I. INTRODUCTION
Inductive Power Transfer (IPT) is a promising way to deliver power from a power source to a load or multiple loads via electromagnetic coupling in order to enhance system flexibility [1]-[17]. Nowadays, IPT systems have been employed in numerous applications which include low power wireless charging of biomedical implants [10], electric vehicle charging systems [16], and public transport systems [17].
Only one primary track with an elongate loop or a pad is supplied by a single resonant inverter in conventional IPT systems, and an IPT pick-up consists of a coil of litz wire in close proximity to the track wires positioned to capture magnetic flux around the track conductor as shown in Fig. 1. The magnitude and frequency of the track current, and the magnetic coupling and quality factor of the compensated circuit directly dictate the amount of power that can be transferred across the air gap. As a result, high voltage, high current, high frequency semiconductor devices are used to achieve a high power transfer. However, these semiconductor devices are relatively expensive and may not be easy to purchase.
Fig. 1.Typical IPT system.
Multilevel technology [18]-[20] has advantages in terms of reducing the stress of semiconductor devices, and in implementing high power IPT systems by using low-cost and low-voltage semiconductor devices. However, it is a challenge to implement such systems at high frequency and to get them to work under the soft switch condition. Multi-inverter connected in parallel is another option to realize high power transfer by using low power capacity resonant inverters. A parallel topology for IPT systems by connecting identical LCL-T-based IPT supplies in parallel across a shared ac track inductor was proposed in [8]. This topology can dramatically improve the system’s transfer power, availability and reliability. However, large circulating currents among the inverter modules may be generated by the component tolerance, and the control strategy used to minimize the circulating currents is complex.
Multi-coil connected with multi-inverter is employed in induction heating to enhance the magnetic fields, which can enhance the total output power by using multiple low power inverters [21]-[26]. On the one hand, the limitations of its single operation can be removed in aspects like heat dissipation, cost, short time overload, and component limitations. On the other hand, the multi-coils connected with multi-inverter also brings convenience in terms of maintenance and flexible operation for maximum efficiency and reliability. However, the mutual inductances among the coils makes it difficult to control the resonant currents flowing through the coils. An additional decoupling transformer is one of the solution to mitigate the influence of mutual inductances [25]-[26]. However, this comes with an increase in cost.
This paper presents a new IPT topology based on dual coupled tracks connected to double resonant inverters to meet the demand of high-power applications. The mutual inductance of the dual coupled tracks is utilized to achieve better power sharing between the inverters or to improve the power distribution by configuring the resonant capacitor. Resonant inverters with different power capacities can be chosen to achieve maximum power transfer by altering the additional capacitors with a careful design. An experimental setup with a total transfer power of 1.4kW is employed to verify the proposed system under power ratios of 1:1 and 1:2 between the two inverters with an approximate transfer efficiency of 88.5%. According to the results, an attractive option for integrating low-power inverters of identical or different power capacities with dual coupled tracks is built to meet the demands of high-power applications.
The rest of this paper is organized as follows. A review of IPT systems based on a single track is shown in In Section II. In Section Ⅲ, a detailed description of the structure design and principle analysis of an IPT system based on dual coupled tracks connected with double resonant inverters is given; and the parameter design and power distribution method for the proposed IPT system is analyzed in detail. Then, Section Ⅳ shows steady-state results of an experimental system operating at 1.4kW. Some conclusions are then given in Section V.
II. REVIEW OF IPT SYSTEMS BASED ON A SINGLE TRACK
A conventional IPT system based on a single primary track is shown in Fig. 2. It comprises a high frequency H-bridge resonant inverter, a full-bridge rectifier, and resonant tanks. LP and LS are the inductances of the primary track and the pick-up coil, respectively. CP and CS are the resonant capacitors used to compensate the primary track LP and the pick-up LS. The equivalent series resistances of the track and the pick-up coil are R1 and RS, which can be neglected since their values are relatively small compared to that of the load. The mutual inductances between the pick-up coil and the primary tracks are denoted as M.
Fig. 2.The structure of the IPT system based on single track.
The inverter is controlled by the phase-shift technique, which generates a fixed-frequency ac output voltage uP as shown in Fig. 3. The operating frequency of the inverter is equal to the resonant frequency
According to [5], the RMS (Root Mean Square) of the track current can be obtained as:
According to [5], the transfer power can be calculated by:
Fig. 3.Principal operation waveforms of inverter.
Therefore, the transfer power of IPT systems can be upgraded by enhancing the equivalent track current.
