Wind is rapidly becoming an important renewable energy source as the worry about declining fossil fuel reserves and the global warming associated with their use continues to grow. There has been a great deal of success in generating power from large windmills, which accounted for 160 GW of power production in 2009. [1] While this accounts for only 2% of worldwide electrical energy consumption, wind-powered generation increased 31.7% from 2008 to 2009 while worldwide primary energy consumption slightly decreased in the same timeframe. [1,2]
Even though wind power generation is growing, there are a number of shortcomings of current generating techniques using windmills. In particular, wind intermittency, costly and easily damaged machinery, and large land usage requirements (in addition to aesthetic and wildlife safety concerns) are some of the problems that need to be overcome. [3,4] A relatively new idea for wind power generation that can overcome many of these shortcomings uses large kites to extract power from high-altitude winds. In this scheme, very large and relatively inexpensive kites are tethered to ground-based generators. As the kite pulls on the tethers, power is generated. The details of the generation depends upon the exact scheme, but at the time of writing of this paper, many groups are working to achieve practical power generation with kites (KiteGen, FlygenKite, Windlift, Festo, and kPower are just a few companies working on this). In this report, one particular kite-powered system will be explained, followed by a detailed analysis of estimates for the power production and cost for this system. Lastly, kite-powered generators will be compared to current windmills.
KiteGen is a company located near Torino, Italy, that is building kite-powered generators. The simplest design is their yo-yo configuration, where a kite is controlled by two tether lines. [5] During the traction phase, the kite is flown in continuous power strokes in a figure-eight-like pattern and pulls on the tether lines. The tether lines are used to transmit power from the kite to the ground as the lines unroll from large drums coupled to electric drives used as generators. When the kite reaches the end of the line extension, the electric drives are driven in reverse and are used to pull in the kite. During this passive phase, the kite can be depowered by pulling in one line more than the other, allowing the kite to extend parallel to the wind, similar to a flag. When the kite is pulled in to the lowest height, the line lengths are equalized and a new traction phase begins. By depowering the kite during the passive phase, less energy is used to pull in the kite than is extracted from the wind during the traction phase, resulting in net power generation. Other groups are working on various competing designs for kite-powered electricity generation, but this report will be focused on KiteGen's yo-yo configuration.
Simulations published by KiteGen, estimate that they can achieve 793 kW average power generation with a kite that is 100 m2 in size using an altitude-varying windspeed between 8 m/s at ground level and 24 m/s at 800 m. [5] By scaling up the size of the kite to 500 m2, 2 MW can be generated at 9 m/s constant windspeed, and much more power at higher windspeeds. In another design, called carousel configuration, they predict that a plant could generate up to 1000 MW mean power with 12 m/s winds and 100 kites that are each 500 m2 in size. [6] In actual prototype tests with small kites, KiteGen was able to generate positive net energy using small kites controlled by humans. [5] More importantly, the power generated matched well to the power predicted by their model, suggesting that their model also provides a good estimate for higher-power generators.
Individual yo-yo configuration generators would be less expensive and lighter than existing windmills since a kite and tether lines weighing about 3 tons altogether would replace the tower and rotor which weigh about 200-300 tons together (the same generator is assumed in both cases). Furthermore, windmills need to be spatially separated in order to achieve maximum performance, while kite-powered generators would extract power from the same amount of air volume with a significantly reduced footprint on the ground. KiteGen predicts they can achieve energy costs of $0.02-$0.05 per kWh, as compared to $0.05-$0.09 per kWh for fossil energy and $0.15 per kWh for current windmills. [5]
In order to trust these numbers from KiteGen, it is necessary to look deeper into the assumptions they make. The most important of these is that sufficient wind is available, followed by the assumption that enough power can be generated by the kite and that this power can be transmitted to the ground. Next, that the kites can be sufficiently controlled, and finally, that these generators would have reduced costs compared to other types of generators.
