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Resonant Converter with Coupling and Load Independent Resonance for Omnidirectional Wireless Power Transfer Application Junjie Feng, Minfan Fu, Qiang Li and Fred C. Lee Center for Power Electronics Systems The Bradley Department of Electrical and Computer Engineering Virginia Polytechnic Institute and State University Blacksburg, VA 24061 USA Abstract—Omnidirectional wireless power transfer (WPT) system has been studied recently due to its better user experience compared with directional WPT system. And this paper focus on resonant converter study in omnidirectional WPT system. At first, three challenges of resonant converter design are identified: I. moving resonant frequency under variable coupling condition; II. voltage controllability under load change; III. complicated system control with coupling between multiple coils. CLCL-LC resonant converter is proposed to solve all the challenges and provide zero voltage switching (ZVS) operation for primary device at resonant frequency. A 6.78MHz CLCL-LC resonant converter for omnidirectional WPT system is built and tested. I. INTRODUCTION Starting from Nicolas Tesla [1], wireless power transfer (WPT) technology has been studied intensely in the past century [2-8]. Up to now, the majority of near field inductive coupling platforms are planar structure [2, 3]. In planar directional WPT system, exact alignment between transmitter coil and receiver coil is required. This characteristics is not user-friendly. Therefore, a well-designed WPT system with omnidirectional power transfer capability is highly attractive in consumer electronics application [4-6]. The focus of these work is how to utilize three dimensional (3D) transmitter coil structure and modulation current to induce omnidirectional magnetic field. Resonant converter study in omnidirectional WPT system is lacked. In this paper, resonant converter design for omnidirectional WPT system is studied. One crucial challenge of resonant converter design in WPT application is variable coupling between transmitter coil and receiver coil. There is no physical connection between transmitter and receiver coil. The position of receiver coil is dependent on users, therefore, coupling coefficient between transmitter coil and receiver coil is not fixed as conventional transformer case. The most efficient operating point of resonant converter is normally at the system resonant frequency. And if the resonant frequency is dependent on coupling, it’s difficult to operate at optimal point when coupling between transmitter and receiver is variable. Therefore, resonant converter with coupling independent resonance is highly attractive in WPT application. This work was supported primarily by the Power Management Consortium (PMC) of Center for Power Electronics System. The second challenge of resonant converter design in wireless charging is voltage controllability under load change. The lithium-ion battery in receiver device can be equivalent to different load at different charging stage in its charging profile. Therefore, extra control circuit is normally needed to keep constant output voltage under load change. To cope with this disadvantage, resonant converter with load independent output voltage characteristics is preferred to achieve good controllability [7,8]. The third challenge in omnidirectional WPT system design is how to decouple multiple transmitter coils from control point of view. In omnidirectional WPT system, multiple transmitter coils structure is always needed to induce magnetic field in different direction [4-6]. And coupling between different transmitter coils makes the system control much more complicated than single transmitter coil case. Therefore, resonant converter, which can decouple electrical information of different transmitter coils to some degree, is advantageous in omnidirectional WPT system. With these three challenges, series-series resonant converter, which is very popular in wireless power transfer research society, is first evaluated in section II [2,5,7,11]. And it cannot satisfy all these requirements simultaneously. Then LLC resonant converter, the popular resonant converter in power electronics society, is also evaluated in this section [9]. In section III, CLCL-LC resonant converter is derived by modifying traditional CLL resonant converter [10]. And CLCL-LC resonant converter can solve all three challenges at the same time. A 6.78MHz CLCL-LC resonant converter is built and tested in section IV. Finally, conclusion is drawn in section V. II. SERIES-SERIES RESONANT CONVERTER AND LLC RESONANT CONVERTER Series-series resonant converter, which is named as seriesseries compensation topology in previous literature, is shown in Fig. 1 [2,5,7,11]. Lp and Ls are the self-inductance of transmitter coil and receiver coil respectively. Cp and Cs are resonant capacitor and they are designed to resonate with Lp and Ls respectively at same frequency. The equivalent circuit of series-series resonant converter is shown in Fig. 2. Transformer T model is utilized to represent coupled coil and equivalent resistor Rrec represents diode bridge with capacitive filter and load