A Three-Coil Inductively Power Transfer System with Constant Voltage Output

Abstract: For a traditional 2-coil system outputting constant voltage (CV), the transfer efficiency decreases drastically as transfer distance increases. To solve this problem, this essay proposes a 3-coil system which could achieve CV output and Zero Phase Angle (ZPA) conditions with specific parameter values. This 3-coil system could partly relief transfer efficiency fall at a long transfer distance, without any complicated controls. In order to achieve CV and ZPA condition, this essay devises the parameter values based on the decoupling 3-coil model, and a prototype is designed accordingly to verify these characteristics. With 10 cm transfer distance, output voltage deviation is 5.5% as the load varies from 12 Ω to 200 Ω, proving that the output voltage almost keeps constant with load change. Furthermore, with software simulation, a comparison experiment between the proposed 3-coil system and a Series-Inductor-Capacitor-Inductor (S-LCL) compensated 2-coil system is built to verify the efficiency improvement. The transfer distance change leads to the differentiation of voltage gain for both 2-coil and 3-coil systems. So, the input voltage for both systems and the compensated capacitor in receiver loop of the 3-coil system are manipulated for keeping 60 V output voltage on the 12 Ω load. With distance increasing from 10 cm to 20 cm, transfer efficiency varies from 92.61 to 48.9% for the 2-coil system, and from 92.89 to 84.26% for the 3-coil system, effectively proving the efficiency improvement. The experiment and simulation results prove the effectiveness of the proposed method.


Introduction
Wireless power transfer (WPT) technology can be roughly divided into far-field technology and near-field technology.Within near-field technology, inductive power transfer (IPT) is one of the most explored technology.It utilizes the magnetic field to transfer power [1][2][3][4], more convenient and safer than traditional plug-in power transfer system.It has the advantages of flexibility, and avoids the electric shock hazard.For application, IPT technology is largely implemented in biomedical implants, wearable electronics, electric automobiles and rail transport [5][6][7][8][9][10].Some applications require constant voltage (CV) for charging, for example, mobile phone [11][12][13][14].
Based on a 2-coil resonant tank, achieving CV output is available [15][16][17][18][19][20][21][22], some of which utilize the control method while others adopt elaborate topology.For instance, by implementing two dc-dc converters, where the boost converter after the rectifier circuit for impedance match and the buck converter before the inverter for input voltage conversion, voltage regulation could be performed by manipulating these two dc-dc converters [15].On the other hand, by using S-LCL topology could also achieving CV [22], which is open loop, has no interconnection between the transmitter and receiver, and easy to control.However, with 2-coil resonant tank, these power transfer methods fail for high efficiency when transfer distance increases, because the magnetic coupling, which plays an important role in power transfer, decreases drastically [23].To relieve the efficiency fall, one method is increasing the working frequency for a high quality factor of the coils so that the conduction loss caused by the coil resistance is reduced [24][25][26], although it was shown later that this method is not suitable for situations requiring a large amount of delivered power which is inversely proportional to frequency [24].Besides, the intermediate coil is another way for improving efficiency [27][28][29][30][31][32], which could create large magnetic coupling with the receiver thus only small current is needed in the primary driving circuit [27].The working mechanism for the relay coil is that it firstly receives the magnetic field from the transmitter coil and then transfers it to the receiver coil, apparently increases the coupling coefficient resulting a higher efficiency [28].The optimal coil geometries for a 3-coil IPT system could be found in [23].
These proposals obviously resolve the low transfer efficiency at large coupling distance, but these systems cannot output CV.Some researchers have noticed this problem, and explore how to achieve CV with a relay coil.For example, a 4-coil IPT system could successfully achieve CV when the working frequency is set to a specific value [24,31].The drawback of this method is that the output voltage involves a lot of variables; a slight change in the system variables may lead to the output voltage deviation.
To reduce the transfer efficiency fall at a larger coupling distance, as well as achieving CV with simple variables, this essay proposes a series-series (SS) compensated 3-coil IPT system.This essay is organized as follows: firstly, analyze the SS compensated 3-coil IPT model, and propose a method to design the parameter values to achieve CV.Besides the 3-coil system, a 2-coil system with S-LCL topology is used to compare the efficiency.Moreover, a prototype based on the 3-coil system is built to verify the feasibility for achieving CV.Finally, with software, the 2-coil system and the 3-coil system are simulated to compare the efficiency as distance changes.

Theoretical Analysis
This section mainly focuses on basic principles of the 3-coil system.For better analyses, this part is designed as follows: Section 2.1 introduces the 3-coil IPT system, its Section 2.1.1 will depict the fundamental configuration as well as Kirchhoff's voltage law (KVL) equations to facilitate later analysis.Section 2.1.2will explain voltage gain and the parameter design process that provides load-independent output voltage.Section 2.1.3will describe transfer efficiency for the proposed 3-coil system.Section 2.1.4will devise parameter values.Following Section 2.2 would illustrate the 2-coil parameter design.