III. ANALYSIS AND DESIGN OF IPT SYSTEMS BASED ON DUAL COUPLED TRACKS
A. Description of the Proposed IPT System
An IPT system based on dual coupled tracks is shown in Fig. 4. The dual tracks are wound in parallel around an E-shaped ferrite core over several-tens of meters as a power transmitter, and each track is connected with an H-bridge resonant inverter as a power supply converter. In addition, all of the inverters share a common DC input voltage. A pick-up coil is wound around an E-shaped ferrite core as a power receiver. The power receiver is intentionally shorter than the power transmitter, so that it can dynamically move over the primary tracks freely.
Fig. 4.The structure of the proposed IPT system.
In order to analyze the magnetic field of the proposed structure, a commercial finite-element analysis software, i.e., Flux is employed to provide the magnetic field image shown in Fig. 5. This is done with an energized current of 10A for a single track, 5A each for dual tracks, and 10A each for dual tracks. It is clear that the magnetic field intensity of 10A for a single track is very close to that of one 5A for each of the dual tracks due to the parallel structure. The magnetic field is dynamically strengthened by increasing the current to 10A each for the dual tracks as the equivalent current increases. In other words, the total magnetic field around the power transmitter is synthesized by the dual tracks’ currents. As a result, the transfer power is enhanced by the synthesized magnetic field, which is energized by the two currents. Under this condition, a relatively large mutual inductance M12 exists between the coupled primary tracks. This large mutual inductance is utilized to obtain better power sharing performance of the IPT system instead of decoupling the inductor behavior to simplify the system as done in classical approaches [25], [26].
Fig. 5.Magnetic field image of the single track and dual tracks structure with different energized currents.
The equivalent circuit of an IPT system with the series-series tuned topology is depicted in Fig. 6. L1, L2 and LS are the inductances of the primary track 1, track 2 and the pick-up coil, respectively. C1, C2 and CS are the resonant capacitors used to compensate the primary tracks L1 and L2, and the pick-up coil LS. The equivalent series resistances of the dual tracks and the pick-up coil are R1, R2, and RS. The mutual inductances between the pick-up coil and the primary dual tracks are M1S and M2S, respectively. A full bridge rectifier is employed to convert high frequency AC power to DC power to feed the load RL. The two-inverter units operate at an identical angular frequency of ω, which can be defined by:
Fig. 6.The equivalent circuit of the proposed series-series tuned IPT system.
For simplicity of analysis and design, the structure of the dual primary tracks are designed identically. In addition, both of the mutual inductances between the pick-up coil and the primary dual tracks are approximately identical, M1S=M2S.
The inverters are controlled by the phase-shift technique, which generates fixed-frequency ac output voltages u1 and u2. Moreover, the voltages are identical to each other by employing synchronous control technology [8], as shown in Fig. 7.
Fig. 7.Principal operation waveforms of inverter 1 and inverter 2.
The fundamental voltage phasor of the inverters can be derived as:
B. Modeling and Analysis of the Proposed IPT System
According to mutual coupling theories, the relationship between the current values and the voltages can be derived as:
where Z1, Z2 and ZS are the impedances of the dual primary tracks and the pick-up, respectively. The impedances can be defined as follow:
For simplicity of the analysis, the equivalent series resistances of the dual tracks and the pick-up coil are neglected since their values are relatively small compared to that of the load. That this is to say, RS=R1=R2=0，Z=Z1=Z2=0, and ZS = R0.
According to [27], the equivalent load R0 of the rectified tank connected to a resistive load RL can be expressed by:
By substituting (4), (6), and (7) into (5), the fundamental current phasor of the dual tracks can be derived by:
The impedances of the H-bridge inverter units can be yielded by:
Under this condition, the H-bridge inverter units’ impedances are not purely resistive due to the mutual inductance between the dual tracks. Therefore, the inverter units are not working under the resonant condition. That is to say, the capacitors are used to compensate the primary track since the traditional method do cannot meet the requirements of the resonance in dual coupled tracks IPT systems.
C. Parameter Design and Power Distribution
According to the aforementioned analysis, in order to minimize the reactive power of the H-bridge inverters, additional capacitors Ce1 and Ce2 are added to ensure that the H-bridge inverters to work under the resonance condition. An equivalent circuit diagram with the additional capacitors is shown in Fig. 8.
Fig. 8.The equivalent circuit diagram with additional compensation capacitors.
