Resonant Converter for Battery Charging Applications With CC/CV Output Profiles

In this paper, a novel resonant circuit topology is proposed for battery charging applications. Compared with traditional implemented circuits, the proposed topology can provide constant current (CC) and constant voltage (CV) charging profiles for different battery states automatically. Specially, zero-voltage-switching (ZVS) turned on of switching devices can be realized at fixed operating frequency for different charging levels, which benefits the transferring efficiency and reduces the voltage stress of the switches. In addition, simple design methodology can be derived to improve system’s practicality and reliability, avoiding complex control strategy. Experimental results obtained from a 200 W prototype system show good agreement with calculated results, validating that the proposed topology can be used for battery charging systems.


I. INTRODUCTION
In recent years, renewable energy and resource has attracted increased interest all over the world. As important storage elements in renewable energy systems, batteries are essential in the development of many industry applications such as consumer electronics, biomedical implants, electric vehicles (EVs) and train power supply [1]- [4]. Particularly, lithium-ion batteries are currently widely used in these applications, as a more economic type of batteries with more cycling times, compared with traditional energy storage batteries.
There are several methods utilized for charging batteries, such as taper current charging, pulse charging, reflex charging and constant voltage or current charging [5]- [10]. For taper current charging method, the current diminishes as the cell voltage builds up, which may cause a serious danger of damaging the cell if the charging rate and duration are not limited. For pulse charging method, the charging rate can be precisely controlled by varying the width of the pulses. However, the best charging duty cycle should be integrated in the controller, which makes the converter and The associate editor coordinating the review of this manuscript and approving it for publication was Gaetano Zizzo . controller complex. Among these methods, the Constantcurrent Constant-voltage (CC/CV) controlled charging method is the most widely used for charging Lithium and some other batteries which may be vulnerable to damage if the upper voltage and current limits are exceeded.
As shown in Fig. 1(a), the charging process contains CC mode before reaching upper voltage limit and CV mode when the current decreases to a trickle charge as the charge approaches completion [11] and [12]. Equivalent DC resistance in Fig. 1(b) can be derived from Fig. 1(a) to show the varying impedance characteristics during charging process with CCCV charging control method. The varied resistance at different charging states influences charging current, voltage and system efficiency essentially. Hence, a converter topology with simple control strategy is preferred to perform the output profiles in Fig. 1, for more reliability and practicality. In addition, the converter topology should be with high efficiency to increase energy utilization.
Battery charging technology based on DC-DC topologies has drawn attention in recent years due to its high equalization accuracy and high efficiency [13]- [18]. Mostly, control schemes for high-frequency DC-DC converters can regulate phase shift or operating frequency to adjust charging current/voltage at various load resistance [13], [14], and [16]- [24]. Among proposed topologies, phase-shifted full bridge (PSFB) converters have been investigated in many aspects due to their simple structures and ZVS features. However, at light-load conditions, it is hard to maintain ZVS conditions for the lagging-leg switches, while minimize conduction loss and ringing for the secondary-side rectifier [25] and [26]. Resonant converters with frequency modulation have been proposed and researched for battery charging, such as LLC topology [27]- [29]. High efficiency and high power density can be achieved with LLC converters operating around the resonant frequency. However, it is difficult to keep high efficiency for wide output voltage range, in particular when the switching frequency is much higher or lower than the resonant frequency. In order to maintain softswitching operation and high efficiency, many studies have been done on different modified circuit topologies or controlling methods. In [30] and [31], synchronous rectifiers (SRs) are integrated into conventional converters to obtain a higher voltage conversion ratio by controlling phase-shifted gate signals for SR switches. In [32] and [33], topologies have been proposed by transforming the structure from full-bridge to half-bridge to extend the output voltage range. However, hard switching may occur in these additional active switches for phase-shifted controlling especially at light load conditions, which leads to a lower efficiency. In order to address the hard switching problems, a variable switching-frequency control strategy for PSFB converters [34] and [35], or a phase-shift modulation method for LLC converters [24] and [36], are implemented under light load condition. Although higher efficiency can be obtained, the control and design methodology is relatively complex and the transition between different control modes slows down the dynamic response.
Therefore, in order to address the aforementioned issues, the paper proposed a new resonant topology for battery charging applications. The advantages of the proposed converter can be summarized as follows: (1) ZVS turned on switching for all primary switches in different charge states; (2) A fixed-frequency resonant operation in both CC and CV charge and hence lower circulating energy; (3) An automatic CC/CV charging patterns without dedicated control strategies at different load resistance.
The proposed system uses a CLCL resonant network and two high-frequency rectifiers, connected in series at input ports and parallel at output ports. The resonant network is fed by a high-frequency converter working at fix operating frequency. A mathematical model is presented to characterize the behavior of the proposed system as well as to show how the unique characteristics can be exploited to maintain a CC or CV charging profile without requiring dedicated control regulations. Experimental results of a prototype 200W system are shown to demonstrate the validity of the proposed topology.

