Wireless Power Transfer to Moving Vehicles

Patrick Landreman
November 21, 2012

Submitted as coursework for PH240, Stanford University, Fall 2012

In February 2012, Stanford University published an article with the auspicious title "Wireless Power could revolutionize highway transportation." [1] The article outlines a method by which electric vehicles could be inductively charged while driving. Power would be transferred to the car by means of resonantly-tuned radio frequency antennas: a receiver built into the underside of the vehicle, and transmitters built into the paved surface of the roadway.

The enthusiasm of this article was based on previous work done at MIT. [2,3] In 2007, an article published in Science showcased the ability to fully power a 60 W light bulb without using wires. The MIT scientists drove alternating currents in a helically-coiled copper wire, resonantly coupling power over a distance of 2 m into an identical coil that powered the bulb. The announcement this year was prompted by an additional computational study from Stanford, which argued that the transfer of power could be made at efficiencies over 90%. [4] The physical process by which power is transferred is well explained in any of the reference papers.

The idea of wirelessly charging a moving vehicle is exciting from an engineering standpoint, and there would be advantages of this proposed infrastructure over the status quo. For instance, in a fully electric transportation system, energy could still be derived from burning fossil fuels, but the reaction could be performed in a few optimized generators instead of a fleet of relatively inefficient engines. While a solar-powered car may have difficulty in cloudy weather, electrical energy from large solar (or wind, etc.) installations could be stored and controllably distributed into the imagined transportation grid.

The benefits of any invention must be weighed against the realities of its implementation to determine whether the idea makes any sense. The viability of a novel infrastructure can be broken into three parts: scientific and technical challenges (does the idea work?), economic challenges (how much does the idea cost?), and safety considerations (what happens when things go wrong?). The goal of this essay, then, is to address the idea of a wireless highway charging system through each of these lenses.

Before diving in, what would this system look like in a real-world application? Using the Nissan Leaf as a benchmark of current electric vehicle technology, the fastest possible charge requires 30 minutes to reach 80% of maximum capacity. [5] The charge rate is tied to physical limitations of the lithium-ion battery - at higher currents, the electrodes degrade and thus battery lifetime. [6] Assuming highway driving speeds of 60 miles per hour, this implies a minimum region of 30 miles to charge a battery. Thus, we are considering huge sections of road with embedded transmitters, each resonantly tuned to the same frequency as an antenna located within each vehicle.

The scientific feasibility of highway charging has been addressed insofar as transferring power to a stationary receiver works. As far as this author is aware, no demonstration has been made of resonant coupling to a moving receiver, nor has anyone analyzed a system with multiple, adjacent transmitters or receivers. These questions turn out to be details compared to the economic and safety considerations of such a system.

From an economic perspective, one cannot install miles of copper wiring into roads throughout the US without paying for it. To get at the cost, we will develop a simple model for the transmission coils based on typical values from the research papers. Consider a transmitter coil as a circular loop of 1 m diameter. Our coil will operate at 10 MHz, at which frequency the skin depth of copper is ~20 μm. [7] The radius of the copper wire is thus chosen to be three times the skin depth. Supposing we want to provide a power, P, to a receiving coil at 100% efficiency, we then need to transfer some energy E in the characteristic coupling time of the ring (~0.1 ms for distances of 2 m). [3] The energy stored in an LC oscillator is E = ┬ŻLI2, thus for a given power we can find the required current. L is approximated analytically from literature and depends quadratically on the number of loops in the ring. [8] To prevent excessive currents from melting the wire, one can increase the number of windings at the expense of more copper. For operating powers of 20-50 kW it is necessary to have roughly 103 windings to achieve currents below 5 A.

The mass of copper necessary for one of these coils is 0.32 kg (copper having a density at room temperature of 8.96 g/cm3). Over the past 5 years, the price of copper has been around $3.5/lb, and thus a single coil would cost $2.45. [9] A mile of such coils (with one coil per meter) would be $3,950. This price is small compared with the millions of dollars required per lane-mile of freeway. [10] Supposing these transmitters were to be installed in all ~6 million kilometers of public US roads, the total mass of copper necessary would be 5 × 109 kg. [11] This amount is one-third of the world mine production of copper in 2010. [9] Including a 1 m2 copper ground plane, as in the most-recent MIT paper, of thickness equal to thrice the skin depth brings the cost per lane-mile to $10,600, and the total mass to 1.3 × 1010 kg.