Overview of the Series-Series 3-Coil IPT System
Figure 1 shows the configuration of the proposed series-series compensated 3-coil IPT system.The circuit consists of a constant voltage source E, a full-bridge inverter Q 1 -Q 4 for a square wave generator, a resonant tank including 3 coils: L 1 , L 2 , L 3 and their resonant capacitor C 1 , C 2 , C 3 , a full-bridge diode rectifier D 1 -D 4 and a load R L .L 1 , L 2 and L 3 represent the transmitter coil, the receiver coil and the relay coil, respectively.M ij (i, j = 1, 2, 3, i = j) means mutual-inductance between coil i and coil j.
Based on Figure 1, r s , r 1 , r 2 , r 3 are the parasite and winding resistance of the source, L 1 , L 2 and L 3 , respectively.Relationship between the inverter output voltage U in and the inverter input voltage E is U in = 2 √ 2E/π.Relationship between the rectifier input voltage U out and the load voltage (U RL ) is For facilitate analysis, the resonant tank circuit could be described in Equation (1) according to Kirchhoff's law.In Equation (1), Xi ( = 1,2,3) represents the imaginary component of equivalent impedance for loop i; Ii represents the current flowing through the loop i; ω represents the working efficiency, R represents the equivalent load, as = 8 / .

Voltage Gain and Methodology for CV Mode
This subsubsection illustrates the voltage gain of the proposed 3-coil system based on Equation (1).The voltage gain GV is defined as the ratio of the output voltage to the input voltage.For simplicity, X1 is set to 0, and the winding resistance ri (i = 1, 2, 3) and rs are neglected, they would be reconsidered in later subsubsection for transfer efficiency.
GV could be calculated as Equation ( 2), with the current derived from Equation (1).
Configuration of the proposed series-series compensated 3-coil IPT (inductive power transfer) system.

Equivalent Circuits and Fundamental Analysis
Figure 2 illustrates the resonant tank of the 3-coil system.Transmitter coil and relay coil are placed on a same plane.The geometric design is shown in Figure 2b: the red loop (Loop 1) is the transmitter coil, the green loop (Loop 2) is the receiver coil, the blue loop (Loop 3) is the relay coil, and the two grey square planes are ferrite bars, one below the transmitter and relay coil, and the other one above the receiver coil.For facilitate analysis, the resonant tank circuit could be described in Equation (1) according to Kirchhoff's law.In Equation (1), Xi ( = 1,2,3) represents the imaginary component of equivalent impedance for loop i; Ii represents the current flowing through the loop i; ω represents the working efficiency, R represents the equivalent load, as = 8 / .

Voltage Gain and Methodology for CV Mode
This subsubsection illustrates the voltage gain of the proposed 3-coil system based on Equation (1).The voltage gain GV is defined as the ratio of the output voltage to the input voltage.For simplicity, X1 is set to 0, and the winding resistance ri (i = 1, 2, 3) and rs are neglected, they would be reconsidered in later subsubsection for transfer efficiency.
GV could be calculated as Equation (2), with the current derived from Equation (1).For facilitate analysis, the resonant tank circuit could be described in Equation (1) according to Kirchhoff's law.In Equation (1), X i (i = 1, 2, 3) represents the imaginary component of equivalent impedance for loop i; I i represents the current flowing through the loop i; ω represents the working efficiency, R represents the equivalent load, as

Voltage Gain and Methodology for CV Mode
This subsubsection illustrates the voltage gain of the proposed 3-coil system based on Equation (1).The voltage gain G V is defined as the ratio of the output voltage to the input voltage.For simplicity, X 1 is set to 0, and the winding resistance r i (i = 1, 2, 3) and r s are neglected, they would be reconsidered in later subsubsection for transfer efficiency.
G V could be calculated as Equation (2), with the current derived from Equation (1).
It is shown in Equation ( 2) that if the D and B equals 0 simultaneously, G V will not change when the load R varies.Based on this principle, B and D should satisfy Equation (4).
It can be seen from the Equation ( 5) that voltage gain is load-independent now, achieving CV output with Equation (4), X 3 , which is the imaginary component of the equivalent impedance for loop 3, could be rewritten as Equation (6).
Z in , the equivalent impedance of the resonant tank, is defined as the ratio of input voltage to the input current, shown in Equation (8).
α, β are the real part and imaginary part of the input impedance of the resonant tank, respectively.To reduce the system's power loss, as well as the capacity requirement for the inverter, the Zero Phase Angle (ZPA) condition should be achieved, β should be set to 0. After some simple mathematical manipulations, X 2 , the imaginary component of the equivalent impedance for loop 2, is derived as Equation (9).
Implementing the new X 2 value, the equivalent impedance Z in is rewritten as Equation (10).
From Equation (10), it's obvious that the equivalent impedance of the resonant tank is pure resistive, avoiding the reactive power dissipation caused by inductor or capacitor, achieving ZPA condition and decreasing the system's power loss and the capacity requirement for the inverter.
Substituting Equation ( 9) into Equation (6), X 3 , the imaginary component of the equivalent impedance for loop 3, could be more concise as Equation (11).
Implementing Equation (9) to Equation (7), G V can be rewritten as Equation (12).Notice that as distance between transmitter and receiver coils varies, M 23 and M 13 also change.
To conclude this subsubsection, if the parameter values satisfy the relationship in Equation ( 9), (11) as well as X 1 = 0, the CV mode could be achieved, as well as ZPA condition.Besides, the G V could be measured with Equation (12).

