Download PROBLEMS FOR CHAPTER 10: Distributed Energy Resources 1

PROBLEMS FOR CHAPTER 10: Distributed Energy Resources
1. Consider the following home electric meter face:
Figure P10.1 Electric meter dials
a. A month ago, the meter dials showed 56000 kWh. What how many kWh have been used
during that month?
b. How much power is being consumed while the dial is spinning at 30 seconds/revolution?
2. Using the definition of rms voltage given in SideBar 10.2, what would be the
rms voltage for the following square wave that randomly jumps back-and-forth
between -1 V to +1V?
Figure P10.2 Find the rms voltage
3. The rate structure for an office building includes an energy charge of
$0.0732/kWh and a summer demand charge of $9/mo per peak kW. As a money
saving strategy, during the 21 days per month that the office is occupied, it has
been decided to shed 10 kW of load for an hour during the period of peak demand
in the summer.
a. How much energy (kWh/mo) will be saved?
b. By what amount will their bill be reduced ($/mo) during those months?
c. What is the value of the energy saved in dollars per kWh saved?
4. Suppose a small business can elect to use either the time-of-use (TOU) rate
schedule shown below or the rate structure involving a demand charge.
During the peak demand period they use 100 kW of power and 24,000 kWh/month, while
off-peak they use 20 kW and 10,000 kWh/month.
Which rate schedule would give the lowest bills?
5. An office building is cooled with an air conditioning (A/C) system having a COP
= 3 (i.e. 3 kWh of heat can be removed from the building using 1 kWh
of electricity fot the A/C). Electricity costs $0.10 / kWh plus demand charges of
$10/mo-kW. Suppose a 100-watt desktop computer is left on 8 hours per day, 5
days/week, 50 weeks/yr, during which time the A/C is always on and the peak
demand occurs.
a. Find the annual cost of electricity for the computer and its associated air conditioning.
b. Find the electricity cost per kWh used by the computer. Compare that with the 10¢/kWh
cost of electric energy.
6. A solar pond consists of a thin layer of fresh water floating on top of a denser
layer of salt water. When the salty layer absorbs sunlight it warms up and much of
that heat is held there by the insulating effect of the fresh water above it (without
the fresh water, the warm salt water would rise to the surface and dissipate its
heat to the atmosphere). A the salty layer of a solar pond can easily reach 90o 100oC (the University of Texas, El Paso, has such a pond that is capable of
producing 100 kW of electrical power).
a. What is the maximum efficiency of a heat engine operating from a 90oC (constant
temperature) solar pond on a 20oC day with the cold sink at ambient temperature?
b. If a real engine is able to achieve half the efficiency of a Carnot engine, how many
kilowatt hours of electricity could be generated per day from a 1 square meter pond that
captures and stores 50 percent of the 5 kWh/m2 per day of solar radiation striking its
surface.
c. For a house that requires 300 kWh per (30-day) month, what area of pond would be
needed?
7. Consider a 40% efficient, 100-kW microturbine having a capacity factor of 0.8.
a. How many kWh/yr will the turbine generate?
b. Suppose the system is rigged for CHP such that half of the waste heat from the turbine is
recovered and used to offset the need for fuel in an 85% efficient, natural-gas-fired
boiler. If natural gas costs $10 per million Btu, what is the economic value of that waste
heat recovery ($/yr)?
c. Without cogeneration, the microturbine generates electricity at a cost of 12¢/kWh. With
the dollars saved in waste heat recovery, what is the net cost of electricity from the CHP
system?
8. If the electricity generated by the CHP system in Problem 10.8 offsets 30%efficient grid power, draw a figure similar to the one shown in Figure 10.12 to
show a complete energy balance and from that find the overall efficiency
improvement of the CHP compared to a separate boiler and grid power.
9. Consider a 7 kW fuel cell used in a combined heat and power application (CHP)
for a proposed green dorm. The fuel cell converts natural gas to electricity with
35% efficiency while 40% of the input fuel ends up as useful heat for the dorm's
water, space heating and space cooling demand. Natural gas costs 90¢/therm (1
therm = 100,000 Btu).
The fuel cell costs $25,000 installed, which is to be paid for with a 6%, 20-year loan (to find
annual payments, multiply the Capital Recovery Factor found in Table 11.2 times the
amount borrowed). The system operates with a capacity factor of 90%. Its (useful) waste
heat displaces the need for heat from an 85% efficient, natural-gas-fired boiler. Following
the procedure presented in Solution Box 10.2, find the cost of electricity from the fuel cell.