An Improved Wireless Battery Charging System

Abstract

This paper presents a direct wireless battery charging system. The output current of the series-series compensated wireless power transfer (SS-WPT) system is used as a current source, and the output voltage of AC-DC converter controls the current source. Therefore, the proposed wireless battery charging system needs no battery charging circuit to carry out charging profiles, and can solve space constraints and thermal problems in many battery applications. In addition, the proposed wireless battery charging system can implement easily most other charging profiles. In this paper, the proposed wireless battery charging system is implemented and the feasibility is verified experimentally according to constant-current constant-voltage charging profile or multi-step current charging profile.

1. Introduction

The use of portable electronic devices and electric vehicles has become more widespread recently, the many electronic devices and electronic vehicles are plugged into wall outlets via power cables for many hours a day, and the use of wired charging apparatuses has become a part of daily life. In this scenario, a large number of wire-chargers are discarded as E (electronics)-waste due to contact failures such as broken wires or short-circuit problems, etc. Due to the increasing E (electronic)-waste problem, there has been increasing interest in the study and development of wireless power transfer (WPT) technology that can be utilized to transfer power to batteries without requiring expensive failure-prone connectors.

WPT technology can provide charging systems with low maintenance costs, high reliability, and the ability to operate even in extreme environments [1]. However, a wireless battery charging system requires more power stages than a wired battery charging system [2,3]. The wireless battery charging system needs a WPT system that consists of a power transmitter and a power receiver. An exclusive controller is also required to regulate the output of WPT system since the power transferred to the receiver of WPT system is not regulated whenever the load changes. The inverter or converter in power electronics is usually controlled by three methods; pulse width modulation (PWM), frequency modulation (FM), and amplitude modulation (AM). The AM method requires an additional stage for the DC-DC converter in order to control the amplitude of the input voltage. On the other hand, both PWM and FM need no additional stage since the inverter or converter uses power semiconductor switches for the power conversion. For this reason, when PWM or FM is applied to the power transmitter of a WPT system, the power transferred to the receiver can be easily regulated. Nevertheless, high current stress and large power loss are generated since the voltage and current in the power transmitter are not in phase. Due to this problem, regulation circuits such as synchronous rectifiers [2,3] or impedance tuners [4] are necessary in the receiver of a WPT system. Furthermore, battery-charging circuits such as low-dropout (LDO) regulators [2,3] or synchronous buck converters [4] are required for the battery charging. Figure 1 shows a conventional wireless battery charging system. As mentioned above, the conventional system consists of the following five key power stages; AC-DC converter, power transmitter of WPT system, power receiver of WPT system, regulation circuit, and battery-charging circuit.

For the wireless battery charging system, the power receiver, regulation circuit, and battery charging circuit must be embedded inside portable electronic devices or electric vehicles, but there is usually not enough space for these power stages. In addition to this problem, the regulation and battery-charging circuits generate huge heat and raise the problem of thermal stress on the electronic devices while being charged.

In this paper, a direct wireless battery charging system is proposed. The regulation and battery charging circuits in the conventional wireless battery charging system are removed, and the battery is charged directly from WPT system. Figure 2 shows the proposed direct wireless battery charging system. As shown in Figure 2, the proposed system is only made of AC-DC converter, power transmitter, and power receiver. The type of the applied WPT system is a series-series compensated wireless power transfer (SS-WPT) system, and it is connected directly to the battery. Generally, the output of SS-WPT system has inherent characteristic as a current source. Hence, without the help of dedicated regulation and battery charging circuits, the battery can be charged directly from the WPT system by adjusting the output voltage of the existing AC-DC converter in front of the WPT system according to the constant-current constant-voltage (CC-CV) charging profile [5,6,7,8,9,10,11] or a multi-step current charging profile [12,13,14,15,16,17,18].

The paper is organized as follows: in Section 2, the inherent current-source characteristics of the SS-WPT system are described. The implementation of the CC-CV charging or MCC charging profile in the proposed wireless battery charging system is explained in Section 3. Experimental verification is presented in Section 4, and finally, Section 5 draws the conclusions.

2. Current Source Characteristic of Series-Series Compensated Wireless Power Transfer

In the proposed wireless battery charging system, the SS-WPT system followed by AC-DC converter consists of a half-bridge inverter, resonant tank, full-bridge rectifier, filter, and load as the battery, as shown in Figure 3. The half-bridge inverter applies a square voltage into the resonant tank. The square voltage, V_square can be described as:

$$V_{square}(t)=\{\begin{array}{c}{V}_{IN}\\ 0\end{array}\begin{array}{c}(0<\omega t\le \mathsf{\pi })\\ (\mathsf{\pi }<\omega t\le 2\mathsf{\pi })\end{array}$$

(1)

where $\omega =2\mathsf{\pi }{f}_S$ and $f_S$ is the switching frequency of the half-bridge inverter in Figure 3.

