Design and implementation of an efficient WPT system

ABSTRACT


INTRODUCTION
In the last years, the enhancing technology of power transfer (WPT) develops quickly. The mobiles or other electronic devices such as laptops or electrical vehicles could be charged by WPT technology. These techniques could be used in places when wiring is difficult to be accomplished [1][2][3][4][5]. Long-range concept of WPT had been formulated after microwave amplifier invention for high power purposes. The possibility of power transmission via electromagnetic waves gained more and more intention for application purposes [6,7]. The works curried out by [7,8] present analytical models for calculating the mutual inductance between planar spiral coils. These models are very useful in the design and optimization of wireless power transfer systems. The proposed models of mutual inductances between coils were derived using the solution of Neumann's integral. An approximate formula for determining the self-resistance of a circular multi-loop inductor having unequal pitches was introduced by [9]. Both proximity and skin effects were included in the suggested formula. Proximity effect was determined using the magnetic fields exerted on a wire due to other wires.
The study conducted by [10] analyzed with a context of non-ferromagnetic metallic plate, the WPT performances. The model of the WPT impedance in the metal environment was built. The proposed system in [11]  between the transmitting and receiving sides, the power was switched to one loop of the inductors for power transmission and power reception.
A WPT system of 13.56 MHz was introduced by [12] and investigated both theoretically and experimentally in addition to simulation. A relative high improvement in efficiency of about 41.7% was achieved. Three phase angles had been designed and analyzed in [13]. Single power amplifier on the primary side and two power amplifiers were located at the secondary side. The proposed multi-degrees method of phase control was capable of achieving simultaneously additional compensation of the reactance, output regulation, and load transformation.
A consistent optimization technique was conducted by [14] for WPT systems equipped with passive element's enhancement beginning from simple reflectors, intermediate relays, and general electromagnetic focusing and guiding structures, like metamaterials and metasurfaces. The proposed work efficiently solved the problem of optimization using arbitrary numbers of passive elements.
The work conducted by [15] presented and explained the published techniques and principles concerning all aspects of inductive link design processes such that no specific preceding information about inductive link designs are required. The work in [16] introduced accurate formulas for calculating mutual inductance between spiral coils using Gaussian integration method. The researches introduced by [17][18][19][20][21][22] concern enhancing coupling coefficients in different environments of inductive links in addition to applications of WPT technologies in contactless electrical vehicles and energizing medical sensors.
In this work, poor efficiency of conventional wireless powering process is enhanced by strengthening the mutual coupling along with power transmission path and conditioning the receiving circuit such that it accomplishes maximum power reception to load node.