Most available wind studies have been from ground level to approximately 100 m. However, Archer and Caldiera have compiled available wind data as a function of altitude and consistency to estimate available wind power. [7] In order to compare these values to the numbers given by KiteGen, a step must first be taken to convert their numbers to wind power densities. According to Archer and Caldiera, the power available in the wind is [7]
| δ = | 1 2 |
ρ v3 |
where δ is the wind power density (kW/m2), ρ is the air mass density at 800 m (approximately 1.12 kg/m3 from standard exponential barametric equations), and v is the wind velocity. From this equation, we find that 9 m/s corresponds to 0.4 kW/m2. Comparing this to the plotted wind power densities in Fig. 3 of Archer and Caldiera, we see that even at 1000 m, most of the world exceeds 0.2 kW/m2 less than 68% of the time annually. [7] In order to get winds with enough power density, the kites need to be extended to much higher altitudes. Between 8000 m and 10000 m, much of the world has greater than 1 kW/m2 at least 68% of the time. [7] Certainly there are locations around the world where wind power is available at lower altitudes, but the large benefits of high-altitude wind are only available at much greater heights.
Given the wind speed assumptions used in the yo-yo configuration simulation presented by Canale, Fagiano and Milanesse, we can attempt to compare the power generated in the simulation to the assumed wind speed. [5] At the average altitude of the kite in the simulation (400 m), the air density is approx 1.17 kg/m3, and they assume windspeeds of 17 m/s. According to to the power density equation above, this leads to a wind power density of 2.9 kW/m2. If we assume a kite size of 100 m2 (the kite area used by canale, Fagiano and Milanese), then this corresponds to a total wind power of 290 kW, which is much less than they claim they can achieve in their paper with a single kite, 793 kW. [5] However, the wind power equation above assumes a stationary wind-power harvester. This is perhaps reasonable for a windmill, but breaks down in the case of a lift-generating wing flying with a large effective wind velocity. If we instead consider the energy density of the air and multiply by the volume of air that the kite interacts with in a certain amount of time, we can estimate the maximum amount of power that the kite could extract from the air. This maximum power is
| Pmax = | 1 2 |
ρ vair2 Aeff vkite |
where ρ is the air density, vair is the wind velocity, vkite is the velocity of the kite with respect to the air, and Aeff is the effective area of the kite. This effective area can be approximated by a lift coefficient times the real area of the kite. Using a kite speed of 105 m/s and a lift coefficient of 0.85 in addition to the same wind speed and air density as above, the maximum available power for a 100 m2 kite with 17 m/s winds is 1500 kW, nearly twice the value they claimed they can extract. [5] This tells us that the power is available.
Canale et al. used standard aerodynamic equations for lift and drag in order to calculate the power generated. [5] This ends up being a much more complicated system of equations that account for many more factors (such as gravity) than the simple approximation above. The largest contributor to the generated power is the lift force produced by the kite multipled by the velocity of the tether lines pulling on the generator. Using mean parameter values listed in that paper along with the standard aerodynamic equations (see Eq. 4 of Canale et al.), a 100 m2 kite in 17 m/s winds can generate a power of 1140 kW, in reasonable agreement with our simple approximation. [5] Due to the success of their experimental trials and the fact that their simulation agrees reasonably with the actual experiment, it seems very believable that given high enough wind velocity, KiteGen will be able to produce a sufficient amount of power with their kites.
In order to transmit the power from the kite to the ground-based generator, the tether lines need to be able to support the load. If 2000 kW peak power is generated by the system (from Fig. 9 of Canale et al.) with a line speed of 2 m/s, the load on the lines at the generator is equivalent to 102 tonnes, or 51 tonnes per line. [5] From Fig. 15 of Canale et al., the 25 mm diameter lines assumed in the simulation would be able to handle this load with a 20% safety margin. [5] This is in agreement with other research. [8] If a breaking stress of 1.25 GPa is assumed (Table I of Lechat et al.), then a line with a diameter of 25 mm could support 63 tonnes, which would be sufficient for the model KiteGen kite. [8]
Good automated control of the kite is extremely critical in order to keep the kites in the sky and generating optimal power. KiteGen presents one model which it uses in the kite simulations presented in Canale et al., but they used a human controller during the actual test flights. [5] However, other groups have successfully demonstrated kite control or have published a number of promising papers on kite control. While difficult, this controls problem does not have any fundamental physical constraints as long as the kites have enough forward velocity to keep moving, and that can be optimized with sufficient research and time.