Efficiency Analysis
This subsubsection illustrates the transfer efficiency for the proposed 3-coil system, with the consideration of the winding resistance r i (i = 1, 2, 3) and the source resistance r s , which are shown in Figure 2.
Figure 2 could be described as the decoupled circuit shown in Figure 3. r a , r b , r c is the reflected impedance from loop 2 to loop 1, from loop 3 to loop 1, from loop 2 to loop 3, respectively, and they are measured in Equation ( 13).
Energies 2018, 11, x FOR PEER REVIEW 5 of 13 Implementing Equation (9) to Equation ( 7), GV can be rewritten as Equation (12).Notice that as distance between transmitter and receiver coils varies, M23 and M13 also change.
To conclude this subsubsection, if the parameter values satisfy the relationship in Equation ( 9), (11) as well as = 0, the CV mode could be achieved, as well as ZPA condition.Besides, the GV could be measured with Equation (12).

Efficiency Analysis
This subsubsection illustrates the transfer efficiency for the proposed 3-coil system, with the consideration of the winding resistance ri (i = 1, 2, 3) and the source resistance rs, which are shown in Figure 2.
Figure 2 could be described as the decoupled circuit shown in Figure 3. ra, rb, rc is the reflected impedance from loop 2 to loop 1, from loop 3 to loop 1, from loop 2 to loop 3, respectively, and they are measured in Equation ( 13).Based on Figure 3, the transfer efficiency could be derived in Equation (14)., , represent the efficiency of loop 1, loop 2 and loop 3, respectively.
Transfer efficiency for the whole system is shown in Equation (15), which is the multiplication of the three efficiencies above.The components R1_23, R3_2 in the numerator are illustrated in Equation ( 16), and R represents the equivalent load, as = 8 / .

Parameter Value Design
This subsubsection illustrates how to design the parameter values for the proposed 3-coil system.Assuming that the voltage on the dc load RL is URL, and input dc voltage is E, the working efficiency is f and = 2π .Based on Equation (12), and the relationship between input voltage and output voltage of the inverter and the rectifier, Equation ( 17) is derived.Based on Figure 3, the transfer efficiency could be derived in Equation (14).η 1 , η 2 , η 3 represent the efficiency of loop 1, loop 2 and loop 3, respectively.
Transfer efficiency for the whole system is shown in Equation ( 15), which is the multiplication of the three efficiencies above.The components R 1_23 , R 3_2 in the numerator are illustrated in Equation ( 16), and R represents the equivalent load, as

Parameter Value Design
This subsubsection illustrates how to design the parameter values for the proposed 3-coil system.Assuming that the voltage on the dc load R L is U RL , and input dc voltage is E, the working efficiency is f and ω = 2π f .Based on Equation (12), and the relationship between input voltage and output voltage of the inverter and the rectifier, Equation ( 17) is derived.
We set U RL = 60 V and E = 120 V in the experiment of verifying the CV feasibility, where the distance between receiver and transmitter keeps 10 cm.According to Equation (17), the ratio of M 23 and M 13 is fixed as 0.5.Then the software ANSYS Maxwell (Ozen Engineering, Inc., Silicon Valley, Sunnyvale, CA, USA) is involved to design the coil size to meet M 23 /M 13 = 0.5, so that the three coils' size, turns, relative position, self-inductance L 1 , L 2 , L 3 as well as the mutual-inductance M 12 are all determined.
Based on aforementioned requirement X 1 = 0, C 1 in the transmitter coil is derived in Equation (18).
Based on Equation ( 11), C 3 in the relay coil is derived in Equation (20).
Based on Equation ( 9), C 2 in the receiver coil is shown in Equation ( 20).
As the capacitor values satisfy Equations ( 18)-( 20), the proposed 3-coil IPT system could achieve CV as well as ZPA condition.
The transfer distance change would lead to differentiation in mutual-inductance, so that the C 2 should be recalculated according to Equation (20).