Assuming that jX1 = (jωCe1)-1 and jX2 = (jωCe2)-1, according to (6), the impedance of the dual primary tracks can be derived by:
For the sake of convenience, the following variables in (11) are defined:
Under these conditions, substituting (4), (7), and (10) into (5), the fundamental current phasor of the dual tracks can be changed to:
The new impedances of the H-bridge inverter units can be yielded by:
In order to let the two H-bridge inverter work under the resonant condition, the H-bridge inverter units’ impedance has to be purely resistive. Meanwhile, to make the two inverter output power levels flexibly configured, is set to be equal to . Re(•) represents the real component operation for (•). That is to say, the output power of inverter 2 is λ times that of inverter 1. Consequently, it is possible to obtain:
The solution of (14) is given by
The value of the additional capacitors can be derived by:
Therefore, by adding the additional capacitors Ce1 and Ce2, the impedances of the H-bridge inverter units are purely resistive as shown below:
The relationship between the dual tracks’ currents can be expressed by:
The output power of each inverter can be derived by:
where (•)* represents the conjugate operation for (•). The total output power (P) of the primary side can be given by:
All in all, the mutual inductance between the dual tracks is compensated by using the additional capacitors, which ensures that the inverters can work under the resonance condition. The inverters’ output power can be effectively allocated by choosing an appropriate value of λ. Moreover, no matter what the value λ is, the total output power of the inverters remains the same.
According to the aforementioned analysis, the voltage ratings of the semiconductor of a conventional IPT system and that of the proposed IPT system are decided by the DC input voltage E. The operating frequency of a conventional IPT system is identical to that of the proposed IPT system with the resonant frequency. Therefore, both the voltage rating and frequency of the semiconductor used for conventional IPT systems and the proposed IPT system are the same.
As can be seen from (1), (7), and (18), if M=M1S and R = R0, it is possible to obtain:
Therefore, the current ratings of the semiconductor for the proposed IPT system are 1/ (λ + 1) or λ/ (λ + 1) times the current ratings of the semiconductor for a conventional IPT system.
D. Track Current Control
In order to simplify the pickup control, it is necessary to regulate the track current at a designed value since the received voltage by a pickup is directly proportional to the track current.
A simplified view of the control loop is illustrated in Fig. 9. The controller controls and regulates the amplitude of the total track current isum (i1+i2) by varying the inverter conduction angle θL shown in Fig. 7, which is the input to the current control loop. The primary objective of the controller is to improve the reference tracking performance of the power supply.
Fig. 9.Current control diagram.
IV. SYSTEM EFFICIENCY
To analyze the system efficiency, the resistances RS, R1, and R2 in Fig. 4 should be considered. Assume that the equivalent series resistances are equal (R1=R2) because the structure of the dual primary tracks are arbitrarily designed identically. λ = 1 is widely used to achieve better power sharing when the H-bridge inverters have identical power capacities. In order to simplify the analysis, the system efficiency is analyzed in detail considering only λ = 1. The impedance of the dual primary circuits can be derived by:
The output power of inverter 1 and inverter 2 can be expressed by:
The voltage phasor of the pick-up coil can be derived by:
The current phasor of the secondary circuit is given by:
The output power of the IPT system is derived by:
Therefore, the efficiency of the IPT system can be derived by:
To achieve maximum efficiency, the equivalent series resistances of the dual tracks and the pick-up coil RS, R1, and R2 should be designed as small as possible.
In order to calculated the maximum efficiency of the IPT system, the derivation of η should be set to zero.
The theoretical optimal load R0 corresponding to the maximum efficiency can be obtained as:
Under this optimal load, the maximum efficiency can be obtained as:
By choosing an optimal load, maximum efficiency can be achieved.
V. EXPERIMENTAL VERIFICATION
A. Prototype System
To validate the proposed topology and power distribution method, an experimental IPT prototype was constructed in a laboratory settings with dual primary tracks connected to dual H-bridge inverters as shown in Fig. 4. The prototype was designed to operate up to 20 kHz and 1.4kW in the experiment. It can implement the power distribution method by choosing proper additional capacitors.
The exterior appearance of the experimental setup is portrayed in Fig. 10. Two inverters are separately powered by a common DC supply, and the AC output of the two H-bridge inverters are connected to the tracks.
Fig. 10.The exterior appearance of the proposed IPT prototype.
The gate pulse signals for the active switches are generated by a TMS320F28335 Digital Signal Processor (DSP, Texas Instrument). A CONCEPT-2SC0108T2A0-17 is adopted as the power MOSFET drive to fulfill the requirements of a high switching frequency.
