Distributed Laser Charging: A Wireless Power Transfer Approach

1 Distrib uted Laser Char ging: A W ireless Po wer T ransfer Approach Qingqing Zhang, Student Member , IEEE, W en Fang, Qingwen Liu ∗ , Senior Member , IEEE, Jun W u, Senior Member , IEEE, Pengfei Xia, Senior Member , IEEE, and Liuqing Y ang, F ellow , IEEE Abstract —Wir eless power transfer (WPT) is a promising solution to pro vide convenient and per petual energy supplies to electronics. T raditional WPT technologies face the challenge of pro viding W att-lev el power over meter -lev el distance for Internet of Things (IoT) and mobile devices, such as sensors, controllers, smart-phones, laptops, etc.. Distributed laser charging (DLC), a new WPT alternative, has the potential to solve these problems and enable WPT with the similar experience as WiFi com- munications. In this paper , we pr esent a multi-module DLC system model, in order to illustrate its ph ysical fundamentals and mathematical formula. This analytical modeling enables the evaluation of power conv ersion or transmission for each individual module, considering the impacts of laser wavelength, transmission attenuation and photovoltaic-cell (PV -cell) tempera- ture. Based on the linear appr oximation of electricity-to-laser and laser -to-electricity power conv ersion validated by measurement and simulation, we deriv e the maximum power transmission efficiency in closed-form. Thus, we demonstrate the variation of the maximum power transmission efficiency depending on the supply power at the transmitter , laser wav elength, transmission distance, and PV -cell temperature. Similar to the maximization of inf ormation transmission capacity in wireless information transfer (WIT), the maximization of the power transmission efficiency is equally important in WPT . Theref ore, this work not only pro vides the insight of DLC in theory , but also offers the guideline of DLC system design in practice. Index T erms —Wireless power transfer , distributed laser charging, power transmission efficiency . I . I N T R OD U C T I O N Internet of Things (IoT) and mobile de vices, such as sensors and smart-phones, are typically powered by batteries that ha ve limited operation time. Sensors for IoT , especially sensors that being deployed in special en vironments such as volcanoes, are difficult to be charged. Meanwhile, carrying a power cord and looking for a power supplier to charge mobile devices incur great incon venience. An alternativ e is thus to transfer power wirelessly , which virtually pro vides perpetual energy supplies. Hence, wireless power transfer (WPT) or wireless charging attracts great attention recently . Three major wireless charging technologies are surve yed in [1, 2]. Inductiv e coupling is safe and simple for implementa- tion. Howe ver , it is limited by a short charging distance from Q. Zhang, W . Fang, Q. Liu, J. W u, and P . Xia, are with the College of Electronic and Information Engineering, T ongji University , Shanghai, China, (email: anne@tongji.edu.cn, wen.fang@tongji.edu.cn, qing- wen.liu@gmail.com, wujun@tongji.edu.cn, pengfei.xia@gmail.com). L. Y ang is with the Department of Electrical and Computer En- gineering, Colorado State University , Fort Collins, CO 80523, USA (email:lqyang@engr .colostate.edu). * Corresponding author. I n t e r - D ron e C h a rg e D L C T ra n smi t t er - 2 D L C T r a n s mit t e r - 1 TV L a p t o p W a t ch C a me ra P h on e P ad D ron e - 1 D ron e - 2 P h o n e S e n s o r Fig. 1 Distributed Laser Charging Applications a few millimeters to centimeters, which is only suitable for contact-charging devices like toothbrush. Magnetic resonance coupling has high charging efficienc y . Howe ver , it is restricted by short charging distances and big coil sizes, which fits home appliances like TV . Electromagnetic (EM) radiation has long effecti ve charging distances. Ho wev er, it suffers from low charging efficienc y and is unsafe when the EM power density e xposure is high, hence is only fa vorable for lo w-power devices like sensors. In a nutshell, these traditional WPT tech- nologies provide great wireless charging abilities for different application scenarios, whereas it is still challenging to of fer sufficient power o ver long distance for safely charging IoT and mobile devices, e.g., smart-sensor , smart-phone, laptop, drone, etc., which usually need W att-le vel power over meter- lev el distances. T o support the po wer and distance requirements for IoT and mobile devices, a distributed laser charging (DLC) system is presented in [3], which could transfer 2-W att power over a 5-meter distance [4]. By using inductiv e coupling or magnetic resonance coupling, IoT and mobile de vices, say sensors and smart-phones, should typically be placed in a special charging cradle with a particular position. Howe ver , the DLC’ s self- aligning feature provides a more con venient way of charging IoT and mobile