Parameter Design for S-LCL Compensated 2-Coil System
Besides verifying the feasibility for CV of the aforementioned 3-coil system, a comparison experiment is also needed to prove that the 3-coil system has higher efficiency than that of 2-coil system as distance increasing.The methodology for designing parameter values in 2-coil system is illustrated in this Section 2.2.
The S-LCL topology of 2-coil circuit is shown in Figure 4.
Energies 2018, 11, x FOR PEER REVIEW 6 of 13 We set = 60 V and = 120 V in the experiment of verifying the CV feasibility, where the distance between receiver and transmitter keeps 10 cm.According to Equation ( 17), the ratio of M23 and M13 is fixed as 0.5.Then the software ANSYS Maxwell (Ozen Engineering, Inc., Silicon Valley, Sunnyvale, CA, USA) is involved to design the coil size to meet / = 0.5, so that the three coils' size, turns, relative position, self-inductance L1, L2, L3 as well as the mutual-inductance M12 are all determined.
Based on aforementioned requirement = 0, C1 in the transmitter coil is derived in Equation ( 18).
Based on Equation (11), C3 in the relay coil is derived in Equation ( 20).
Based on Equation ( 9), C2 in the receiver coil is shown in Equation ( 20).
The transfer distance change would lead to differentiation in mutual-inductance, so that the C2 should be recalculated according to Equation (20).

Parameter Design for S-LCL Compensated 2-Coil System
Besides verifying the feasibility for CV of the aforementioned 3-coil system, a comparison experiment is also needed to prove that the 3-coil system has higher efficiency than that of 2-coil system as distance increasing.The methodology for designing parameter values in 2-coil system is illustrated in this Section 2.2.
The S-LCL topology of 2-coil circuit is shown in Figure 4.The voltage gain GV for the 2-coil system shown in Figure 4 could be derived as Equation (21) based on [22].
For a fair and reasonable efficiency-comparing experiment, we adopted the principle mentioned in reference [33].For a 2-coil system, the power supply drives the transmitter coil and relay coil in series, so that the same copper volume is used in the coupling mechanism for both 2-coil system and The voltage gain G V for the 2-coil system shown in Figure 4 could be derived as Equation (21) based on [22].
For a fair and reasonable efficiency-comparing experiment, we adopted the principle mentioned in reference [33].For a 2-coil system, the power supply drives the transmitter coil and relay coil in series, so that the same copper volume is used in the coupling mechanism for both 2-coil system and 3-coil system.Besides, G V for both systems are designed to be the same value, which varies with transfer distance.G V could be determined with Equation (12).
The capacitor value C p1 in Figure 4 could be derived in Equation (22), based on Equation (21).
Based on Equation ( 22), Inductance values L P1 and L P2 could be measured with Equation (23).
Capacitors C 1 and C 2 resonant with L 1 and L 2 , respectively.Their values are shown in Equation (24).
If the requirements in Equations ( 22)-( 24) are satisfied, the S-LCL compensated 2-coil system could achieve CV as well as ZPA condition [22].

Experimental Analysis
In this experimental part, we firstly build a 3-coil system to test the feasibility for CV.Secondly, with software, we simulate the proposed 3-coil system with the S-LCL 2-coil system, to prove that the former one has higher efficiency as transfer distance changes.
To test the effectiveness of the CV of the 3-coil system, we build an experimental prototype shown in Figure 5a, which includes an oscilloscope (Agilent DSO-X3014T, Santa Clara, CA, USA) to record the experimental output waveforms and a power analyzer (PW6001, HIOKI, Nagano, Japan) to gauge the transfer efficiency between dc source and dc load.The transmitter and receiver coils are wound with Litz wires (0.1 × 400) as shown in Figure 5b.Parameter values are shown in Table 1.
In Figure 5b, loop 1 is the transmitter coil, which connects inverter comprising 4 MOSFETS (C2M0080120D, Cree, Durham, NC, USA); loop 2 is the receiver coil which connects rectifier including 4 diodes (DSEI2X61-06C, IXYS, Milpitas, CA, USA) and the electronic load (IT8518B, ITECH, NanJing, China), loop 3 is the relay coil to generate an enhanced magnetic flux for the power transfer to receiver [19].For size, the transmitter coil's outer diameter is 191.5 mm, the same as receiver coil, and the relay coil 300 mm.For relative position, the relay coil and the transmitter coil are remained in the same plane and same centered, the receiver is parallel with the transmitter and same centered; space between relay coil and transmitter is 40 mm, power transfer distance between receiver and transmitter keeps 100 mm in testing the constant voltage output characteristics of the 3-coil system.
Energies 2018, 11, x FOR PEER REVIEW 7 of 13 3-coil system.Besides, GV for both systems are designed to be the same value, which varies with transfer distance.GV could be determined with Equation (12).The capacitor value Cp1 in Figure 4 could be derived in Equation (22), based on Equation (21).
If the requirements in Equations ( 22)-( 24) are satisfied, the S-LCL compensated 2-coil system could achieve CV as well as ZPA condition [22].

