EPS219 – Energy and the Environment
Homework#8 – Due in class, Thursday, April 2, 2015
1) (10 pts) Explain why a power utility company might be justified in charging
homeowners a monthly “net metering” surcharge if they install rooftop solar
panels.
The cost of maintaining the grid of power lines is still the same, and without the
surcharge for rooftop-solar users, they would have to charge everyone else a
little bit more, and this might adversely affect low-income people who could
never afford to install solar panels.
[other answers possible]
2) (10 pts) Explain why a power utility company might not be justified in
charging homeowners a monthly “net metering” surcharge if they install rooftop
solar panels.
The solar panels would be operating during the day, when power companies
have their heaviest load and often have to produce extra electricity at greater
costs (such as with gas or natural gas-fired turbines) during the day to meet
demands. So, solar panels lessen the utility companies need to produce costly
electricity.
3) (10 pts) Explain how the evolution of the way that electric power utilities
charge homeowners for electricity has paralleled the history of how individuals
have paid for cell-phone usage.
For both, there used to a flat rate for usage. Now, both have varying plans that
offer users different rates at different times.
4) (5 pts) Explain the difference between the “shifting” and “curtailing” options
for “Demand Response” programs.
With curtailing, consumers will actually use less electricity. With shifting,
consumers still end up using the same amount of electricity, but move some of it
to off-peak times.
5) (15 pts) The gradient of the Mississippi River is about 0.37 ft/mile as it passes
through New Orleans. Suppose that you dammed the river so that the reservoir
extended 3 miles behind a hydroelectric dam. How much power could you
theoretically get out of the dam? (Hint: You will need to find on the web what the
discharge of the River is.)
Answer: (15 pts) (Can be done two different ways)
(From my powerpoint lecture) Power (kW) = 5.9 x Flow (m3/s) x Head (m)
Head = 0.37 ft/mi x 3 mi = 1.1 ft = 0.34 m
Average Flow = ~ 17,000 m3/s [Answer can vary]
Power = 5.9 x 17,000 x .34 = 34,000 kW = 34 MW [Answer can vary][In this case,
the “5.9” accounts for a loss in efficiency]
Or
E = mgh so Power = mgh/s = volume x density x g x h /s =
(17,000 m3/s)(1000 kg/m3)(9.8 m/s2)(0.34m)= 57 MW [This doesn’t take loss
of efficiency into effect]
6) (10 pts) Explain why are there two high tides and two low tides each day?
Answer: (10 pts) Because there are two bulges from the tides, one on the front
and back of the earth. So, as Earth rotates over a day, a point on Earth will pass
through both bulges, so will experience two high tides.
7) (20 pts) Suppose you are a municipal electricity supplier and you need to
provide a steady source of power. Explain what the separate concerns are for
each of hydroelectric, wind, tidal, and ocean wave energy in terms of providing a
steady and continuous power source (i.e., what are the forms and sources of the
uncertainties in continuity?)
Answer: (20 pts)
Hydroelectric – mostly quite constant, but the amount of power can change over
longer periods of time (months to decades) if the amount of rainfall changes
between seasons or over the course of an extended drought.
Wind – Very unpredictable. Can change over many different time scales, from
minutes to days. One day it can be very windy, the next, not windy at all.
Tidal – VERY predictable, but the magnitude varies significantly over both daily
and monthly cycles. But you know what they will be.
Ocean waves – Like wind, it can change over minutes to days. Some days the
wave can be small, sometimes large.
8) (10 pts) Explain why a hydroelectric dam reservoir tends to fill up with silt
over time.
Flowing water can carry more sediment when it is flowing than when it is
standing still. The water that flows from a river into a dam reservoir is initially
carrying sediment, but when the water stops moving, the sediment drops out,
and the dam can fill us with silt.
9) (10 pts) Explain how a hydroelectric power plant built in the mountains is
likely to be less disruptive to the region than a plant built in a relatively flat
region.
In a mountainous area where the sides of the canyon are steep, a relatively small
area is flooded to make the dam reservoir. In the flat region, the same vertical
height for the dam could result in a very large area that gets flooded, displacing
many more people from their homes.