Wireless charging system for electric bicycle application

Received Dec 12, 2019 Revised Apr 26, 2020 Accepted May 21, 2020 This paper presents a design of the wireless charging system for e-byke applications. The double-side LCC compensation circuit is used to achieve high efficiency and reduce the volt-ampere rating. A new constant current/voltage (CC/CV) charging control method at the transmitter side is proposed to avoid dual side wireless communication. This paper also presents a simple method of estimating both the coupling coefficient and load impedance only from the transmitter side. A wireless charging system of 2.5kW is built. Error in the CC/CV charging mode is 3.3% and 1.12%, respectively. System efficiency reaches 92.1% in CC charging mode.


INTRODUCTION
Recently, electric bicycles (e-bike) are widely used instead of the motorcycle to reduce air pollution in the world. The users are almost students and women. Therefore, a convenient and safe charging method is necessary. Based on wireless power transfer (WPT) technology, wireless charging systems could be done automatically and safely without any human contact with electricity [1][2][3].
In wireless charging systems, the power can be transferred from the transmitter side to the receiver side over a short air gap [4]. These systems have a low coupling coefficient leads to high reactive power and low energy transfer efficiency. Therefore, the compensation circuit is used to reduce reactive power and improve system efficiency. There are four basic compensation circuits, which are series-series, seriesparallel, parallel-series, and parallel-parallel [5]. These compensations are simple, easy to design, and it is sensitive to the variation of parameters [6]. Besides, some other compensation circuits are used to improve efficiency as LCL, CLL, LCC compensation circuits. However, the LCL compensation circuit requires a large compensation inductance value, close to the coil's inductance value [7,8]. A capacitor is added to the LCL compensation circuit to reduce the size, the cost of circuit components that creates an LCC compensation circuit [9]. Also, the LCC compensation circuit has resonant frequency independent of the coupling coefficient, load, and the soft-switching condition for the electronic devices reached [10][11][12].
In [13], The CLL/S compensation circuit is used to limit the inverter current. However, the parameters of the compensation circuit are relatively large that is difficult to design high power systems. Besides, efficiency is slightly lower than the double-sided LCC compensation circuit. The other problem with wireless charging is that the CC/CV charging modes are required to achieve high charging efficiency and lithium-ion pin protection [14,15]. Therefore, a proper charging control strategy is required. The charging control methods in the WPT system consists of three types: transmitter side control, receiver side control, and dual side control [16][17][18]. In these methods, the transmitter side control is preferred because it doesn't require any additional DC/DC converter. However, parameters as load, coupling coefficient must be known to control at the transmitter side. Moreover, in the wireless charging, the voltage/current of the battery varies during the charging process [5,19]. Therefore, the battery is considered a variable load during charging. Besides, to high-efficiency charging, the e-bike must park in alignment with the transmitter to receive energy from the transmitter. However, that is not always possible. When e-bikes park in misalignment, the coupling coefficient also varies with each charging [20,21]. In the wireless charging, these parameters are difficult to obtain without using wireless communications.
The CC/CV charging is performed by designing a hybrid compensation circuit in [22]. However, the system is complicated because it needs to add capacitors, inductors, and switches. In [23], the CC/CV is performed via AC switches that the system requests weak communication. However, it leads to control deviations when the communication signal jammed. In [24], the CC / CV charging achieved through coil and compensation circuit design. However, the design method is complicated. The switching frequency must switch between the CC and CV charging modes. In [25], the CC/CV charging has performed at only the primary side. However, the load estimation method is complicated, which used the quadrature transformation algorithm to measure active power. Also, the mutual inductance was not estimated resulting in inflexible control.
In this paper, the LCC compensation circuit is designed for both transmitter and receiver to high efficiency and small compensation circuit elements value. Then, a new CC/CV charging control method only on the transmitter side is implement that base on a new high accuracy estimation method of both parameters like the coupling coefficient and load. A 2.5 kW wireless charging system has built to verify the feasibility of the proposed method. Section 2 presents a system structure and LCC compensation circuit design. Section 3 presents the CC/CV charging control method. Section 4 presents the simulation and experimental results. Conclusions are given in section 5.