Experimental Analysis
In this experimental part, we firstly build a 3-coil system to test the feasibility for CV.Secondly, with software, we simulate the proposed 3-coil system with the S-LCL 2-coil system, to prove that the former one has higher efficiency as transfer distance changes.
To test the effectiveness of the CV of the 3-coil system, we build an experimental prototype shown in Figure 5a, which includes an oscilloscope (Agilent DSO-X3014T, Santa Clara, CA, USA) to record the experimental output waveforms and a power analyzer ( PW6001, HIOKI, Nagano, Japan) to gauge the transfer efficiency between dc source and dc load.The transmitter and receiver coils are wound with Litz wires (0.1 × 400) as shown in Figure 5b.Parameter values are shown in Table 1.
In Figure 5b, loop 1 is the transmitter coil, which connects inverter comprising 4 MOSFETS (C2M0080120D, Cree, Durham, NC, USA); loop 2 is the receiver coil which connects rectifier including 4 diodes (DSEI2X61-06C, IXYS, Milpitas, CA, USA) and the electronic load (IT8518B, ITECH, NanJing, China), loop 3 is the relay coil to generate an enhanced magnetic flux for the power transfer to receiver [19].For size, the transmitter coil's outer diameter is 191.5 mm, the same as receiver coil, and the relay coil 300 mm.For relative position, the relay coil and the transmitter coil are remained in the same plane and same centered, the receiver is parallel with the transmitter and same centered; space between relay coil and transmitter is 40 mm, power transfer distance between receiver and transmitter keeps 100 mm in testing the constant voltage output characteristics of the 3coil system.To verify that the output voltage could keep constant as load varies, we change the load from 12 Ω to 200 Ω. Figure 6 shows the DC-DC efficiency and output voltage respectively while load varies.To verify that the output voltage could keep constant as load varies, we change the load from 12 Ω to 200 Ω. Figure 6 shows the DC-DC efficiency and output voltage respectively while load varies.From Figure 6, the maximum voltage is 63.85 V, the minimum voltage is 60.39 V. Obviously, constant voltage output is achieved with only 5.5% output voltage changing rate as load varies from 12 Ω to 200 Ω.It would show later in Figure 7 that when load varies from 12 Ω to 120 Ω, the voltage changing rate decreases to 5.1%.
Figure 7 shows the waveforms of voltage Vin output from the inverter, current Iin output from the rectifier, voltage VB on the load, current IB going through the load.Figure 7a shows these waveforms corresponding to 12 Ω, with VB = 60.39V and IB = 5.03 A, meaning that the output power is 303.76W, and the transfer efficiency is 90.58%.Figure 7b shows the waveforms corresponding to 120 Ω, with VB = 63.64 V and IB = 0.53 A, meaning that the output power is 33.62 W, and the transfer efficiency is 72.46%.Comparing these two working conditions, we can conclude that the voltage changing rate is 5.1%, almost achieving constant voltage output goal.From Figure 6, the maximum voltage is 63.85 V, the minimum voltage is 60.39 V. Obviously, constant voltage output is achieved with only 5.5% output voltage changing rate as load varies from 12 Ω to 200 Ω.It would show later in Figure 7 that when load varies from 12 Ω to 120 Ω, the voltage changing rate decreases to 5.1%.
Figure 7 shows the waveforms of voltage V in output from the inverter, current I in output from the rectifier, voltage V B on the load, current I B going through the load.Figure 7a shows these waveforms corresponding to 12 Ω, with V B = 60.39V and I B = 5.03 A, meaning that the output power is 303.76W, and the transfer efficiency is 90.58%.Figure 7b shows the waveforms corresponding to 120 Ω, with V B = 63.64 V and I B = 0.53 A, meaning that the output power is 33.62 W, and the transfer efficiency is 72.46%.Comparing these two working conditions, we can conclude that the voltage changing rate is 5.1%, almost achieving constant voltage output goal.To verify that the output voltage could keep constant as load varies, we change the load from 12 Ω to 200 Ω. Figure 6 shows the DC-DC efficiency and output voltage respectively while load varies.From Figure 6, the maximum voltage is 63.85 V, the minimum voltage is 60.39 V. Obviously, constant voltage output is achieved with only 5.5% output voltage changing rate as load varies from 12 Ω to 200 Ω.It would show later in Figure 7 that when load varies from 12 Ω to 120 Ω, the voltage changing rate decreases to 5.1%.