de vices without specific positioning or track- ing, as long as the transmitter and the receiv er are in the line of sight (LOS) of each other . Dif ferent from EM radiation, DLC’ s 2 wireless power transfer can be stopped immediately when this LOS is blocked by any object, which ensures the safety of DLC system. The size of the DLC recei ver is sufficiently small to be embedded in a sensor or a smart-phone. The DLC transmitter can be installed on the ceiling like a lightbulb . In addition, multiple de vices can be charged simultaneously by a single DLC transmitter [5–7]. Therefore, DLC can provide IoT and mobile de vices with safe WPT capability , which enables people to charge their devices with the similar experience as W iFi communications. Fig. 1 illustrates the DLC potential applications. In Fig. 1, in the room, DLC T ransmitter-1 is combined with a light- emitting diode (LED) array and become a DLC-equipped lightbulb . Thus Transmitter -1 can be con veniently installed on the ceiling, and then provide wireless power to IoT and mobile devices within its coverage. In the outdoor scenario, Drone-1 is equipped with a DLC transmitter , which can charge IoT and mobile de vices on demand. At the same time, a DLC receiver is also embedded in Drone-1. Thus, it can be remotely charged by DLC T ransmitter-2, which acts as the po wer-supply base station on the ground. In addition, Drone-2 equipped with both DLC transmitter and receiver can play the role of a relay to receiv e power from DLC T ransmitter-2 and transmit power to Drone-1 simultaneously . Similar to the maximization of the information trans- mission capacity of wireless channels in wireless information transfer (WIT), an important research topic in WPT is to maximize the power or ener gy tr ansmission efficiency [8]. The wireless charging efficiency of a DLC system is affected by many factors, including laser wa velength, electricity-to- laser conv ersion ef ficiency , laser transmission attenuation, and laser-to-electricity conv ersion ef ficiency [9–12]. In this pa- per , we focus our study on the modeling of DLC system and its performance ev aluation. In order to understand the fundamental mechanism of DLC system, we separate the DLC system into multiple conceptually independent modules. Thus, the corresponding power con version or transmission for each module can be in vestigated individually , considering the impacts of laser wav elength, transmission attenuation, and photov oltaic-cell (PV -cell) temperature. Finally , the maximum power transmission efficiency in closed-form can be obtained from this modular analysis. In this paper , a multi-module system model is proposed to describe the DLC system. The physical mechanism and mathematical formula are presented to describe the relation- ship between the stimulating electrical power and the output power , as well as the ef ficiency . The relationship between the supply power and the laser power , the relationship between the receiv ed laser po wer and the output power , and thus the rela- tionship between the output po wer and the supply power are all depicted by both analytical results and illustrative graphs. The relationship between the electricity-to-laser con version efficienc y and the supply power , the relationship between the laser-to-electricity conv ersion efficiency and the receiv ed laser power , and thus the relationship between the maximum power transmission ef ficiency and the supply po wer are captured by closed-form expressions as well as being illustrated by figures. As a result, this work not only provides the insight of DLC DL C T ra ns m it t er DL C Re ce iv e r I n t r a - ca v i t y L a s er P o we r Su ppl ier G a i n M edium PV + - P o we r O ut pu t E x t er na l - ca v i t y L a s er R eso na nt C a v it y R 2 ： 95 % Re f lec t iv it y E lec t ric it y - to - L a s er Co nv er s io n T ra n s m i t t er P o we r S u p p ly L a s er - to - E lec t ric it y Co n v ers io n Re ce i v er P o we r O ut pu t L a s er T ra n s mi s s i o n R 1 ： 1 0 0 % Ref lect iv it y Fig. 2 Distributed Laser Charging System Diagram DL C T ra ns m it t er DL C Re ce iv e r I n t r a - ca v i t y L a s er P o we r Su ppl ier G a i n M edium PV + - P o we r O ut pu t E x t er na l - ca v i t y L a s er R eso na nt C a v it y R 2 ： 95 % Re f lec t iv it y E lec t ric it y - to - L a s er Co nv er s io n T ra n s m i t t er P o we r S u p p ly L a s er - to - E lec t ric it y Co n v ers io n Re ce i v er P o we r O ut pu t L a s er T ra n s mi s s i o n R 1 ： 1 0 0 % Ref lect iv it y Fig. 3 Distributed Laser Charging System Model in theory , but also of fers the design guideline for DLC system implementation in practice. In the rest of this paper , we will first revie w the DLC system and present the multi-module system model. Then, we will illustrate the analytical modeling of each module to in vestigate the corresponding working principles. After that, we