The dual tracks are wound with Litz wire around an E type ferrite core, and the pick-up coil is also wound around an E type ferrite core with Litz wire. The ferrite core sizes are shown in Fig. 11. The air gap between the tracks and the secondary pick-up coil is set to be 5cm.
Fig. 11.The tracks and the pick-up coil wound around ferrite core with Litz wire.
The mutual and track inductances were measured by an Agilent E4980A LCR meter. Moreover, an oscilloscope Agilent MSO-X 4034A was used to measure and display the current and voltage waveforms of interest by means of N2780B current probes and N2891A differential probes, respectively.
The design specifications of the prototype and the experimental setup are listed in TABLE I.
TABLE ITHE CONFIGURATION OF THE IPT SYSTEM
B. Experimental Results
Without a loss of generality, two settings (λ = 1 and λ = 2) are performed to validate the performance of the proposed algorithm. The additional compensation capacitors are calculated as Ce1 = Ce2 = 1.04μF and Ce1 = 4Ce2 = 0.52μF according to (16). Under these conditions, a number of experimental results have been tested by altering θL. However, only three sets of experimental waveforms are provided in Fig. 12 and Fig. 13 due to limitation on the paper’s length.
Fig. 12.Output currents and voltages of the inverters: (a) λ = 1 and θL = π∕2, (b) λ = 1 and θL = π∕3, and (c) λ = 2 and θL = π∕2.
Fig. 13.Pick-up output current and voltage: (a) λ = 1 and θL = π∕2, (b) λ = 1 and θL = π∕3, and (c) λ = 2 and θL = π∕2.
The output currents i1, i2 and voltages u1 , u2 of the two H-bridge inverters are illustrated in Fig. 12 for the corresponding measured waveforms. isum is the sum of the two inverter currents i1 and i2 . In Fig. 12 (a) and (b), show that the currents of the two inverters are identical when λ = 1 with θL = π/2 and θL = π/3. In this case, the output current of one inverter is not only in phase with that of the other, but also in phase with the output voltage. This shows that both of the inverters are working under the resonance condition. When λ = 2, the current of the first inverter is in phase with the other but with twice the magnitude as shown in Fig. 12(c). The voltage and current waveforms of the load are illustrated in Fig. 13 and the measured powers (P1 and P2 are the output power of inverter 1 and inverter 2, and Po is the load consumption power) are listed in TABLE II
TABLE IIPERFORMANCE OF PROPOSED IPT SYSTEM UNDER VARIOUCSONDITIONS
The output power of Case A is approximately the same as that of Case C. The output power of both of the inverters in Case A are nearly identical, while the output power of one inverter in Case C is nearly twice as that of the other. This means the power sharing of the two inverters can be achieved by the proposed method. The output power and the system’s efficiency decrease as θL goes down for both cases, as shown in Fig. 15.
To provide a clear comparison of the different operating conditions, the experimental values of the output powers of each inverter and total output power against θL are given in Fig. 14. The experimental results clearly show that wide-range output power regulation can be attained by altering θL, and that power sharing can be achieved by the proposed method.
Fig. 14.Relation between the output power of the inverters and θL.
Fig. 15.Relation between the efficiency and θL.
The dynamic current response with λ = 1 is shown in Fig. 16 with two test cases. One is for changing the reference amplitude value of the current isum from 18A to 24A and the other is for changing it from 24A to 18A. The blue line is the summation of the total track current isum, and the red line is the first track current i1. It needs only 15ms to settle down to the reference current for both cases, which shows the good performance of the dynamic response. In addition, i1 is half of isum for both cases.
Fig. 16.Closed loop system response to step change in reference track current: (a) From 18A to 24 A and (b) From 24A to 18A.
In conclusion, according to the aforementioned experimental results, the power distribution of the two inverters can be allocated by adopting different values of λ , which validates the proposed power distribution and control methods.
VI. CONCLUSION
A novel IPT system based on dual coupled primary tracks is proposed in this paper. The structure of an IPT system has been explained and described in detail. In addition, the magnetic, system’s efficiency and the control strategy are provided to analyze the characteristic of the proposed IPT system. The mutual inductance of the dual coupled tracks is utilized to achieve better power sharing between the inverters or to improve the power distribution by configuring additional capacitors. Furthermore, both of the inverters can work under resonance conditions. The output power can be continuously regulated by altering the output voltage pulse width of the inverters. A 1.4kW experimental prototype is set up and tested to verify power ratios of 1:1 and 1:2 with a transfer efficiency up to 88.7%. The experimental results verify the performance of the proposed IPT system and the power distribution approach, which is suitable for high power IPT applications with various power level requirements.
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