Figure 7 shows the waveforms of voltage Vin output from the inverter, current Iin output from the rectifier, voltage VB on the load, current IB going through the load.Figure 7a shows these waveforms corresponding to 12 Ω, with VB = 60.39V and IB = 5.03 A, meaning that the output power is 303.76W, and the transfer efficiency is 90.58%.Figure 7b shows the waveforms corresponding to 120 Ω, with VB = 63.64 V and IB = 0.53 A, meaning that the output power is 33.62 W, and the transfer efficiency is 72.46%.Comparing these two working conditions, we can conclude that the voltage changing rate is 5.1%, almost achieving constant voltage output goal.To prove that the 3-coil system could relieve efficiency falls better than the 2-coil system, we built an S-LCL compensated 2-coil system simulating model with the resonant tank shown in Figure 4.The magnetic simulations are run in ANSOFT Maxwell (Ozen Engineering, Inc., Silicon Valley, Sunnyvale, CA, USA), getting mutual-inductances and self-inductances.MATLAB/Simulink (2014a, Natick, MA, USA) was used to build the system, which could simulate the current and analyze the efficiency.
The coupling mechanism for the 3-coil system in Maxwell simulation is shown in Figure 2b.Coupling mechanism of the transmitter side for the 2-coil system is connecting transmitter coil and relay coil in series.Loop 3 and loop 1 is same centered, and the outer diameter for loop 3 is 300 mm, the gap between loop 1 and loop 3 is 40 mm; loop 1 and loop 2 both have 191.5 mm diameter.These 3 coils each has 10 turns, the winding resistance r1, r2, r3 is 0.18 Ω, 0.18 Ω, and 0.29 Ω respectively.Based on the waveforms of Figure 8, it's very clear that V in and I in correspond simultaneously to the MOSFET gate driving signal: as the MOSFET turn-on signal V GS goes high, V DS and I in both immediately respond, V DS drops almost to zero as I in starts flowing from drain terminal to source terminal of the MOSFET, proving that the output voltage V in and the output current I in are in the same phase, with no reactive power dissipation.
Figure 9 shows the transient waveforms of V in and I in V B and I B respectively, as switching load from 12 Ω to 50 Ω and inversely switching.It's clear that during the switching period, V B keeps almost constant, and waveforms of I in and V in have no obvious overshoot or undershoot, avoiding spike pulse and achieving stability.To prove that the 3-coil system could relieve efficiency falls better than the 2-coil system, we built an S-LCL compensated 2-coil system simulating model with the resonant tank shown in Figure 4.The magnetic simulations are run in ANSOFT Maxwell (Ozen Engineering, Inc., Silicon Valley, Sunnyvale, CA, USA), getting mutual-inductances and self-inductances.MATLAB/Simulink (2014a, Natick, MA, USA) was used to build the system, which could simulate the current and analyze the efficiency.
The coupling mechanism for the 3-coil system in Maxwell simulation is shown in Figure 2b.Coupling mechanism of the transmitter side for the 2-coil system is connecting transmitter coil and relay coil in series.Loop 3 and loop 1 is same centered, and the outer diameter for loop 3 is 300 mm, the gap between loop 1 and loop 3 is 40 mm; loop 1 and loop 2 both have 191.5 mm diameter.These 3 coils each has 10 turns, the winding resistance r1, r2, r3 is 0.18 Ω, 0.18 Ω, and 0.29 Ω respectively.To prove that the 3-coil system could relieve efficiency falls better than the 2-coil system, we built an S-LCL compensated 2-coil system simulating model with the resonant tank shown in Figure 4.The magnetic simulations are run in ANSOFT Maxwell (Ozen Engineering, Inc., Silicon Valley, Sunnyvale, CA, USA), getting mutual-inductances and self-inductances.MATLAB/Simulink (2014a, Natick, MA, USA) was used to build the system, which could simulate the current and analyze the efficiency.
The coupling mechanism for the 3-coil system in Maxwell simulation is shown in Figure 2b.Coupling mechanism of the transmitter side for the 2-coil system is connecting transmitter coil and relay coil in series.Loop 3 and loop 1 is same centered, and the outer diameter for loop 3 is 300 mm, the gap between loop 1 and loop 3 is 40 mm; loop 1 and loop 2 both have 191.5 mm diameter.These 3 coils each has 10 turns, the winding resistance r 1 , r 2 , r 3 is 0.18 Ω, 0.18 Ω, and 0.29 Ω respectively.Taking 10 mm steps, increasing transfer distance from 100 mm to 200 mm, the mutual-inductance between each coil for both systems got with ANSOFT Maxwell are show in Table 2, where subscription 1, 2 and 3 represent transmitter coil, receiver coil and relay coil, respectively; the changing trend is shown in Figure 10.Taking 10 mm steps, increasing transfer distance from 100 mm to 200 mm, the mutual-inductance between each coil for both systems got with ANSOFT Maxwell are show in Table , where subscription 1, 2 and 3 represent transmitter coil, receiver coil and relay coil, respectively; the changing trend is shown in Figure 10.To verify that the proposed CV model could reduce efficiency fall when transfer distance increases, we simulate the proposed 3-coil system (shown in Figure 1) and the S-LCL compensated 2-coil system (shown in Figure 4) with MATLAB/Simulink.The requirements for a 3-coil system are: setting the load resistance as 12 Ω, keeping the output voltage as 60 V by manually adjusting the input