The resonant tank consists of s transmitter coil, receiver coil, transmitter capacitor, and receiver capacitor. The capacitors in the resonant tank resonate with coils and improve the conversion efficiency of the system. Since the capacitors are in series with coils, the structure is called series-series (SS) compensation [19,20]. Since the series-series compensated resonant tank acts as a band pass filter, the effect of any harmonic components in the input square voltage V_square can be neglected, except for its fundamental component. Then, the transmitter and receiver voltages in the resonant tank are sinusoidal and expressed as V_T and V_R, respectively. The transmitter and receiver currents are also sinusoidal and expressed as I_T and I_R, respectively. The load represented as R_L can be described with an equivalent load resistance R_eq [20]:

$$R_{eq}=\frac{8}{{\mathsf{\pi }}^2}{R}_L$$

(2)

Figure 4a shows the equivalent circuit of the SS-WPT system in Figure 3, which consists of a sinusoidal transmitter voltage V_T, capacitors, a coupled-inductor model, and an equivalent load resistance R_eq. The components in the receiver side can be transformed into the transmitter side by the effective transformer turns-ratio, n. Here, the term n can be expressed as:

$$n=\sqrt{L_T/L_R}$$

(3)

where L_T and L_R are the transmitter coil’s self-inductance and receiver coil’s self-inductance, respectively.

The modified equivalent circuit of SS-WPT system can be represented with coupling coefficient κ, L_T, and C_T as shown in Figure 4b, assuming n = 1 and C_T = C_R. Figure 5 shows the modified equivalent circuit of SS-WPT system in frequency-domain.

The series impedance Z_S and parallel impedance Z_P are expressed as:

$$Z_S=j\omega L_T(1-\frac{{\omega }^2}{{\omega }_r^2})-j\kappa \omega L_T=-j\kappa {\omega }_r{L}_T=-j\kappa Z_O\mathrm{and}$$

(4)

$$Z_P=j\kappa \omega L_T=j\kappa {\omega }_r{L}_T=j\kappa Z_O$$

(5)

where ω_r is the resonant angular frequency and Z_O is the characteristic impedance. The series impedance Z_S and parallel impedance Z_P have the same magnitude, but different phase. To define the characteristics between input and output parameters, the resonant tank can be described as the transmission matrix in Equation (6). From Equation (6), the relationship between input and output parameters can be obtained in as Equation (7):

$$\left[\begin{array}{c}{V}_T\\ I_T\end{array}\right]=\left[\begin{array}{cc}0& -j\kappa Z_O\\ -j\frac{1}{\kappa Z_O}& 0\end{array}\right]\left[\begin{array}{c}n{V}_R\\ I_R/n\end{array}\right]$$

(6)

$$V_T=-j\kappa Z_O{I}_R/n\mathrm{and}{I}_T=-j\kappa \frac{1}{Z_O}n{V}_R$$

(7)

In Equation (7), it is known that the sinusoidal receiver current I_R is proportional to the sinusoidal transmitter voltage V_T. This means that SS-WPT system driven by the fixed output voltage of AC-DC converter behaves as a constant current-source. In addition, if the magnitude of the output voltage of AC-DC converter is controlled, the SS-WPT system is able to be a voltage controlled current-source at the resonant frequency. From Equation (7), the battery charging current, I_ch of the SS-WPT system in Figure 3 can be described with the input voltage V_IN as follows:

$$I_{ch}=\frac{4}{{\mathsf{\pi }}^2}·\frac{n{V}_{IN}}{\kappa Z_O}$$

(8)

Then, the output voltage V_O can be expressed with the I_ch as in Equation (9):

$$V_O=I_{ch}{R}_L=\frac{4}{{\mathsf{\pi }}^2}·\frac{n{V}_{IN}}{\kappa Z_O}{R}_L$$

(9)

Since the output voltage V_O of SS-WPT system is clamped at the battery voltage V_bat, the load resistance R_L can be determined from the V_bat and I_ch:

$$R_L=\frac{V_{bat}}{I_{ch}}$$

(10)

3. Implementation of CC-CV and MCC Charging

When the battery is not charged, it can be approximately modeled as only a capacitor with a high capacitance. At this state, the battery voltage V_bat is called open circuit voltage V_OC. On the other hand, when the battery is charged by the charging current I_ch, the battery voltage V_bat is called closed circuit voltage V_CC, which is lower than V_OC due to the IR voltage drop V_η across the overpotential resistance R_η and the voltage drop V_P by polarization. The relationship between V_OC and V_CC can be expressed as:

$$V_{CC}=V_{OC}+V_{\eta }+V_P$$

(11)

In order to charge the battery fully, the open circuit voltage V_OC should be able to arrive at the maximum allowable battery voltage V_{max_bat}. However, although the V_CC observed externally while being charged can reach to the V_{max_bat}, the V_OC is always lower than the V_{max_bat} due to the two voltage drops in Equation (11). To solve this, the charging current I_ch should be reduced to a predetermined small value I_sm at the end-of-charge because the V_η and V_P are proportional to the I_ch.

