Page 1 of 3 ER 100/200, Fall 2007 Topics Covered: Conservation & Efficiency; Grid T&D; EJ Problem Set #5 Due Thursday, 11/8 at 5pm. Total Points: 100 Cost of Conserved Energy [40 points] 1. After doing your Energy Audit for Problem Set 3, you are alarmed by how much electricity your apartment uses. You ask your landlady if she is willing to invest in more efficient appliances. She says she will consider it, but wants to know how much it will cost. You research replacements for your three most electricity-hungry appliances, and these are the best options you can find: Existing appliances Proposed new appliances Model kWh/yr Resale Model kWh/yr Price Lifetime Fridge Maytag RB19KN-4A 850 $65 Whirlpool ET8WTMXK 412 $714 10 y Washer Maytag LAT9800AAW 380 $35 LG WM2016CW 155 $759 15 y Dishwasher Gen. Electric GSD4360L 414 $50 Hotpoint HDA3500NWW 333 $248 12 y a. How much energy (in kWh/yr) would each of these appliances save, compared to the ones you currently have? (3 pts) b. What is the cost of conserved energy per kWh for each of these new appliances over their lifetime? (Assume a discount rate of 6%, and assume you are able to sell the old appliances on Craigslist at the resale prices above.) (10 pts) c. So far, your landlady is not convinced. “There must be cheaper ways to save electricity,” she says. “Instead, what if you replaced all the lightbulbs with compact fluorescents?” You do some more research and come up with the following data: Number of lights needed Hrs used per light per day Wattage per bulb Price per bulb Lifetime of bulb Incandescent 12 2.5 75 $0.49 0.6 yrs CFL 12 2.5 19 $4.29 6.0 yrs i. How much energy, in kWh/yr, could you save by switching to CFLs? (4 pts) ii. What is the cost of conserved energy per kWh for a CFL? (Note the different lifetimes of incandescent bulbs versus CFLs – the best way to account for this is to compare the levelized annual capital cost for each technology. Also, to simplify the calculations, assume that all your current bulbs are ready to be replaced now.) (8 pts) d. Now that you have collected this information on the cost of conserved energy, present it in the form of a graph (like the one on Hirsh p. 152, and on slide 18 of lecture 14) with “cost per kWh” on the y-axis and “kWh saved per year” on the x-axis. Which of your energy-saving options is the cheapest and which is the most expensive? (10 pts)Page 2 of 3 e. On your graph, plot the retail price of electricity as a horizontal line. (Use the baseline PG&E price of $0.11/kWh given on Dan’s utility bill from PS2.) What does this tell you about which of the energy-saving options you should invest in? Explain to your landlady in a few sentences. (5 pts) f. [ER200N only] List five oversimplifications of this analysis, and speculate on how the cost of conserved energy for these technologies might look different in a more detailed analysis. (10 pts) Transmission and Distribution of Electricity [20 points] 2. The Cahora Bassa dam, located in Mozambique, is the highest dam in Africa (171 m). The hydroelectric facility within the dam generates 1890 MW. Nearly all of this power goes to South Africa. The power station is linked from Northern Mozambique to Pretoria, 1,680 km away, by a 533 kV high-voltage DC (HVDC) power line. a. The transmission line consists of two bundles of four 611 mm2 cables made of aluminum with a steel core for strength and structural support. Calculate the resistance of the lines. (7 points) Hint: Assume that each cable has a cross-sectional area that is 1/3 steel and 2/3 aluminum. The resistance (R) for a conducting cable is given by R = ρ L/A where ρ = resistivity; L = length; and A = cross sectional area. ρsteel = 7.2 x10-7 Ω·m and ρAl = 2.7x10-8 Ω·m. Treat each cable as if it consisted of one steel and one aluminum resistor arranged in parallel. Also, note that for simplicity you may calculate Rsteel and Ralum by including all eight cables in the area calculation for each, because this is equivalent to calculating the resistance of multiple identical cables in parallel. Two resistors (R1 and R2) in parallel add in the following way: 121TotalR1R1R−+= b. How much current flows through the transmission lines? What is the power loss in the line? What is the percentage of power lost in the transmission lines relative to the power generated? (7 points) c. What would the power loss be if the power were transmitted using 333 kV AC transmission lines, which are popular for shorter distance transmission in Southern Africa (assume the same cables are used). Percentage of power lost? (6 points) Environmental Justice [28 points] 3. In this problem we will review some of the information on toxics releases that is available to the public. Go to the EPA’s Toxics Release Inventory website (http://www.epa.gov/tri/) and read a little about the program by following the “What is TRI?” link. Then go to the TRI Explorer program (http://www.epa.gov/triexplorer/) which provides access to the TRI database to answer these questions: a. Who were the three largest toxic polluters in Contra Costa County in 2005? How many of the top-20 polluters are energy-related? Hint: Click on the “Facility Report” link on the left-hand side of the page, and complete the relevant information. After you generate the report, sort the list of companies by “Total On-Site and Off-Site Disposal or Other Releases” by clicking on the appropriate triangle. (4 points) b. Examine the data provided for the top energy-related polluter, and perhaps visit their website, to get more information about them:Page 3 of 3 i. In a sentence, what does this company do? (1 point) ii. List the top three pollutants being emitted by this facility by weight into the air and for water. Use the categories “Point Source Air Emissions” and “Surface Water Discharges.” Which other pollutants on the list concern you and why, even though the magnitude of their emissions is not as great? (4 pts) iii. Have the company’s emissions gotten better or worse over time? (You can answer this question in words and/or graphically.) How would you explain the trend in emissions over time, if any? To answer this question you may want to visit Scorecard (http://www.scorecard.org) which provides the historical data for these companies in a format that is easier to analyze. (4 points)