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.

1. 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.

2. 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 2.1.2 will explain voltage gain and the parameter design process that provides load-independent output voltage. Section 2.1.3 will describe transfer efficiency for the proposed 3-coil system. Section 2.1.4 will devise parameter values. Following Section 2.2 would illustrate the 2-coil parameter design.

2.1. 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 Q₁–Q₄ for a square wave generator, a resonant tank including 3 coils: L₁, L₂, L₃ and their resonant capacitor C₁, C₂, C₃, a full-bridge diode rectifier D₁–D₄ and a load R_L. L₁, L₂ and L₃ 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, r₁, r₂, r₃ are the parasite and winding resistance of the source, L₁, L₂ and L₃, respectively. Relationship between the inverter output voltage U_in and the inverter input voltage E is $U_{in}=2\sqrt{2}E/\pi$. Relationship between the rectifier input voltage U_out and the load voltage (U_RL) is $U_{out}=2\sqrt{2}{U}_{RL}/\pi$.

2.1.1. 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), 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 $R=8R_L/{\pi }^2$.

$$\left[\begin{array}{c}{U}_{in}\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccc}j{X}_1+r_1+r_s& -j\omega M_{12}& -j\omega M_{13}\\ -j\omega M_{12}& j\omega X_2+r_2+R& j\omega M_{23}\\ -j\omega M_{13}& j\omega M_{23}& j\omega X_3+r_3\end{array}\right]\cdot \left[\begin{array}{c}{I}_1\\ I_2\\ I_3\end{array}\right]$$

(1)

2.1.2. 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, X₁ 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).

$$G_V=\frac{I_{2}R}{U_{in}}=\frac{A{R}^2+BR}{C{R}^2+D}$$

(2)

$$\begin{array}{l}A=\omega M_{23}{M}_{13}^3-X_3{M}_{12}{M}_{13}^3\\ B=j\left(X_3{M}_{12}-\omega M_{13}{M}_{23}\right)\left(X_3{M}_{12}^2-2\omega M_{12}{M}_{13}{M}_{23}+X_2{M}_{13}^2\right)\\ C=\omega M_{13}^4\\ D=\omega {\left(X_3{M}_{12}^2-2\omega M_{12}{M}_{13}{M}_{23}+X_2{M}_{13}^2\right)}^2\end{array}$$

(3)

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).

$$\left[\begin{array}{c}B\\ D\end{array}\right]=\left[\begin{array}{c}j\left(X_3{M}_{12}-\omega M_{13}{M}_{23}\right)\left(X_3{M}_{12}^2-2\omega M_{12}{M}_{13}{M}_{23}+X_2{M}_{13}^2\right)\\ \omega {\left(X_3{M}_{12}^2-2\omega M_{12}{M}_{13}{M}_{23}+X_2{M}_{13}^2\right)}^2\end{array}\right]=\left[\begin{array}{c}0\\ 0\end{array}\right]$$

(4)

By substituting Equation (4) into Equations (3) and (2), Equation (2) could be rewritten as Equation (5).

$$G_V=\frac{A}{C}=\frac{\omega M_{23}-X_3{M}_{12}}{\omega M_{13}}$$

(5)

It can be seen from the Equation (5) that voltage gain is load-independent now, achieving CV output with Equation (4), X₃, which is the imaginary component of the equivalent impedance for loop 3, could be rewritten as Equation (6).

$$X_3=\frac{X_2{M}_{13}^2-2\omega M_{12}{M}_{13}{M}_{23}}{M_{12}^2}$$

(6)

By substituting Equation (6) into Equation Equation (5), G_V could be more concise as Equation (7).

$$G_V=\frac{X_2{M}_{13}-\omega M_{12}{M}_{23}}{\omega M_{12}{M}_{13}}$$

(7)

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).

$$Z_{in}=\frac{U_{in}}{I_1}=\alpha +j\beta$$

(8)

$\alpha , \beta$ 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, $\beta$ should be set to 0. After some simple mathematical manipulations, X₂, the imaginary component of the equivalent impedance for loop 2, is derived as Equation (9).

$$X_2=\frac{2\omega M_{12}{M}_{23}}{M_{13}}$$

(9)

Implementing the new X₂ value, the equivalent impedance Z_in is rewritten as Equation (10).

$$Z_{in}=\frac{M_{13}^2}{M_{23}^2}R$$

(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), X₃, the imaginary component of the equivalent impedance for loop 3, could be more concise as Equation (11).

$$X_3=0$$

(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, M₂₃ and M₁₃ also change.

$$G_V=\frac{M_{23}}{M_{13}}$$

(12)

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).