Regardless of costs or resources, human safety is arguably the most important consideration is such an infrastructure if to be ubiquitous. Radio frequency magnetic fields are capable of inducing circulating currents in human tissue, resulting in heating and ultimately burning. [12] As mentioned earlier, the penetration depth of MHz-frequency fields is sub- millimeter, and thus persons inside a vehicle could be shielded. Motorcyclists, highway workers, or pedestrians would not have this shielding. In the range of 10 MHz the IEEE has determined the maximum admissible rms magnetic field strength is 1.6 A/m. When powering a 60 W light bulb, the MIT scientists noted that the electric and magnetic fields near their resonant coils were between 1-8 A/m, and additional design considerations would be necessary to make real devices compliant. The Nissan Leaf consumes 765 J/m, which at 60 mph corresponds to a power of (765 J/m)(1609.34 m/mile)(60 mile/hr)/(3600 s/hr) = 20.514 kW. [13] The minimum power to sustain a vehicle at highway speeds is three orders of magnitude higher than a light bulb, and thus the fields involved must be considered. We can make a simple estimate, noting that the energy stored in a magnetic field goes as H2, thus the required field should be ~30 times larger. Using the simple transmission coil as before, we can obtain the current necessary to supply 20 kW. The magnetic field due to a circular current is known analytically, being strongest close to the wire and lower in the center or above the loop. [14] For this power, assuming lossless energy transfer, the rms magnetic field one meter above the center of the loop would be 52 A/m. For a real antenna with losses this strength will need to be even higher. The field falls below 1 A/m at ~4 m to the side of the coil.

An additional safety consideration is that of magnetically-stored data. Credit cards and hard disks are two examples of critical data that is potentially vulnerable to large magnetic fields. The coercivity of these materials is approximately 2000-4000 Oe, requiring fields of ~8000 Oe to completely degauss the magnetic domains. [15,16] These fields are massive compared to the tens of A/m associated with our model coil, and so it is unlikely that the proposed highway system would create a risk for magnetic storage media. Furthermore, magnetically-sensitive components of vehicles on the road could be shielded by a thin metal casing as described previously, if the chassis of the vehicle does not already provide the required shielding.

From this simple analysis, there are two major conclusions that may be drawn. First, converting the US roadway system to charge electric vehicles through resonant coupling will require amounts of copper that are large compared to the quantity produced within the US each year. The amounts of metal involved are not impossible, and a more precise economic evaluation is warranted. Second, and more pressing, the magnetic fields required to power a small car at highway speeds are 50x larger than standards for safe levels, even under static, idealized conditions. To a small degree, the costs and danger posed by magnetic fields can be mitigated by restricting charging coils to "short" (multi-mile) segments. However, finite charging regions will necessarily operate at higher powers, making the fields more dangerous in the vicinity. Reducing the operating frequency would allow higher tolerable fields, but the materials cost will increase with the skin depth of copper. Ultimately, any design for such a highway system will have to address the problem of passing 20 kW through the air without endangering innocent bystanders before it can be considered viable.

© Patrick Landreman. 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] M. Schwartz, "Wireless Power Could Revolutionize Highway Transportation, Stanford Researchers Say," Stanford Report, 1 Feb 12.

[2] A. Karalis, J. D. Joannopoulos and M. Soljacic. "Efficient Wireless Non-Radiative Mid-Range Energy Transfer," Ann. Phys. 323, 34 (2008).

[3] A. Kurs et al., "Wireless Power Transfer via Strongly Coupled Magnetic Resonances," Science 317, 83 (2007).

[4] X. Yu et al., "Wireless Energy Transfer With the Presence of Metallic Planes," Appl. Phys. Lett. 99, 214102 (2011).

[5] 2012 Leaf Owner's Manual, Nissan Motor Co., Ltd., Publication No. OM2E-OZZEOU2, April 2012, p. EV- 11.

[6] R. A. Leising et al., "A Study of the Overcharge Reaction of Lithium-Ion Batteries," J. Power Sources, 97-98, 681 (2001).

[7] U. S Inan and A. Inan, Electromagnetic Waves (Prentice Hall, 1999).

[8] E. B. Rosa and F. W. Grover, "Formulas and Tables For the Calculation of Mutual and Self-Inductance," Bull. Bureau Stds. 8, 1 (1912).

[9] M. E. Schlesigner et al., Extractive Metallurgy of Copper, 5th Ed., (Elsevier, 2011), Ch. 2.

[10] T. E. Keeler and K. A. Small, "Optimal Peak-Load Pricing, Investment, and Service Levels on Urban Expressways," J. Political Econ. 85, 1 (1977).

[11] R. T. T. Forman, "Estimate of the Area Affected Ecologically by the Road System in the United States," Conservation Biol. 14. 1 (2001).

[12] "IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency", IEEE C95.1-2005, 19 Apr 06.

[13] N. Bunkley, "Nissan Says Its Electric Leaf Gets Equivalent of 99 M.P.G.," New York Times, 22 Nov 10.

[14] J. D. Jackson, Classical Electrodynamics, 3rd Ed., (Wiley, 1998), ch. 5.

[15] P. Gutmann, "Secure Deletion of Data from Magnetic and Solid-State Memory", in Sixth USENIX Security Symposium Proceedings (Usenix Assn., 1996), p 77.

[16] J. Kay, "Magnetic Stripe Cards," JTI Technologies, Ltd., April 2000.