will ev aluate the performance of each module and deri ve the maximum DLC power transmission efficiency in closed- form. Finally , we will gi ve summarizing remarks and discuss open issues for future research. I I . D L C S Y S T E M DLC is a WPT technology based on the distributed res- onating laser presented in [3]. Traditional laser systems belong to the scope of inte grated resonating laser , since all optical components are integrated in one single device. Howe ver , in DLC systems, the optical components are divided into two separate parts, the transmitter and the receiv er , respecti vely . Therefore, the laser in DLC systems falls within the scope of distributed resonating laser . Fig. 2 shows the DLC system diagram described in [3]. A retro-reflector mirror R1 with 100% reflectivity and a gain medium are implemented at the transmitter . While in the recei ver , a retro-reflector mirror R2 with ex emplary 95% partial reflectivity is contained. R1, R2 and the gain medium consist the resonant ca vity , within which photons are amplified and form intra-ca vity resonating laser . Photons that pass through R2 generates the external-cavity laser . The external-ca vity laser power can be con verted to electrical power by a photov oltaic-panel (PV -panel) installed behind mirror R2, which is similar to a solar panel. Fig. 2 includes the power supplier at the transmitter and the power output at the receiv er for the comprehensiv e DLC system design. As specified in [3], in the DLC system, photons is amplified without concerning about the incident angle, as long as they trav el along LOS of R1 and R2. Hence, the intra- cavity laser generated by the resonator can be self-aligned without specific positioning or tracking. This feature enables users to charge their devices without placing them in a specific position cautiously . Besides self-alignment, the DLC system is intrinsically-safe, since objects blocking the line-of-sight 3 of intra-cavity laser can stop the laser immediately . These features offer DLC the capability of safely charging devices ov er long distance. Fig. 3 presents the system model to elaborate the wireless power transfer in the DLC system. This model illustrates a theoretical framew ork of power transfer by electricity-to- laser conv ersion, laser transmission, and laser-to-electricity con version. The physical fundamentals and mathematical for- mulations of this modular model will be specified in the following section. I I I . A N A L Y T I C A L M O D E L I N G In this section, we will discuss each module of the DLC model in Fig. 3 and describe its wireless power transfer mechanism analytically . At the DLC transmitter , the po wer supplier provides electrical power to generate the intra-cavity laser . W e will first introduce the electricity-to-laser conv ersion. Then, the intra-ca vity laser will trav el through the air and arriv e at the DLC receiv er . W e will discuss the intra-cavity laser po wer attenuation along its transmission. At the DLC receiv er , the intra-cavity laser will partially go through the mirror R2 and form the external-ca vity laser, then the external- cavity laser will be con verted into electricity by a PV -panel. W e will analyze this laser-to-electricity conv ersion based on the PV engineering. Finally , the PV -panel output electrical power can be used to charge electronics. Based on the above analytical modeling, we will obtain the power conv ersion and transmission efficiency of each module and the ov erall power transmission efficienc y . A. Electricity-to-Laser Con version At the DLC transmitter, the electrical power P s is pro- vided by the power supplier , which depends on the stimulating current I t and voltage V t as: P s = I t V t . (1) The supply power P s can stimulate the gain medium to generate laser . Thus, the electrical power can be conv erted to the laser po wer . W e denote P l as the external-ca vity laser power when the intra-cavity laser transmission ef ficiency is 100%. It is well-known that laser can be generated, only when I t provided by the po wer supplier is ov er a certain threshold [13]. In the laser diode physics, the laser power P l relies on I t . Their relationship can be depicted as [13]: P l = ζ hυ q ( I t − I th ) , (2) where ζ is the modified coef ficient, h is the Plunk constant, υ is the laser frequency , q is the electronic charge constant, and I th is the current threshold. Thus, the electricity-to-laser con version efficienc y η el can be figured out as: η el = P l P s . (3) PV - p a n e l I o P r V o Fig. 4 PV -panel Power Con version Circuit Model B. Laser T ransmission Laser power transmission attenuation means that laser power decreases along with its transmission through the air , which is similar to EM wa ve propagation power loss [14]. The laser po wer attenuation lev el depends on the transmission distance and air quality [15, 16]. Relying on the above laser- generation