2.1.3. 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).

$$r_a=\mathrm{Re}\left(-j\omega M_{12}\frac{I_2}{I_1}\right),r_b=\mathrm{Re}\left(-j\omega M_{13}\frac{I_3}{I_1}\right),r_c=\mathrm{Re}\left(j\omega M_{23}\frac{I_2}{I_3}\right)$$

(13)

Based on Figure 3, the transfer efficiency could be derived in Equation (14). ${\eta }_1,{\eta }_2,{\eta }_3$ represent the efficiency of loop 1, loop 2 and loop 3, respectively.

$${\eta }_1=\frac{r_a+r_b}{r_a+r_b+r_1+r_s},{\eta }_2=\frac{R}{R+r_2},{\eta }_3=\frac{r_c}{r_c+r_3}$$

(14)

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 $R=8R_L/{\pi }^2$.

$$\eta ={\eta }_1{\eta }_2{\eta }_3=\frac{R_{1\_23}{R}_{3\_2}R}{\left(r_1+r_s+R_{1\_23}\right)\left(r_3+R_{3\_2}\right)\left(r_2+R\right)}$$

(15)

$$R_{1\_23}=\mathrm{Re}\left(-j\omega M_{12}\frac{I_2}{I_1}\right)+\mathrm{Re}\left(-j\omega M_{13}\frac{I_3}{I_1}\right),R_{3\_2}=\mathrm{Re}\left(j\omega M_{23}\frac{I_2}{I_3}\right)$$

(16)

2.1.4. 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 $\omega =2\mathsf{\pi }f$. Based on Equation (12), and the relationship between input voltage and output voltage of the inverter and the rectifier, Equation (17) is derived.

$$G_V=\frac{M_{23}}{M_{13}}=\frac{U_{RL}}{E}$$

(17)

We set $U_{RL}=60\mathrm{V}$ and $E=120\mathrm{V}$ 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 $M_{23}/M_{13}=0.5$, 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 $X_1=0$, C₁ in the transmitter coil is derived in Equation (18).

$$C_1=\frac{1}{{\omega }^2{L}_1}$$

(18)

Based on Equation (11), C₃ in the relay coil is derived in Equation (20).

$$C_3=\frac{1}{{\omega }^2{L}_3}$$

(19)

Based on Equation (9), C₂ in the receiver coil is shown in Equation (20).

$$C_2=\frac{M_{13}}{{\omega }^2\left(L_2{M}_{13}-2M_{12}{M}_{23}\right)}$$

(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 C₂ should be recalculated according to Equation (20).

2.2. 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 G_V for the 2-coil system shown in Figure 4 could be derived as Equation (21) based on [22].

$$G_V=\left|\frac{U_{RL}}{E}\right|=\frac{1}{{\omega }^{2}M{C}_{p1}}$$

(21)

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).

$$C_{p1}=\frac{1}{{\omega }^{2}M{G}_V}$$

(22)

Based on Equation (22), Inductance values L_P1 and L_P2 could be measured with Equation (23).

$$L_{P1}=\frac{1}{{\omega }^2{C}_{P1}},L_{P2}=L_{P1}$$

(23)

Capacitors C₁ and C₂ resonant with L₁ and L₂, respectively. Their values are shown in Equation (24).

$$C_1=\frac{1}{{\omega }^2{L}_1},C_2=\frac{1}{{\omega }^2{L}_2}$$

(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].

3. 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. Parameter values for 3-coil system.

