Adaptive Resonant Beam Charging for Intelligent Wireless ... · system implementation; 3) we analyze the ARBC system performance considering various conditions including beam wavelength,

1

Adaptive Resonant Beam Charging forIntelligent Wireless Power Transfer

Qingqing Zhang, Wen Fang, Mingliang Xiong, Qingwen Liu∗, Jun Wu, and Pengfei Xia

Abstract—As a long-range high-power wireless power trans-fer (WPT) technology, resonant beam charging (RBC) cantransmit Watt-level power over long distance for the devices inthe internet of things (IoT). Due to its open-loop architecture,RBC faces the challenge of providing dynamic current andvoltage to optimize battery charging performance. In RBC,battery overcharge may cause energy waste, thermal effects,and even safety issues. On the other hand, battery underchargemay lead to charging time extension and significant batterycapacity reduction. In this paper, we present an adaptive resonantbeam charging (ARBC) system for battery charging optimization.Based on RBC, ARBC uses a feedback system to control thesupplied power dynamically according to the battery preferredcharging values. Moreover, in order to transform the receivedcurrent and voltage to match the battery preferred chargingvalues, ARBC adopts a direct current to direct current (DC-DC)conversion circuit. Relying on the analytical models for RBCpower transmission, we obtain the end-to-end power transferrelationship in the approximate linear closed-form of ARBC.Thus, the battery preferred charging power at the receiver canbe mapped to the supplied power at the transmitter for feedbackcontrol. Numerical evaluation demonstrates that ARBC can save61% battery charging energy and 53%-60% supplied energycompared with RBC. Furthermore, ARBC has high energy-saving gain over RBC when the WPT is unefficient. ARBC inWPT is similar to link adaption in wireless communications. Bothof them play the important roles in their respective areas.

I. INTRODUCTION

Internet of things (IoT) takes significant strides and hasbecome the driving force of scientific revolution and indus-trial transformation [1]. However, IoT development faces thechallenge of device power endurance. Meanwhile, dramaticgrowth of the multimedia process in mobile devices leads tosignificant energy consumption [2], [3]. Carrying a power cordand looking for power supply cause inconvenience for users.Hence, wireless power transfer (WPT) technology becomes anattractive solution for the power hunger [4], [5], [6].

To provide perpetual power supply for mobile devices,WPT should provide high power over long distance. The ex-isting WPT technologies include inductive coupling, magnetic

The material in this paper was presented in part at the 2017 IEEE86th Vehicular Technology Conference (VTC2017-Fall), Toronto, Canada,September 24-27, 2017.

Q. Zhang, W. Fang, M. Xiong, Q. Liu, J. Wu, P. Xia, arewith Department of Computer Science and Technology, Tongji Univer-sity, Shanghai, People’s Republic of China (e-mail: [email protected],[email protected], [email protected], [email protected], [email protected], [email protected]).

* Corresponding author.Copyright (c) 2012 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

TV

Sweeping Robot

Smartphone

Floor Lamp

Lamp

Laptop

Air Conditioner

Stereo

Air Purifiers

Electric

Curtain

Ceiling Light

Fig. 1: An Example Application Scenario

resonance, radio frequency and laser. However, the transmis-sion distances of inductive coupling and magnetic resonanceare only within millimeter or centimeter, which can not supportlong distance WPT [7], [8]. Radio frequency and laser areunsafe when transmitting Watt-level power [9], [10].

To support Watt-level power transmission over meter-level distance safely, Wi-Charge has published the wirelesspower delivery products and has received the FDA safetyapproval [11]. The Wi-Charge transmitter can deliver up to3 Watts power over 5 meters to multiple receivers simulta-neously through infrared beams while guaranteeing the safetyand mobility [11], [12]. The resonant beam charging (RBC),i.e. distributed laser charging (DLC), was at first presented in[13].

The RBC mechanism, mathematical models and featuresare depicted in [14], [15]. The self-aligning feature of RBCprovides users a convenient way to charge their devices with-out specific aiming or tracking, as long as the transmitter andthe receiver are in the line-of-sight (LOS) of each other. RBCsupports charging multi-device simultaneously, which is likemulti WiFi-devices connecting to a single access point[11],[14], [15]. Additionally, once there is an obstacle between theRBC transmitter and receiver, WPT can be cut off right away.Therefore, the RBC system guarantees safety.

On the other hand, to keep all IoT devices accessing to theRBC system working as long as possible for fairness, the firstaccess first charge (FAFC) scheduling algorithm was presentedin [16]. Multi-device can be selected to charge with theirbatteries’ preferred charging power according to the accessingorder, while all receivers discharge depending on their usingstatues during a time slot.

As smart-home has become an important IoT application

arX

iv:1

809.

0936

4v1

[cs

.SY

] 2

5 Se

p 20

18

2

IntracavityResonant

Beam

PV-panel

R2: 95% Reflectivity R1: 100% Reflectivity

Transmitter

Power

Monitor

Power

Controller

Receiver

Feedback Channel

Feedback System

RBC System

ARBC System

DC-DC

Converter

External-cavityBeam

Power

Supply

+ -Power

Output

Gain

Medium

Fig. 2: Adaptive Resonant Beam Charging System Diagram

area, Fig. 1 gives an example of RBC application in an indoorscenario. In Fig. 1, the ceiling light is the RBC-equippedlight bulb where a RBC transmitter is embedded in. All theelectronic devices embedded with the RBC receivers in thecoverage of the RBC transmitter can be charged wirelesslyand simultaneously.

However, the preferred charging current, voltage, andthus power of battery, such as the most widely used Li-ionbattery, keep changing during the charging period [17], [18].If the transmitter could adjust the emitted power accordingto the battery preferred value, battery charging performanceand wireless power transfer efficiency can be optimized. Tothis end, an adaptive resonant beam charging (ARBC) systembased on the RBC system is introduced in this article.