Design of the proposed efficient WPT system
The inductive mutual coupling Mab between two 1-turn planar spiral coils is shown in Figure 1a. The mutual inductance between these two coils is given by [7] ⁄ 1 (1) Where, a and b are the outer radii of the first and second coils, respectively. µ0 is the permeability of free space and z is the distance between the centers of the two coils, which are aligned coaxially. For multi-turns planar spiral coils, (1) can be modified to Where, N1 and N2 are the numbers of turns of the first and second coils, respectively. If two inductively coupled coils are forming a resonant inductive link shown in Figure 1b, then the link currents and voltages at resonance frequency can be given by , ≫ Where, L1 and L2 are self-inductances of the first and second coils, respectively. M12 is the mutual inductance between the two coils. R1 and R2 are the AC resistances of the first and second coils, respectively. C1 and C2 are the tuning capacitances of the sending (transmitting) and receiving circuits, respectively, whereas ω0=2πf0 is the inductive link operating angular frequency. Rrefl is defined by The output voltage V2 is determined by The link input power Pi, output power P0, and efficiency η can be given by , ≫ Where, Q1, Q2, and QL are the quality factors of the first coil, second coil, and load, respectively at resonance frequency f0. Q1, Q2, and QL are defined by ω0L1/R1, ω0L2/R2, and RL/ω0L2, respectively. k12 is the coefficient of coupling between the two coils and is defined by (12) For loosely coupled inductive link (11) can closely be approximated to According to (11), the efficiency of WPT process is directly proportional to the square of the coupling coefficient. The proposed efficient WPT system can be depicted by block diagram of Figure 2.  It is obvious that the proposed system shown in Figure 2 comprises four series WPT systems. In this work, three resonating coils are inserted on the path joining the transmitting and receiving coils. The locations of resonating coils are selected such that maximum power is transferred between each two adjacent coils. Figure 3 shows the alignment of coils in the proposed inductive link. The first coil from the left is L1, which represents the transmitting coil and its distance z12 from the second coil L2 (first resonator coil) is 156cm. At 227cm to the right of the first resonator is located the third coil L3 (second resonator coil), whereas the fourth coil L4 (third resonator coil) is located at 140cm to right of the second resonator. Three similar receiving coils L5, L6, and L7 are oriented 50cm to the right of the third resonator and each adjacent coils are 20cm apart. The transmitting coil is shown in Figure 4a. It is wound with 12.667 turn's copper pipe having an outer diameter of 19.05 mm and wall thickness of 0.91mm. The coil outer diameter is 62cm, whereas its inner diameter is 12cm. The first resonator shown in Figure 4b is a planar spiral coil wound with 5.5 turn's copper pipe having outer diameter of 19.05 mm and wall thickness of 0.91mm. The coil outer and inner diameters are 150cm and 30cm, respectively. The second resonator shown in Figure 4c is a planar spiral coil wound with 7.25 turn's copper pipe having outer diameter of 6.35 mm and wall thickness of 0.71mm. The coil outer diameter is 110cm and its inner diameter is 20cm. The third resonator shown in Figure 4d is a conical coil wound with 9.25 turn's copper pipe, which has an outer diameter of 19.05 mm and wall thickness of 0.91mm. The coil outer and inner diameters are 72cm and 20cm, respectively. The coil length is 68cm. The receiving circuit is shown in Figure 5. It is composed of three similar planar spiral coils connected in parallel. Each coil is wound with 6 turn's copper pipe having outer diameter of 6.35 mm and wall thickness of 0.71mm. The coil outer and inner diameters are 33.5cm and 6cm, respectively. The coils in the proposed WPT system are wound with pipe conductors in order to decrease their AC resistances by decreasing the skin effect, which has great impact on the quality factors of coils. Decreasing the AC resistances of coils increases the coils quality factor, which in turn increases the link efficiency governed by (11) or (13), which is applicable for loosely coupled inductive links. The proposed WPT system depicted in Figure 2 can be schematically represented by the circuit shown Figure 6. In this Figure, R1, R2, R3, R4, R5, R6, and R7 are the AC resistances of the coils L1, L2, L3, L4, L5, L6, and L7, respectively. C1, C 2, C 3, C 4, and C 5 are tuning capacitors of transmitting, first resonator, second resonator, third resonator, and receiving circuits, respectively. Each M represents the mutual inductance between two certain coils. For example M12 represents the mutual inductance between L1 and L2. M12 is equal to M21 (M12=M21) and this is applicable for each two coils.  The inductances of planar spiral coils can be calculated by [15] . 0.2 Where, the average diameter is denoted by davg = 0.5(do+di). di and d0 are the inner and outer diameters of the coil, respectively, while β is the fill-factor, which is given by (15) The inductance of the conical coil shown in Figure 7 can be calculated as follows [23]: Where, n, di, s, and Y are coil number of turns, inner diameter, distance between two adjacent turns, and coil angle, respectively. Y and s are defined by  (16) to (18) gives Lcon=22 µH. The DC resistances of all coils in the proposed WPT system can be calculated by (19) Where, lC, σCu, w, and wth, are the coil length, conductivity of copper, outer diameter of coil pipe conductor, and wall thickness of the pipe. The calculated inductances and DC resistances are listed in Table 1. The mutual inductances between coils can be calculated using (3). The coefficients of coupling between coils are calculated according to (12). The calculated mutual inductances and their corresponding coefficients of coupling are listed in Table 2. The AC resistance RAC of a coil wound with copper conductors can be calculated by [24] (20) Where, RDC, σCu, w, and δCu are the DC resistance of the coil, conductivity of copper, outer diameter of the coil conductor, and copper skin depth at f0. Respectively. Applying (20) using the conductor outer diameters and calculated DC resistance in Table 1, the AC resistances of all coils are calculated and listed in Table 3.   Since the transmitting coil (L1) and the three resonating coils (L2, L3, and L4) are operating within loosely coupled conditions, then the tuning capacitors C2, C3, and C4 shown in Figure 6 can be determined as 9.25nF, 7.5345nF, and 10.034463nF, respectively.The circuit elements C1 and L1 in Figure 6 are parts of the output circuit of the class-E power amplifier, which represents the power transmitter of the proposed efficient WPT system. The series combination formed by C1 and L1 Are designed to resonate at a frequency slightly less than f0 and their equivalent impedance at the resonance frequency f0 is R1+jX, where X is defined by [25] 1.152 (22) Where, R represents the resistive load of class-E power amplifier and can be determined by (23) The tuning capacitor C5 of the receiving coils shown in Figure 6 can be approximately determined in a different procedure. Figure 8 models the receiving coils without C5 and RL. Since the receiving circuit is symmetrical around the branch including L6, then I5=I7 and I6=-2I5. Consequently, the impedance ZRCV of the parallel-connected receiving coils can be determined by Where, I1, I 2, I 3, I 4, I 5, I 6, and I 7 are the currents flowing through coils L1, L2, L3, L4, L5, L6, and L7, respectively. Since, L1 and C1 are parts of the class-E driving power amplifier and resonate at a frequency slightly less than the link resonance frequency f0, the inductive reactance X represents their equivalent reactance at f0. Z55, Z56, Z57, Z65, Z66, Z67, Z75, Z76, and Z77 are defined by According to the block diagram of the overall proposed WPT system, there are four series WPT systems namely WPT1, WPT2, WPT3, and WPT4. The first three systems WPT1, WPT2, and WPT3 are loosely coupled systems due to the relatively large distances between their transmitting and receiving coils, thus the first WPT system (WPT1) can be analyzed separately from other systems. Figure 9 shows the model of the resonant inductive link corresponding to WPT1 system. At resonance frequency f0, the reflected resistance Rrefl from the secondary side (first, second, and third resonators) in the primary side (transmitting coil) is determined according to Equation (7) as 1.56Ω. V´ in Figure 9 represents the voltage across the resistive load of class-E power amplifier. According to [25], V´ has an amplitude of Vom and phase of φ=-32.4 0 . The maximum possible value of Vom is 1.074VDD=1.074×12V=12.888V, thus the voltage Vi can be determined by Substituting all calculated mutual inductances, coil's self-inductances, coil's AC resistances, X, and C5 into (26) and (27) gives  Figure 9. Modeling of the first WPT system (WPT1). (32) % 100% .

