Figure 1. Proposed setup of a rectangular area with a moving receiver

and a single small transmitter

Study of Wireless Power Systems with Two-Dimensionally Moving Receivers

Stijn Wielandt, Jean-Pierre Goemaere, Lieven De Strycker and Nobby Stevens DraMCo, Faculty of Engineering Technology

ESAT, KU Leuven Gebroeders De Smetstraat 1, 9000 Gent, Belgium

stijn.wielandt@kuleuven.be, info@dramco.be

Abstract—The advantages of wirelessly powering electronic devices are numerous, but the technology is generally not being applied to moving devices because existing solutions are complex or offer poor efficiency. This paper describes a wireless power system for receivers moving between uniformly distributed points in a rectangular area. The proposed solution consists of a single small wireless power transmitter, offering both low complexity and high efficiency. Simulations were performed to determine the optimal transmitter location, shape and transmitted power. Also a statistical analysis of the receiver buffer size was performed. As a result of these simulations, a design flow was proposed that permits the use of existing technologies for the considered setup.

Keywords-wireless power; moving receiver; transmitter shape; buffer size

I. INTRODUCTION In the past few years, the number of wireless power

systems has increased rapidly. This evolution is due to the numerous advantages that are involved in this technology. In the medical industry, the lack of connectors plays a key role in the development of powered implants or more hygienic external devices [1]. In consumer electronics, wireless power brings an increased ease of use and robustness, since connectors for a galvanic power link become unnecessary. Another reason for the increase of wireless power applications is the foundation of several consortia and the resulting standardization. The Wireless Power Consortium and the Alliance for Wireless Power (A4WP) developed respectively the Qi standard [2] and Rezence [3], while similar efforts are being made by the Power Matters Alliance [4] and the IEEE Wireless Power and Charging Systems Working Group [5]. All of these standards rely on an alternating magnetic field with a frequency ranging from 100 kHz up to several MHz. They are aimed at providing up to tens of watts of power to immobile devices in close proximity of the power transmitter. Some measures have been taken in order to handle misalignment of the power receiver. For example, the Qi standard provides the possibility of using multiple transmitter coils in a matrix configuration. In this case, only the transmitter coil that provides the highest link efficiency will be used. However, a lot of electronic devices are continuously moving and lose their functionality when they reside motionless on a charging pad, e.g., a wireless computer mouse, a robot vacuum cleaner, robot

toys,... Some devices don’t even allow for static charging, such as transmitters or sensors attached to animals. This paper focuses on wirelessly powering this kind of two-dimensionally moving devices. In order to enable continuous wireless power transmission while these devices are moving, one can choose between different designs of the wireless power system. The first option involves the use of a matrix of transmitter coils, covering the complete area of operation [6], comparable to the Qi transmitter coil matrix [2]. A comparable solution involves the use of one transmitter coil and a matrix of resonators, increasing the range of the power transmitter [7]. However, these solutions are expensive and invasive due to complex driver circuitry and the number of coils to be installed. Another option is the installation of a single transmitter coil that covers the complete area of operation. This requires a very large transmitter coil compared to the receiver coil, resulting in a very low coupling factor and consequently a low link efficiency, making it only suitable for low power receivers (e.g., RFID tags) [8]. The option we will consider in this paper concerns the use of a single small transmitter coil, positioned strategically in order to provide the receiver with energy every time it passes over the transmitter coil. In order to provide the receiver load with a continuous energy supply, a sufficiently large energy buffer is indispensible. This last option was not found in literature and forms the subject of this paper, applied to receivers that move between uniformly distributed points in a rectangular space, as shown in Fig. 1.

The authors would like to thank the Flemish Agency for Innovation by Science and Technology (IWT), the German Federation of Industrial Research Associations (AIF) and the European Collective Research Networking (CORNET) group to support this research.

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Figure 3. Probability of receiver passing, divided into 6 intervals

(high probability =light, low probability = dark)

Figure 2. Maximal achievable link efficiency as a function of k with

QTx = QRx = 50

This paper is organized as follows. Section II illustrates the potential improvement of the link efficiency when the dimensions of the transmitter coil are reduced. In Section III simulations are presented for transmitter optimization with respect to the location, shape and transmitted power. Section IV focuses on the receiver side, with a specific emphasis on buffer size statistics. Section V presents a design flow for the proposed wireless power system. The conclusions and future work are discussed in section VI.

II. LINK EFFICIENCY IMPROVEMENT In inductively coupled wireless power systems (e.g. Qi or

Powermat), the maximal achievable link efficiency ηlink,max is expressed by (1) [1]. It is only a function of the quality factors of the transmitter and receiver coil (respectively QTx and QRx) and the coupling coefficient k between these coils. k is a value between 0 and 1 that can be defined as the ratio of the magnetic flux that is coupled into the receiver coil to the magnetic flux that is generated by the transmitter coil. Fig. 2 depicts (1) with a variable k and constant quality factors of 50, which is a common value. According to Finkenzeller et al., one can state that a decrease of the transmitter radius with a factor of 10 roughly increases the coupling coefficient with a factor of 30 as long as the receiver coil is much smaller than the transmitter coil and the coils are coaxially aligned, close to each other, [9]. Fig. 2 illustrates the potential increase in link efficiency that can be achieved by reducing the size of the transmitter coil. For example, consider a transmitter coil with a radius of 100 times the receiver coil radius. When the transmitter radius decreases with a factor of 10, the coupling factor increases from 0.1 % to 3 %, yielding an increase of the maximal achievable link efficiency from 0.6 % to 29 %.

