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Wind Energy Garage

Beyond the Wind Turbine Power Curve

Problem

As electric vehicles (EVs) gain in popularity the burden they put on the electric grid also increases. In 2022 just a week after approving a plan to ban the sale of new gasoline cars, California asked electric vehicle owners to limit when they plugged in to charge. [1] In July of 2022 Tesla told users in Texas not to charge their cars during a heat wave. The Electric Reliability Council of Texas (ERCOT) made this request in an effort to prevent the grid from being pushed to near-emergency conditions. [2]

Solution

One solution is to add more gigantic wind farms and huge solar arrays that can produce megawatts of electricity which needs to be routed to where it is used. Another solution is to produce the energy right where it is needed. The Wind Energy Garage (WEG) captures the energy that strikes the side of a garage and converts it to electricity to charge a hybrid plug-in vehicle. Such a garage would require a windy area with a minimum of obstructions to the wind to be practical.

The way the WEG converts the kinetic energy of the wind striking the side of the garage into rotation around a vertical shaft is totally different from a typical wind turbine. It doesn t have many of the drawbacks that a wind turbine has. In the WEG mechanism the wind hits the propeller in the direction it needs to go rather than hitting it at an angle. There is less stress on the propeller which can be translated into captured energy. Plus, the WEB mechanism can handle gusts and much higher wind speeds than a turbine.

It can be mathematically shown that the wind speed should slow down to 1/3 after it passes by the wind turbine blades to be most efficient. But how do you design turbine blades to do that? In the WEG the propellers need to be constrained to move 1/3 as fast as the entering wind. This can be done by adding additional load on the generator which will be converted to energy. Somewhat similar to how a hybrid vehicle captures energy when it brakes. I believe that instead of the power curve flattening out at 25 mph a WEG will continue to capture energy exponentially.

A Garage Designed to Charge a Hybrid Plug-In

Where I live it is rural and there aren't many charging stations nearby. It is also very cold and very windy. For the sake of discussion, I will use the Toyota Prius Primes specifications although any hybrid plug-in would work similarly. My commute is about 50 miles round trip so if I had a Toyota Prius Prime, I could get to work on the electric charge and get back on gas. I like the idea of using gas when I need to, and using free energy from wind and solar when it is available. The 2023 Toyota Prius Prime has a 13.6 kWh battery pack. Imagine coming home from work and fully charging your vehicle overnight with energy captured during the day.

How it works

The basic shape of the Wind Energy Garage might be a dome shape or a hexagonal shape. In this document I will describe a hexagonal shaped building. Each side of the hexagon is 24 feet which would allow two vehicles to use the garage. The bottom story of the garage will have windows and doors and a charger. The second story is where the wind energy is captured and converted to rotational energy to run the generator on the bottom floor. The second story has windows I will call flaps that only open inward. When the wind hits one side of the building the flaps open on that side and causes a pressure difference from the ambient air.

If the sides of the second floor are filled up with flap openings as much as possible the area would be about 30' by 10'. 300 hundred square feet is about the same area as the area swept by a 10 foot radius wind turbine. You might ask why not just mount a 10 foot turbine on the top of the garage but as I will explain, the WEG has some advantages over a turbine.

In addition to the pressure caused by the wind hitting the building there is a Bernoulli effect at the top of the building which lowers the pressure in the central cylinder effectively pulling out air, so it doesn't impede the mechanism. The top of the structure is rounded so the wind is moving faster going over the top. This is similar to the lift on an airplane wing and its effect here is to suck out the air out of the center of the wind energy mechanism.

If you are interested in the mechanism inside the WEG you can sign a non-disclosure agreement and I will explain it in more detail. In essence, instead of blades that convert the kinetic energy of the wind into rotational torque, the WEG mechanism operates more like a disk in a tube being blown by the wind to do work. So fine tuning the WEG mechanism is totally different from a wind turbine. With a wind turbine the blades are often tilted to be more efficient at different speeds. A typical wind turbine power curve is shown in figure 1. With the WEG, the wind forces are in the direction the mechanism is designed to rotate and not perpendicular to it.