100%
(33) The above overall link efficiency corresponds to wirelessly energizing a load circuit located at 6.61m from the power source taking into account strengthening the inductive coupling environment and conditioning the power receiving circuit for maximum power reception. If only one receiving coil is used and located at the same distance from the power source without using resonators for strengthening the inductive coupling, then according to (13), the efficiency for single coil receiving circuit without using resonators is calculated at RL=130Ω as follows: The overall link efficiency of the proposed system at a load of 130Ω is calculated as To show the significance of the efficiency enhancement processed in this work, what is known as the efficiency gain Geff adopted here reflects this as follows: . .

241.184
(36) Many techniques are exploited in the design of the WPT transmitter to target relatively remote electrical nodes required to be wirelessly energized. The most efficient technique is class-E power amplifier, which is a switch mode power amplifier characterized by high efficiency and high power. Therefore such kind of power amplifiers are recommended to be adopted in the design of WPT systems. Figure 10 shows the PSpice design of the proposed efficient WPT system.
The class-E power amplifier in the proposed system is loaded by an RLC combination composed of a series RLC circuit represented by C1, L1, and R1 shunted by a capacitor CSH. L1 and R1 represent the inductance and AC resistance of the transmitting coil, respectively. C1 is a tuning capacitor resonates with L1 at a frequency slightly less than f0, whereas CSH resonates with the series RLC (C1, L1, and R1) circuit at f0. Using (22) at an operating frequency of 338.6 kHz, C1 is calculated as 4.8631nF. CSH is determined by [25]

RESULTS AND DISCUSSION
The proposed efficient WPT system was first designed on PSpice, tested, and then practically implemented, thus in this work, there are simulative results, which are validated by experimental results.

Simulation results
The MOSFET triggering voltage signal VS is a square wave voltage having a 338.6 kHz frequency and ±10V voltage levels. The DC current IDC of the system power amplifier and the output received voltage vo during 50Ω resistance are shown in Figure 11(a). The DC input current is about 2.5A and the output received AC voltage is about 5.36V peak value. The system input power is IDCVDC, which is equal to   2.5A×12V=30W, while the received output AC power can be calculated as 0.5(vop) 2 /RL=0.5(5.36V) 2 /50Ω= 0.29W. Here vop represents the peak value of vo. Thus the overall system efficiency can be calculated as (0.29W/30W)×100%=0.967%. Figure 11(b) shows the AC currents i1, i2, i3, and i4, which are respectively corresponding to transmitting coil, first, second, and third resonator's currents during loading the proposed WPT system with 50Ω resistance. The results reveal the peak values of the AC currents i1, i2, i3, and i4 of 8.6A, 10.81A, 6.29A, and 5.2A, respectively. Figure 11(c) shows the receiving coil's currents i5, i6, and i7, in addition to the receiving tuning capacitor current i8 during loading the proposed WPT system with 50Ω resistance. The results reveal peak values of the AC currents i5, i6, and i7 of 0.516A, 0.4085A, and 0.409A, respectively. Figure 11(d) shows the AC voltages v1, v2, v3, and v4 which are respectively corresponding to the transmitting coil, first, second, and third resonators during loading the proposed WPT system with 50Ω resistance. The results reveal peak values of the AC voltages v1, v2, v3, and v4 of 858.4V, 550V, 390V, and 240V, respectively.
(a) (b) (c) (d) Figure 11. The proposed WPT system currents and voltages during 50Ω load. (a) DC input current and the received AC voltage, (b) the transmitting coil, first, second, and third resonator's currents, (c) the transmitting coil, first, second, and third resonator's voltages, (d) the receiving currents.
The overall WPT system was extra tested at different loading conditions Table 4 summarizes the efficiency changes as load resistance varied from 12.5Ω to 125Ω, while Figure 12 shows a graph reflecting the efficiency changes with load variations.

