Hydropower Generation in the Florida Keys

By: Joe Pritzkow

B.S. Civil Engineering

University of Wisconsin-Madison

 

 
ABSTRACT
PROPOSED DESIGN
DESIGN PARAMETERS
CALCULATIONS
FEASIBILITY
CONCLUSION

ABSTRACT:

Since 1975, oil demand in the world has increased from roughly 22 million barrels per day to its current 77 million barrels per day. At this current rate of consumption, oil reserves would be depleted by the year 2048, since the world’s total oil reserves are estimated to be around 1225 billion barrels (BP Statistical Review, 2003). Given the projected rate of consumption, however, these reserves could be diminished by as early as 2042 (International Energy Agency, 2003). In order to protect these oil reserves, an alternative source of energy needs to be implemented soon, or the world will be facing an energy crisis in the near future.

Hydropower is a clean, renewable, and reliable energy source which can help reduce oil demand and the resulting pollution. Below is a pie chart from March of 2001 showing theUnited States’ generation of electricity based on different production sources. As you can see, hydroelectric power accounts for 9.8% of the total U.S. annual electricity production. This is attributed to the more than 2000 hydropower plants in the U.S. This chart also shows that 2% of the total electricity generation comes directly from petroleum. This may not seem like a lot of oil, but to put it in perspective, the world generates roughly 23%-25% of its electricity from hydropower. This is equivalent to approximately 675,000 MW of power, which would require around 3.6 billion barrels of oil to produce. Now the number seems quite significant.

Source: EIA, Electric Power Monthly, March 2001. Table 3

This project focuses on the feasibility of producing hydropower in the Florida Keys. The Florida Keys were chosen because they demonstrate a strong underwater current caused primarily by the rise and fall of daily tides. This strong underwater current is directly related to the potential the water has to create electricity when using an underwater turbine, which is the hydropower device that will be analyzed. 



PROPOSED DESIGN:

In order to determine the feasibility of producing hydropower in the Florida Keys, we must first develop a model to show how the electricity will be produced. As mentioned earlier, an underwater turbine will be used to generate the electricity. Below are two examples of different types of turbines that may be used. The turbines on the right sit at the ocean floor, while the turbines on the left can have their height adjusted for optimal electricity production. For this study, the turbines on the right will be the ones used. This is primarily because the areas where these turbines will be located, as is discussed later, will have high amounts of water traffic, and therefore, need to be located at a depth that won’t interfere with boater activity.

Once the turbines are set in place, they will be attached to a generator. In order to reduce the height of the turbines above the ocean floor, the generator will be located below the turbines under the ocean floor. The generator is the device that is used to convert the mechanical energy of the rotating turbines caused by the moving water, into electrical energy. Below is a schematic of how the generator converts mechanical energy into electrical energy.

http://www.eia.doe.gov/electricity.html

The force of the flowing water will cause the turbines to rotate. As they rotate, this rotation is transferred to a shaft which travels down to the generator. The generator is based on the principle of “electromagnetic induction”, discovered in 1831 by British scientist Michael Faraday. The principle of electromagnetic induction is this: if an electric conductor, like a copper wire, is moved through a magnetic field, electric current will be induced, or begin to flow, in the conductor. This is because the magnet causes the electrons in the electrical conductor to transfer position throughout the conductor. The movement of electrons is defined as electricity. So the rotating shaft is connected to copper coils inside the generator, and surrounded by a large magnet to create a strong magnetic field. This creates an electric current, which can then be transferred to transmission lines. For the purposed of this design, the transmission lines will run below the ocean floor to reduce the risk of corrosion and damage. The transmission lines will then carry the electrical energy, harnessed from the generator in the form of alternating current (AC), to a transformer located on land. The transformer will then transform the alternating current to a higher voltage current which can then be used for residential and industrial uses.



DESIGN PARAMETERS:

Now that the general concept of how electricity will be produced from the underwater current is understood, we must analyze the important design parameters that must be established to optimize the design. 

1)The correct location must be chosen. The reason for this is because the amount of electricity produced is directly proportional to the speed of rotation of the turbines. The speed of rotation of the turbines is directly proportional to the velocity of the water. Therefore, the locations where the underwater velocity is a maximum are optimal. Below is a map showing the Florida Keys. As you can see, and as the name suggests, the Florida Keys are made up of many islands, or keys, connected by a single highway. 

Earth’s centrifugal force and the gravitational attraction forces due to earth, the moon, the sun, and other planets, produces tides, or the periodic rise and fall of water levels. There are two types of tides, high tides, or flood tides, when water flows in from the ocean, and low tides, or ebb tides, when water flows away from shore and back out into the ocean. Additional monthly and annual lunar cycles vary the strength of these currents. The Keys are a unique situation though, because the incoming water due to flood tides doesn’t want to stop at the Keys, but rather, wants to flow through them and into the Gulf of Mexico. This causes increased flowrates through the gaps between adjacent keys, somewhat similar to the flowrate of the Gulf Stream. The same phenomenon occurs when ebb tides begin, and the water flows out from the Gulf of Mexico. Therefore, for optimum electricity production, the turbines need to be placed in locations where the water is flowing through the gaps.This will provide maximum rotation of the turbines. 

                                                                                                            Possible Locations

One advantage of this type of hydropower is that it is a very reliable energy source. This is because the energy source is independent of weather and climate change, as it follows the predictable relationship of the lunar orbit, which is known many years in advance.