The contributions of this paper can be summarized asfollows: 1) we propose the ARBC system design, which canautomatically adjust the resonant beam power relying on thefeedback control; 2) we illustrate the working flow, create themathematical model, and present the control algorithm of theARBC system, which provide the guidelines for the ARBCsystem implementation; 3) we analyze the ARBC systemperformance considering various conditions including beamwavelength, PV-cell temperature, air quality, etc.. We find 61%battery charging energy and 53%-60% supplied energy can besaved by the ARBC system compared with the RBC system.

In this paper, RBC will be briefly introduced at first.Then, we will introduce the ARBC system. The modules andworking mechanisms of the ARBC system will be depictedin the following. The ARBC system design, including themathematical modeling and the control algorithm, will bepresented to quantitatively analyze the ARBC model. Based onthe system design, we will evaluate the system performance byusing MATLAB and Simulink. Finally, the conclusions will begiven and the open issues for future research will be discussed.

II. SYSTEM ARCHITECTURE

In this section, we will briefly introduce the RBC systemat first [13]. Then, we will propose the ARBC system basedon the RBC system.

A. RBC System

Fig. 2 shows the RBC system, where the transmitterand the receiver are separated in space. A power supply, aretro-reflector R1 with 100% reflectivity and a gain medium,which is used to amplify photons, are included in the RBCtransmitter. While in the RBC receiver, a retro-reflector R2with 95% reflectivity is contained. A photoelectric conversioncomponent, such as photovoltaic-panel (PV-panel), is installedbehind R2 at the receiver.

In the RBC system, the electrical power provided by thepower supply is converted to the intra-cavity resonant beampower. Then, the intra-cavity resonant beam travels through theair from the transmitter to the receiver with certain attenuation.At the receiver, the intra-cavity resonant beam can be partiallyconverted to the external-cavity beam after passing throughR2. Then, the PV-panel converts the external-cavity beampower to the electrical power. Thus, batteries can be chargedby the electrical power.

1) Electricity-to-Beam Conversion: The power supplyprovides electrical power Ps to pump the gain medium. Psdepends on the stimulating current It and voltage Vt as:

Ps = ItVt. (1)

Then, the intra-cavity resonant beam can be stimulatedout from the gain medium. If there is no transmission attenu-ation, the external-cavity resonant beam power at the receiverPbt can be derived as [19]:

Pbt = γhν

q(It − Ith), (2)

where γ is the modified coefficient, h is the Plunk constant,ν is the beam frequency, q is the electronic charge constant,and Ith is the current threshold.

2) Beam Transmission: The intra-cavity resonant beamtravels through the air and arrives at the RBC receiver. Duringthe transmission, the beam power suffers from attenuation,which is similar to electromagnetic (EM) wave propagationpower loss [20].

The beam transmission efficiency ηbt can be modeled as[21]:

ηbt =PbrPbt

= e−σR, (3)

where Pbr is the received external-cavity beam power at thereceiver, σ is the beam attenuation coefficient, and R is thetransmission radius. When R is close to zero, ηbt approaches100%, and thus Pbr is approximate to Pbt.

3) Beam-to-Electricity Conversion: At the receiver, theexternal-cavity beam power Pbr can be received by a PV-panel and then be converted to electrical power [22], [23].The relationship between the PV-panel output current Io,pvand voltage Vo,pv can be depicted as:

Io,pv = Isc − Is(eVo,pv/Vm − 1), (4)

where Isc is the PV-panel short-circuit current, and Is is thesaturation current, i.e., the diode leakage current density in theabsence of light. Vm is the “thermal voltage”, which can bedefined as:

Vm =nkT

q, (5)

3

where n is the PV-panel ideality factor, k is the Boltzmannconstant, and T is the PV-cell temperature. Then, the PV-paneloutput power Po,pv can be obtained as:

Po,pv = Io,pvVo,pv. (6)

In the RBC system, the electrical power Po,pv can finallybe used to charge batteries.

B. ARBC System

The RBC system can transmit Watt-level power over longdistance [13]. However, there exist some concerns with theRBC system:

1) To optimize battery charging performance, the batterycharging current and voltage should be dynamically changedduring the charging period, which will be discussed in detailin the following. However, the RBC system can only chargebatteries with constant current and voltage.

2) The RBC resonant beam power propagation lossdepends on transmission radius and medium obstacle along theLOS path between the transmitter and the receiver [13]. Thus,the space-time varying propagation loss requires dynamicpower supply compensation.

3) If the PV-panel output power at the RBC receiver is notfully converted to the battery power, the extra energy usuallycauses thermal effects, which may lead to PV-panel conversionefficiency reduction, battery damage, and even danger.

To deal with these issues, an intuitive idea is to control thetransmission power by adaptively sending the value of batterypreferred power from the receiver to the transmitter through afeedback channel. The similar mechanism for signal transmis-sion is well-known as link adaption in wireless communicationfor optimizing the information delivery [24].

At first, we need to specify the adaption goal to optimizebattery charging performance. Battery charging profile is thealgorithm of using dynamic current and voltage in batterycharging process. Battery performance, in terms of achievablecapacity and charging speed, depends on the battery chargingprofile. For example, the preferred battery charging profile ofLi-ion battery is known as the constant current - constantvoltage (CC-CV) profile to achieve the maximum batterycapacity [18].

On the other hand, the PV-panel output current andvoltage may not be the battery preferred charging values, theDC-DC converter can take the role of converting the PV-paneloutput values to the battery preferred ones.