mechanism, the intra-cavity laser can transmit from the transmitter to the receiv er . During the transmission, laser may experience power attenuation. For simplicity , we assume that the laser diameter is a constant. This assumption could be validated by controlling aperture diameters of the DLC transmitter and receiv er [15]. The laser transmission efficienc y η lt can be modeled as [15]: η lt = P r P l = e − αd , (4) where P r is the external-ca vity laser po wer received at the DLC receiv er , α is the laser attenuation coefficient, and d is the distance. When d is close to zero, the laser transmission ef- ficiency approaches 100%. In this situation, P r is approximate to P l . α can be depicted as: α = σ κ  λ χ  − ρ , (5) where σ and χ are two constants, κ is the visibility , λ is the wav elength, and ρ is the size distribution of the scattering particles. ρ depends on visibility , which will be discussed later . C. Laser-to-Electricity Conver sion At the DLC receiv er, the external-cavity laser power can be con verted to electrical power . T o illustrate the laser -to- electricity con version mechanism, the single-diode equi valent T ABLE I T ransmission or Conv ersion Efficiency Parameter Symbol Electricity-to-laser conversion efficiency η el Laser transmission efficiency η lt Laser -to-electricity con version efficiency η le The overall DLC power transmission efficiency η o 4 0 2 4 6 8 Stimulating Current I t (A) 0 10 20 30 40 Power (W) I th = 0.5 A 3.5 4 4.5 5 5.5 Stimulating Voltage V t (V) Measured Supply Power P s Formula Laser Power P l Measured Laser Power P l Measured Voltage V t Fig. 5 Electricity-to-Laser Con version Power , V oltage and Current (810nm) circuit model of a PV -panel is depicted in Fig. 4 [17]. The PV - panel output voltage V o , and current I o can be characterized as [17]: I o = I sc − I s ( e V o /V m − 1) , (6) where I sc is the PV -panel short-circuit current, I s is the saturation current, i.e., the diode leakage current density in the absence of light, and V m is the “thermal voltage”, which can be defined as: V m = nk T q , (7) where n is the PV -panel ideality factor , k is the Boltzmann constant, and T is the absolute PV -cell temperature. Then, the PV -panel output power P o , which relies on I o and V o , can be obtained as: P o = I o V o . (8) Therefore, the laser -to-electricity con version efficienc y , i.e. the PV -panel con version efficienc y , η le depends on P o and P r , which can be depicted as: η le = P o P r = I o V o P r . (9) In summary , the PV -panel conv erts the receiv ed laser power P r to the output power P o with the efficienc y η le . D. DLC P ower T ransmission Efficiency Based on the above analysis for each individual module of the DLC system model, the DLC po wer transmission efficienc y from the po wer supplier at the transmitter to the power output at the receiv er can be depicted as: η o = η el η lt η le . (10) The conv ersion or transmission ef ficiency of each module and the DLC power transmission efficienc y are listed in T able I. The numerical e valuation of the DLC system model will be presented in the next section. 0 2 4 6 8 Stimulating Current I t (A) 0 20 40 60 Power (W) I th = 0.6 A 0 5 10 15 Stimulating Voltage V t (V) Measured Supply Power P s Formula Laser Power P l Measured Laser Power P l Measured Voltage V t Fig. 6 Electricity-to-Laser Con version Power , V oltage and Current (1550nm) I V . N U M E R I C A L E V A L UA T I O N Based on the analytical modeling in the previous section, we can find that the DLC system efficienc y varies with laser wa velength, transmission attenuation and PV -cell temperature. Their impacts on the performance of each module as well as the o verall DLC system will be discussed in this section. The numerical ev aluation is implemented in MA TLAB and Simulink. A. Electricity-to-Laser Con version Electrical supply po wer P s provided by the po wer sup- plier at the transmitter depending on the stimulating current I t and voltage V t , as in (1). Based on the measurement of I t , V t , and thus P s , for the laser systems ( λ is 800-820nm and 1540-1560nm, respectiv ely) in [9, 10], the measured supply power P s , the measured laser po wer P l , the stimulating current I t , and the stimulating v oltage V t are shown for 810nm and 1550nm in Fig. 5 and Fig. 6, respectiv ely . From the dashed- lines for the measured laser power in Fig. 5 and Fig. 6, the modified coef ficient ζ in (2) can be determined and listed in T able II. Thus, from (2), the formulated laser power curves are giv en as the solid-lines in Fig. 5 and Fig. 6, respecti vely . T ABLE II Electricity-to-Laser Con version Parameters Parameter Symbol V alue 810nm 1550nm Boltzmann constant k 1 . 38064852 × 10 − 23 J /K Planck constant h 6 . 62606957 × 10 − 34 J · s Electronic charge constant q 1 . 6 × 10 − 19 C Laser wavelength λ 810 nm 1550 nm Laser frequency υ 3 . 7 × 10 14 H z 1 . 