II. PROPOSED RESONANT CONVERTER
The proposed resonant topology, which uses a half-bridge converter, a resonant network and two identical rectifiers, is shown in Fig. 2. The CLCL resonant network consists of the capacitors C i , C t and the inductors L i , L t [37]. Meanwhile, the capacitor C t is employed as DC blocking capacitor for the half-bridge converter. The input AC ports of the highfrequency rectifiers are in series, while the output DC ports are in parallel, for adding the transferred power from Part 1 and Part 2. The resistor R L serves as a battery load with various DC resistance depending on the charging state.
The converter is operated at the desired frequency, which can be expressed as: Proposed resonant converter topology.  For the CLCLresonant topolog as depicted in Fig. 3, the input impedance is constantly resistanceunder tuning frequency in (1) [37], which can be expressed by: Substituting (1) to (2), the impedance can be calculated as: Meanwhile, under tuning condition as (1), the output current of the circuit in Fig. 3 can be derived as: The harmonic components in input current of the CLCL resonant network are sensitive to the values of L t and C t . For example, Fig. 4 gives calculated waveforms of input current at different L t . As can be seen, both turn-on and turn-off switching states have changed with the variations of resonant component values. Higher harmonic components may result into worse EMC performance and lower system efficiency due to high-frequency skin effect. With a resonant value of 10 L i , Case 3 shows nearly sinusoidal current waveforms. Therefore, in order to minimize the influence by harmonic components, L t can be larger than L i .
The schematic diagram in Fig. 2 can be further simplified by one voltage source u i and Z 1 , Z 2 to represent impedances of Part 1 and Part 2, as shown in Fig. 5. If the value of R L is small, the impedance Z 1 is much larger than Z 2 since L i and C i form a network close to parallel resonant. Therefore, the magnitude of u o2 is much smaller than u i . Fig. 6(a) shows typical waveforms during this period. As evident from (4), the output current i o1 is determined by the input voltage u o1 , performing CC state. As R L turns to be larger, the impedance of Z 1 is decreased while Z 2 is increased. As evident from the waveforms in Fig. 6(b), both Part 1 and Part 2 transfer power to the load. Since the impedance of Z 1 and Z 2 is close to resistance, ZVS can be achieved during this period. If the load resistance becomes larger, Z 2 is much larger than Z 1 , which results in large magnitude of u o2 , as shown in Fig. 6(c). During this period, CV performance can be achieved. In general, the proposed topology consists of two different parts, as Part 1 to perform CC characteristics (as proved by (4)) and Part 2 to perform CV characteristics. By cascading these two parts together, they can play a leading role at different load resistance as shown in Fig. 6.
It should be noted that the input voltage u i is in phase with i o2 . As a result, the transferred power can be given by: Under tuned condition, the current i o1 is determined by the input voltage of the CLCL network as: The relationship of u o2 and the output voltage U o , transferred by a rectifier in Part 2 shown in Fig. 2, can be determined as: By substituting (6) and (7) into (5), the resonant current i o2 can be derived as: where M t and N t are given by: VOLUME 8, 2020 By substituting (8)-(10) into (5), the output voltage and current can be derived as: Equation (11) and (12) represents the relationship between the output current/voltage and the equivalent load resistance. By substituting determined resonant values into (11) and (12),  Fig. 7, where the system was tuned at 200 kHz and the input voltage is 100 V. The resonant components C t , L t , C i , L i are designed as 10 nF, 71 µH, 80 nF and 7.9 µH. As can be seen, I o is kept almost constant when the load resistance is less than 15 . After that, U o becomes constant while I o decreases, as R L is increased. Compared with the CC/CV profiles shown in Fig. 1, results in Fig. 7 indicate the output characteristics of the proposed topology is in good agreement with the trend of CC/CV curves at different load resistance. The largest difference is about 8% at the end of CC mode and the beginning of CV mode, since there is a soft transient process from CC to CV modes due to the natural feature of the proposed topology. The deviation of calculated and expected values in Fig. 7 comes from the difference between simplified fundamental analysis method at resonant frequency as shown in (1)-(12) and the nonlinear switching system.
The input voltage U d and the resonant parameters play an important role in regulating the output power. Therefore, Fig. 8 shows variations in I o , U o as a function of R L where the system was operating at different U d and L i . As evident from Fig. 8(a) Based on above analysis, under tuning conditions in (1), the output profiles perform CC states at small load resistance and CV states at large load resistance, as can be seen in Fig. 7. The profile is coincident with characteristics of charging batteries.
Furtherly, the proposed charging topology can be converted to an isolated version with a transformer T r1 , as shown in Fig. 9. A DC block capacitor C DB is employed to block the DC component of the voltage generated from the halfbridge converter. As can be seen, the working principle is the same as discussed before. Efficiency is a little lower than the proposed topology in Fig. 2, because of the high-frequency transformer. However, the output voltage and current values can be adjusted by changing the turn ratio of the transformer.  Compared with traditional PSFB or LLC converters, ZVS switching can be obtained easily without dedicated controllers or additional active switches, which can benefit the system design and increase the reliability. The drawback of the proposed topology is the extra rectifier, which may increase the cost of the system. However, from another view, more distributed diodes may benefit the design of cooling system especially at high transferred power level.