Parameter	Value	Parameter	Value
Frequency f/kHz	200	Capacitor C2/nF	13.681
Input voltage E/V	120	Capacitor C3/nF	6.701
Self-inductance L1/uH	53.76	Transfer distance gap/mm	100
Self-inductance L2/uH	56.69	Outer radius of Loop 1 R1/mm	95.75
Self-inductance L3/uH	94.497	Outer radius of Loop 2 R2/mm	95.75
Mutual inductance M12/uH	9.5425	Outer radius of Loop 3 R3/mm	150
Mutual inductance M13/uH	23.255	Number of turns for Loop 1 N1	10
Mutual inductance M23/uH	12.675	Number of turns for Loop 2 N2	10
Capacitor C1/nF	11.779	Number of turns for Loop 3 N3	10

.

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.

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 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 = 60.39 V and I_B = 5.03 A, meaning that the output power is 303.76 W, 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.

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.

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. 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. Parameters for coupling mechanism for both systems.

Model	gap/mm	100.00	110.00	120.00	130.00	140.00	150.00	160.00	170.00	180.00	190.00	200.00
3 coil	L1/uH	62.51	62.23	61.94	61.87	61.73	61.64	61.49	61.54	61.54	61.46	61.56
	L2/uH	62.57	62.35	61.96	61.98	61.82	61.61	61.57	61.73	61.65	61.71	61.61
	L3/uH	107.14	106.82	106.20	106.26	105.53	105.54	105.57	105.37	105.25	105.42	105.32
	M12/uH	9.93	8.38	7.13	6.09	5.23	4.52	3.92	3.41	2.98	2.61	2.30
	M13/uH	23.66	23.20	22.91	22.71	22.51	22.40	22.34	22.27	22.28	22.19	22.16
	M23/uH	13.04	11.46	10.09	8.92	7.88	7.00	6.23	5.55	4.96	4.44	3.98
2 coil	L1/uH	216.98	215.45	213.96	213.54	212.29	211.99	211.75	211.46	211.34	211.27	211.19
	L2/uH	62.57	62.35	61.96	61.98	61.82	61.61	61.57	61.73	61.65	61.71	61.61
	M/uH	22.97	19.84	17.22	15.00	13.11	11.52	10.16	8.96	7.94	7.05	6.28

, 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 L_p1, L_p2, and C_p1 to keep 60 V output voltage. The simulation results are shown in

Table 3. Simulating result.

Model	gap/mm	100.00	110.00	120.00	130.00	140.00	150.00	160.00	170.00	180.00	190.00	200.00
3 coil	Pin/w	329.80	325.70	323.10	326.40	327.60	331.90	332.60	336.10	344.40	347.70	356.20
	Pout/w	306.30	302.20	299.20	301.10	300.70	301.90	300.10	299.10	301.30	299.60	300.10
	η/%	92.89	92.78	92.62	92.24	91.79	90.96	90.24	88.99	87.50	86.15	84.26
	URL/V	60.62	60.22	59.92	60.11	60.07	60.19	60.01	59.91	60.13	59.96	60.01
	E/V	117.20	129.50	144.10	161.80	181.00	203.00	226.50	253.00	284.00	315.00	351.00
	I1/A	3.13	2.80	2.50	2.25	2.03	1.84	1.67	1.53	1.42	1.33	1.27
	I2/A	5.61	5.58	5.53	5.57	5.56	5.57	5.56	5.55	5.57	5.55	5.56
	I3/A	4.21	4.43	4.78	5.28	5.87	6.56	7.30	8.16	9.14	10.17	11.34
2 coil	Pin/w	325.00	324.20	325.40	328.40	334.60	345.50	362.30	390.80	435.80	504.50	613.60
	Pout/w	301.00	300.50	300.70	300.70	300.70	300.50	300.10	300.20	299.30	299.30	300.20
	η/%	92.61	92.69	92.41	91.57	89.87	86.98	82.81	76.81	68.67	59.33	48.92
	URL/V	60.10	60.05	60.07	60.07	60.07	60.05	60.01	60.02	59.93	59.93	60.02
	E/V	117.20	129.50	144.10	161.80	181.00	203.00	226.50	253.00	284.00	315.00	351.00
	I1/A	3.12	2.82	2.55	2.33	2.33	2.01	1.88	1.80	1.76	1.81	1.96
	I2/A	3.53	4.54	5.86	7.58	9.74	12.47	15.81	20.04	25.41	31.76	39.75

. Where I₁, I₂ and I₃ 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 (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.

4. 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.