3.1. CC-CV Charging Profile

Figure 6a shows the concept on implementation of constant-current and constant-voltage charging in the proposed system. On the CC phase of the CC-CV charging, the relative high current is required for I_ch for the fast charge. Since the charging current I_ch of SS-WPT system is proportional to the input voltage V_IN as in Equation (8), this means that the output voltage of AC-DC converter in the proposed wireless charging system (or V_IN) must be set high. According to this principle, a fixed high V_IN is required for a constant high I_ch in the proposed system and then, the I_ch will charge the battery directly until the closed circuit voltage V_CC reaches the maximum allowable battery voltage V_{max_bat}, as shown in Figure 6a.

On the CV phase, the I_ch begins to decreasing and the decreasing I_ch reduces the two voltage drops of V_η and V_P to allow the open circuit voltage V_OC to reach the maximum allowable battery voltage V_{max_bat}. At the end of CV phase, the I_ch reaches the predetermined small current I_sm. For this mechanism, the proposed system must reduce the output voltage of AC-DC converter on CV phase. As a result, the I_ch of SS-WPT system will decrease and the open circuit voltage V_OC will continue to increase. The two voltage drops V_η and V_P will decrease gradually on the CV phase. On the other hand, the closed circuit voltage V_OC will be hold at the maximum allowable battery voltage V_{max_bat} due to the constant sum of the increased open circuit voltage V_OC and the decreased two voltage drops V_η and V_P.

When CC-CV charging is implemented in the conventional system, any transient phase may occur during the switching time from CC control mode to CV control mode [7]. However, in the proposed wireless battery charging system, the current source characteristic of SS-WPT system is used on the CC phase and only the voltage feedback loop is required on the CV phase. This means that in the proposed system, the CC phase is always switched into the CV phase smoothly.

3.2. MCC Charging Profile

Figure 6b shows the concept on implementation of multi-current charging in the proposed system. The MCC charging is composed of various CC phases with different constant magnitudes for I_ch. In this profile, whenever the closed circuit voltage V_CC reaches the predetermined voltage V_{pre_bat}, the charging currents I_ch is steped down in turn. On the last CC phase of the MCC charging, the I_ch should be stepped down to the predetermined small current I_sm to charge the battery fully, as shown in Figure 6b. In the proposed wireless battery charging system, this mechanism can be implemented by stepping down the output voltage of AC-DC converter in turn according to the MCC charging profile.

3.3. Other Charging Profile

The battery is charged generally from one current source, and the battery charging circuit carries out the role of the current source in the conventional wireless charging system. On the other hand, the SS-WPT system is used as a current source for the battery charging in the proposed wireless charging system. The current-level of the current source by the SS-WPT can be adjusted variously by changing the output voltage of AC-DC converter, as analyzed in Equation (8). From this, it is noted that most other charging techniques such as constant power charging [21,22,23,24], boost charging [25], varying current decay [26], and optimal charging based on temperature rise and charge time [27] can be implemented easily by the use of the proposed system.

4. Experimental Verification

4.1. Experimental Conditions

A prototype was made to verify the proposed wireless battery charging system. Symmetric wire-wound spiral coils (inner diameter: 30 mm and outer diameter: 70 mm) with ferrite sheet (width: 90 mm, length: 75 mm, and height: 500 μm) are fabricated as illustrated in Figure 7. Symmetric wire-wound spiral coils are separated by the air gap of 15 mm. The thickness of transmitter case is 1 mm, and the thickness of receiver case is 1 mm. The parameters in Figure 3 for the experiment are listed in

Table 1. Parameters for experiments.

Symbol	Description	Values/Part Name
LT	Self-inductance of transmitter coil	50 μH
LR	Self-inductance of receiver coil	50 μH
κ	Coupling coefficient	0.4
n	Turns-ratio	1 (27:27)
CT	Transmitter capacitance	78 nF
CR	Receiver capacitance	78 nF
Q1, Q2	Switches	50CN10N
D1–D4	Diodes	PMEG4030ER
fr	Resonant frequency	80 kHz

.

The lithium-ion batteries used for the experiment are prismatic 3100 mAh batteries (Samsung, city, country) which have the minimum allowable battery voltage V_{min_bat} of 3.4 V and a maximum allowable battery voltage V_{max_bat} of 4.3 V. One battery is charged according to the CC-CV charging profile, and another battery is charged based on the MCC charging profile. The input voltage V_IN, the charging current I_ch, and the closed circuit voltage V_CC are simultaneously recorded by a MV1000 digital recorder (Yokogawa, Japan).