III. EXPERIMENTAL RESULTS AND DISCUSSIONS
A resonant system with the circuit in Fig. 2 was designed and built to validate the viability of the proposed topology, as shown in Fig. 10. The system comprises a 200 W converter and two high-frequency rectifiers, which were connected by a CLCL network. Fig. 11 illustrates the steps to design the system parameters. Firstly, the CC and CV values and the resonant frequency should be determined. For charging batteries, the CC charging value is usually specified from manufacturers as the maximum charging rate which the battery can be fully charged while avoiding damaging by overcharging. Meanwhile, the CV charging value should be predetermined according to the battery cell upper voltage limit, which is known as the float level during the CV mode. After selecting specific batteries, the U o , I o can be determined firstly. The optimum switching frequency is found on the basis of design tradeoffs amongst converter's efficiency, size, weight and cost. Higher frequencies may produce smaller solution size using lower valued resonant inductors and capacitors, but decrease efficiency and impact thermal performance with higher magnetic core and copper losses in passive resonant elements. In this design, the switching frequency is selected as 100 kHz for the switching device IPP200N25N3G.
As shown in Fig. 5 and Fig. 6, if the load resistance R L is very small, the impedance Z 1 is much larger than Z 2 as can be seen in (3), Fig. 6 and Fig. 7. Therefore, the CC current value can be simplistically determined as shown in (4). According to the selected switching frequency, L i is calculated as: Thus, a close resonant inductor L i is selected as 33.4 µH due to dead-time effect of half-bridge converter.
As a result, the resonant capacitor C i can be calculated as 75.8 nF by (1). An approximate value 74.2 nF is achieved by combinations of several resonant capacitors shown in Fig. 10.  According to Fig. 4, the inductor L t is determined as much larger than L i to minimize the influence by harmonic components. Here, L t is determined as 135.2 µH, as 4L i to eliminate the harmonics in current. Substituting L t into (1), C t is derived as 24.8 nF. As a result, a capacitor of 25 nF is selected into the resonant topology.
If the load resistance R L is large, the impedance Z 2 is much larger than Z 1 as shown in Section II, thus Part 2 plays the most important role in these conditions, which means the CV value U o is determined as: Thus, the input voltage U d is derived as 200 V. The parameters of the prototype are given in Table 1.
The experimental results of output voltage and current are compared with the calculated values, as shown in Fig. 12. When the load resistance is less than 28 , the output current decreases slowly, while the output voltage increases markedly. After that, the output voltage keeps almost constant and the output current decreases dramatically. Both the simulated and experimental results are in good agreement, confirming the accuracy of the calculated model.  According to the analysis presented in Section II, the relative phase between u i and i o2 is not influenced by the variations in the load resistance. Thus, the experimental waveforms taken from the prototype, where R L is 12.6 , 32.1 , and 65 , are shown in Fig. 13. As evident from the results, the phase between u i and i o2 is almost zero with the increased resistance. The magnitude of i o2 increases firstly, then decreases. As a result, ZVS of the switching devices can be realized at fixed operating frequency for different load resistance, which means under tuning conditions in (1), the output profiles perform CC states at small load resistance and CV states at large load resistance as shown in Fig. 12. As a result, the performance of the proposed topology is coincident with characteristics of charging batteries.  The total efficiency was measured with different load resistance as shown in Fig. 14. As evident from the results, the efficiency changes slightly for CV charging state, while the efficiency increases for CC charging state because the losses of diodes account for a larger proportion for low voltage and high current charging state. The peak efficiency of the system is 95.4%.
In order to illustrate the efficiency performance at different load resistance, Fig. 15 gives the loss distributions for different operating conditions. When R L is 13 for CC charging state, the diode losses in Part 1 in Fig. 2 accounts for the largest proportion of the total losses. As R L becomes larger, the diodes loss in Part 2 takes larger proportion. Meanwhile, the core losses in the inductor L t increases first and then decreases obviously, as the load resistance is increased. It should be noted that the switching losses P sw is relatively very small owing to the ZVS switching performance.
To sum up, the benefits of the proposed resonant topology are as follows: (1) The experimental current i o2 and voltage u i of the designed converter indicate that ZVS turn on for all primary switches can be achieved during both CC and CV charge states at different load resistance. Thereby, the efficiency of the proposed resonant converter is promoted, especially with light load.
(2) The switching frequency is fixed and closed to the resonant frequency, which is beneficial for transferring efficiency and reducing the voltage stress of the switches. (3) No dedicated control strategy is utilized for CC/CV output characteristics, which can improve the system reliability and practicality.
In general, a comparison between the proposed topology and existing works has been listed in Table 2, to shown the advantages of the new topology as discussed above.

IV. CONCLUSION
A novel resonant converter topology has been proposed for battery charging applications. The proposed topology utilizes a CLCL resonant network and two high-frequency rectifiers to realize CC or CV charging states with different load resistance automatically, without a dedicated sophisticated controller. ZVS turn on can be achieved for all switches in the proposed converter, which benefits the transferring efficiency and voltage stress. The novel resonant circuit has been described in detail and calculated to show the unique characteristic of power transfer. Experimental results of a prototype 200 W system have been presented to demonstrate the applicability of the proposed converter.