Calculations and design

Instructions

Assignments are to be done individually. If you write calculations by hand, make sure they are legible and neat. Assignments are to be submitted no later than 5pm on Friday the 29 of May. Late assignments will be penalized by 10% per day late (the day starts at 5pm).

 

Scenario

You have been hired to provide a renewable power solution for a luxury resort hotel. The resort is located on a beautiful and scenic beach surrounded by hills and mountains. There is a river with a waterfall, which flows into a large bay.

 

During the three months of peak-season, the hotel accommodates 450 guests. In the two months of off-season, the number of guests is as low at 50 guests. The number of staff is always 50. The maximum power required by the hotel is during the peak-season and is 20kWh/day/person (staff and guests). In the off-season, the power consumption is 25kWh/day/person.

 

The resort does not own the surrounding land. If any power systems were installed on the surrounding land, it would cost $0.01/kWh of energy produced.

 

You measure the ocean wavelength of approximately 14m. You also measure the radius of wave motion on the surface of the water to be 1m.

The current on the ocean floor at 40m depth is only 1m/s.

The bay is approximately only 100m x 1km with a maximum depth in spring tide of 45m. The average spring tide height variation is 15m. The average neap tide height variation is only 10m.

 

Behind the scenic hills, is a narrow strip of land approximately 200m wide and 5 km long. The land is flat and level with trees, hedges, shrubs and foot-high grass. The wind speeds data measured at 5m from ground level, is this area is as follows:

 

0-2m/s for 10% of the time

2-4m/s for 10% of the time

4-6m/s for 15% of the time

6-8m/s for 20% of the time

8-10m/s for 15% of the time

10-12m/s for 15% of the time

12-14m/s for 5% of the time

14-16m/s for 5% of the time

Greater than 16m/s for 5% of the time

 

A river runs from the hills into a waterfall and then into the bay. You have assessed that the part of the river that is of interest has a length of approximately 10km with a gradient of 1:1000. At the end of this section of interest is the waterfall. The waterfall is approximately 10m high with approximately 10m3/s of water flowing. This waterfall is one of the more popular tourist attractions for resort visitors.

 

The resort has indicated is has an available budget of $100,000. Any more than that will require a bank loan, with 6% interest, charged monthly. There is no maximum loan amount. For any system you design, the annual maintenance and operation 1.5% of capital cost. Annual levelized replacement cost for all equipment is 1% of capital cost.

 

Other details required for any system designed:

Hydropower: any penstock will have a roughness factor of = 0.002.

 

Ocean power: ocean current systems are horizontal axis. They have a rated speed of 1m/s, diameter of 20m, total efficiency of 20%.

 

Tidal power: operates in both directions to get power in both high tide and low tide.

 

Wave power systems: no information is available.

 

Wind power: The 15m radius 200kW HAWT that you may purchase have a cut-in speed of 4m/s, rated speed of 10m/s and cut-out speed of 16m/s. The 1kW VAWT system is a Savonius turbine and has a cut-in speed of 2m/s and a rated speed of 8m/s. It has a total efficiency of 30%.

 

Make any other assumptions as required, unless specified in the remainder of the questions.

 

Questions

1. Design a Pelton Wheel to produce all the required power. Is it feasible to have a Pelton Wheel provide all the power?

[10 marks]

 

2. How many hours during the year will the HAWT run at rated speed? How many hours will the VAWT run at rated speed?

[4 marks]

 

3. Assuming there was battery storage for any “down time” in energy production, what is the minimum number of HAWTs needed to support this new community?

[7 marks]

 

4. Assuming there was battery storage for any “down time” in energy production, what is the minimum number of VAWTs needed to support this new community?

[6 marks]

 

5. How much power could be produced by a tidal barrage system? Discuss your solution.

[4 marks]

 

6. If you were to use ocean currents, how many horizontal axis ocean current systems would be needed to provide all the required power? Discuss your solution.

[4 marks]

 

7. If you could install wave energy converters to harness 1km wavefront, how efficient would the designed system need to be? Discuss your solution.

[5 marks]

 

8. How much would a HAWT system cost to run if it was to provide all the energy required, assuming the wind turbines have a 20-year life span, capital cost of $2/W (rated power), and excess energy is not sold into the grid. If energy could be sold for $0.10/kWh, how much profit could the resort make in the off-season?

[5 marks]