To ensure the kite will keep moving, we need an aerodynamic force in the forward direction of the kite. This can be achieved simply by altering the angle between the kite and the wind in order to make the lift force (normally perpendicular to the effective wind direction) act partially in the forward direction of the kite. This results in more forward acceleration with less force on the lines, and so there is a tradeoff between keeping the kite flying, and producing power.
If we use the same aerodynamic equations as Canale et al., we see that this force in the forward direction depends greatly upon the angle of attack, positive for some angles and negative for others. [5] However, an average force of zero is all that is necessary to keep the kite flying, so the angle can be controlled to ensure there is enough forward momentum. This indicates the importance of the control algorithms for flying the kites, which is a major area of research. Due to the successful tests and simulations by KiteGen, we can assume that enough forward velocity can be obtained.KiteGen estimates that they can achieve energy costs of $0.02-$0.05 per kWh, in comparison to $0.05-$0.09 per kWh for fossil fuels, or $0.15 per kWh for current wind farms. [5] They predict that the cost of a complete KiteGen system would be less than an order of magnitude below the cost of a windmill rated for the same power, would weigh about an order of magnitude less, and could require nearly and order of magnitude less land for the same power. [5,6] Even if the generator for a kite-powered system is the same cost, the kite and lines would cost less than the rotor blades and tower combined. [5] It is very difficult to estimate actual construction and running costs for a system that is in such an early phase, but the power generation estimates suggest that it is not unrealistic that kite-powered generators could cost less than windmills. However, the electricity costs for fossil fuels given in Canale et al. appear to be exaggerated when compared to other sets of data. [5] Estimates for the cost of energy from coal and gas are around $0.03 to $0.04 per kWh, and $0.05 per kWh for nuclear power. [10] As a result, comparing KiteGen's cost estimates to the current market, kite-generated power is not liekly to be substantially cheaper than other electricity sources, especially coal and gas. However, kite power could still be competitive, and has potential to be cheaper than electricity from current windmills.
Kite-powered generators have many advantages over windmill generators, assuming the same power can be produced. First, the actual generator is located on the ground instead of on top of an 80 meter tower, greatly simplifying engineering and reducing costs. Second, the expensive and large rotor blades are replaced by a relatively inexpensive kite and set of lines. Third, the amount of land required by the kite generators is can be as much as 9 times less than the land required by a windmill farm producing the same amount of energy. [5] Kites have the potential to harness wind at much higher altitudes than windmills, giving access to stronger and more consistent winds. Kite generators also have greater ease of scalability as bigger generators can be built, and more kites can be added in carousel configuration, but stability and manufacturing difficulties limit the size of windmills. Furthermore, damage to a kite or lines is less costly than repairing windmill blades, and kites could be actively controlled to avoid planes and even wildlife. [5]
Besides being a proven and more mature technology, windmills do not have any major advantages over kite-powered generators. If the predictions by KiteGen and other companies about the potential of kite power are close to accurate, they will likely have a large impact upon wind power.
According to the calculations above, the predictions published by KiteGen appear quite optimistic, but perhaps not unrealistic. Significant improvement seems to be achieved by going to 400 m altitude, but the real potential for consistent and powerful wind lies at an even higher altitude. The drag and weight of lines will play an even more important role at this height, and so more detailed studies will need to be performed. However, the kites are able to extract sufficient power from the wind, and control systems are already effective enough to keep a kite flying. Also, Kite systems have the potential to be competitively inexpensive, and to be more scalable than current windmills. Wind intermittency will still be a very large problem, and so wind power will need to be coupled with more consistent power plants unless the current technology for energy storage is greatly improved. In conclusion, While kite-powered generators will likely not replace traditional power plants immediately, they have a lot of potential to start replacing windmill farms in the near future.
© Darin Sleiter. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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