By incorporating the feedback system and the DC-DCconverter into the RBC system, the ARBC system architecturecan be depicted as in Fig. 2. The feedback system crosses overthe two ends of the ARBC system, which consists of powermonitor and power controller.

The ARBC operation flow is depicted in Fig. 3 as:1) The power monitor gets the values of battery preferred

charging current, voltage, and cut-off time;2) If the preferred charging current is lower than 20 mA,

the charging procedure ends. Or, turn to 3);3) If the charging time cuts off, the charging procedure

ends. Or, turn to 4);

Begin

Preferred current valueis lower than 20 mA?

The preferred charging values are sent to the power

controller through the feedback channel

Intra-cavity resonant beam is stimulated out

Beam transmission

DC-DC converter converts the PV-panel output current

and voltage to the battery preferred ones

Finish charging

End

Charging battery

Receiver beam power is converted to electrical power

Power monitor gets battery charging profile

(voltage, current, and charging time）

N

Y

Charging time cuts off?

N

Y

Fig. 3: ARBC Flow Chart

4) The power monitor sends the preferred charging powerto the power controller;

5) After receiving the preferred charging values, thepower controller informs the power supply to generate the cor-responding electrical power. The electrical power has effectson the gain medium to stimulate out the intra-cavity resonantbeam;

6) The resonant beam travels through the air from thetransmitter and arrives at the receiver;

7) The receiver beam power is converted to the electricalpower by the PV-panel at the receiver;

8) The DC-DC converter converts the PV-panel outputcurrent and voltage to the battery preferred values;

9) The battery is charged with the preferred current andvoltage;

10) The power monitor updates the values of batterypreferred charging current, voltage, and cut-off time accordingto the battery status.

Repeating this flow, the battery can be charged with thepreferred values during the whole charging procedure.

To specify the ARBC system in detail, the battery charg-ing profile, the DC-DC converter and the feedback mechanismis discussed in the following.

1) Li-ion Battery Charging Profile: Different kinds ofbatteries may have different charging profiles given the chem-ical characteristics [25]. Li-ion battery is the most widely usedrechargeable battery for IoT and mobile devices. In traditionalcharging systems, including the RBC system, batteries are

4

0

200

400

600

800

1000

1200

Cha

rgin

g C

urre

nt (

mA

)

CurrentVoltage

0 0.5 1 1.5 2 2.5 3 3.5 4

Charging Time (h)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Cha

rgin

g V

olta

ge (

V)

Stage1 TC

Stage2 CC

Stage3 CV

Stage4 CT

Fig. 4: Li-ion Battery Charging Profile

charged with fixed power. However, for Li-ion battery, evenslightly undercharging can lead to significant capacity reduc-tion [26]. For example, 1.2% undercharge of the optimal full-charge voltage may result in 9% capacity reduction. On theother hand, overcharge may damage the battery and even causedanger. Therefore, offering controllable current and voltage isimportant to charge Li-ion battery safely as well as achieveits full capacity.

We discuss here the Li-ion battery preferred chargingprofile, which includes four stages as in Fig. 4. As an instanceof a single cell Li-ion battery with 1000 mAh capacity, thebattery can theoretically provide one hour of operating timewhen discharged at a constant current of 1000 mA. We outlinethe stages of battery charging profile as [27], [26]:

Stage 1: Trickle Charge (TC) - When the battery voltageis below 3.0 V, the battery is charged with the current whichincreases towards 200 mA. The voltage rises to 3.0 V.

Stage 2: Constant Current (CC) Charge - After the batteryvoltage has risen above 3.0 V, the TC-CC threshold, thecharging current switches to constant value between 200 mAto 1000 mA. The voltage rises towards 4.2 V.

Stage 3: Constant Voltage (CV) Charge - When the cellvoltage reaches the CC-CV threshold, 4.2 V, the CC stageends and the CV stage begins. In order to maximize capacity,the voltage variation tolerance should be less than 1%. Thecurrent decreases towards 20 mA.

Stage 4: Charge Termination (CT) - Two approachesare typically used to terminate charging: 1) minimum currentcharge or 2) timer cutoff. However, a combination of thetwo techniques may also be applied. In the minimum currentapproach, battery charge is terminated when the current dimin-ishes below 20 mA, the minimum current threshold, duringthe CV stage. In the timer cutoff approach, for example, 2.4-hour timer starts when the CV stage is invoked. The charge isterminated after 3.6-hour during the CV stage.

It takes 4 hours to fully charge a deeply depleted batteryto maximize the battery capacity. The charging speed isaffected by CC in Stage 2 [18]. For example, if CC is 700 mA,50% to 70% capacity can be charged at the end of Stage 2.

连续模式：Vo/Vi = -D/(1-D)D=Vo/(Vo+Vi)

不连续模式：Vo/Vi = -ViD2T/(2LIo)

D=Vo/(Vo+Vi)

+

-

-

+

Io,pv

Vo,pv

Io,dc

Vo,dcL

Fig. 5: Buck-Boost DC-DC Converter

This is the secret that many “fast-charging” techniques relyon. If CC is 200 mA, much longer time is needed to finishStage 2, however, nearly 100% capacity can be achieved at theend of Stage 2. It is the tradeoff between charging speed andachieved capacity, which can be controlled by CC at Stage 2.

Compared with fixed-charging system, dynamicallycharging, according to the above charging profile, can not onlyavoid overcharge or undercharge, but also reduce potentialdamage to battery or safety concern.

2) DC-DC Conversion: The PV-panel output currentIo,pv and voltage Vo,pv may not be optimal for batterycharging. At first, Io,pv and Vo,pv may be dynamic due tothe variance of Pbr and PV-panel characteristics. Secondly,the preferred battery charging current and voltage vary withdifferent battery conditions, as discussed above. Therefore,converting Io,pv and Vo,pv to the battery preferred valuesbecomes imperative.

