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| Fig. 1: An example of a wave energy conversion device. Pictured is the Pelamis Wave Energy Converter at the European Marine Energy Centre in 2008. (Source: Wikimedia Commons) |
The term "wave energy" refers to the energy in the periodic waves that arise from the friction of wind on the ocean. There are other methods of extracting energy from the ocean such as from the tides, currents, thermal gradients, and salinity gradients. [1] As many large cities are located near bodies of water, waves have been touted as a possible source of large amounts of renewable energy. For context, the energy of the waves impinging on the coast of San Francisco, California have a power density of 25 kW/m as compared to both wind and solar, which each have a maximum power density of 1 kW/m2, with 12 m/s winds and full sun exposure, respectively. [2] Comparing a linear power density (i.e. wave power) and areal power density (i.e. wind power) is not straightforward. This will be important for comparisons later.
Estimations have shown that the total energy one could extract from waves around the globe per year clocks in at 8,000-80,000 TWh per year, which we can compare to the total global energy expenditure of 162,494 TWh in 2017. [1] In addition, waves are present throughout the day and are a relatively consistent source of energy in the night. Although this is better than the situation of solar, this would mean that similar amounts of energy are produced during the night and day, while the average consumer uses less energy at night. Also, waves are less consistent than solar during the day. In addition, there are other, more major shortcomings of wave power both physically and economically.
First, we give a brief overview on the physical background on wave power. The amount of power in a deep-water wave (where the depth of the water is greater than half the wavelength of the wave) in an idealized environment is given by: [3]
| P | = | ρ g2 T H2 32π |
Here, ρ is the density of water (997 kg m-3), g is the acceleration due to gravity (9.8 m s-2), T is the period of the wave (we will use a conservative value of 10 s), and H is the height of the wave (for deep waters this is about 2.5 m). [4,5] Using these values we get a power density of:
| P | = | ρ g2 T H2 32π |
= | 997 kg m-3 × (9.8 m
s-2)2 × 10 s ×
(2.5 m)2 32π |
= | 59.5 kW m-1 |
We can take the power generated per meter and multiply it by the total length of the mainland US pacific coastline (2.0 × 106 m), for example, to obtain a total power generation of 119 GW. [6] Finally, multiplying this by the amount of time in a year, we would obtain a total energy output in a year of 3.8 × 1018 J = 1056 TWh.
This value is clearly large; the total energy produced by the state of California in 2019 was 255 TWh. [7] Note that this is the theoretical value, which does not account for inefficiencies. In addition, there has been little consensus on the best design or method for harnessing wave energy. Some designs have been able to reach 20% efficiency in 25 kW/m waters, which corresponds to a 5 kW/m power density. [8] However, as evidenced by the lack of wave power in our society, these have only been done on prototypes and may not be suited for practical scenarios.
As a short note, there are many different devices and techniques one can use to extract energy from waves. The different types of wave energy conversion (WEC) devices are: attenuators, point absorbers, and terminators. [1] Fig. 1 is an example of a wave energy converter. We will not go into detail here about the different mechanisms and principles behind these devices, as we are solely considering the practicality of wave power.
One problem with wave power is its use of space. We notice a clear comparison to make between wave power and wind power. For this exercise, we use the power density values from S. J. Lim of 1 kW/m2 for wind power and 25 kW/m for wave power. [1] Suppose we had 120 meters of coastline to place either a wave energy converter or a wind turbine. One of the leading turbines in 2013 (the Siemens SWT-3.6-12) was 120 meters in diameter, meaning that it covers an area of about 11304 m2. [9] From this, a single ideal wind turbine generates a power of 11304 m2 × 1 kW m-2 = 11304 kW. If we were to take up the same length of coastline with an ideal wave energy converter, the energy produced would be 120 m × 25 kW m-1 = 3000 kW. The power produced by a wind turbine scales quadratically with length, while the power produced by a wave energy converter scales linearly with length. At the scales of modern wind turbines, the power generated from waves is overshadowed by that of wind power.
One may still think that wave power is a worthwhile investment, as more energy is better than less. However, another problem wave energy faces at the moment is its cost. The current cost of harnessing wave energy (as of 2015) is $0.87/kWh. [10] This high value is attributed to many challenges wave power faces, including: [10]
Engineering difficulties in optimizing energy extraction.
Issues with maintaining a system that can survive marine environments for long amounts of time.
Difficulty in obtaining permits and the ability to test prototypes.
Underdeveloped markets and supply chains.
As a comparison, wind and solar have cheaper costs of $0.01/kWh-$0.04/kWh as of 2018 and $0.06/kWh-$0.16/kWh as of 2017, respectively. [11,12] This means that, although wave power has a some advantages, its price cannot be justified.
The United States Department of Energy plans to reduce the cost of wave energy from $0.87/kWh to $0.17/kWh, which may allow wave energy to be viable in the future. [10]
Wave power is not only an inefficient use of the wind power out at sea, it is also a very expensive source of energy in its current state. However, if the cost of wave power were to drastically decrease, we may see wave power emerge as a supplementary source of energy.
© Mark Zic. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. 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.
[1] S. J. Lim, "Wave Energy Converters," Physics 240, Stanford University, Fall 2013.
[2] B. Czech and P. Bauer, "Wave Energy Converter Concepts: Design Challenges and Classification," IEEE Ind. Electron. M. 6, 4 (2012).
[3] E. Bonifacio, "Wave Energy," Physics 240, Stanford University, Fall 2010.
[4] W. H. Munk, "Origin and Generation of Waves," Coast. Eng. Proc. 1, 1 (1950).
[5] S. K. Gulev and V. Grigorieva, "Last Century Changes in Ocean Wind Wave Height From Global Visual Wave Data," Geophys. Res. Lett. 31, L24302 (2004).
[6] H. A. Karo, "World Coastline Measurements," Int. Hydrogr. Rev. 33, 131 (2018).
[7] "Electric Power Annual 2019," U.S. Energy Information Administration, October 2020.
[8] T. Aderinto and H. Li, "Review on Power Performance and Efficiency of Wave Energy Converters," Energies 12, 4329 (2019).
[9] P. Higgins and A. Foley, "The Evolution of Offshore Wind Power in the United Kingdom," Renew. Sustain. Energy Rev 37, 599 (2014).
[10] A LiVecchi et al., "Powering the Blue Economy," U.S. Office of Energy Efficiency and Renewable Energy, DOE/GO-102019-5157,April 2019.
[11] R. Wiser et al., "2018 Wind Technologies Market Report," U.S. Office of Energy Efficiency and Renewable Energy, DOE/GO-102019-5191, August 2019.
[12] "The SunShot 2030 Goals: 3¢ per Kilowatt Hour for PV and 5¢ per Kilowatt Hour for Dispatchable CSP," U.S. Office of Energy Efficiency and Renewable Energy, DOE/EE-1501, August 2017.
