# Solve the problems technique 1) Problem statement 2) Schematic 3) Assumptions and Approximations 4)

Solve the problems technique

1) Problem statement

2) Schematic

3) Assumptions and Approximations

4) Physical laws

5) Properties

6) Calculations

7) Reasoning, Verification and Discussion

Question 1 The following table gives capital costs and variable costs for a coal plant, a natural gas combined-cycle plant, and a natural-gas-fired gas turbine: COAL CC GT

Capital Cost ($/kW)

$ 1,500.00 $ 1,000.00 $ 500.00

Variable Cost (c/kWh) 2.50 4.00 8.00

The utility uses a fixed charge rate of 0.10/yr for capital costs. Its load duration curve is shown as follows: a. Draw the screening curves for each type of power plant. b. Suggest a least-cost combination of power plants for this utility. c. Estimate the capacity factor for each type of power plant. d. How much electricity would each type of power plant generate each year? e. What annual revenue would the utility need to receive from each type of power plant? f. What would be the cost of electricity from each type of power plant? Question 2 Suppose 0.01 m3/s of water is taken from a creek and delivered through 150 m of pipe to a 40% efficient turbine/generator 50 m lower than the source. a. Assuming locally available Poly pipe comes in 1 cm diameter increments (starting with 2 cm), pick a pipe size to keep flow to less than a recommended speed of 2 m/s. b. In a 30-day month, how much energy would be provided? c. With a 5-nozzle Pelton wheel, what diameter jets would be appropriate? Question 3 Set up a cash-flow analysis spreadsheet for a photovoltaic system that costs $12,000, generates 8000 kWh/yr and is paid for with a 6%, 20-year loan. Assume a tax bracket of 30.5%, initial cost of utility electricity 10¢/kWh, utility electricity rate escalation 5%/yr, and personal discount rate of 10%. Question 4 Consider a PV array charging batteries for an off-the-grid, stand-alone system near Perth. You plan to run everything in the house on 240 V AC. a. Suppose the load is estimated to consist of the following 240 V AC appliances. Supplement load data given below with values from Table 9.10 in the textbook. i. A 19 cu. ft. Refrigerator/freezer ii. A 1000 W microwave oven used 15 minutes/day iii. Five 20-W compact fluorescent lamps, each used 8 hours per day iv. A horizontal-axis washing machine used 3 hours/week v. A 24-V well pump that delivers 288 gal/day at 1.6 gpm of water from 100 ft depth vi. A 19-in. colour TV used 2 hrs/day and drawing standby power the other 22 hrs/day vii. A satellite receiver system for the TV, used 2 hrs/day and in standby mode 22 hrs. viii. A laptop computer used 4 hrs/day ix. Six 3-W transformer units for chargers that run all day long Find the total watt-hrs per day needed by these appliances. b. Pick an appropriate system voltage. c. How many amp-hours/day would the battery bank have to deliver if the loads are all AC provided by a 85% efficient inverter? d. How many amp-hours/day would have to be delivered to the batteries if they have a Coulomb efficiency of 90%? e. Suppose 5% of the PV output is lost due to dirt, etc. How many amp-hours/day should the PVs provide before that derating? f. Using the worst month in Perth with North facing flat panels inclined at latitude angle, how many Astro Power APex 90-watt modules with DC, STC rated current 5.3 A and rated voltage 17.1 V would be needed in series and parallel? If they cost $400 each, what is the cost of PVs? g. What is the maximum current that you might expect in the wires connecting the array to the battery system (just use the rated current)? h. If your design goal is to provide needed electricity 95% of the time, about how many days of usable battery storage would you need? i. If a C/48 discharge rate is assumed along with 20oC, what should be the rated (nominal) Ahr capacity of the deep-cycle lead-acid battery bank? j. Suppose you use Concorde PVX 1080 batteries. How many batteries in series and how many in parallel would you recommend? At $160 each, how much would the batteries cost? k. Assume a power control unit with inverter costs $1.00/W and they come in 500 W increments. You want one big enough to cover all your appliances on at once. Pick one inverter. How much would it cost? l. Draw the system “wiring” diagram showing series/parallel combinations of the PV modules and batteries, similar to Figure 9.51 in the textbook. m. What would the total system cost be? n. Using the average annual insolation in Perth, estimate the average amp-hours/day (at the system voltage) that the PVs could deliver all year long. If all of that electricity is run through the batteries and inverter and ends up being used in the house, how many kWh/year would be delivered? Question 5 For the following turbines and average Rayleigh wind speeds, set up a spreadsheet to find the total annual energy delivered and compare that with an estimate obtained using the simple correlation given in (6.65) in the textbook: a. Bonus 300 kW / 33.4 m, 7 m/s average wind speed b. NEG/Micon 1000 kW / 60 m, 8 m/s average wind speed c. Vestas 600 kW / 42 m, 8 m/s average wind speed d. Whisper 0.9 kW / 2.13 m, 5 m/s average wind speed. CLICK HERE…….