2) The optimum location must be chosen in term of depth. That is because if you are too deep, the underwater velocity is lower. Conversely, if you are too shallow, while you have a much higher water velocity, you risk damage to boats. Based on the relationship between water depth and water velocity, it was determined that a depth of 10 meters would be sufficient to provide enough underwater velocity for electrical generation and provide enough clearance for ongoing vessels. 

3) The optimum size of the propellers on the turbines must be selected. This parameter is partially restricted due to the available depth before the turbines will interfere with vessels on the surface. For the purposes of this design, it was assumed that the propeller size would be 4 feet, making the overall size of the turbine approximately 8.4 feet.                           




4) The angle of the incoming and outgoing current must be determined for optimal placement of the turbines. The goal here is to place the turbines at a 90° angle to the direction of water flow. To simplify this analysis, since the location of the turbines will be in gaps between adjacent keys, it can be assumed that the water will be coming in at a 90° angle if the turbines are parallel to the adjacent land.

5) Screens must be used on the turbines to avoid harm to aquatic species and humans. Since many of the areas these turbines would be located in are home to aquatic wildlife, the correct safety precautions must be taken. These areas are also home to many lobster hunters and scuba divers, and these screens would help reduce the risk of the turbines to humans.

6) Corrosion resistant materials must be used for the turbines and generators. This is because metals corrode in the presence of saltwater. Alternative non-corrosive materials must be chosen such as Superferritic Stainless Steels and Nickel Base Alloys.



CALCULATIONS:

Now that an understanding has been developed as to what type of system will be used and analyzed, calculations can be conducted to determine if the proposed design is feasible. First, properties of the water must be determined. If a proposed depth of 10 meters is used as the location of the turbines, we can determine if the water is shallow, deep, or intermediate. This is done by calculating d/L, with L being the wavelength. Based on data from the Florida Keys Weather Service, the average wavelength was assumed to be 37 meters. This yields a d/L value of 0.27, classifying the water as intermediate water.

To calculate the underwater velocity, the intermediate wave velocity equation can be used. This equation is shown below:

u=?Hcoshk(z+d)cos(kx-wt)/Tsinhkd

H=wave height=2ak=wave number=2?/Lw=angular frequency=2?/TT=wave period

Based on this equation, the underwater velocity, u, equates to 0.327 m/s during normal flow. This number was verified using the Delaware Wave Calculator. However, this u value doesn’t represent the underwater velocity during peak conditions, when peak tides occur. There is no equation to calculate the underwater velocity for this phenomenon. Therefore, an assumption must be made. To determine the underwater velocity during peak tides, it was assumed that the underwater current behaves similar to that of rip currents. This assumption was made based on personal experience I have had with both rip currents in California and the currents in the Florida Keys while lobster hunting. Typical values of the water velocity during rip currents range from 2 ft/sec to 10 ft/sec. Therefore, a conservative value of 4 ft/sec was chosen. This is equivalent to a u value of 1.308 m/s. 

Now that we know the underwater velocities, we must determine the power that can be generated based on these velocities. To do this, we will apply the wave power equation for hydropower generation:

MW = Q*h*e/11.81

Q=flow (1000 ft/sec)h=head (ft)e=efficiency of turbine/generator 

Typically, this equation is used to calculate the MW (megawatt) production of hydroelectric dams, which is why the variable h is included. To use this equation for the purposes of this project, h will be assumed to be 24.4 feet.

e is the efficiency of the turbine and generator to convert the potential energy of the water into electricity. It is nearly impossible to develop a perfect model that converts 100% of the potential energy to electricity. Therefore, an efficiency value of 0.85, or 85%, will be used.

The flow, Q, can be calculated by multiplying the underwater velocity by the area of the turbines through which it will flow. During normal flow Q1 is equal to 0.0593 (1000 ft3/sec). During peak flow, however, Q2 is equal to 0.238 (1000 ft3/sec). Now it must be determined how long the underwater velocity represents peak conditions, and how long it represents normal conditions. Based on my experience in the area, I assumed that 86% of the day, conditions were normal. The other 16% of the day, the conditions were peak. This produces the following power equation:

MW = 0.16(Q2*h*e/11.81) + .84(Q1*h*e/11.8) = 0.145 MW

This is equivalent to 145 kilowatts. Now it must be determined if this quantity is significant enough to the Florida Keys to make it a feasible alternative.



FEASIBILITY:

Since there are so many Keys in the Florida Keys, just one will be analyzed to determine the feasibility. The Key I chose was Duck Key, which is where I go lobster hunting. The current population of Duck Key is approximately 500 people, based on information from the Florida City Data Council. On average, each person uses 3000 kwh/year. Therefore, the total Duck Key demand is 1,500,000 kwh/year. On average, each turbine produces 145 kilowatts, which is equal to 1,015,000 kwh/year if the turbine is operating 100% of the time. Typically, turbines only operate 80% of the time due to maintenance and repair. This reduces the annual turbine production to 812,000 kwh/year. Therefore, one turbine could supply Duck Key with 54% of its electrical demand. 

It is important to note that these numbers are all rough estimations. Exact numbers are hard to determine since there are so many variables such as the size of the copper coil and magnet in the generator, the resistance to rotation the turbine propellers exhibit, and the type of turbine used, to name a few. 



CONCLUSION:

Based on the calculations, it seems like hydropower is a feasible alternative energy source in the Florida Keys. The initial cost will be expensive, but over time, hydropower will supply a clean and reliable energy source that could help reduce the cost of electricity in the Florida Keys. The uniqueness of the Keys makes it an ideal location for investigation into the possibility of hydropower generation. I believe this rare opportunity must be explored.