LU Chao ( )， LI Xunbo ()， FENG Daiwei ()， OUYANG Zhiyuan ()， LI Youcheng ()

School of Mechatronics Engineering， University of Electronic Science and Technology of China， Chengdu 611731， China

Abstract： Along with the prosperous of magnetic coupled inductive power transfer (MCIPT) technology which is widely used in industrial applications such as electric vehicle charging， the topology of double D coils(DD coils) with a spatial quadrature Q coil arises with great research interest. The Q coil， however， has been thoroughly studied by adding to the receiving side but seldom to the transmitting side. By using finite element simulation， this paper presents a preliminary study on the effectiveness of Q coil in the transmitting side， and its inner dimension is optimized for optimal compensating the misalignment between the transmitting and receiver sides. Simulation results show that the windings of the Q coil should be placed in the center of the aperture of the DD coils， and these results render a useful guidance for mechanical structural design and circuit controller design of MCIPT.

Key words： structural optimization; particle swarm optimization; inductive power transfer; finite element analysis

Introduction

Because of its high safety， high convenience and high reliablility， magnetic coupling inductive power transfer (MCIPT) was an engineering curiosity in the past three decades. MCIPT began with industrial applications such as clean factories[1-3]， lighting applications[4]， instrumentation and electronic systems[5-7]，etc. Recently its applications have shifted to designs that can meet the challenge of powering electric vehicles under both stationary and dynamic conditions[8-10].

With the success of such systems， the focus of the last decade has been on developing systems that have improved tolerance to misalignment and can handle the variation in coupling which result. This has required improvements in magnetic design and control of power so that practical systems can now be considered for stationary charging systems without alignment aid， although dynamic power transfer to things on the move is still a challenge[11].

To date， circular designs are by far the most common coupler topology; these are the most intuitive and have been derived from pot cores[12-13]. The relationship between the size of a pad (primary or secondary magnetic inductive coupler) and its ability to throw flux to a secondary pad placed above it has been explained using the concept of fundamental flux path height[14]. In this sense， the flux path height of a circular pad is approximately proportional to one quarter of the pad diameter[15]. It is meaningful to increase this height for improving the tolerance of both the air gap between primary and secondary pads and their misalignment. Consequently， polarized couplers have recently been investigated which have a flux path height approximately to half of the pad length[16-17]. By sitting flattened DD coils on a Ferrite base in both primary and secondary pad which placed face to face， a new single sided flux path pad topology which can significantly improve coupling effectiveness has attracted great research interest， and is often labeled as DD. As the secondary (receiver) DD coils can only couple horizontal flux components， the tolerance of the receiver pad can be significantly improved if a second receiver coil is added. This spatial quadrature coil should be designed and optimized along with the DD structure to balance the capture of vertical and horizontal flux in a similar way to the quadrature receivers developed for material handling systems， this combined structure is referred to as DD structure plus Q structure(DDQ structure)[10， 18]. It is so far in literature the Q coil only added in the secondary (receiver) pad has been studied as which can balance performance and circuit complexity， the Q coil added in the primary (transmitting) pad was seldom studied， and is the scope of this research.

Using finite element simulation， this paper presents a preliminary study on the effectiveness of Q coil in the primary pad， and begins with its structural optimization to find the best way on how to place it. The content of this paper is as follows. Section 1 gives a brief introduction of the MCIPT with DDQ topology， and then followed by specifying the content and objective of the optimization in section 2; Section 3 describes the simulation settings， and the simulation results are analyzed in section 4 and concluded in section 5.

1 Principe of the Magnetic Coupled Inductive Power Transfer System

1.1 Mechanical structure

The power pad structure of the primary side of the MCIPT with DDQ topology can be depicted as shown in Fig. 1. By placing a secondary counterpart face to face over the primary one， a single-sided flux path can be produced when current is fed into the DD coils and Q coil on the primary pad， and thus electric power can be transferred from the primary to the secondary. Neglecting the power supply， electric control circuits and mechanical shield， the kernel mechanical structure of the transmitting (primary) and receiving (secondary) part is much simple. Usually the DD coils and Q coil(DDQ coils) made of Litz-wire and used to reshape the flux path. Therefore the coupling effects are enhanced.