voltage.The requirements for 2-coil system are: setting the load resistance as 12 Ω, keeping the same input voltage as its 3-coil counterpart, adjusting parameter Lp1, Lp2, and Cp1 to keep 60 V output voltage.The simulation results are shown in Table 3.Where I1, I2 and I3 are the current flowing through transmitter coil, receiver coil and relay coil, respectively.To verify that the proposed CV model could reduce efficiency fall when transfer distance increases, we simulate the proposed 3-coil system (shown in Figure 1) and the S-LCL compensated 2-coil system (shown in Figure 4) with MATLAB/Simulink.The requirements for a 3-coil system are: setting the load resistance as 12 Ω, keeping the output voltage as 60 V by manually adjusting the input voltage.The requirements for 2-coil system are: setting the load resistance as 12 Ω, keeping the same input voltage as its 3-coil counterpart, adjusting parameter L p1 , L p2 , and C p1 to keep 60 V output voltage.The simulation results are shown in Table 3.Where I 1 , I 2 and I 3 are the current flowing through transmitter coil, receiver coil and relay coil, respectively.Based on data in Table 3, for the 2-coil system, currents (I 1 , I 2 ) versus transfer distance are drawn in Figure 11.It's obvious that as transfer distance increases, I 1 decreases firstly, but when the coupling coefficient becomes very week, loss of system becomes excessive large, resulting I 1 increases.For I 2 , it increases from 3.5 A to 39.7 A, leading to increasing loss and decreasing efficiency.
Based on data in Table 3, for the 2-coil system, currents (I1, I2) versus transfer distance are drawn in Figure 11.It's obvious that as transfer distance increases, I1 decreases firstly, but when the coupling coefficient becomes very week, loss of system becomes excessive large, resulting I1 increases.For I2, it increases from 3.5 A to 39.7 A, leading to increasing loss and decreasing efficiency.
For the 3-coil system, currents (I1, I2, I3) versus transfer distance are drawn in Figure 12  For the two systems, their efficiency trends are shown in Figure 13.It could be seen that as transfer distance increases, the efficiency decreases from 92.61 to 48.9% for the 2-coil system, and it decreases from 92.89 to 84.26% for the 3-coil system.Proving that the proposed model could improve the transfer efficiency as power transfer distance increases.For the 3-coil system, currents (I 1 , I 2 , I 3 ) versus transfer distance are drawn in Figure 12.It's clear that as transfer distance increases, I 1 decreases continually, I 2 keeps almost constant, and I 3 increases from 4.2 A to 11.3 A, leading to lower efficiency but better than that of 2-coil system.Based on data in Table 3, for the 2-coil system, currents (I1, I2) versus transfer distance are drawn in Figure 11.It's obvious that as transfer distance increases, I1 decreases firstly, but when the coupling coefficient becomes very week, loss of system becomes excessive large, resulting I1 increases.For I2, it increases from 3.5 A to 39.7 A, leading to increasing loss and decreasing efficiency.
For the 3-coil system, currents (I1, I2, I3) versus transfer distance are drawn in Figure 12.It's clear that as transfer distance increases, I1 decreases continually, I2 keeps almost constant, and I3 increases from 4.2 A to 11.3 A, leading to lower efficiency but better than that of 2-coil system.For the two systems, their efficiency trends are shown in Figure 13.It could be seen that as transfer distance increases, the efficiency decreases from 92.61 to 48.9% for the 2-coil system, and it decreases from 92.89 to 84.26% for the 3-coil system.Proving that the proposed model could improve the transfer efficiency as power transfer distance increases.For the two systems, their efficiency trends are shown in Figure 13.It could be seen that as transfer distance increases, the efficiency decreases from 92.61 to 48.9% for the 2-coil system, and it decreases from 92.89 to 84.26% for the 3-coil system.Proving that the proposed model could improve the transfer efficiency as power transfer distance increases.Based on data in Table 3, for the 2-coil system, currents (I1, I2) versus transfer distance are drawn in Figure 11.It's obvious that as transfer distance increases, I1 decreases firstly, but when the coupling coefficient becomes very week, loss of system becomes excessive large, resulting I1 increases.For I2, it increases from 3.5 A to 39.7 A, leading to increasing loss and decreasing efficiency.
For the 3-coil system, currents (I1, I2, I3) versus transfer distance are drawn in Figure 12  For the two systems, their efficiency trends are shown in Figure 13.It could be seen that as transfer distance increases, the efficiency decreases from 92.61 to 48.9% for the 2-coil system, and it decreases from 92.89 to 84.26% for the 3-coil system.Proving that the proposed model could improve the transfer efficiency as power transfer distance increases.