In solar power systems, it is well-known to adopt a DC-DC converter between PV-panel and power load to obtainthe preferred current and voltage [28]. There are three DC-DC converter types – boost converter, buck converter andbuck-boost converter. At the ARBC receiver, the buck-boostconverter is adopted [29]. As depicted in Fig. 5, the DC-DC converter, a programmable integrated circuit, can convertthe input current and voltage, which are the PV-panel outputcurrent Io,pv and voltage Vo,pv , to the output current Io,dc andvoltage Vo,dc, which are the battery preferred charging currentand voltage.

There are two working modes of the buck-boost DC-DC converter according to whether the current through theinductor falls to zero during a working period. If the currentthrough the inductor never falls to zero, it is called thecontinuous mode. Otherwise, it is the discontinuous mode.

When working at the continuous mode, the relationshipbetween Vo,pv and Vo,dc can be depicted as:

Vo,dcVo,pv

= − D

1−D, (7)

where D is the duty cycle, which means the switch closingtime of the whole working time t. While, if working at thediscontinuous mode, Vo,pv and Vo,dc are related as:

Vo,dcVo,pv

= −Vo,pvD2 t

2 L Io,pv, (8)

where L is the inductor.Then, the DC-DC converter output current and voltage are

converted to the battery preferred charging current and voltage.Thus, batteries can be charged with the preferred values.

5

0 10 20 30 40

Supplied Power Ps (W)

0

5

10

15

20T

rans

mitt

er B

eam

Pow

er P

bt (

W)

Measured Curve (810nm) Formulated Curve (810nm) Measured Curve (1550nm) Formulated Curve (1550nm)

Fig. 6: Transmitter Beam Power vs. Supplied Power

TABLE I: Curve-fitting Coefficients for Beam Power

Beam Wavelength a1 b1810 nm 0.445 -0.751550 nm 0.34 -1.1

3) Feedback Mechanism: To charge batteries dynami-cally and continuously, we should track the preferred batterycharging current, voltage, and thus power, and send the infor-mation to the power supply during the charging procedure. Inthe feedback system, the power monitor at the ARBC receivertakes the role of tracking the battery status and obtainingthe charging values of current and voltage. After that, theexpected charging power can be calculated as the product ofthe preferred current and voltage.

Then, the adjustment or requirement of the transmittingpower will be sent to the power controller by the powermonitor through the feedback channel. The feedback channelcan be established relying on various wireless communica-tion technologies, e.g., WiFi, Bluetooth, infra-communication.Alternatively, the decision logic can be implemented in thepower controller, if the power monitor can feedback the batterycharging related information to the power controller.

Thus, the battery can be charged with preferred currentand voltage continuously. Thereafter, the intelligent wirelesscharging technology can be realized to optimize battery per-formance. This architecture is capable to support chargingdifferent kinds of batteries with diverse charging profiles, suchas Li-ion, Ni-MH, etc..

In summary, the proposed ARBC mechanism for optimiz-ing wireless charging performance is similar to the link adap-

TABLE II: Beam Transmission Parameters

Parameter ValueClear Air Haze Fog

τ 10 km 3 km 0.4 kmθ 1.3 0.16τ + 0.34 0

0 10 20 30 40 50

Beam Transmission Radius R (km)

0

20%

40%

60%

80%

100%

Bea

m T

rans

mis

sion

Effi

cien

cy

bt

clear air (1550nm)clear air (810nm) haze (1550nm) haze (810nm) fog (1550nm) fog (810nm)

Fig. 7: Beam Transmission Efficiency vs. Radius

tion widely-used in wireless communications for optimizinginformation delivery.

In the next section, we will present the numerical modelsand performance evaluation of the ARBC system.

III. ARBC SYSTEM DESIGN

To design the ARBC system, the power relationshipbetween the battery preferred charging power and the suppliedpower should be obtained. So, we will introduce the numericalmodels at first in this section. Based on these models, we willdesign the system control algorithm to describe the ARBCsystem in detail.

A. Mathematical Modeling

We at first introduce the electricity-to-beam conver-sion model, the beam transmission model, and the beam-to-electricity conversion model. Based on these models, theARBC end-to-end power transfer relationship between thebattery power and the supplied power can be obtained, whichoffers a quantitative and intuitive tool to evaluate the ARBCsystem.

1) Electricity-to-Beam Conversion: From [30], [31], themeasured values of stimulation current It, stimulation voltageVt and the resonant beam power Pbt for the beam wavelengthof 810 nm and 1550 nm can be obtained, respectively. Then,the supplied electrical power Ps can be calculated accordingto (1). According to [14], [15], Ps is verified to be linearlyrelated with Pbt. The relationship between Pbt and Ps can bedescribed as:

Pbt ≈ a1Ps + b1, (9)

where a1 and b1 are two coefficients, of which the values arelisted in Table I.

In Fig. 6, the dot-dash-line and the dot-line depict themeasured relationships between Pbt and Ps when the beamwavelength takes 810 nm and 1550 nm, respectively. While,the solid-line and the dash-line are the formulated fittingcurves for 810 nm and 1550 nm based on (9). As can be

6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

PV-panel Output Voltage Vo,pv

(V)

0

2

4

6

8

10P

V-p

anel

Out

put P

ower

P

o,pv

(

W)

Pbr

=15W, =810nm

Pbr

=10W, =810nm

Pbr

=5W, =810nm

Pbr

=1W, =810nm

Pbr

=15W, =1550nm

Pbr

=10W, =1550nm

Pbr

=5W, =1550nm

Pbr

=1W, =1550nm

Fig. 8: PV-panel Output Power vs. Voltage (25◦C)

seen, the formulated curves match the measured ones verywell, which validates the linear approximation.