resistor. The voltage gain characteristics in different coupling condition with variable load resistance is shown in Fig. 3, with only fundamental component of input voltage source considered. Fig. 4 LLC resonant Converter Fig.1 Series-series resonant converter (a). k=0.4 (b).k=0.2 Fig.5 LLC voltage gain curve in different coupling There is two resonant frequency characteristics as shown in Fig.5. Fig.2 Equivalent Circuit of SS resonant converter (a). k=0.4 (b).k=0.2 Fig.3 Voltage gain curve of SS resonant converter in different coupling There is three resonant frequency fo, f1, and f2 in gain characteristics as shown in Fig.3: f1= 1 2π (1 + k ) L p C p (1) f2= 1 2π (1 − k ) L p C p (2) 1 1 = 2π L pC p 2π LsCs (3) fo= As illustrated by Fig.3, resonant frequency f1 and f2 is dependent of coupling condition and constant voltage characteristics can be achieved at these frequency. Resonant frequency fo is independent of coupling condition, but voltage gain at fo fluctuates a lot under load change. Therefore, series-series resonant converter cannot achieve coupling independent resonance and load independent voltage output characteristics simultaneously. Other than series-series resonant converter, LLC resonant converter, which is very popular in power electronics society, is also evaluated in this section [9]. The coupled coil is represented by cantilever model in LLC circuit diagram as shown in Fig. 4 [12]. LLC voltage gain characteristics in different coupling condition with variable load resistance is shown in Fig. 5, with only fundamental component of input voltage source considered. f1 in gain 1 2π Lk C p (4) 1 2π ( L p + Lm )C p (5) fo= f1= f o, In LLC resonant converter, resonant frequency fo is the most efficient operation point with zero voltage switching in wide load range [9]. In WPT application, this optimal point is sensitive to coupling change because it’s determined by leakage inductance. Therefore, it’s difficult to operate at this point in variable coupling case. As for resonant frequency f1, there is no constant voltage output characteristics although it is independent of coupling. Therefore, LLC resonant converter cannot satisfy all the requirement either. New resonant converter topology is preferred to solve all the challenges mentioned in introduction section. III. CLCL-LC RESONANT CONVERTER CLL resonant converter, which is LLC-like resonant converter, is first evaluated in this section [10]. The circuit diagram of CLL resonant converter is shown in Fig. 6, and coupled coils is represented by transformer T model. In order to identify the resonant frequency with voltage source output characteristics in CLL resonant converter, equivalent circuit with one branch in series with load is derived with Thevenin’s theorem and Norton’s theorem as shown in Fig. 7[13]. Fig. 6 CLL resonant Converter Fig. 9 CLL-LC resonant Converter Fig. 7 Equivalent Circuit of CLL resonant Converter In the equivalent circuit, the impedance of resonant network in series with load is zero at resonant frequency with voltage source output characteristics. According to this criteria, the resonant frequency fo can be calculated as: 1 fo= 2 2π ( Lr // 2 N Lsk Lm + N Lsk L pk + Lm L pk N 2 Lsk + Lm )Cr (6) The voltage source resonant frequency fo is still related to leakage inductance and magnetizing inductance, which is dependent on coupling condition. Therefore, resonant frequency with voltage source output characteristics in CLL is also dependent of coupling. The voltage gain characteristics in different coupling condition with variable load of CLL resonant converter is shown in Fig. 8. Compared with LLC resonant converter, resonant frequency fo in CLL is less sensitive to coupling change. (a). k=0.4 Fig. 10 Equivalent Circuit of CLL-LC resonant Converter (b).k=0.2 Fig.8 CLL voltage gain curve in different coupling In the equivalent circuit of CLL resonant converter, there are only Lm and Lsk between input source and load at resonant frequency of Lr, Cr due to their high impedance. Lm and Lsk in series is equivalent to self-inductance (Ls) of receiver coil, which is independent of coupling. Then if another capacitor Cs is added to resonate with Ls at this frequency, a series resonant frequency can be formed. With Cs added in receiver side, CLL-LC resonant converter is formed as illustrated in Fig.9. The equivalent circuit and voltage gain characteristics in different coupling condition is shown in Fig. 10 and Fig. 11. In Fig. 10, the power will go through Lm, Lsk and Cs as the blue arrow due to high impedance formed by Lr and Cr at their resonant frequency. If Cs is designed to resonate with self-inductance Ls at this frequency, then coupling independent fo with voltage source output characteristics can be obtained. This can be verified in Fig. 11, the resonant frequency fo is fixed at 6.78MHz in different coupling condition. 