Experimental results
The results introduced here are reflecting the performance of the whole proposed system during energizing a 50Ω resistive load, lighting a LED, and charging 1.2V rechargeable battery. Figure 13(a) shows the oscilloscope reading of the transmitting coil and first resonator voltages, which have peak to peak values of 900V and 280V, respectively. The oscilloscope voltage gain for both channel are 10V/cm. The yellow reading corresponds to transmitter voltage, while the blue one corresponds to first resonator voltage. Figure  13(b) shows the oscilloscope reading of the second coil and third resonator voltages, which have peak to peak values of 188V and 96V, respectively. The oscilloscope voltage gain for both channel are 10V/cm and the yellow reading corresponds to first resonator voltage, while the blue corresponds to second resonator voltage. Figure 13(c) shows the oscilloscope reading of the receiving circuit voltage, which has peak to peak value of 2.56V during energizing 50Ω resistive load.
(a) (b) (c) Figure 13. The AC voltages of (a) the transmitting coil and first resonator, (b) second and third resonators, (c) receiving circuit during loading the proposed WPT system with 50Ω resistance. Figure 14(a) shows the oscilloscope reading of the receiving circuit voltage of 4.8V peak to peak during lighting a LED shown in Figure 14 Figure 15(a) shows the oscilloscope reading of the receiving circuit voltage, which has peak to peak value of 4.28V during charging a 1.2V rechargeable battery shown in Figure 15 Figure 16 shows the oscilloscope reading of the voltage of a receiving circuit having a single coil instead of three coils during 50Ω load. The oscilloscope reading is 1.28V peak to peak value. Figure 16. The voltage of a single coil receiving circuit in the proposed WPT system during energizing 50Ω resistive load. Figure 17 shows voltage and current readings of the DC power supply. The voltage reading is 12V DC, while the current reading is 1.9A DC. The input DC power is Pi=IDCVDC=1.9A×12V=22.8W, while the AC received power P0 for three coil receiving circuit is calculated as P0=0.25(vopp) 2 /RL=0.25(2.56V) 2 /50Ω=0.032768W. Therefore, the overall system efficiency is calculated as ηoverall=(P0/Pi)×100%= 0.144%. The received output power for single coil receiving circuit is 0.25(1.28V) 2 /50Ω=0.008192W. The system efficiency for single coil receiving circuit is 0.036%. Therefore, the proposed WPT system with three parallel connected receiving coils has an overall efficiency four times greater than that of a same system having single receiving coil. This means utilizing parallel connected coils in the receiving circuit significantly enhances the overall system efficiency.  The effects of resonators on received AC power are addressed in this work. Table 5 lists the received AC power and efficiency for all important cases of removing resonators from the circuit of the practical WPT system taking into account a DC input power of 22.8W, which is taken as reference power during the calculation of efficiency.

CONCLUSION
In this work, an adaptive efficient WPT system is introduced. This system is carried out on PSpice and validated experimentally. Both simulative and experimental WPT system have accomplished significant enhancement in efficiency. The proposed WPT systems has three resonators and three parallel connected identical receiving coils located at 6.61m from the power transmitter. The efficiency enhancement approaches thousands times the efficiency of a conventional WPT system having similar power transmitter located at the same distance from the receiving circuit, which has a single coil identical to those in the proposed efficient WPT system. The conclusions of this work are summarized in: Both simulative and practical systems have demonstrated that efficiency enhancement can be accomplished through inserting resonators along with energy transmission path. Both simulative and practical systems have demonstrated that efficiency enhancement can be accomplished through the modification of the receiving circuit using parallel connected receiving coils. More power can be received when the reactance of the equivalent receiving coil is much less than the load impedance. Energy transmission can approach distant nodes via inserting more resonators along the path toward the targeted node. Heavier power transmission requires lower frequency range, but bigger sending and receiving antennas.
Both systems show similar responses, which they differ in amounts, but exhibit similar behaviors. The differences in amounts are due to commercial tuning capacitors which have dielectric resistances responsible for causing significant reduction in the resonant currents in all resonator circuits.