2) Beam Transmission: In different transmission sce-narios, the intra-cavity resonant beam power takes differentattenuation according to (3). The attenuation coefficient σ canbe depicted as [21]:

σ =3.91

τ

( λ

550 nm

)−θ, (10)

where τ is the visibility, and θ is the size distribution of thescattering particles.

We consider three typical scenarios, i.e., clear air, hazeand fog here. θ can be specified as [32]:

θ =

1.3 for clear air (6 km ≤ τ ≤ 50 km),0.16τ + 0.34 for haze (1 km ≤ τ ≤ 6 km),0 for fog (τ ≤ 0.5 km).

(11)These transmission parameters are listed in Table II.

Fig. 7 illustrates how ηbt varies with the transmissionradius R under three different air quality and two differentbeam wavelengths. We can see that, ηbt decays exponentiallywith the increment of R. Meanwhile, for the same beamwavelength, ηbt has much steeper shape with the decrementof τ . It means that ηbt declines faster with the air qualitydeclining, i.e., the visibility gets low.

TABLE III: PV-panel Simulation Parameters

Parameter Value810 nm 1550 nm

Short-circuit current 0.16732A 0.305AOpen-circuit voltage 1.2V 0.464VIrradiance used for

measurement36.5W/cm2 2.7187W/cm2

Laser frequency 3.7037× 1014Hz 1.9355× 1014HzQuality factor 1.5 1.1

Number of series cells 72PV-panel material GaAs-based GaSb-based

Measurement temperature 25◦C 120◦C

In addition, in the clear air and the haze scenarios, giventhe same radius R, the beam power attenuates faster for theshort beam wavelength. When θ takes 0 in the fog scenario,for 810 nm and 1550 nm, ηbt has the same attenuation pattern.

3) Beam-to-Electricity Conversion: At the ARBC re-ceiver, various factors like the input beam power Pbr, the beamwavelength λ, and the PV-cell temperature T affect the PV-panel power conversion. We simulate the beam-to-electricityconversion procedure with the standard solar cell Simulinkmodel [15]. Table III lists all the simulation parameters.

When the PV-cell temperature T is 25◦C (298K), Fig. 8illustrates the influences that Pbr and λ have on the PV-paneloutput power Po,pv based on (4), (5) and (6).

From Fig. 8, Po,pv goes up gradually to the peak andthen declines sharply to the bottom. The PV-panel outputsmore power with the increment of Pbr. The dots in Fig. 8are the maximum power points (MPPs) of the curves, whichhave been proved that uniquely exist [33]. Similarly, the MPPswhen T takes 0◦C (273K) and 50◦C (323K) can be obtained.

To obtain the maximum efficiency of the ARBC system,the PV-panel is expected to work at MPPs. Moreover, themaximum Po,pv should be the preferred battery chargingpower Pb. The dots in Fig. 9 are the MPPs obtained underdifferent PV-cell temperatures (0◦C, 25◦C and 50◦C) andbeam wavelengths (810 nm and 1550 nm). From Fig. 9, therelationship between Pb and Pbr can be obtained by the linearcurve-fitting approximation as [14], [15]:

Pb ≈ a2Pbr + b2, (12)

where a2 and b2 are the linear curve fitting coefficients. Toprovide more details about how Pb changes with Pbr underdifferent temperature, values of a2 and b2 when the PV-celltemperature takes 0◦C, 5◦C, 10◦C, 15◦C, 20◦C, 25◦C, 30◦C,35◦C, 40◦C, 45◦C, and 50◦C are listed in Table IV.

Fig. 9 depicts the linear relationship between Pb and Pbrfor 810 nm and 1550 nm, respectively. The linear fitting lines

TABLE IV: Curve-fitting Coefficients for Battery Power

Beam Wavelength Temperature a2 b2810 nm 0◦C 0.6084 -0.08382

5◦C 0.6087 -0.0850610◦C 0.6089 -0.0862815◦C 0.6092 -0.0874920◦C 0.6094 -0.0886825◦C 0.6096 -0.0898730◦C 0.6098 -0.0910235◦C 0.6100 -0.0921740◦C 0.6102 -0.0933145◦C 0.6103 -0.0944350◦C 0.6105 -0.09557

1550 nm 0◦C 0.6043 -0.12755◦C 0.5964 -0.129410◦C 0.5885 -0.131715◦C 0.5806 -0.133820◦C 0.5727 -0.135825◦C 0.5649 -0.138230◦C 0.5569 -0.139835◦C 0.5491 -0.142440◦C 0.5412 -0.144045◦C 0.5334 -0.146450◦C 0.5255 -0.1483

7

0 5 10 15

Received Beam Power Pbr

(W)

0

2

4

6

8

10B

atte

ry P

ower

P

b

(W

)

T=0°C, =810nm

T=25°C, =810nm

T=50°C, =810nm

T=0°C, =1550nm

T=25°C, =1550nm

T=50°C, =1550nm

9.95 10 10.055.9

5.95

6

6.05

Fig. 9: Battery Power vs. Received Beam Power

match the measured Pb and Pbr, which are marked by the dots,very well. With the increment of T , for same Pbr, the valueof Pb diminishes. On the other hand, the 1550 nm system ismore temperature-dependent than the 810 nm system.

4) End-to-End Transmission: Efficiency of battery charg-ing, DC-DC conversion and feedback affect the end-to-endpower transmission efficiency. We can assume there is almostno energy loss if the battery is charged with preferred powervalues. We also assume that the feedback system and theDC-DC converter cause almost no energy loss [34]. Thus,the ARBC end-to-end power transmission mathematical modelcan be built based on the numerical models.