(Dvorak)

Figure 1

In Figure 1 the rated speed starts at 12 meters/sec (26.8 mph) and levels off until the cut-out speed at 23 meters/sec (53.6 mph). One reason the power stays at the rated output is because the turbine can be damaged at higher wind speeds. Because of its design, the WEG is able to use the energy from higher wind speeds, but it requires the rotation of the shaft to be approximately equal to 1/3 of the wind speed. If there was a gear shifting mechanism to adjust the shaft rotation to the optimum value while maximizing the output of the electric generator that would help. Another possibility is to engage more electric generators as the wind speed increases to keep the rotation speed at maximum efficiency while producing as much energy as possible.

No device that captures energy from the wind can exceed the Betz limit and it can be shown that a wind turbine is most efficient when the downward wind speed is 1/3 of the upward wind speed. (Cole) But it isn't clear how things can be tweaked to achieve this. The goal is to make the wind turbine as efficient as possible by adjusting the shape of the blades and to tilt them at different angles for different wind speeds. The WEG, on the other hand, can use a feedback loop to keep the rotation speed close to 1/3 the wind speed by increasing or decreasing the load on the generator.

Work needs to be done in designing such an electric generator with a wind speed feedback system to keep generating the optimum amount of energy at higher speeds. At least in the WEG the electric generator is on the bottom floor of a two-story building and not at the top of a 50-foot tower.

As I have said, the typical wind turbine power curve flattens out after it reaches the rated wind speed. It stays at that level until the wind reaches the cut out wind speed where the turbine shuts down to avoid damage. Because the energy in the wind is proportional to the wind speed cubed there is a huge amount of energy that can be collected at wind speeds between the rated speed and the cut-out speed.

Figure 2 shows the theoretical (all friction and other losses ignored) energy of the wind as speed cubed to show how much energy is available at higher wind speeds. How much is usable has to be determined. The 18.5 kWh battery from Fortress Power (Power) has a maximum charge rate of 180 amps at 50 volts which is 9,000 watts. The WEG might be able to generate that from a wind speed of 30 mph so anything more than that would be unusable to charge the battery but could be fed back into the electric grid.

Figure 2

 

Determining the Rotation Speed to Extract the Most Energy

We have said that the objects in the WEG mechanism that are doing work to generate electricity should move at 1/3 the outside wind speed. Without going into the design details of the WEG mechanism we can think of it as a disk being blown down a tube. As with all wind capturing devices this disk in a tube is limited by the Betz limit. The Betz limit is an important concept in understanding how much energy can be extracted from the wind. The Betz ratio is the maximum work that can be done by the wind entering an area divided by the total kinetic energy of the wind entering that same area.

To understand where the value of 1/3 the wind speed comes from we can imagine a simplified ideal engine with no friction that is doing the work.

Ideal Wind Engine

Imagine a tube oriented parallel with the wind that has a thin disk inside it. As the wind enters the tube it hits the disk which causes a pressure on the disk that moves the disk down the tube doing work. So, the amount of work done by the disk is the force on the disk times the distance it moves. One might ask what the speed of the disk should be to extract the most work out of the wind. Obviously, if the disk is not moving the pressure would be the maximum but since the disk is not moving it isn't doing any work. And if the disk is moving as fast as the wind there is no force on the disk and again there is no work being done. Clearly, there is an optimum speed at which the disk should move to maximize the amount of work done.

 

A diagram of a tube

Description automatically generated

Figure 3

We show the calculations to obtain the optimum speed of 1/3 the wind speed on the 1/3 Wind Speed Difference and the Betz Limit page. Instead of tweaking blade shapes for a conventional wind turbine we have two goals for the WEG mechanism. One, reduce all friction that would reduce the efficiency and two, vary the load on the electric generator so that the most electricity possible is generated. By varying the load on the generator and possibly shifting gears the speed of the propellers can be kept at around 1/3 the wind speed.

 



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