(1)

III. TRANSMITTER OPTIMIZATION When designing a wireless power system with a single

small transmitter coil for sporadically powering a moving

receiver, it is imperative to start with a statistical study on the movement of the receiver. The statistical properties of the receiver will determine the optimal transmitter location, shape and the transmitted power. The simulations in this paper start with a presumption of a receiver, moving between uniformly distributed points in a rectangular area with dimensions a and b, as presented in Fig. 1. This kind of location distribution might for example resemble the movements of a robot in a room. It could also represent the positional variation of humans or animals in a rectangular area, or even the movement of a computer mouse on a desktop. However, one should keep in mind that extra boundary conditions might be imposed, due to the presence of obstacles. This may lead to different statistical properties.

A. Transmitter location In order to study the travelled path of a receiver, Matlab

was used to perform simulations of a receiver travelling between 5·106 uniformly distributed points in a rectangular area that was divided into 2.5·105 equal patches. Each of these patches received a score, representing the number of times that the receiver crossed the patch. Consequently, these scores are a measure for the probability of finding the receiver at a certain position. Fig. 3 visualizes these scores, indicating that the transmitter passes the most in the middle of the rectangular area. Hence, this is the most obvious location to position the wireless power transmitter.

B. Shape of the transmission area Apart from the location of the transmitter coil, we can also

determine the optimal shape of the area in which power should be transmitted wirelessly. Note that this shape is not necessarily the shape of the transmitter coil, but rather an area in which a certain amount of power can be transferred. Fig. 3 indicates that the highest probability of a receiver being at a certain location, can be found in an elliptical area in the middle of the rectangle. However, this elliptical area evolves into a rectangular area as the threshold of the score is being lowered. Simulations have pointed out that the shape of the area can be approximated well by a superellipse, as defined in (2) [10]. With the origin of the coordinate system located in the lower left corner of the rectangular area, as depicted in Fig. 3, (a/2, b/2) represents the middle of the rectangle, while ra and rb represent the radius of the superellipse along respectively the x-axis and the y-axis.

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Figure 4. Exponent n as a function of parameter s

Figure 5. Ratio of travelled distance in transmission area to total

travelled distance as a function of s

(2)

The values ra and rb can be expressed as a function of the rectangle’s dimensions and a parameter s, as displayed in (3). The parameter s is a value between 0 and 1, indicating the ratio of ra and rb to respectively a/2 and b/2. As a consequence, it is a measure for the transmitter area size. The value of exponent n as a function of s was determined from simulations and is presented in Fig. 4. This curve displays very high values of n for s approaching to 1. This means that the shape of the superellipse comes close to the rectangular operation area. Furthermore, when s is smaller than 0.3, n will be equal to 2, which means that the shape of the transmission area is a perfect ellipse (or a perfect circle, when a = b).

(3)

C. Transferred power The amount of energy that is being consumed by the power

receiver in a certain period of time should be provided wirelessly by the power transmitter. But since wireless power transmission only takes place sporadically, when the receiver is located in the transmission area, this amount of energy should be transferred in a shorter period of time, and buffered in the receiver. Since power can be expressed as the amount of energy consumed during a period of time, this means that the power delivered to the receiver PTx should be a factor 1/p higher than the power consumed by the receiver electronics PRx, as expressed in (4). Remark that PTx represents the power that should be delivered to the receiver. The effectively

transmitted power will be higher, due to the imperfect link efficiency. p represents the ratio of the travelled distance in the transmission area to the total travelled distance. Note that this approach presumes a constant amount of energy is required per unit of travelled distance, since it relies on a ratio of distance units rather than a ratio of time units. The value of p as a function of s was determined in simulations and is presented in Fig. 5. This graph shows us for example that if a transmission area with an s value of 0.1 is selected, the transferred power PTx should be at least 55 times higher than PRx.

