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Effect of Surrounding Conductive Object on Four-Plate Capacitive

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Effect of Surrounding Conductive Object on Four-Plate Capacitive Effect of Surrounding Conductive Object on Four- Plate Capacitive Power Transfer System Qi Zhu, Lixiang Jackie Zou, Shaoge Zang, Mei Su, and Aiguo Patrick Hu Abstract- In this paper, the effect of a surrounding conductive in the secondary side as power receivers. The typical structure object on a typical capacitive power transfer (CPT) system with of a four-plate CPT system is shown in Fig. 1. two pairs of parallel plates is studied by considering the mutual Based on the above typical structure, some fundamental coupling between the conductive object and the plates. A studies have been done. C. Liu et al. studied the coupling mathematical model is established based on a 5*5 mutual mechanism [15], steady-state analysis [16], power flow control capacitance matrix by using a larger additional conductive plate to represent the surrounding conductive object. Based on the [17], 2D alignment analysis [18] and generalized coupling proposed model, the effect of the additional conductive plate on modeling [19] of a four-plate CPT system. L. Huang et al. the CPT system is analyzed in detail. The electric field distribution studied compensation networks for improving the performance of the CPT system including the additional plate is simulated by of a four-plate CPT system [20-21], the accurate steady-state ANSYS Maxwell. A practical CPT system consisting of four modeling considering cross-coupling for a four-plate CPT 100mm*100mm square aluminum plates and one 300mm*300mm system [22] and the definition of mutual coupling among four square aluminum plate is built to verify the modeling and analysis. plates [23]. Four-plate CPT systems have been further Both theoretical and experimental results show that the output developed for high-power applications. F. Lu et al. proposed a voltage of the CPT system decreases when the additional double-sided LCLC compensated four-plate CPT system to conductive plate is placed closer to the CPT system. It has found that the additional plate can effectively shield the electric field transfer 2.4kW power with 90.8% efficiency through an air gap outside the plate, and it attracts the electric field in-between the distance of 150mm [11]. The typical structure of two pairs of four plates of the CPT system and the additional plate. It has also parallel plates is replaced by a stacked four-plate structure to found that the voltage potential difference between the additional save space in electric vehicle charging applications, and the plate and the reference plate of the CPT system remains almost system achieved 1.88kW power with 85.87% efficiency constant even when the distance between them changes. The through a 150mm air gap [12]. Two of the four plates are further findings are useful for guiding the design of CPT systems, replaced by the vehicle chassis and earth ground, with only two particularly the electric field shielding. external plates required for electric vehicle charging [14]. Constant-voltage and constant-current modes were also found Index Terms- Capacitive power transfer (CPT), electric field distribution, four-plate CPT system, mutual capacitance matrix, in a four-plate CPT system with double-sided LC compensation surrounding conductive object. [24]. However in practice, a four-plate CPT system is quite I. INTRODUCTION sensitive to the surroundings, especially with a conductive object around it. The presence of this external object will Capacitive Power Transfer (CPT) based on electric field change the existing electric field coupling generated by the four coupling is an alternative Wireless Power Transfer (WPT) plates and further affect the system output performance. solution. It enables power transfer through metal barriers with Theoretically, the original 4*4 mutual capacitance matrix lower power losses and EMI compared to Inductive Power contributed by the four plates should be correspondingly Transfer (IPT) [1, 2]. This technology has been widely used in modified to a 5*5 matrix considering this external object. both low-power and high-power applications, such as Hence, the effect of this external object on the four-plate system integrated circuits [3], biomedical devices [4, 5], mobile can be mathematically described by considering the additional devices [6, 7], synchronous machines [8-10] and electric elements in the 5*5 matrix. This study can be used to guide the vehicles [11-14]. Normally, a typical CPT system requires two practical design of CPT systems by considering the effects of pairs of parallel metal plates to form electric field coupling and surrounding conductive objects. provide a power flow path. Two metal plates are used in