Figure 8 shows the measured I_ch by changing the input voltage V_IN of SS-WPT system. As shown in Figure 8, the charging current I_ch of the proposed system increases linearly from 100 mA to 1000 mA when adjusting the V_IN from 3.61 V to 27.46 V. From this result, it is confirmed that the SS-WPT system behaves as a voltage controlled current source at the resonant frequency. The voltage controlled current source will charge the two batteries from the minimum allowable battery voltage V_{min_bat} of 3.4 V to the maximum allowable battery voltage V_{max_bat} of 4.3 V. And the I_ch at the end of CV phase is set to the predetermined small current I_sm of 100 mA.

4.2. CC and CV Charging Profile

Figure 9 shows the measured curves of CC-CV charging in the proposed system. The input voltage V_IN is set at 27.46 V to obtain the charging current I_ch of 1000 mA on the CC phase. Then, the I_ch of 1000 mA starts to charge the battery. The closed circuit voltage V_CC increases sharply due to the two voltage drops of V_η and V_P at the start point of the CC phase, and then reaches the maximum allowable battery voltage V_{max_bat} of 4.3 V from 3.9 V, as shown in Figure 9. Figure 10 shows the measured key waveforms in the SS-WPT system while the closed circuit voltage V_CC moves from 3.9 V to 4.3 V. As shown in Figure 10, the key waveforms at the V_CC of 3.9 V is nearly similar to that at 4.3 V. At the end of CC phase, the V_CC reaches the V_{max_bat} of 4.3 V, but the open circuit voltage V_OC will be not 4.3 V due to the two voltage drops V_η and V_P.

On the CV phase after the CC phase, the I_ch is decreased by reducing the V_IN in order to charge the battery fully. Then, the two voltage drops of V_η and V_P is reduced and the open circuit voltage V_OC of the battery will arrives at the V_{max_bat} of 4.3 V. Figure 11 shows the key waveforms in SS-WPT system on the CV phase. Since the WPT system operates at the resonant frequency, the input square voltage V_square and the transmitter resonant current I_T are almost in phase. Also, the receiver resonant current I_R leads the I_T by about π/2. When the I_ch reaches the predetermined small current I_sm of 100 mA, the CC-CV charging profile ends. The total charging time t_ch is 13,540 s.

Concretely, the charging times on the CC phase is 9238 s and the CV phase needs a time of 4302 s. With this experiment, it is also confirmed that the total charging time t_ch measured in the proposed wireless battery charging system is almost equal to that of the conventional wired battery charging system (13,200 s) under the same conditions.

4.3. MCC Charging Profile

Another battery is charged according to the MCC charging profile consisting of four CC phases. Figure 12 shows the measured curves of MCC charging in the proposed system. While charging the battery, the constant charging current I_ch is stepped down as follows: CC₁ phase (1000 mA)–CC₂ phase (800 mA)–CC₃ phase (600 mA)–CC₄ phase (400 mA)–CC₅ phase (100 mA), as shown in Figure 12. The I_ch on the last CC phase is set to the predetermined small current I_sm of 100 mA to charge the battery fully. The output voltage of AC-DC converter is stepped down to 27.46 V, 22.06 V, 16.38 V, 11.39 V, and 3.61 V in sequence in order to obtain the constant I_ch of 1000 mA, 800 mA, 600 mA, 400 mA, and 100 mA, respectively.

The maximum allowable battery voltage V_{max_bat} is selected as the predetermined battery voltage V_{pre_bat}. As a result, when the closed circuit voltage V_CC reaches the V_{max_bat} of 4.3 V, the I_ch are stepped down as shown in Figure 12. The total charging time t_ch under this MCC charging condition is 16,892 s.

5. Conclusions

This paper proposes a direct wireless battery charging system. Since the proposed system takes advantage of the inherent current-source characteristic of SS-WPT system, the regulation and battery-charging circuits in the conventional system are eliminated and hence it can be easily implemented in many battery applications such as portable electronic devices and electric vehicles, etc. In addition, a voltage controlled current source implemented by changing the output voltage of AC-DC converter in the proposed system can directly charge the battery. This enables us to easily implement various battery charging profiles such as CC-CV, MCC, etc. without an exclusive current feedback loop. In this paper, the abovementioned merits of the proposed system were analyzed in detail and the feasibility was verified with experiments based on a prototype of the proposed system, using Samsung prismatic 3100 mAh lithium-ion batteries, and a CC-CV charging profile. From the results, it can be stated that the proposed system will be more competitive than the conventional system.