SYSTEM STRUCTURE AND LCC COMPENSATION CIRCUIT DESIGN
The wireless charging system structure is shown in Figure 1. At the transmitter side, the DC voltage is converted into a high-frequency alternating voltage by a single-phase inverter for the magnetic coupler. The transmitter side controller performs CC/CV charging control through measuring resonant current and inverter DC input power. The primary side LCC compensation circuit is used to reduce reactive power, and achieve soft switching for MOSFETs. Then, energy is transferred to the receiver side via the magnetic coupler. The receiver side LCC compensation circuit is used to maximize transfer efficiency. The obtained AC voltage on the receiver coil via the LCC compensation circuit is rectified and filtered to charge for the battery. At the transmitter side, the equivalent load, and the coupling coefficient are estimated. Then, the transmitter side controller is designed to control CC/CV charging modes.
Transmitter side controller Transmitter side When the battery charging process is slow, the battery can be modeled as a resistor R eb which depends on the battery's state of charge [5,25]. The battery equivalent resistance can be expressed as (1) where U b , I b is the charging voltage, charging current, respectively. When ignoring power losses on rectifiers, the equivalent load resistance/current seen from the input of the rectifier is expressed as follows: When the inverter output voltage and rectifier input voltage are approximated as sinusoidal sources, the equivalent circuit is given in Figure 2. Where L i is coil's self-inductance, M is the mutual inductance, L fi , C fi , C i are compensation inductor and capacitors; i (i= 1,2) index of parameters at the transmitter, receiver side, respectively.
Ignore internal resistance of coils, the fundamental harmonics approximation method is used to analyze the working principle of the resonant circuit. The transmitter and receiver coil have designed the same. Therefore, the following parameters are the same: The resonance frequency is design to be equal to the inverter switching frequency, ω = 2πf sw . Parameter's relationship in the resonant circuit is shown as follows.
The system output power can be expressed as follows Combine (5), (6), and (7), the compensation circuit parameters for the system are calculated and depicted in Table 1.

PROPOSED TRANSMITTER SIDE CONTROLLER 3.1. Theoretical analysis
Analyzing the circuit of Figure 2 when considering the internal resistance of the transmitter and receiver coils, the following relationships have drawn: where R i is coil internal resistances, I 1 is resonant current on transmitter coil. At a fixed resonant frequency, from (8), (9) show that I eL , U eL depends on k, R eL, and resonant current I 1 . The coupling coefficient (k) varies according to the position between the receiver and transmitter. The equivalent resistance (R eL ) varies according to the battery charging state. If these parameters are estimated, the CC/CV charging is possible via transmitter side resonant current adjustment. The resonant current is expressed by: It shows that the transmitter resonant current I 1 could be controlled by regulating inverter output voltage (U AB ). The phase-shift method is used to adjust the RMS of U AB . The PWM signals for S 1~S4 and the phase-shift inverter output voltage is given in Figure 3. Through the first harmonic approximation, U AB is given as [26]: where α is the phase-shift angle of the resonant inverter. The equations (8) to (11) show the ability to control CC / CV charging by adjusting the phase shift angle of the inverter.

Estimate the coupling coefficient and equivalent resistance from only the transmitter side
To make estimates of coupling coefficiency and equivalent resistance only from the transmitter side, the circuit diagram Figure 2 is analyzed. The equivalent impedance of the receiver side seen into the receiver coil can be expressed: The equivalent impedance of the transmitter side seen into the transmitter coil can be expressed: If the losses on the compensation circuit elements are ignored, then: Where P DC is inverter input DC power. Combining the equations (14) and (16), the coupling coefficient can be expressed: Usually, the wireless charging system for e-bike is the static charging system. When starting charging, the vehicle position is fixed. Therefore, from equations (12) and (17), the parameters are estimated by the following two steps: Step 1: When starting the charging process, the rectifier and battery are cut off and replaced by an optimum resistance (R L.opt ) as shown in Figure 1. The coupling coefficient is estimated as (17). Then, the coupling coefficient value is remembered.
Step 2: After the coupling coefficient value has been collected, the optimum resistance load is cut off. The equivalent resistance value is estimated continuously during charging: Thus, by measuring the values of inverter input DC power and RMS of resonant current, the coupling coefficient and equivalent resistance are estimated.