Based on (3), (9) and (12), given the beam transmissionefficiency ηbt, the battery charging power Pb changes depend-ing on the supplied power Ps as:

Pb ≈ a2ηbtPbt + b2

= a1a2ηbtPs + (a2b1ηbt + b2).(13)

Hence, Pb depends on Ps linearly. For the 810 nm system,Fig. 10 depicts the linear relationship under three different Twhen ηbt takes 100% and 50%, respectively. While, Fig. 11depicts the same relationships for the1550 nm system.

The linear relationship between Pb and Ps provides anintuitive and quantitive way to understand the end-to-endpower transfer in the ARBC system.

B. Control Algorithm

Based on the mathematical modeling, given the batterypreferred charging current, voltage, and thus power, the sup-plied power can be calculated out with reference to the end-to-end transmission efficiency. To demonstrate the chargingoperation of the ARBC system, we give the charging algorithmin Algorithm 1 as:

1) The power controller gets the battery preferred charg-ing power Pb, current Ib, voltage Vb or cut-off time t from thepower monitor.

2) If Ib is lower than 20 mA or t equals to 3.6 h, thecharging procedure ends. Otherwise, the power controller in-

0 5 10 15 20 25 30 35 40

Supplied Power Ps (W)

0

2

4

6

8

10

12

Bat

tery

Pow

er

Pb

(W

)

T=0°C, bt

=100%

T=25°C, bt

=100%

T=50°C, bt

=100%

T=0°C, bt

=50%

T=25°C, bt

=50%

T=50°C, bt

=50%

24.95 256.22

6.23

6.24

24.98 24.99 25

3.07

3.072

Fig. 10: Battery Power vs. Supplied Power (810 nm)

forms the power supply to generate Ps from Pb with referenceto the end-to-end transmission efficiency.

3) Ps effects on the gain medium, and the resonant beamcan be stimulated out.

4) The PV-panel can convert the beam power to theelectrical power Ppv , while the output current and voltage areIpv and Vpv .

5) The DC-DC converter converts Ipv and Vpv to Ib andVb. Thus, the battery can be charged with preferred values.

6) The power monitor updates Ib and Vb according tothe next battery state, and sends them to the power controller.Then, turn to 2).

Repeating these steps, the battery can be charged withthe battery preferred charging values dynamically during thewhole ARBC procedure.

Algorithm 1 Adaptive Resonant Beam Charging

1: Begin2: The power monitor gets the preferred charging power Pb,

current Ib, voltage Vb and cut-off time t3: while Ib ≥ 20 mA and t ≤ 3.6 h do4: Ps ← Pb/(ηebηbtηpv) // The power monitor computesPs, and sends it to the power controller

5: Pbt ← Psηeb // Transmitter beam power6: Pbr ← Pbtηbt // Receiver beam power7: Pb ← Pbrηpv // PV-panel output power8: if Ipv 6= Ib and Vpv 6= Vb then // DC-DC conversion9: Ib ← Ipv

10: Vb → Vpv11: end if12: Charge the battery with Ib and Vb13: The power monitor updates Pb, Ib and Vb according

to the next battery state14: end while15: Stop Charging16: End

8

0 5 10 15 20 25 30 35 40

Supplied Power Ps (W)

0

2

4

6

8B

atte

ry P

ower

P

b

(W

)

T=0°C, bt

=100%

T=25°C, bt

=100%

T=50°C, bt

=100%

T=0°C, bt

=50%

T=25°C, bt

=50%

T=50°C, bt

=50%

Fig. 11: Battery Power vs. Supplied Power (1550 nm)

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Bat

tery

Pow

er P

b (W

)

5.96Wh

15.20Wh

RBCARBC

Fig. 12: Battery Power in ARBC and RBC

IV. PERFORMANCE EVALUATION

Based on the ARBC system design, the batteries accessedto the ARBC system can be charged with their preferredvalues. Therefore, the system performance can be evaluated.In terms of battery charging and power supply, the advantagesof the ARBC system over the RBC system will be validatedby the performance comparisons in this section. The numericalevaluations are implemented in MATLAB and Simulink.

A. Battery Charging Performance

In traditional wireless charging systems, including theRBC system, charging stages can not be tracked withoutadaptive function. Hence, batteries are charged with fixedcurrent or voltage. We take 4.2 W (constant current 1 A andconstant voltage 4.2 V) for Li-ion battery charging power. Thesolid-line in Fig. 12 shows the constant battery charging power.It is an horizontal line without any changes during the RBCprocedure.

However, batteries can be charged dynamically in theARBC system. According to the Li-ion battery charging profile

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

2

4

6

8

10

12

14

16

18

20

22

Sup

plie

d P

ower

Ps (

W)

RBC

ARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

0.495 0.5 0.50515.06

15.09

15.12

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°C

R=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 13: Supplied Power with Different Radius and Tempera-ture for 810 nm (Clear Air)

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

5

10

15

20

25

30

35

40

45

Sup

plie

d P

ower

Ps (

W)RBC

ARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°C

R=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 14: Supplied Power with Different Radius and Tempera-ture for 810 nm (Haze)

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

0.5

1

1.5

2

2.5

3

Sup

plie

d P

ower

Ps (

W)

105

RBC

ARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

0 2 40

900

1800

2700

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°C

0 2 40

20

40

60

R=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 15: Supplied Power with Different Radius and Tempera-ture for 810 nm (Fog)

9

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

5

10

15

20

25

Sup

plie

d P

ower

Ps (

W)

RBCARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°C

R=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 16: Supplied Power with Different Radius and Tempera-ture for 1550 nm (Clear Air)

