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The Power of Tides

The Power of Tides. Energy for the Lower East Side. Alannah Bennie, James Davis, Andriy Goltsev , Bruno Pinto, Tracy Tran. Outline. Introduction Motivation Methodology Results Impact. Problem. We want to harness the power of tidal currents into energy that can be used as electricity

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The Power of Tides

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  1. The Power of Tides Energy for the Lower East Side Alannah Bennie, James Davis, AndriyGoltsev, Bruno Pinto, Tracy Tran

  2. Outline • Introduction • Motivation • Methodology • Results • Impact

  3. Problem • We want to harness the power of tidal currentsinto energy that can be used as electricity • How many turbines can we put into the East River around downtown Manhattan to power the Lower East Side?

  4. Why Tidal Energy • Tidal energy is a clean alternative that we can use efficiently without harm to the environment • Highly reliable: Tides will always exist due to the gravitational forces exerted by the Moon, Sun, and the rotation of the Earth • Predictable: The size and time of tides can be predicted very efficiently

  5. What are tides? • Tides – the alternate rising and falling of the sea, usually twice in each lunar day at a particular place, due to the attraction of the moon and sun • Currents generated by tides

  6. Tides • Flood tide – tide propagates onshore • High tide – water level reaches highest point • Ebb tide – tide moves out to sea • Low tide – water level reaches lowest point • Slack tide – period of reversing wave (low current velocity)

  7. The East River • Not a river • A tidal strait connecting the Atlantic Ocean to the Long Island Sound • Semidiurnal tides • Flow of the river • What makes up velocity • Direction

  8. Background • Our region is bounded by: (40.715 N,73.977 W) (40.707 N,73.997 W) (40.704 N,73.996 W) (40.708 N,73.976 W)

  9. Background • Video of Tidal Turbine • Size of turbine • Each turbine has a rotor diameter of 4 meters • Type of turbine • Modeled after turbines used by Verdant Power (2007) • Efficiency • We are looking at a turbine efficiency of around 40%

  10. Methodology • Data from the National Oceanic and Atmospheric Administration (NOAA) • Tidal velocity • Daily • 2007-2011

  11. Monthly Mean Tidal Velocities

  12. Methodology • Use polynomial interpolation to gather a velocity field • Interpolation is a method of constructing new data points within the range of a discrete set of known data points. • Polynomial interpolation is the interpolation of a given data set by a polynomial

  13. Polynomial Interpolation • Since we are working with four data points, we need to find a third degree polynomial of the form: • Thus, given any set of coordinates in our region, (x,y), we can use this polynomial to determine the velocity at that point P(x,y) = a0+ a1 x+ a2y+ a3x2+ a4xy+ a5y2+ a6x3+ a7x2 y+ a8 x y2+ a9y3

  14. Polynomial Interpolation • Because we know the velocities at our four collection points, we will use polynomial interpolation to find a set of polynomials which go exactly through these points

  15. Polynomial Interpolation • Begin by defining the matrix that will be used to create our interpolating polynomials • The matrix is a 4 x 10 since there are 4 data points with coordinates and 10 terms in the polynomial that we are seeking

  16. Polynomial Interpolation • Now create a system of equations, so that we can solve for the coefficients of our interpolating polynomials • Here is the average tidal velocity at

  17. Polynomial Interpolation • Finally, we have found our coefficients and therefore our interpolating polynomials • Since we looked at the average tidal velocities (mps) per month over the course of 5 years, we have 12 separate polynomials (one for each month) • We can use these polynomials to find the velocity at any location in any month