9 × 10 14 H z Stimulation current threshold I th 0 . 5 A 0 . 6 A Modified coefficient ζ 1 . 5 3 . 52 P l -P s curve fitting parameter a 1 0 . 445 0 . 34 P l -P s curve fitting parameter b 1 − 0 . 75 − 1 . 1 5 0 10 20 30 40 50 Supply Power P s (W) 0 5 10 15 20 25 Laser Power P l (W) Formulated Curve (810nm) Measured Curve (810nm) Formulated Curve (1550nm) Measured Curve (1550nm) Fig. 7 Laser Power vs. Supply Power 0 10 20 30 40 Supply Power P s (W) 0 10% 20% 30% 40% 50% Electricity-to-Laser Conversion Efficiency el 810nm 1550nm Fig. 8 Electricity-to-Laser Conv ersion Ef ficiency vs. Supply Power In Fig. 5 and Fig. 6, the relationship between P l and P s is illustrated in Fig. 7. W e adopt the linear formula to approximate this power con version as: P l ≈ a 1 P s + b 1 . (11) The measured and formulated curves in Fig. 7 depict the linear approximation between P l and P s based on (11), when the wa velength λ is about 810nm and 1550nm, respecti vely . W e can find that the fitting curves match the measurement very well in the giv en supply power and laser po wer range in Fig. 7. From (3) and (11), we can obtain the electricity-to-laser con version ef ficiency η el as: η el = P l P s = a 1 + b 1 P s . (12) The solid-line and dashed-line in Fig. 8 illustrate η el for 810nm and 1550nm, respectiv ely . The initial P s supply power threshold in Fig. 8 is corresponding to the current threshold 0 10 20 30 40 50 Distance d (km) 0 20% 40% 60% 80% 100% Laser Transmission Efficiency lt clear air (1550nm) clear air (810nm) haze (1550nm) haze (810nm) fog (1550nm) fog (810nm) Fig. 9 Laser T ransmission Efficiency vs. Distance I th for P l in Fig. 5 and Fig. 6. In Fig. 8, η el starts to increase dramatically from the initial supply power P s threshold and will reach the plateau as P s increases. The plateau of η el for 810nm laser is around 43%, which is higher than 31% for 1550nm laser . B. Laser T ransmission From (4) and (5), the laser po wer attenuation coefficient in transmission can be determined under three typical sce- narios, i.e., clear air , haze, and fog. For the three scenarios, the size distribution of the scattering particles ρ in (5) can be specified as [16]: ρ =    1 . 3 for clear air (6 k m ≤ κ ≤ 50 k m ) , 0 . 16 κ + 0 . 34 for haze (1 k m ≤ κ ≤ 6 k m ) , 0 for fog ( κ ≤ 0 . 5 k m ) , (13) where κ is the visibility . Along with ρ , the other attenuation parameters are listed in T able III. Thus, the relationship between η lt and the trans- mission distance d can be obtained from (4) and (5), which is illustrated in Fig. 9. It is clear that η lt decays exponentially to zero as d increases. Meanwhile, for the same laser wav elength, laser po wer attenuation depends on the visibility κ . Laser power attenuation increases when κ decreases. As can be seen in Fig. 9, for clear air , haze and fog, given the same d , the laser power attenuation for short-wav elength is more than that of long-wa velength. For clear air and haze, laser attenuation for 810nm is much more than that of 1550nm. Howe ver , for fog, since ρ takes 0 for both 810nm and 1550nm, the coefficient T ABLE III Laser T ransmission Parameters Parameter V alue Clear Air Haze Fog σ 3 . 92 χ 550 nm κ 10 km 3 km 0 . 4 k m ρ 1 . 3 0 . 16 κ + 0 . 34 0 6 0 10 20 30 40 50 60 70 80 90 PV-panel Output Voltage V o (V) 0 40 80 120 PV-panel Output Current I o (mA) P r = 1 W P r = 5 W P r = 10 W P r = 15 W Fig. 10 PV -panel Output Current vs. V oltage ( λ = 810nm) 0 10 20 30 40 50 PV-panel Output Voltage V o (V) 0 50 100 150 200 PV-panel Output Current I o (mA) P r = 1 W P r = 5 W P r = 10 W P r = 15 W Fig. 11 PV -panel Output Current vs. V oltage ( λ = 1550nm) α has the same value. Therefore, the laser attenuation in fog does not dependent on λ . C. Laser-to-Electricity Conver sion At the DLC receiv er, PV -panel takes the role of con- verting laser po wer to electrical power . PV -panel con version efficienc y relies on laser po wer, wav elength, and cell temper- ature. With reference to (6)-(7), we can obtain the PV -panel output current, voltage, and thus power , giv en the parameters listed in T able IV. Fig. 10-17 demonstrate their relationships for different laser wa velength using the standard solar cell Simulink model [18]. Fig. 10 shows the relationship between PV -panel output current I o and voltage V o with different input laser power , i.e., the e xternal-cavity laser po wer P r at the recei ver , for the GaAs-based PV -panel with 810nm laser at 25 ◦ C [19]. Similarly , Fig. 11 is for the GaSb-based PV -panel with 1550nm laser at 25 ◦ C [20]. The PV -panel output power P o can be deriv ed from the corresponding I o and V o based on Fig. 10 0 10 20 30 40 50 60 70 80 90 PV-panel Output Voltage V o (V) 0 2 4 6 8 PV-panel Output Power P o (W) P r = 1 W P r = 5 W P r = 10 W P r = 15 W Fig. 12 PV -panel Output Power vs. V oltage ( λ = 810nm) T ABLE IV Laser-to-Electricity Conv ersion Parameters Parameter Symbol V alue 810nm 1550nm Short-circuit current I sc 0 . 