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

5

10

15

20

25

30

35

40

45

50

Sup

plie

d P

ower

Ps (

W)

RBC

ARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°CR=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 17: Supplied Power with Different Radius and Tempera-ture for 1550 nm (Haze)

0 0.5 1 1.5 2 2.5 3 3.5 4

Hours (h)

0

0.5

1

1.5

2

2.5

3

3.5

Sup

plie

d P

ower

Ps (

W)

105

RBC

ARBC

R=1km, T=50°C

R=1km, T=25°C

R=1km, T=0°C

0 2 40

900

1800

2700

R=0.5km, T=50°C

R=0.5km, T=25°C

R=0.5km, T=0°C

0 2 40

20

40

60

R=0.1km, T=50°C

R=0.1km, T=25°C

R=0.1km, T=0°C

Fig. 18: Supplied Power with Different Radius and Tempera-ture for 1550 nm (Fog)

0.1km 53.32% c01 53.32%0.5km 53.83% c05 53.83%1km 54.42% c1 54.42% 0.5332 0.53830.1km 53.71% h01 53.71%0.5km 55.44% h05 55.44%1km 56.95% h1 56.95%0.1km 57.02% f01 57.02%0.5km 59.55% f05 59.55%1km 59.60% f1 59.60%

25℃25℃25℃25℃50℃50℃50℃50℃

53.32%53.83%

54.42%

53.71%

55.44%

56.95% 57.02%

59.55% 59.60%

49.0%

51.0%

53.0%

55.0%

57.0%

59.0%

61.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 19: The Percent of Saved Supplied Energy under 0◦C(λ=810 nm)

0.1km 53.23% c01 Clear Air 53.23%0.5km 53.75% c05 Clear Air 53.75%1km 54.34% c1 Clear Air 54.34% 0.53230.1km 53.62% h01 Haze 53.62%0.5km 55.36% h05 Haze 55.36%1km 56.86% h1 Haze 56.86%0.1km 56.93% f01 Fog 56.93%0.5km 59.46% f05 Fog 59.46%1km 59.51% f1 Fog 59.51%

25℃25℃25℃25℃50℃50℃50℃50℃

53.23%53.75%

54.34%

53.62%

55.36%

56.86% 56.93%

59.46% 59.51%

49.0%

51.0%

53.0%

55.0%

57.0%

59.0%

61.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 20: The Percent of Saved Supplied Energy under 25◦C(λ=810 nm)

0.1km 53.16% c01 53.16%0.5km 53.68% c05 53.68% 0.5316 0.5368 0.5426 0.53551km 54.26% c1 54.26%0.1km 53.55% h01 53.55%0.5km 55.29% h05 55.29%1km 56.79% h1 56.79%0.1km 56.86% f01 56.86%0.5km 59.38% f05 59.38%1km 59.44% f1 59.44%

53.16%53.68%

54.26%

53.55%

55.29%

56.79% 56.86%

59.38% 59.44%

49.0%

51.0%

53.0%

55.0%

57.0%

59.0%

61.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 21: The Percent of Saved Supplied Energy under 50◦C(λ=810 nm)

10

0.1km 52.86% c01 52.86%0.5km 53.36% c05 53.36%1km 53.94% c1 53.94%0.1km 53.24% h01 53.24%0.5km 54.94% h05 54.94%1km 56.40% h1 56.40%0.1km 56.47% f01 56.47%0.5km 58.94% f05 58.94%1km 58.99% f1 58.99%

25℃25℃25℃25℃50℃50℃50℃50℃

52.86%

53.36%

53.94%

53.24%

54.94%

56.40% 56.47%

58.94% 58.99%

49.0%

50.0%

51.0%

52.0%

53.0%

54.0%

55.0%

56.0%

57.0%

58.0%

59.0%

60.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 22: The Percent of Saved Supplied Energy under 0◦C(λ=1550 nm)

0.1km 53.10% c01 Clear Air 53.10%0.5km 53.58% c05 Clear Air 53.58%1km 54.12% c1 Clear Air 54.12%0.1km 53.46% h01 Haze 53.46%0.5km 55.06% h05 Haze 55.06%1km 56.43% h1 Haze 56.43%0.1km 56.50% f01 Fog 56.50%0.5km 58.79% f05 Fog 58.79%1km 58.84% f1 Fog 58.84%

25℃25℃25℃25℃50℃50℃50℃50℃

53.10%

53.58%

54.12%

53.46%

55.06%

56.43% 56.50%

58.79% 58.84%

50.0%

51.0%

52.0%

53.0%

54.0%

55.0%

56.0%

57.0%

58.0%

59.0%

60.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 23: The Percent of Saved Supplied Energy under 25◦C(λ=1550 nm)

0.1km 53.35% c01 Clear Air 53.35%0.5km 53.79% c05 Clear Air 53.79%1km 54.30% c1 Clear Air 54.30%0.1km 53.69% h01 Haze 53.69%0.5km 55.18% h05 Haze 55.18%1km 56.46% h1 Haze 56.46%0.1km 56.52% f01 Fog 56.52%0.5km 58.66% f05 Fog 58.66%1km 58.70% f1 Fog 58.70%

25℃25℃25℃25℃50℃50℃50℃50℃

53.35%

53.79%

54.30%

53.69%

55.18%

56.46% 56.52%

58.66% 58.70%

50.0%

51.0%

52.0%

53.0%

54.0%

55.0%

56.0%

57.0%

58.0%

59.0%

60.0%

0.1km 0.5km 1km 0.1km 0.5km 1km 0.1km 0.5km 1km

Sav

ed E

ner

gy P

erce

nt

Air Condition

Beam Transmission Radius

Clear Air Haze Fog

Fig. 24: The Percent of Saved Supplied Energy under 50◦C(λ=1550 nm)

in Fig. 4, the preferred battery charging power can be obtainedaccording to the preferred charging current and voltage. Thedash-line in Fig. 12 shows the preferred battery charging powerchanges during the ARBC procedure.

