The power of tides
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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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The power of tides

The Power of Tides

Energy for the Lower East Side

Alannah Bennie, James Davis, AndriyGoltsev, Bruno Pinto, Tracy Tran


Outline

Outline

  • Introduction

  • Motivation

  • Methodology

  • Results

  • Impact


Problem

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?


Why tidal energy

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


What are tides

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


Tides

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)


The east river

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


Background

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)


Background1

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%


Methodology

Methodology

  • Data from the National Oceanic and Atmospheric Administration (NOAA)

    • Tidal velocity

    • Daily

    • 2007-2011


Monthly mean tidal velocities

Monthly Mean Tidal Velocities


Methodology1

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


Polynomial interpolation

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


Polynomial interpolation1

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


Polynomial interpolation2

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


Polynomial interpolation3

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


Polynomial interpolation4

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


Our polynomials

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


Polynomial interpolation5

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


Tidal velocity contour mps

Tidal Velocity Contour (mps)


Polynomial interpolation6

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


Placement of the turbines

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


Placement of the turbines1

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


Placement of the turbines2

Placement of the Turbines

  • Using the fact that the

    line thru pt1 and pt2 y = -5.80563 x + 310.327

    line thru pt2 and pt3y = 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


Methodology2

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)


Facts

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


Results

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


Discussion

Discussion

  • Limiting parameters

    • Velocity

    • Turbine efficiency


Comparison

Comparison


Comparison1

Comparison


Costs

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.


Bibliography

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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