16732 A 0 . 305 A Open-circuit voltage V oc 1 . 2 V 0 . 464 V Irradiance used for measurement I r 0 36 . 5 W/cm 2 2 . 7187 W/cm 2 Laser frequency υ 3 . 7037 × 10 14 H z 1 . 9355 × 10 14 H z Quality factor n 1 . 5 1 . 1 Number of series cells N 72 PV -panel material GaAs-based GaSb-based Measurement temperature T 25 ◦ C 120 ◦ C Simulation temperature 0 ◦ C / 25 ◦ C / 50 ◦ C P m -P r curve fitting parameter a 2 0.546/0.541/0.537 0.543/0.498/0.453 P m -P r curve fitting parameter b 2 -0.213/-0.231/-0.249 -0.276/-0.299/-0.321 and Fig. 11. Thus, Fig. 12 and Fig. 13 depict the relationship between P o and V o for 810nm and 1550nm, respectiv ely . From Fig. 12 and Fig. 13, giv en P r , we can figure out the maximum output po wer, which is defined as the maximum power point (MPP) and marked by the dots on the corresponding output po wer curves. W e denote P m as the MPP of P o . From [21], P m is pro ved as the unique output po wer , i.e., the corresponding current and v oltage are unique, given the receiv ed laser power P r . For e xample, given P r = 10 W , the MPP is unique as 4.64W for 1550nm, which is depicted by the dots in Fig. 11 and 13. The corresponding unique I o and V o are 121.3mA and 38.3V , respectiv ely . In Fig. 10 and Fig. 11, given P r , I o keeps almost a constant when V o is belo w the MPP . Ho wever , I o drops rapidly 7 0 10 20 30 40 50 PV-panel Output Voltage V o (V) 0 2 4 6 8 PV-panel Output Power P o (W) P r = 1 W P r = 5 W P r = 10 W P r = 15 W Fig. 13 PV -panel Output Power vs. V oltage ( λ = 1550nm) 0 10 20 30 40 50 60 70 80 90 PV-panel Output Voltage V o (V) 0 20 40 60 80 PV-panel Output Current I o (mA) 0 ° C 25 ° C 50 ° C 73 74 75 76 67 69 71 Fig. 14 PV -panel Output Current vs. V oltage ( λ = 810nm) 0 10 20 30 40 50 PV-panel Output Voltage V o (V) 0 20 40 60 80 100 120 140 PV-panel Output Current I o (mA) 0 ° C 25 ° C 50 ° C Fig. 15 PV -panel Output Current vs. V oltage ( λ = 1550nm) 0 10 20 30 40 50 60 70 80 90 PV-panel Output Voltage V o (V) 0 1 2 3 4 5 6 PV-panel Output Power P o (W) 0 ° C 25 ° C 50 ° C 73 75 77 5 5.1 5.2 5.3 Fig. 16 PV -panel Output Power vs. V oltage ( λ = 810nm) 0 10 20 30 40 50 PV-panel Output Voltage V o (V) 0 1 2 3 4 5 6 PV-panel Output Power P o (W) 0 ° C 25 ° C 50 ° C Fig. 17 PV -panel Output Power vs. V oltage ( λ = 1550nm) 0 5 10 15 20 Received Laser Power P r (W) 0 2 4 6 8 10 12 Maximum Output Power P m (W) 0 ° C 25 ° C 50 ° C 17 17.5 18 9 9.2 9.4 Fig. 18 Maximum Output Power vs. Receiv ed Laser Po wer ( λ = 810nm) 8 0 5 10 15 Received Laser Power P r (W) 0 2 4 6 8 Maximum Output Power P m (W) 0 ° C 25 ° C 50 ° C Fig. 19 Maximum Output Power vs. Receiv ed Laser Po wer ( λ = 1550nm) when V o is over the MPP . For the same V o , I o increases when P r increases. When I o is close to zero, V o is the open-circuit voltage, which increases when P r increases. From Fig. 12 and Fig. 13, giv en P r , P o increases when V o increases until it reaches the MPP . Howe ver , P o drops dramatically when V o is abov e the corresponding voltage for MPP . For a gi ven voltage V o , the output power P o increases when the input laser power P r increases. Besides input laser power , PV -cell temperature also im- pacts the PV -panel output current, v oltage, and power . Giv en the three cell temperatures (0 ◦ C, 25 ◦ C, 50 ◦ C), for λ = 810nm and P r = 10W power , Fig. 14 and Fig. 16 depict the variation of I o and P o on different V o , respectively . Similarly , for λ = 1550nm and P r = 10W power , Fig. 15 and Fig. 17 show the PV -panel output I o , V o and P o for these cell temperatures. From Fig. 14 and Fig. 15, I o keeps almost as a constant when V o is belo w a certain value. Gi ven dif ferent cell tem- peratures, I o curves start dropping at different V o . The turning voltage is low when the temperature is high. From Fig. 16 and Fig. 17, P o is low when the temperature is high. Additionally , the MPP increases as the cell temperature declines. Based on the MPP dots in Fig. 10 and Fig. 12 for different P r and Fig. 14 and Fig. 16 for different cell temperatures, we can obtain the MPP dots in Fig. 18, which illustrates P m versus P r for 810nm. Similarly , Fig. 19 demonstrates P m versus P r for 1550nm. In order to ev aluate the relationship between P m and P r , we adopt the approximation formula by using the curve fitting method as: P m ≈ a 2 P r + b 2 , (14) where a 2 and b 2 are the linear curv e fitting coefficients for different wav elengths and cell temperatures, which are listed in T able IV. From Fig. 18 and Fig. 19, we can find that the approximate lines based on (14) matches the MPP dots very well. W e denote η lem as the maximum PV -panel con version efficienc y when P o is P m . Based on (9) and (14), η lem can 0 5 10 15 20 Received Laser Power P r (W) 0 10% 20% 30% 40% 50% 60% Maximum Laser-to-Electricity Conversion Efficiency lem 0 ° C 25 ° C 50 ° C 15 20 25 52% 53% 54% Fig. 20 Maximum