Conclusions
This essay proposes a SS compensated 3-coil IPT system to achieve CV and ZPA conditions, solving the efficiency decreasing problem in long distance coupling for the traditional 2-coil IPT system.This proposal has no complicated control circuit, and the output voltage only involves the ratio of mutual-inductances between the coils.In the CV verification experiment, the voltage change rate is 5.5% as the load varies from 12 Ω to 200 Ω, with 100 mm transfer distance.In the simulated comparing experiment, as transfer distance increases from 10 cm to 20 cm, transfer efficiency for 2-coil system decreases from 92.61 to 48.9%, for 3-coil system from 92.89 to 84.26%.The experiment results prove that the proposed prototype could achieve CV and that the 3-coil system has a higher efficiency than the 2-coil system when increasing transfer distance.Thus, the proposal is feasible and effective to achieve CV as well as ZPA conditions.

Figure 3 .
Figure 3. Decoupled circuit of resonant tank for the proposed 3-coil system.

Figure 3 .
Figure 3. Decoupled circuit of resonant tank for the proposed 3-coil system.

Figure 5 .
Figure 5. (a) Prototype of the 3-coil system (b) Resonant tank of the 3-coil system.

Figure 5 .
Figure 5. (a) Prototype of the 3-coil system (b) Resonant tank of the 3-coil system.

Figure 6 .
Figure 6.Output voltage and efficiency respectively versus load resistance for the 3-coil system.

Figure 6 .
Figure 6.Output voltage and efficiency respectively versus load resistance for the 3-coil system.

Figure 8 13 Figure 8 Figure 8 .
Figure 8 shows the waveforms of the voltage V in and the current I in respectively, and the voltage V GS and the voltage V DS between gate and source, drain and source of the MOSFET respectively.Energies 2018, 11, x FOR PEER REVIEW 9 of 13 Figure 8 shows the waveforms of the voltage Vin and the current Iin respectively, and the voltage VGS and the voltage VDS between gate and source, drain and source of the MOSFET respectively.

Figure 9
shows the transient waveforms of Vin and Iin VB and IB respectively, as switching load from 12 Ω to 50 Ω and inversely switching.It's clear that during the switching period, VB keeps almost constant, and waveforms of Iin and Vin have no obvious overshoot or undershoot, avoiding spike pulse and achieving stability.

Figure 8 .
Figure 8. Experimental waves of V in , I in , V DS , V GS .

Energies 2018 , 13 Figure 8 Figure 8 .
Figure 8 shows the waveforms of the voltage Vin and the current Iin respectively, and the voltage VGS and the voltage VDS between gate and source, drain and source of the MOSFET respectively.

Figure 9
shows the transient waveforms of Vin and Iin VB and IB respectively, as switching load from 12 Ω to 50 Ω and inversely switching.It's clear that during the switching period, VB keeps almost constant, and waveforms of Iin and Vin have no obvious overshoot or undershoot, avoiding spike pulse and achieving stability.

Figure 9 .
Figure 9.The transient waveforms of V in , I in , V B , I B when the load switches between 12 Ω and 50 Ω.

Table 2 .
Parameters for coupling mechanism for both systems.

Table 2 .
Parameters for coupling mechanism for both systems.
. It's clear that as transfer distance increases, I1 decreases continually, I2 keeps almost constant, and I3 increases from 4.2 A to 11.3 A, leading to lower efficiency but better than that of 2-coil system.
Current Versus Transfer Distance for 2-coil System.
. It's clear that as transfer distance increases, I1 decreases continually, I2 keeps almost constant, and I3 increases from 4.2 A to 11.3 A, leading to lower efficiency but better than that of 2-coil system.Current Versus Transfer Distance for 2-coil System.