Energy & Environment I NAME: ANSWERS

HW#4

Due Friday, October 26, 2001

ANSWERS MUST BE TURNED IN ON THESE SHEETS IN THE SPACES PROVIDED. YOU MUST SHOW ALL WORK.

ANSWERS IN BOLD RED.
    1. Fig 2.6, p 55, of the text tells you how much energy the average American uses in one year. Convert this to kwh. Fig 1.8, p 12, of the text tells you how much of this is used for residential purposes. Determine how much energy (as kwh) the average American uses for residential purposes.

      2. (2pt) ANSWER for annual per capita energy use as kwh:

      350 GJ = 350,000,000 kJ/(3600 kJ/kwh) = 97,222 kwh

      (3pt) ANSWER for annual per capita residential energy use as kwh:

      Figure 1.8 shows the residential energy as 20% of the total. Thus: 0.20 x 97,222 = 19,444 kwh.

      Suppose you are an average American energy-wise, and you wish to generate an amount of electrical energy equal to one-half the per capita annual residential energy consumption. That is, you decide to mount on your roof solar PV panels that over the year would generate an amount of electrical energy equal to one-half the per capita annual residential energy consumption. Determine the capital cost of your solar PV system, the roof area required (as sq meters), and the cost of the electricity generated (as cents/kwh, assuming a 30 year lifetime of the system, and simple economics, ie, cost/kwh = capital cost/total kwh generated over 30 years).

      Note:

      Unit cost of solar PV system = $7500/kw-rated-peak.

      Solar panel power rating = 0.12 kw-rated-peak/sq meter.

      Capacity factor for Seattle = 0.12 = average kw actually generated/kw-rated-peak.

      (2pt) ANSWER for electrical energy as kwh you wish to annually produce with your solar PV system:

      19,444 kw/2 = 9722 kwh

      (4pt) ANSWER for the electrical energy as kwh your solar PV system would annually produce if it continuously ran at the rated-peak power:

      9722 kwh/capacity factor = 9722 kwh/0.12 = 81,019 kwh

      (4pt) ANSWER for the rated-peak power of your solar PV system as kw:

      81,019 kwh/(8760 hr) = 9.25 kw

      (4pt) ANSWER for the area of your solar PV system as sq meters:

      9.25 kw/(0.12 kw/m2) = 77 m2

      (3pt) ANSWER for the total cost of your solar PV system as $:

      9.25 kw-rated-peak x $7500/kw-rated-peak = $69,375

      (4pt) ANSWER for the unit cost of the electricity produced by your solar PV system as cents/kwh:

      $69,375/(9722 kwh/yr x 30 yr) = 0.24 $/kwh = 24 cents/kwh

      Are you ready to buy a solar PV system and install it?

      (3pt) ANSWER with your reason:

      The cost of the electricity generated is very expensive compared to our current price of about 6 cents/kwh. Thus, on these economic grounds, I would not buy a solar PV for my Seattle area home.

      What if you lived in Honolulu, where the capacity factor is at least 0.20 and the residential cost of electricity is about 15 cents/kwh? Would you buy now?

      (6pt) ANSWER backed up with your reason:

      This is a different situation. Except for the summertime, Honolulu

      receives considerably more solar energy per day than Seattle. Thus, the capacity factor is greater than that for Seattle. Thus, in Honolulu solar PV electricity can be generated for 24 x 0.12/0.20 = 14 cents/kwh. This is competitive with utility electricity. Thus, I’d buy a solar PV system in Honolulu. (It would provide security since utility electricity in Honolulu is highly dependent on the burning of oil imported to Hawaii.)
    2. If you were an average American energy-wise, how much energy (as kwh) would you annually use for transportation?

      3. (3pt) ANSWER for amount of energy as kwh annually used for transportation by an average American:

      Figure 1.8 shows 27% of our energy use is for transportation. Thus, the per capita use for transportation is 0.27 x 97,222 kwh = 26,250 kwh

      Now determine your personal annual transportation energy use (as kwh). That is, determine how much you annually use for your car, for riding in friends’ and relatives’ cars, for riding the bus, and for riding in trains and airplanes.

      ANSWER with calculation for the energy (kwh) you use per year driving your car:

      (Miles driven per yr)/(average miles per gallon)/(average number of persons in your car) x (125,000 BTU/gallon) / (3412 Btu/kwh).

      ANSWER with calculation for the amount of energy (kwh) annually used by friends and relatives transporting you:

      (Miles driven per yr)/(average miles per gallon)/(average number of persons in the car) x (125,000 BTU/gallon) / (3412 Btu/kwh).

      (If you cannot estimate the mileage your friends’ and relatives’ cars get, then you could resort to using the value of 3840 BTU per passenger-mile given by Bodansky in Table 21.3, p. 21:4. Muliply this by the number of miles you traveled in your friends’ and relatives’ cars.

      ANSWER with calculation for the amount of energy (kwh) annually used by you in riding the bus:

      Estimate the number of miles you travel per year in buses. Then multiply this by the BTUs per passenger-mile given by Bodansky.

      ANSWER with calculation for the amount of energy (kwh) annually used by you in riding in trains and airplanes:

      Estimate the number of miles you travel per year in trains and airplanes. Then multiply this by the BTUs per passenger-mile given by Bodansky. (Or better yet, find and use updated figures for the BTUs per PM.)

      (21pt) ANSWER for your total annual use of energy (kwh) for transportation:

      Add up the values above to obtain your total.

      How do you compare with the national average?

      (3pt) Explain:

      Compare and comment.

      Are you overlooking any transportation energy you used?

      (8pt) Explain:

      Yes. The above estimate of your personal use of energy for transportation neglects the transportation energy associated with goods and services you purchase over a year. It also needs the taxes you paid for military use of transportation energy.
    3. During the winter of 2000-01, the spot price for natural gas in California peaked at about $30 per million BTUs. In order to break even, what would have been the price of the electricity produced by a gas-fired power generator? Note: the fuel cost is the main cost borne by the power generator.

(15pt) ANSWER with calculation for the break-even unit cost of electricity produced from natural gas having a price of $30/million BTU.

Assume 50% efficiency for generating electricity from natural gas (in combined cycle power plants). Then, from 1 million BTUs of gas, 1,000,000 BTU/(3412 BTU/kwh)/2 = 146.5 kwh of electricity are generated. Thus, the break-even price would be $30/146.5 kwh = 0.205 $/kwh = 20.5 cents/kwh. (This might explain some of the high cost of wholesale electricity in California last winter.)

Compare your answer to the break-even cost of electricity produced from $2 per million BTU gas (the current spot price) and $1.2 per million BTU coal.

Be sure to consider the efficiency of generating electricity from natural gas, and from coal.

(5pt) ANSWER with calculation for the break-even unit cost of electricity produced from natural gas having a price of $2/million BTU.

20.5 cents/kwh x 2/30 = 1.4 cents/kwh.

(10pt) ANSWER with calculation for the break-even unit cost of electricity produced from coal having a price of $1.2/million BTU.

The efficiency is now 33%. Thus, 1,000,000 BTU/(3412 BTU/kwh)/3 = 97.7 kwh of electricity are generated. The break-even price would be $1.2/97.7 kwh = 0.012 $/kwh = 1.2 cents/kwh. (Additionally, operating costs and payoff of the capital investment might be greater than for a gas-fired plant. However, some of the old, "grandfathered" coal-fired plants are fairly cheap to run.)