Laser-to-Electricity Con version Efficienc y vs. Receiv ed Laser Power ( λ = 810nm) 0 5 10 15 Received Laser Power P r (W) 0 10% 20% 30% 40% 50% 60% Maximum Laser-to-Electricity Conversion Efficiency lem 0 ° C 25 ° C 50 ° C Fig. 21 Maximum Laser-to-Electricity Con version Efficienc y vs. Receiv ed Laser Power ( λ = 1550nm) be depicted as: η lem = P m P r = a 2 + b 2 P r . (15) Fig. 20 and Fig. 21 show ho w η lem varies with the receiv ed laser power P r for 810nm and 1550nm, respectively . From Fig. 20 and Fig. 21, the changing trend of η lem is similar with that of η el in Fig. 8. η lem is low when cell temperature is high. The impact of cell temperature on η lem is bigger for 1550nm than that of 810nm, comparing Fig. 20 and Fig. 21. D. DLC P ower T ransmission Efficiency The relationship between the laser po wer P l and the sup- ply power P s is demonstrated by (11), when the transmission distance d is close to zero in the electricity-to-laser con version. The relationship between P l and the receiv ed laser po wer P r due to laser transmission is illustrated in (4). The relationship between P r and the maximum PV -panel output power P m in 9 0 10 20 30 40 Supply Power P s (W) 0 2 4 6 8 10 Maximum Output Power P m (W) 0 ° C, lt =100% 25 ° C, lt =100% 50 ° C, lt =100% 0 ° C, lt =50% 25 ° C, lt =50% 50 ° C, lt =50% 39.5 40 40.5 41 8.8 9 9.2 39 40 41 4.3 4.4 4.5 Fig. 22 Maximum Output Po wer vs. Supply Power ( λ = 810nm) 0 10 20 30 40 Supply Power P s (W) 0 2 4 6 8 Maximum Output Power P m (W) 0 ° C, lt =100% 25 ° C, lt =100% 50 ° C, lt =100% 0 ° C, lt =50% 25 ° C, lt =50% 50 ° C, lt =50% Fig. 23 Maximum Output Po wer vs. Supply Power ( λ = 1550nm) 0 10 20 30 40 Supply Power P s (W) 0 5% 10% 15% 20% 25% Maximum Power Transmission Efficiency om 0 ° C, lt =100% 25 ° C, lt =100% 50 ° C, lt =100% 0 ° C, lt =50% 25 ° C, lt =50% 50 ° C, lt =50% 29 30 31 21.5% 22% 22.5% 29 30 31 10.4% 10.6% 10.8% Fig. 24 Maximum Po wer T ransmission Efficiency vs. Supply Power ( λ = 810nm) 0 10 20 30 40 Supply Power P s (W) 0 5% 10% 15% 20% Maximum Power Transmission Efficiency om 0 ° C, lt =100% 25 ° C, lt =100% 50 ° C, lt =100% 0 ° C, lt =50% 25 ° C, lt =50% 50 ° C, lt =50% Fig. 25 Maximum Po wer T ransmission Efficiency vs. Supply Power ( λ = 1550nm) 0 5 10 15 20 25 30 35 Distance d (km) 0 5% 10% 15% 20% 25% Maximum Power Transmission Efficiency om 0 ° C, 810nm 25 ° C, 810nm 50 ° C, 810nm 0 ° C, 1550nm 25 ° C, 1550nm 50 ° C, 1550nm 1.8 2 2.2 14% 14.5% 15% Fig. 26 Maximum Power T ransmission Efficiency vs. Distance (Clear Air) 0 1 2 3 4 5 6 Distance d (km) 0 5% 10% 15% 20% 25% Maximum Power Transmission Efficiency om 0 ° C, 810nm 25 ° C, 810nm 50 ° C, 810nm 0 ° C, 1550nm 25 ° C, 1550nm 50 ° C, 1550nm 0.7 0.75 0.8 11% 11.5% 12% Fig. 27 Maximum Power T ransmission Efficiency vs. Distance (Haze) 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Distance d (km) 0 5% 10% 15% 20% 25% Maximum Power Transmission Efficiency om 0 ° C, 810nm 25 ° C, 810nm 50 ° C, 810nm 0 ° C, 1550nm 25 ° C, 1550nm 50 ° C, 1550nm 0.095 0.1 0.105 8% 8.25% 8.5% Fig. 28 Maximum Power T ransmission Efficiency vs. Distance (Fog) the laser-to-electricity conv ersion is shown in (14). Thus, from (11), (4) and (14), we can obtain the relationship between P s at the transmitter and P m at the receiv er as: P m = a 2 η lt P l + b 2 = a 1 a 2 η lt P s + ( a 2 b 1 η lt + b 2 ) . (16) Fig. 22 depicts the linear relationship between P m and P s for η lt = 100% and η lt = 50%, respectiv ely , when PV -cell temperature is 0 ◦ C, 25 ◦ C, 50 ◦ C, and λ = 810nm. Meanwhile, Fig. 23 illustrates the similar circumstances for λ = 1550nm. From (10), we denote η om as the maximum power transmission efficiency , when P o is P m , i.e. η le approaches η lem . From (3), (4), (9), (10), (12) and (15), the maximum power transmission efficienc y η lem can be obtained as: η om = η el η lt η lem = η el η lt ( a 2 + b 2 η el η lt P s ) = a 1 a 2 η lt + a 2 b 1 η lt + b 2 P s = a 1 a 2 e − αd + a 2 b 1 e − αd + b 2 P s . (17) Fig. 24 shows the relationship between η om and P s when η lt are 100% and 50% and cell temperatures are 0 ◦ C, 25 ◦ C, and 50 ◦ C for 810nm. Fig. 25 shows the same circumstances for 1550nm. η om raises up with P s increasing at first, then it reaches the plateau. The gro wth pattern of η om in Fig. 24 and Fig. 25 is similar as η el in Fig. 8 and η lem in Fig. 20 and Fig. 21. η om depends not only on the supply power P s but also on the distance d . Fig. 26 depicts the relationship between η om and d for dif ferent laser wav elength and PV -cell temperature, when P s = 40W and air quality is clear . Fig. 27 and Fig. 28 illustrate η om for the similar situation when air condition is haze and fog, respectiv ely . Fig. 29 describes ho w η om changes ov er η lt under clear air when P s is 40W . 