Analysis of the proposed controller
The block diagram of the closed-loop control is given in Figure 4. The RMS of resonant current and input DC power of the inverter is measured. First, the coupling coefficient is estimated by (17) and remembered. Later, the equivalent load is estimated according to (18) during process CC/CV charging. Final, the value of equipment load current /voltage is calculated by (7), (8). The value of I eL /U eL is compared with I eL.ref /U eL.ref , the errors are fed into the PI (CC/CV) controller that creates the phase-shifted angle. The transfer function of the object is identified by PSIM simulation software. Then, CC/CV charging controller designed as bellow. Thus, the CC/CV charging process is performed.

Simulation results
The circular coil structure is used to build the transmitter and receiver. When misalignment between the transmitter and receiver is variation, 2D/ 3D FEA simulation results of the coupling coefficient are shown in Figure 5. The results show that when misalignment between the transmitter and the receiver increases, the coupling coefficient decreases. The coupling coefficient equal to 0.25 is the highest when the transmitter and receiver align.
The wireless dynamic charging system is simulated by PSIM software to evaluate the proposed designs. Simulation model using the parameters given in Table 1. Figure 5b (k.est) show the estimation result of the coupling coefficient that estimated an error of less than 2%. simulation and the estimation result Figure 6 shows the results of a closed-loop simulation of the CC/CV charging process. The coupling coefficient is estimated at the beginning of the charging process. The value of equivalent load impedance is changed within a range of 10 Ω to 200 Ω during simulation, which corresponds to the charging state of the battery. Figure 6(a) shows CC charging mode simulation results with a reference value of 7.5 A. When the battery equivalent resistance (R eb ) changes from 15Ω to 25 Ω, simulation results indicate that: battery current is maintained to reference value with an error of 3.3%, battery voltage increases from 112V to 180V, estimated load resistance (R eb.est ) varies from 15.3 Ω to 24.8 Ω with an estimation error of 1.4%. Figure 6(b) shows CV charging mode simulation results with a reference value of 400 V. When the battery equivalent resistance (R eb ) changes from 120Ω to 150Ω, simulation results indicate that: battery voltage is maintained to reference value with an error of 1.12%, battery current decreases from 3,29 A to 2.64 A, estimated load resistance (R eb.est ) varies from 118Ω to 147Ω with an estimation error of 1.8%. Figure 7 gives waveform simulation results in the cases in Figure 6 at steady-sate. Figure 7(a) shows to control the constant charging current in the simulation case, the phase-shift angle (α) reduces from 28 0 to  Figure 7(a) shows to control the constant charging voltage in the simulation case, the phase-shift angle increase from 97 0 to 113 0 . The voltage/current waveform of the MOSFET, in this case, is shown in Figure 7(c). The two legs of the inverter are operated in two different states of soft switching. The S1/S4 MOSFET operates in the zero voltage switching condition and S3/S2 MOSFET operates in the zero current switching condition. The S1/S4 has turn-off loss and S3/S2 has turn on-loss. The ZVS/ZCS condition depends on the phase-shift angle and load.

Experiment results
A wireless charging system with a 2.5kW has built in the laboratory as in Figure 8. Polypropylene film capacitors are used in compensation circuits to reduce losses and increase high current tolerance in highfrequency systems. C3M0280090D SICs are used to improve inverter efficiency.
The experimental result waveforms of inverter output voltage/current in CC charging mode are shown in Figure 9. During the CC charging process, current charging is maintained by 8.5A, the ZVS is achieved perfectly, the ZCS condition is also almost achieved. The maximum efficiency reaches 92.1% at 2.5 kW in the CC charging mode when the receiver and transmitter are aligned.

CONCLUSION
The paper proposes to perform a wireless charging system for e-byke. The double-sided LCC compensation circuit is designed that the advantage of high efficiency and resonant frequency regardless of the coupling coefficient and load. The CC/CV charging control is performed only from the transmitter side. Also, the paper proposes a simple method to estimate both the load and the coupling coefficient based on measured parameters such as RMS of resonant current and input DC power of the inverter. The simulation and experimental results verify the feasibility of the proposed method. A 2.5 kW wireless charging system is built. The maximum charging efficiency reaches 92.1%.