the In this paper, the effect of a surrounding conductive object primary side as power transmitters, and the other two are used on a typical four-plate CPT system will be studied by considering the mutual coupling between this external object Primary Side Secondary Side and one of the four plates. A larger additional conductive plate will be used to represent this external object, and a mathematical model based on a 5*5 mutual capacitance matrix AC Load Voltage will be established to describe the relationship between the additional plate and the CPT system. The effect of the Compensation Electric Compensation additional plate on the CPT system will be analyzed in detail. Network Coupler Network The electric field distribution of the CPT system with an Fig. 1. Typical structure of a four-plate CPT system. additional conductive plate will be simulated in ANSYS Maxwell. A practical CPT system with an additional conductive The 5*5 mutual capacitance matrix of a four-plate CPT plate will be built to verify the modeling and analysis. system with a surrounding conductive object can be described The rest of this paper is organized as follows: The modeling as follows: 퐶 −퐶 −퐶 −퐶 −퐶 of a four-plate CPT system with a surrounding conductive 푄1 푚,1 푚,12 푚,13 푚,14 푚,15 푉1 푄2 −퐶푚,12 퐶푚,2 −퐶푚,23 −퐶푚,24 −퐶푚,25 푉2 object is introduced in Section II. The electric field distribution 푄 −퐶 −퐶 퐶 −퐶 −퐶 푉 3 = 푚,13 푚,23 푚,3 푚,34 푚,35 3 analysis with or without the surrounding conductive object is 푄4 −퐶 −퐶 −퐶 퐶 −퐶 푉4 presented in Section III. Practical considerations related to the 푚,14 푚,24 푚,34 푚,4 푚,45 [푄5] [−퐶푚,15 −퐶푚,25 −퐶푚,35 −퐶푚,45 퐶푚,5 ] [푉5] surrounding conductive object are given in Section IV. A four- (1) plate CPT system with one surrounding conductive plate is where, established in Section V. A conclusion about the effect of a 퐶푚,1 = 퐶푚,12 + 퐶푚,13 + 퐶푚,14 + 퐶푚,15 conductive object on a four-plate CPT system is drawn in 퐶푚,2 = 퐶푚,12 + 퐶푚,23 + 퐶푚,24 + 퐶푚,25 Section VI. 퐶푚,3 = 퐶푚,13 + 퐶푚,23 + 퐶푚,34 + 퐶푚,35 퐶푚,4 = 퐶푚,14 + 퐶푚,24 + 퐶푚,34 + 퐶푚,45 II. MODELING A FOUR-PLATE CAPACITIVE POWER 퐶푚,5 = 퐶푚,15 + 퐶푚,25 + 퐶푚,35 + 퐶푚,45 TRANSFER SYSTEM WITH A SURROUNDING CONDUCTIVE Assume that Plate 1 and 2 are chosen as the primary power OBJECT transmitters, and Plate 3 and 4 are chosen as the secondary power receiver. The source voltage, current and angular A four-plate CPT system can be simplified as four metal frequency are VS, IS and 휔, respectively, and the voltage and plates with an AC voltage source and a load, regardless of the current of the load RL are VL and IL, respectively. The physical power converter and compensation network used in a typical connection and equivalent circuit of a four-plate CPT system CPT system. The placement of two pairs of parallel metal plates with a surrounding conductive object are shown in Fig. 3. is taken to represent the capacitive coupler in a typical four- Let Plate 2 be the reference plate, then 푉2 = 0, 푉푠 = 푉1 , plate CPT system in this paper. Normally, the performance of a 푉퐿 = 푉3 − 푉4. According to the law of charge conservation, it four-plate CPT system is sensitive to a nearby conductive object. can be drawn that 푄1 + 푄2 + 푄3 + 푄4 + 푄5 = 0. According to Since some capacitance exists between any two electrical Kirchhoff’s current law, (1) can be reduced to the following conductors in proximity, the presence of a nearby conductive matrix: object changes the electric field distribution of a four-plate CPT system. A larger metallic plate is used to represent the Voltage Source surrounding conductive object in this paper. Plate1 Plate2 Assume that two pairs of metal plates are identical and placed in parallel in space, Plate 1, Plate 2, Plate 3 and Plate 4. A Capacitive Coupler surrounding conductive object, Plate 5, is placed close to these Plate3 Plate4 Load four plates. The quantity of electric charge on each plate is Q1, Q2, Q3, Q4 and Q5, respectively. The electric potential of each plate is V1, V2, V3, V4 and V5, respectively. The mutual capacitance between every two plates is Cm,12, Cm,13, Cm,14, Cm,15, Cm,23, Cm,24, Cm,25, Cm,34, Cm,35 and Cm,45. Cm,ij indicates how many charges on Plate i are contributed by the potential Plate5 difference between Plate i and j. The self-capacitance of each Surrounding Object plate is ignored because the distance between any two plates is (a) much smaller than the distance between one plate and the VS IS ground reference at infinity. The block diagram of four plates and one surrounding conductive object is shown in Fig. 2. Plate 1 Cm,12 Plate 2 Capacitive Coupler Cm,14 Q ,V Q ,V 1 1 2 2 Cm,13 Cm,24 Plate1 Cm,12 Plate2 Cm,15 Cm,25 Cm,23 Cm,13 Cm,14 Cm,23 Cm,24 Plate3 Plate4 Plate 3 Plate 4 Cm,34 Q3,V3 Cm,34 Q4,V4 IL Cm,15 Cm,25 RL Cm,35 Cm,45 Cm,35 Cm,45 VL Plate5 Plate 5 Q ,V 5 5 (b) Surrounding Object Fig.
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