N OWADAYS, environmental problems and traditional en- ergy depletion are becoming increasingly serious. Electric vehicles (EVs) have drawn much attention owning to their environmental-friendly characteristic [1]- [3]. The on-board battery charger (OBC) is a crucial technology for the development of EVs. Generally, OBC is a two-stage system, which is composed of a power factor correction circuit and a dc/dc converter. For the dc-dc converter, LLC resonant converters have been widely used in this field owning to their features such as: wide input and output voltage range; soft switching capability; and high power density [4]- [18].
For a lithium battery cell, constant current (CC) and constant voltage (CV) charging are required. In order to regulate the output of an LLC resonant converter, frequency modulation (FM) or combining FM with phase-shift modulation (PSM) are frequently adopted. In [4]- [11], the FM is applied to regulate the output of the LLC resonant converter. The design optimization [9] and the control strategies [7] of the LLC resonant converter in the wide output voltage range application is discussed. Specifically, optimized design methodologies for LLC resonant converter based on time-weighted average efficiency and based on time-domain analysis are proposed in [11]. However, the main disadvantage of the FM in wide output voltage range applications is that a wide switching frequency range is required. This will cause some problems, such as poor electromagnetic interference (EMI) performance, complicated design of magnetic components, low power density, and high conduction losses. In addition, in order to satisfy the wide output voltage requirement and obtain a low voltage gain, the switching frequency above the series resonant frequency has to be applied. However, in this case, the zero-current switching (ZCS) for the secondary diodes is lost, and this will lead to undesired decrease in efficiency.
In order to narrow the operating frequency range, a control strategy combining the FM and the PSM is proposed in [12]- [15]. Different combination strategies are analyzed and proposed to improve the system efficiency. However, the PSM is not preferred for heavy load conditions due to its high turn-OFF current for the primary switches when compared with the FM. In addition, it still suffers from variable frequency range, and complicates control algorithms. Therefore, the problems of EMI and magnetic components design still remain.
To further narrow the switching frequency range, some topologies based on the modification of an LLC converter structure are proposed [16], [17]. However, these topologies require additional switches that operate at hard switching and cause additional power losses. In [18], a dual full-bridge LLC resonant converter topology is proposed. An additional switch and a resonant capacitor are required to adjust the operation modes of the LLC resonant converter, namely constant output current mode and constant output voltage mode. However, although the constant output voltage mode is verified and has been widely used, the constant output current mode, especially its accuracy, still needs to be proved, which will be discussed in Section II. In addition, all of these topologies still need to adopt FM, PSM, or pulsewidth modulation (PWM) to implement closed-loop control. Although the switching frequency range has been reduced, the abovementioned problems are still present.
In addition to FM and PSM, the magnetic control (MC) is also a feasible control strategy for resonant converters. It has been adopted in many applications, including LED drivers, resonant converters, and inverters [19]- [24]. In order to solve the abovementioned problems, in this paper, a dual half-bridge LLC resonant converter with MC (or variable inductor control) is proposed. Instead of using FM or PSM, the variable inductor is adopted to regulate the output. Therefore, a constant duty cycle and switching frequency for the primary switches can be achieved, which simplifies the EMI and magnetic components design. Moreover, by carefully designing the resonant networks, the zero-voltage switching (ZVS) operation for primary switches and ZCS operation for secondary diodes can be achieved. Compared with the topology given in [18], the proposed topology has the following advantages.
1) Owning to the MC, constant duty cycle and constant switching frequency for primary switches can be achieved. 2) No additional switch and resonant capacitor are required, thus the system structure is simplified. 3) In addition, switching the capacitor and sudden changes in the resonant capacitor value will result in overshoot or other problems that may damage the converter. In the proposed MC method, the resonant inductor value can be adjusted continuously without abrupt change. 4) The control principle for MC is a simple voltagecontrolled current source, which can simplify the control circuit design compared with other control strategies. 5) The function decoupling idea is adopted. One of the LLC resonant converters is always operating at the series resonant frequency and handling most of the output power, whereas another LLC resonant converter adopts MC to regulate the output so that the averaged efficiency can be improved. This paper is organized as follows: examinations of constant output voltage and constant output current mode are implemented in Section II. In Section III, the MC strategy is briefly introduced and the operation analysis for the proposed topology is presented. Then, the detailed parameter design procedures are presented in Section IV. Finally, a 320-W experimental prototype is built to verify the theoretical analysis.
In this part, the constant output voltage and constant output current modes of an LLC resonant converter are examined. Fig. 1 shows the topology of a half-bridge LLC resonant converter and the converter model obtained by using the fundamental harmonic approximation (FHA) method, where V ac is the fundamental harmonic of the resonant network input voltage and V p1 is the fundamental harmonic of the transformer primary side voltage. There are two resonant frequencies in an LLC resonant converter. First one is the series resonant frequency f r , which is determined by resonant capacitor C r and resonant inductor L r . The second one is the parallel resonant frequency f m , which is determined by resonant capacitor C r , resonant inductor L r , and magnetizing inductor L m . Both resonant frequencies are given by the following equations:
Theoretically, at the series resonant frequency, the output voltage of the LLC resonant converter is independent of load, and at the parallel resonant frequency, the output current is independent of load. In the following part, the theoretical analysis will be discussed, and the experimental results will be used to examine the accuracy of the constant output voltage and constant output current characteristics. In this research, the resonant inductor is separated from the transformer, so the leakage inductance is very small compared with the magnetizing inductance and resonant inductance, which makes the secondary leakage inductance effects ignorable. However, if the integrated transformer is adopted, where the secondary leakage inductance is not small anymore, its effects must be analyzed as presented in [25] and [26]. Therefore, in this research, the secondary leakage inductance effects are ignored.