  18. Our Polynomials P1[x,y] = 0.000299263 + 0.00984117 x + 0.362105 x2 + 15.4992 x3 + 0.0120129 y + 0.200942 x y + 0.679683 x2 y + 0.366569 y2 - 14.844 x y2 + 5.37202 y3 P2[x,y] = 0.000289367 + 0.00957213 x + 0.35658 x2 + 15.4945 x3 + 0.0115257 y + 0.191041 x y + 0.67966 x2 y + 0.348566 y2 - 14.8392 x y2 + 5.37048 y3 P3[x,y] = 0.000288423 + 0.00954475 x + 0.355857 x2 + 15.4786 x3 + 0.0114819 y + 0.190195 x y + 0.678976 x2 y + 0.347027 y2 - 14.8239 x y2 + 5.36498 y3 P4[x,y] = 0.000281853 + 0.00937133 x + 0.352788 x2 +15.5226 x3 + 0.01115 y + 0.183318 x y + 0.681046 x2 y + 0.334526 y2 - 14.8659 x y2 + 5.38031 y3 P5[x,y] = 0.00029242 + 0.00965699 x + 0.358498 x2 + 15.5127 x3 + 0.011673 y + 0.193988 x y + 0.680411 x2 y + 0.353925 y2 - 14.8568 x y2 + 5.37678 y3 P6[x,y] = 0.000297207 + 0.00978715 x + 0.361172 x2 + 15.5152 x3 + 0.0119087 y + 0.198776 x y + 0.680429 x2 y + 0.362631 y2 - 14.8593 x y2 + 5.37758 y3 P7[x,y] = 0.00029066 + 0.00960398 x + 0.356925 x2 + 15.4654 x3 + 0.0115946 y + 0.192525 x y + 0.678349 x2 y + 0.351262 y2 - 14.8114 x y2 + 5.36038 y3 P8[x,y] = 0.00029513 + 0.00971291 x + 0.35798 x2 + 15.3541 x3 + 0.0118348 y + 0.197724 x y + 0.673347 x2 y + 0.360707 y2 - 14.7051 x y2 + 5.32176 y3 P9[x,y] = 0.000282421 + 0.00938159 x + 0.352511 x2 + 15.4761 x3 + 0.0111863 y + 0.184186 x y + 0.67898 x2 y + 0.336101 y2 - 14.8214 x y2 + 5.36418 y3 P10[x,y] = 0.000279165 + 0.00929402 x + 0.350803 x2 + 15.4833 x3 + 0.0110244 y + 0.180872 x y + 0.679356 x2 y + 0.330076 y2 - 14.8281 x y2 + 5.36669 y3 P11[x,y] = 0.000291449 + 0.00963447 x + 0.358401 x2 + 15.5473 x3 + 0.0116189 y + 0.19279 x y + 0.681959 x2 y + 0.351751 y2 - 14.8898 x y2 + 5.38879 y3 P12[x,y] = 0.000292155 + 0.00965048 x + 0.358429 x2 + 15.5188 x3 + 0.0116588 y + 0.193682 x y + 0.680686 x2 y + 0.35337 y2 - 14.8626 x y2 + 5.37891 y3

  19. Polynomial Interpolation • Our polynomials appear similar which is due to the fact the tidal velocities have minimal seasonal change • This was verified when we plotted our contour maps of the velocities and saw that they all looked the same

  20. Tidal Velocity Contour (mps)

  21. Polynomial Interpolation • Pros • No error at the data points • Easy to program • Able to determine an interpolating polynomial just given a set of points • Cons • It is only an approximation • Accuracy dependent on the number of points you interpolate • Not the best technique for multivariate interpolation

  22. Placement of the Turbines • Each Turbine needs to be approx. 9.8 – 24.4 meters (32-80 ft) apart (Verdant Power, 2007) • 1 degree of latitude = 111047.863 meters (364330.26 ft) • 1 degree of longitude = 84515.306 meters (277281.19 ft) • We decided to place the turbines 12.2 meters (40 ft) apart

  23. Placement of the Turbines • Using Mathematica, given a min/max latitude and longitude we were able find all points that lie 40 feet apart from one another in a set area • We then had to use basic mathematics to confine the points to our particular area

  24. Placement of the Turbines • Using the fact that the line thru pt1 and pt2 y = -5.80563 x + 310.327 line thru pt2 and pt3 y = 0.327377 x + 60.6708 line thru pt3 and pt4 y = -5.70626 x + 306.265 line thru pt4 and pt1 y = 0.292453 x + 62.0709 We used these lines to constrain the points to our study area

  25. Methodology • In an optimal environment, the available power in water can be calculated from the following equation: = turbine efficiency = water density ( kg/m3 ) A = turbine swept area ( m2 ) V = water velocity ( m/s ) P = power (watts)

  26. Facts • Total number of homes in the Lower East Side: 1546 • On average, a household in America uses 10,000 kWh per year • Total energy needed: 15,460,000 kWh per year

  27. Results • Total number of turbines: 3794 • Total energy from turbines: 21893.9 kWh • Total power output in a year: 1.91791 × 108 kWh • Total # of homes we could power in a year: 19179.1

  28. Discussion • Limiting parameters • Velocity • Turbine efficiency

  29. Comparison

  30. Comparison

  31. Costs • The turbines cost $2,000-$2,500 per kilowatt installed • Total Cost for 3794 turbines: 44 - 54 million dollars • Who pays: • In 2010, conEd gained a revenue of 25.8 ¢ per kWh to residents and 20.4 ¢ per kWh for commercial and industrial. • The average yearly revenue for residencies alone would be approximately 49 million dollars. conEd would start profiting from the turbines in about a year after they are installed.

  32. Bibliography • Hardisty, Jack. "The Analysis of Tidal Stream Power." West Sussex, UK: John Wiley & Sons, Ltd, 2009. 109-111. • NOAA. Tidal Current Predictions. 25 1 2011. <http://tidesandcurrents.noaa.gov/curr_pred.html>. • Power, Verdant. The RITE Project.2007. 2011 <http://www.theriteproject.com/>. • Yun Seng Lim, Siong Lee Koh. "Analytical assessments on the potential of harnessing tidal currents for electricity generation in Malaysia." Renewable Energy (2010): 1024-1032.

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