0 20% 40% 60% 80% 100% Laser Transmission Efficiency lt 0 5% 10% 15% 20% 25% Maximum Power Transmission Efficiency om ° C ° C ° C ° C ° C ° C 63% 64% 65% 14% 15% Fig. 29 Maximum Power T ransmission Efficienc y vs. Laser T ransmission Efficienc y From Fig. 26 and Fig. 27, η om decreases when d in- creases. η om of 810nm laser is higher than that of 1550nm laser when d is short. Howe ver , η om for 810nm is lower than that of 1550nm when d is long. From Fig. 28, η om of 810nm laser alw ays keep higher than that of 1550nm laser until η om decrease to 0. At the same time, as described above, the cell temperature has bigger impact on η om for 1550nm than that of 810nm. From Fig. 29, η om increases linearly as η lt enhances based on (17). Fig. 29 provides a guideline of designing the DLC systems. For example, if 20% of DLC maximum trans- mission ef ficiency is expected, the 1550nm DLC system can not meet the requirement, howe ver , the 810nm DLC system is preferred. Meanwhile, when deploying the DLC system, the transmission ef ficiency at a certain distance pro vides the theoretical reference to determine the radius, i.e., the coverage, which is similar to the base station coverage analysis in mobile communications [22, 23]. Therefore, the maximum economic benefits can be obtained by minimizing the number of DLC transmitters to cov er a gi ven area [24]. This analysis provides a guideline for the efficient deployment of the DLC systems. In summary , the numerical ev aluation in this section validates the analytical model presented in Section III. At first, for the three modules: electricity-to-laser conv ersion, laser transmission, laser-to-electricity conv ersion, the con version or transmission ef ficiency of each module is quantitatively analyzed. Secondly , through numerical analysis, we obtain the approximate linear relationship between the supply po wer P s at the transmitter and the maximum PV -panel output power P m at the recei ver . Next, the maximum DLC power transmission efficienc y η om in closed-form is deri ved. Finally , based on the maximum power transmission ef ficiency , DLC system design and dev elopment guidelines are provided, for example, ho w to select the laser wa velength and determine the coverage of the DLC systems. 11 V . C O N C L U S I O N S This paper presents the distributed laser charging technol- ogy for wireless power transfer . The multi-module analytical modeling of distrib uted laser charging pro vides the in-depth view of its physical mechanism and mathematical formulation. The numerical ev aluation illustrates the power con version or transmission in each module under the impacts of laser wav e- length, transmission attenuation, and PV -cell temperature. The linear approximation is adopted and validated by measurement and simulation for electricity-to-laser and laser-to-electricity power con version. Thus the maximum power transmission efficienc y in closed-form is deriv ed and its performance de- pending on the supply power , laser wav elength, transmission distance, and PV -cell temperature is illustrated by figures. Therefore, this paper not only provides the theoretical insight, but also offers the practical guideline in system design and deployment of distributed laser charging. Due to the space limitation, there are serval important issues unaddressed in this paper and left for our future work, some of which are briefly discussed here: • The PV -panel efficiency used in the DLC system is about 50%, which is not much efficient. More studies on the PV -panel types, the ef ficiency analyzation, and the total efficienc y of the DLC system could be improved in the future. • Only 810nm and 1550nm laser wavelengths are consid- ered in this paper . W ider range of wav elengths can be studied to make the DLC system more uni versal in the future work. • T o conv ert the PV -panel output current and voltage to different preferred charging current and voltage for dif- ferent applications, the circuit or device that can conv ert a source of direct current from one voltage lev el to another is worth to be discussed in the future. • The point-to-point charging procedure is well illustrated in this paper . On this basis, the accessing protocols, the scheduling algorithms, the influencing factors of po wer con version and transmission, and the system optimiza- tion for charging batteries adaptively in the the point- to-multiple-point wireless char ging scenario should be another interesting topic to discuss. • Since point-to-multiple-point wireless po wer transfer is naturally supported by distributed laser charging systems, the network architecture of WPT becomes an interesting research topic worthy of further inv estigation. The related protocols and algorithms to effecti vely operate WPT networks could be dev eloped, e.g., WPT network access protocols, WPT scheduling algorithms and so on [1]. • It is interesting to in vestigate the potential simultaneous wireless information and power transfer (SWIPT) in dis- tributed laser charing systems. 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