Fig.1 Layout of the DDQ pad mechanical structure

1.2 Analysis of the resonant circuit

Figure 2 shows a four-coil MCIPT system using the transformer model with two full-bridge invertors. This system also consist of two square wave generators， two resonators and two output rectifiers， and all of them are connected in parallel. The two full-bridge invertors should work in phase， and by tuning the ratio of the current fed into the DD coils and that into the Q coil in the primary side， the misalignment in thex-direction (see in Fig. 1) between the secondary pad and the primary pad can be well compensated. It’s worth denoting that with Q coil in the transmitter pad， the Q coil in the receiver pad is thus optional.

Fig.2 Layout of the MCIPT circuit

Since the DD coils and Q coil are working in phase， they can be treated as one for simplification of analysis and then can be modeled as an ordinary coupling inductors as shown in Fig.3， in which the inductorsL1，L2andLMaccount for the primary coil inductance， secondary coil inductances， and mutual inductance， respectively. The reason that it can be processed this way lies in that the four coil associated circuits can be tuned and controlled to work in the resonant state by carefully tuning the serially connected capacitors (C1，C2，C3，C4) in Fig. 2， separately.

Fig.3 Coupling inductor model of MCIPT

The voltages and currents of the input and output ports of the coupling inductor model is expressed in Formula(1).

(1)

Typically in electric vehicle charging systems， the primary and secondary pads are made mechanically the same， whatever in coils and pad sizes， which means thatL1=L2=L. With the capacitors taking into consideration and taking the SS topology (capacitors are connected in series both in primary and secondary as shown in Fig. 4) as an example ， the alternating curent(AC) equivalent circuit of the system is obtained as shown in Fig. 5 by using the fundamental approximation， which can be used to simplify the analysis， and where theLSdenotes the equal primary and secondary leakage inductances.

Fig.4 MCIPT with SS topology

Fig. 5 AC equivalent circuit

Fig.6 Norton equivalent circuit

2 Content and Objective of Optimization

The main aim of this paper is to explore how the size and placement of the Q coil affects the power transfer effectiveness in the conditions of different misalignment between the primary and secondary pad， and then to find out the optimal mechanical size.

The key parameter to be optimized in this study is the inside dimension of the Q coilWQas shown in Fig. 7. To simplify the optimization analysis， the Ferrite base is fixed to be 200 mm×160 mm， and the coil widths are set to be 30 mm for both the DD coils and the Q coil.

Fig.7 Dimensions of the DD-Pad

Another problem that should be figured out in this study is how to specify the amplitude of the current fed into Q coil versus the current fed into the DD coils. The result would be a very useful guidance for circuit controller design.

3 Optimization Simulation Settings

The optimization is conducted by simulation; the software “JMAG” and finite-element analysis are adopted in this study.

3.1 2-D simulation model

A 2-D model of MCIPT was built in JMAG with DDQ transmitting coils in primary side and DD receiving coils in the secondary side as shown in Fig.8. Here the Q coil is only placed in the primary pad. Without the interaction of the Q coil in the secondary pad， the effect of how the inside dimension of Q coil influence the power transmission can be more clearly demonstrated， and the simulation can be simplified as well.

Fig.8 2-D model in JMAG

The winding corners are omitted in 2-D model to reduce the complexity， which may be questioned that it would result innon-negligible simulation accuracy. Actually， this has been found to have little effect.

To mimic the real situation， a physical pad as shown in Fig.9 was made in accordance with the models in simulation， and its parameters were precisely measured and used for simulation parameter settings， and these parameters are listed in Table 1.

Fig.9 Physical pad of DDQ topology

It’s worth noting that the internal resistance of the Q coil increases with increase of its internal dimensionWQ. This variation can be well compensated in simulation by varying its internal resistance， as which is proportional to the total length of the Litz-wire of the Q coil. Its self-inductance， however， does not vary withWQ， since the number of its coil turns is fixed to be 12.

Table 1 Physical parameters of coils

3.2 Schematic of variation of WQ and misalignment

In JMAG， the study with case control is adopted in the simulation， the parameterWQand misalignment between primary and secondary pad varies in each case. The minimum and maximum of 40 mm and 140 mm， separately， which can be graphically represented in Fig.10.

