the rate of return is
6%, 20%
6.
A wind power turbine produces a
maximum electrical output of 500 kilowatts.
The turbine has a 15-year lifetime and the discount rate is 10%. The
wind turbine costs $1 million for equipment prior to installation. Operation
and maintenance costs are $50,000 per year. The capacity factor depends on
where the turbine is installed. The
power producer is considering two possible sites. A nearby site has a capacity
factor of 30%, and construction and installation would add $100,000 to the
cost. A more distant site with a more favorable wind resource has a capacity
factor of 38%, but construction costs are $250,000. Which site is better, if the goal is produce
the cheapest electricity?
A more expensive turbine would last for 20
years instead of 15 years and would give a capacity factors of 33% and 41%
instead of 30% and 38%. The better turbine costs $1.5 million. Is it worth
buying the more costly turbine?