(4)

IV. RECEIVER DESIGN Since power is being delivered to the receiver only when it

travels over the transmission area, a certain kind of energy buffer is indispensible to provide the receiver electronics with energy as long as it travels outside the transmission area. The distance d(s) that the receiver should be able to travel on a single charge can be determined by means of a statistical analysis of the movements of the receiver. However, this distance depends on the shape of the transmission area (a function of s) and the dimensions of the rectangle (a and b). Therefore, simulations of a receiver traveling in a unit square operation area (a = b = 1 m) were performed first. This enables us to define a parameter D as a function of s and a certainty percentage. D represents the traveled distance that will not be exceeded in a unit square without crossing the transmission area, with a given certainty. Fig. 6 depicts 4 curves D(s) for a certainty of 50 %, 84 %, 97.7 % and 99.85 %, comparable to the upper border of respectively 0σ, 1σ, 2σ and 3σ in standard deviations [11]. Selecting the most appropriate curve is a trade-off between buffer size and operation reliability. Some applications might require very high reliability (e.g., a device that needs a continuous energy flow to keep moving), while other applications tolerate temporary outages (e.g. a transmitter attached to an animal). When a value for D(s) is selected, a value for d(s) can be determined for specific rectangular

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Figure 6. 99.85 %, 97.7 %, 84 % and 50 % boundaries for distance

factor D(s)

dimensions a and b using (5). Subsequently the buffer size can be determined with (6) if the required energy per unit of traveled distance E1m [J/m] is known.

(5)

(6)

One can verify that the buffer size Ebuffer should be 32.25 J for a setup with a = 1 m, b = 2 m, s = 0.1, E1m = 1.2 J/m and the 97.7% D(s) curve. Above these considerations, one should also consider the charging and discharging efficiency of the buffer in the given conditions of use for practical applications.

V. PROPOSED DESIGN FLOW Given the obtained results, a design flow is proposed for

the development of wireless power systems for randomly moving devices in a rectangular region. At the start, a, b, PRx and E1m are supposed to be known parameters. The first step involves a statistical analysis of the movements of the receiver. If it exhibits the same behaviour as described in this paper (i.e. moving between uniformly distributed points in the rectangular space), one can proceed with the next steps. Otherwise, the research in section III and IV should be performed again for the given distribution. In the second step, a value for s is chosen together with an achievable value of PTx for the given application, based on Fig. 5 and (4). Subsequently, the shape of the transmission area and Ebuffer are determined, based on Fig. 2 and Fig. 4. Following this step, an estimation of ηlink,max can be performed. If ηlink,max is too low, s should be decreased. If Ebuffer or PTx are too high, s should be increased. When Ebuffer, PTx, and the shape of the transmission area are laid down, a common design sequence for a wireless power system can be followed (e.g. as described in [1]). This allows any (commercial) technology to be used for wirelessly powering moving devices,

whether it is based on inductive coupling, capacitive coupling or magnetic resonance.

VI. CONCLUSIONS AND FUTURE WORK Devices moving between uniformly distributed points in a

rectangular area can be powered wirelessly with only one small transmitter coil. This setup can provide both high efficiency and low system complexity. Simulations illustrated that the optimal area for wireless power transfer has a superellipse shape and is located in the center of the rectangular area. The power to be transferred was also determined in simulations, indicating that a smaller wireless power transfer area demands for a higher transmitted power. An energy buffer is indispensible in this kind of systems in order to provide a continuous energy flow to the receiver electronics. The buffer size depends on both the size of the power transfer area and the desired operation reliability, as demonstrated by numerical simulations. Finally, a design flow was proposed, resulting in a traditional wireless power design process, allowing implementations with existing (commercial) technologies.

Future work involves the study of multiple moving receivers in a single area. Also receivers moving between differently distributed points will be studied, even in open space.

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and Application to Biomedical Systems”, ser. Analog circuits and signal processing. Springer London, Limited, 2009

[2] Wireless Power Consortium, “Qi: System Description Wireless Power Transfer” July 2013. [Online]. Available: http://www.wirelesspowerconsortium.com/downloads/

[3] Rezence, Alliance for Wireless Power, 2014. [Online]. Available: http://www.rezence.com

[4] Power Matters Alliance, 2014 [Online]. Available: http://www.powermatters.com

[5] S. Yu, “IEEE to help wireless device users cut the power cord with launch of new working group to develop IEEE P2100.1™ standard specifications for wireless power and charging systems” October 2013 [Online]. Available: http://standards.ieee.org/news/2013

[6] Q. Xu, H. Wang, Z. Gao, Z. Mao, J. He and M. Sun, "A Novel Mat-Based System for Position-Varying Wireless Power Transfer to Biomedical Implants," Magnetics, IEEE Transactions on , vol.49, no.8, pp.4774,4779, Aug. 2013

[7] A. Shimada, Y. Ito, H. Uehara and T. Ohira "Effect of hop counts on power division ratio in multi-hop power transfer via magnetic resonance," Wireless Power Transfer (WPT), 2013 IEEE , vol., no., pp.179,182, 15-16 May 2013

[8] Azad, U.; Jing, H.C.; Wang, Y.E., "Link Budget and Capacity Performance of Inductively Coupled Resonant Loops," Antennas and Propagation, IEEE Transactions on , vol.60, no.5, pp.2453,2461, May 2012

[9] K. Finkenzeller, “RFID Handbook”, 2nd ed. England: John Wiley and Sons Inc, 2002.

[10] Rosin, P.L., "Fitting superellipses," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.22, no.7, pp.726,732, Jul 2000

[11] C. Walck, “Hand-book on Statistical Distributions for experimentalists”, University of Stockholm, September 2007

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