(a) Minimum WQ

(b) Maximum WQ

The aligned position and its maximum x-direction misaligned position (50 mm) can be depicted in Fig.11.

(a) Aligned position

(b) Maximum misaligned position

3.3 Simulation circuit

Two alternative currents are directly fed into DD and Q coils as shown in Fig. 12，and they are in phase but with different current amplitude. The parameters of DD coils and Q coil of both the primary and secondary side are set as shown in Table 1.

Compared with Fig. 2， the capacitors connect to coils are omitted. In real applications， the capacitors are used and tuned for resonance， but in simulation， sinusoidal currents (AC1 and AC2) make the coils resonate in nature， and leave the resonance capacitors unnecessary. As this study focus on the optimization of shaping the Q coil，i.e. its optimal internal dimensionWQ， the details of the real circuit is not in this scope， the output full-wave rectifiers as shown in Fig. 2 is also neglected， instead， a resistance loadRL=30 Ω is directly connect to the secondary DD coils.

Fig.12 Simulation circuit

Compared with Fig. 2， the capacitors connect to coils are omitted. In real applications， the capacitors are used and tuned for resonance， but in simulation， sinusoidal currents (AC1 and AC2) make the coils resonate in nature， and leave the resonance capacitors unnecessary. As this study focus on the optimization of shaping the Q coil，i.e. its optimal internal dimensionWQ， the details of the real circuit is not in this scope， the output full-wave rectifiers as shown in Fig. 2 is also neglected， instead， a resistance loadRL=30 Ω is directly connect to the secondary DD coils.

4 Simulation Results and Analysis

The frequency of both AC1 and AC2 are 30 kHz， and their current amplitudes are 2 A and 1 A， separately.

4.1 Optimal WQ

With the simulation settings described above， the active electric power consumed byRLwith variousWQand misalignment is shown in Fig. 13. The power is small comparing to the pad size， because the current AC1 and AC2 are set relatively small， which does not make this MCIPT work at its suitable conditions. It does not affect the simulation results， as the transmitting power capacity is not in the scope of this study， however.

Fig.13 Effects on active power transfer of WQ and misalignment

It can be shown in Fig. 13 that at each given misalignment， the power presents bi-directional changes withWQ， and all the peak values appear atWQ=70 mm， which clearly demonstrates that the optimal inter dimension of Q coil in the transmitting pad is 70 mm. There is an exception at the case that when the primary and secondary pad are aligned，i.e.Misalignment=0 mm， as the Q coil has no effects on power transmitting in this condition， the power does not vary withWQ.

4.2 Active misalignment compensation of Q coil

It can also be shown in Fig. 13 that at each givenWQ， the power also presents bi-directional changes with misalignments， and all the peak values appear atMisalignment=-20 mm. Special attention should be paid that this optimal misalignment associates with the current ratio of AC1 to AC2. In this case， it is shown that when AC1=2 A， AC2=1 A， the misalignment which can be best compensated is the -20 mm. It’s worthy of noting that the misalignment can be compensated in both the positive and negative direction of the x direction. For example， if AC2 were set to be -1 A and all the other parameters remained the same， the best compensated misalignment should be 20 mm.

In the case thatWQ=70 mm andMisalignment=-20 mm， the flux path can be clearly illustrated in Fig.14. In contrast to the center line of primary pad， the flux path is reshaped to be left-side concentrated by the Q coil， and this gives a physical insight into how the Q coil can actively compensate the misalignments. Figure 14 also gives a clear instruction on the best way to place the Q coil， that is the windings of the Q coil should be located in the center of the aperture of the DD coil.

5 Conclusions

By using finite element simulation analysis， this paper explores how the size and placement of the Q coil in a magnetic coupling inductive power transfer system with DDQ topology in the transmitting pad affects the power transfer effectiveness in the conditions of different misalignment between the primary and secondary pad. Simulation results have shown that (1) the best way to place the Q coil is that the windings of the Q coil should be located in the center of the aperture of the DD coils; (2) a physical insight into how the Q coil can actively compensate the misalignments. Meanwhile， these results produce useful guidance to the optimization of mechanicalstructural design and electric circuit controller design.

Fig.14 Flux path