From Fig. 12, we can recognize the big power consump-tion gap between the RBC system and the ARBC system. Theareas under the battery charging power in Fig. 12 stand forthe consumed battery charging energy. The RBC procedureconsumed energy is 15.20 Wh, while the ARBC procedureonly consumes 5.96 Wh. That is to say, during the wholecharging procedure, the ARBC system could save 9.24 Whenergy. In summary, 61% battery charging energy can be savedby the ARBC system compared with the RBC system.

B. Power Supply Performance

For different transmission radius R, air quality, beamwavelength λ, and PV-cell temperature T , the supplied powerPs takes different values in the ARBC system. That is, Psdepends on R, T , λ and air quality. For λ=810 nm, Figs. 13,14 and 15 show how Ps changes with different radius R underdifferent air quality (clear air, haze and fog) and differenttemperature T (0◦C, 25◦C and 50◦C), respectively. Figs. 16,17, and 18 illustrate Ps in the same scenarios for λ=1550 nm,respectively.

Form Figs. 13-18, when R increases, ηbt becomes small.Thus, Ps needs to be enhanced to compensate the power atten-uation. Since the PV-panel takes lower conversion efficiencyas T goes up, Ps and T show a negative correlation. Moreover,with the same R, T and λ, Ps increases when the air visibilitydecreases. This is due to the attenuation of ηbt becomes higherwith the air quality getting worse. To obtain the preferredbattery charging power, Ps increases as ηbt attenuates.

Then, the corresponding consumed supplied energy dur-ing the charging procedure can be obtained as in Table ??.It can be observed that, for the same beam wavelength,the consumed supplied power keeps the upward trend as Tincreases within certain radius under certain air quality. TheARBC system consumes much less supplied energy in all thelisted scenarios for both 810 nm and 1550 nm compared withthe RBC system.

Thereafter, for the same charging procedure, the suppliedenergy saved by the ARBC system compared with the RBCsystem can then be obtained. Figs. 19, 20 and 21 show thesaved supplied energy percentage for 810 nm under 0◦C, 25◦Cand 50◦C, respectively. Figs. 22, 23 and 24 show the savedsupplied energy percentage in the same scenarios for 1550 nm.

From Figs. 19-24, under the same air quality, the percent-age of saved energy goes up with R increasing under the sameT . With the same R and T , the percentage of saved energygoes up as the air quality declines. Since whether R increasesor air quality declines, ηbt decreases, and thus Ps needs tobe increased. The increment of Ps leads to thermal effectand energy loss. Therefore, to obtain same battery chargingpower, the smaller Ps is preferred by ARBC compared withRBC. Hence, less energy will loss in the ARBC system, andmore energy will be saved. This validates that the necessity ofadopting the ARBC system increases as the preferred supplied

11

power Ps rising. Moreover, in the above scenarios, 53%-60%supplied energy can be saved by the ARBC system no matterfor the 810 nm or the 1550 nm system.

C. Summary

The ARBC mechanism introduced in Section III is nu-merically evaluated. Based on the end-to-end power conver-sion analysis, we quantitatively demonstrate the variation ofthe supplied power during battery charging period procedure.The supplied power depends on the PV-cell temperature, beamtransmission efficiency, and beam wavelength. Furthermore,we obtain the battery charging energy and the supplied energysaved by the ARBC system compared with the RBC systemin different scenarios.

The observations from the above analysis include:• With the increment of either the transmission radius R or

the PV-cell temperature T , the preferred supplied powerPs takes an upward trend in the ARBC system.

• The supplied power Ps shows a negative correlation withthe air quality. That is to say, with the improvement ofthe air quality, i.e., the enhancement of the visibility,less supplied power is required to get the certain batterycharging power.

• For the same air quality and transmission radius R,the consumed supplied energy goes up with the PV-celltemperature T increasing for the RBC system and theARBC system.

• For the same air quality, the percentage of the ARBCsystem saved energy goes up as the transmission radiusR increases.

• For the same transmission radius R, the ARBC systemsaves more energy with the air quality going down.

• For battery charging, 61% energy can be saved by theARBC system compared with the RBC system.

• For the power supply, 53%-60% supplied energy is savedby the ARBC system compared with the RBC system.

V. CONCLUSIONS

An adaptive resonant beam charging (ARBC) system isintroduced in this paper based on the resonant beam chargingsystem (RBC). The system design and numerical analysis ofthe ARBC system are presented to optimize battery chargingperformance in terms of battery charging profile. Given thesupplied power, the battery charging power is influencedby various factors, including beam wavelength, beam trans-mission efficiency and PV-cell temperature etc.. Numericalanalysis illustrates that 61% battery charging energy and 53%-60% supplied energy can be saved by the ARBC systemcompared with the RBC system.

Several issues in this area are worth of further research:• The analysis in this paper is under ideal assumptions.

For example, the feedback and measurement errors areinevitable in the practical system, which should be con-sidered in the future.

• For different beam wavelengths, the saved energy variesas the PV-cell temperature changing

• Different battery types have different battery chargingprofiles. Therefore, studying their impacts on ARBC isone of the future research areas.

VI. ACKNOWLEDGMENT

The authors would like to thank the editors and the anony-mous reviewers. At the same time, we would like to thankcolleagues in our laboratory. Thank Hao Deng and MingqingLiu for their valuable suggestions, and thank Aozhou Wu forpolishing the figures.

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