1 1 fo= = (7) 2π Lr Cr 2π Ls Cs (a). k=0.4 (b).k=0.2 Fig.11 CLL-LC voltage gain curve in different coupling In the gain characteristics of CLL-LC resonant converter, resonant frequency fo is in positive slope region. Therefore, zero voltage switching (ZVS) operation of primary device would be a great concern. To ensure ZVS operation, inductive input impedance is necessary to let input current lag switching node voltage [11]. The phase of input impedance with different load in k=0.4 is plotted in Fig.12. As demonstrated by Fig. 12, the phase of input impedance of CLL-LC is negative, which means capacitive input impedance. Therefore, there is no ZVS operation at fo in CLL-LC resonant converter. This is detrimental for switching device when operating at 6.78MHz. The system performance also suffers due to large switching loss and EMI problem associated with hard switching. Fig. 12 CLL-LC’s Input impedance To achieve ZVS operation, another capacitor Cp, is added in CLL-LC resonant converter as shown in Fig. 13. The criteria for designing Cp is making sure input impedance of CLCL-LC resonant converter is inductive. One example design is shown in Fig.14. The input impedance is always inductive at fo with different load condition to achieve ZVS operation in CLCL-LC resonant converter. Fig.16 Current source mechanism of CLCL-LC resonant converter Fig. 13. CLCL-LC resonant converter Fig. 14 CLCL-LC’s Input impedance The voltage gain characteristics of CLCL-LC resonant converter in different coupling is shown in Fig. 15. As shown in this figure, a coupling independent resonant frequency fo with voltage source output characteristics is achieved with ZVS operation. Therefore, the first two challenge mentioned in section I is solved with CLCL-LC resonant converter. In summary, CLCL-LC resonant converter can solve all the challenges mentioned before: 1: coupling independent resonance frequency fo; 2: voltage source output characteristics at fo; 3: decoupled system control variable at fo. Besides, ZVS operation can also be achieved in CLCL-LC resonant converter at fo. Therefore, CLCL-LC resonant converter is very promising circuit topology for omnidirectional WPT application. Other than CLCL-LC resonant converter, LCCL-LC resonant converter as shown in Fig. 17, has very similar characteristics. In the future, more resonant converter topologies with similar characteristics will be studied in systematic way. Fig.17 LCCL-LC Resonant converter (a). k=0.4 (b).k=0.2 Fig.15 CLCL-LC voltage gain curve in different coupling In WPT application, the power received by receiver coil is determined by transmitter coil current and coupling condition between them [14-15]. Therefore, transmitter coil current is important control variable in system control. And there are multiple transmitter coils in omnidirectional WPT system. The system control will be much complicated if transmitter coil current is impacted by each other due to some unintentional coupling. In CLCL-LC resonant converter, the transmitter coil current has current source output characteristics due to resonance of Lr and Cr. The mechanism of constant transmitter coil current is explained by Fig. 16. In Fig. 16, square wave voltage source in series with capacitor can be equivalent to input current source in parallel with capacitor. Due to Lr and Cr at resonant frequency fo, the transmitter coil current is determined by this current source. Since the transmitter coil current is decoupled between different coils, the system control will be much simpler. IV. EXPERIMENT RESULT The experiment setup of our omnidirectional WPT system is shown in Fig.18. There are multiple transmitter coils in our platform. In transmitter side circuit, EPC 8009 half bridge demo board is utilized to provide square voltage source for resonant tank. In receiver side, diode bridge with capacitor rectifies 6.78MHz AC power to DC power. The resonant tank parameter of CLCL-LC converter is provided in Table I. Fig.18 Experiment setup The experiment waveform of CLCL-LC converter is shown in Fig. 19. The pink waveform is 6.78MHz switching node voltage waveform of half bridge, red waveform is the input current waveform and blue curve is the output voltage waveform after diode bridge. The waveform is very clear, benefit from ZVS operation of primary device. Output voltage is 5V, which can be directly connect to cell phone for charging. The system efficiency from input to output is around 60% with coupling coefficient of 0.15. TABLE I Switching frequency fs Lr Cr Cp Lp Ls Cs R 6.78MHz 1uH 550pF 120pF 5.6uH 5uH 110pF 10Ω Fig. 19 CLLC-LC’s Experiment waveform IV. CONCLUSION First, three challenges in resonant converter design for omnidirectional WPT system are identified in section I. Then series-series resonant converter and LLC resonant converter are evaluated in section II. Both of them cannot solve all three challenges at the same time. Starting from CLL resonant converter, CLCL-LC resonant converter is proposed to satisfy all the requirement. And more resonant topologies with similar characteristics can be derived with our methodology. Finally, a 6.78MHz CLCL-LC resonant converter is built. ZVS operation at resonant frequency is achieved and the system efficiency is around 60%. ACKNOWLEDGMENT This work was supported by the Power Management Consortium in CPES, Virginia Tech. REFERENCES [1]. N. Tesla, Apparatus for transmitting electrical energy, US patent 1,119,732, December 1914. [2]. C. Wang, O. Stielau and G. 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