Based on Fig. 1(b), the output voltage of the LLC resonant converter can be derived according to the voltage divider law as follows:
At the series resonant frequency, resonant capacitor C r is resonating with the resonant inductor L r , so the term (1/C r s + L r s) equals 0. Then, (3) can be simplified as
Based on (7), it can be seen that at the series resonant frequency, the output voltage is independent of the load, so it is in the constant output voltage mode.
By dividing both sides of (3) by R ac and rearranging the result, one can obtain
At the parallel resonant frequency, resonant capacitor C r and resonant inductor L r are resonating with magnetizing inductor L m , so the term (L m s + L r s + 1/C r s) equals 0. Then, (8) can be simplified as
It can be seen that the output current is independent of the load for this condition.
In order to examine the constant output voltage and constant output current characteristics, an LLC resonant converter with the parameters shown in Table I is built.
According to (7), at the series resonant frequency, the output voltage is kept constant at 20 V, by taking diode forward voltage into consideration, and the output voltage should be kept constant at 19 V. Fig. 2 shows the experimental waveforms including the input voltage V in , the resonant inductor current i Lr , the output voltage V o , and the output current I o at series resonant frequency with different loads.
By substituting s = 2πf s j (where f s = f m ) into ( 9), one can calculate that the theoretical constant output current is 1.29 A. Fig. 3 shows the experimental waveforms when the converter is operating at parallel resonant frequency with different loads. The accuracies of the constant output voltage and constant output current modes are obtained by calculating the relative error of the theoretical value and experimental value as illustrated in Fig. 4. It can be seen that the accuracy of constant output voltage mode is much higher than that of the constant output current mode, and the accuracy varies slightly with the load. In comparison with the constant output voltage characteristic, the constant output current characteristic has considerable errors, which will finally lead to a relatively wide switching frequency range to keep the output current constant. This phenomenon can easily be understood by examining the principle of the FHA method, only the fundamental harmonic is considered. When the switching frequency is close to the series resonant frequency, the resonant current is more sinusoidal and FHA provides more accurate results. However, when the switching frequency is away from the series resonant frequency, the waveform is distorted and many harmonics are added (see Fig. 3), which leads to the poor accuracy of the constant output current mode. In addition, if the LLC resonant converter operates at parallel resonant frequency, the ZVS operation for the primary switches is lost, which is not preferred for MOSFETs. In [18], both the constant output current and constant output voltage modes are adopted. However, due to the poor accuracy of the constant output current characteristic, a relatively wide switching frequency operation range is still required. Because of the high accuracy of the constant output voltage mode at the series resonant frequency operating point, only this mode is used in the proposed topology.
In this part, the operation principle of the MC is briefly introduced, and then, the operation analysis for the proposed converter is presented. Finally, based on the battery charging profile, the design considerations for the proposed converter are elaborated.
The structure of the variable inductor using a double E-core is shown in Fig. 5. The control winding or auxiliary winding is divided into two identical portions with the number of turns N DC , which is mounted on the lateral legs of the core. The inductor winding or main winding with the number of turns N AC is placed on the air-gapped middle leg of the core. The dc bias current allows for the modification of the inductance of the main winding. The typical relationship between dc bias current and variable inductance value is shown in Fig. 6. It can be seen that the variable inductance value is inversely proportional to the dc bias current.
In the proposed method, the inductance value of the variable inductor is controlled. The control scheme is shown in Fig. 7. During the CC charge mode, the error is obtained by comparing the reference current and the feedback current, and then applied to the proportion integration (PI) controller. Similarly, during the CV charge mode, the error is obtained by comparing the reference voltage and the feedback voltage and then the error is applied to the PI controller. The PI controller generates the control signal that is used to adjust the dc bias current. Consequently, the inductance value of the variable inductor is adjusted to regulate the output current or voltage of the second LLC resonant converter.
The proposed converter is shown in Fig. 8. The converter mainly includes the following parts: 1) half-bridge inverter, which is shared by two LLC resonant converters; 2) two LLC resonant networks, LLC 1 operates at the fixed operating point, whereas LLC 2 adopts MC to regulate the output; and 3) two rectifier networks, which are connected in series in order to reduce the voltage stress on each diode. Therefore, a low-voltage rating diode can be selected to achieve higher efficiency.
Fig. 9 shows the voltage gain curves versus normalized switching frequency
where the resistive curve is the operating points when resonant network input current is in phase with its input voltage. It can be seen that the line f n = 1 and the resistive curve have divided the LLC resonant converter operation into three regions, namely region 1, region 2, and region 3. It is well known that in region 1, ZVS operation for primary switches is achieved, but ZCS operation for secondary diodes is lost. For region 2, both ZVS operation for primary switches and ZCS operation for secondary diodes can be achieved. For region 3, ZCS operation for primary switches and secondary diodes are achieved. Since MOSFETs are preferred to operate under ZVS, region 2 is the most suitable operation region for the LLC resonant converter. Operation in region 2 can be guaranteed if: the switching frequency is below or equal to the resonant frequency; and the voltage gain is monotonously decreasing with the increase in normalized switching frequency within the operating range.
In addition, a lower f n leads to a higher voltage gain. Similarly, a lower Q results in a higher voltage gain. For the MC, the switching frequency is fixed, whereas the resonant inductance is adjustable, which means that the series resonant frequency is not constant. So, the normalized switching frequency is adjustable. At the CC charge mode, the output voltage is increasing and a higher voltage gain is required. Therefore, the variable inductance value is reduced to increase the series resonant frequency and reduce the normalized switching frequency, finally increasing the voltage gain and keeping the output current constant. At CV charge mode, the output voltage needs to be kept constant while the quality factor Q is reducing during the CV charge stage and the voltage gain is increased. So, the variable inductance value should be increased to reduce the series resonant frequency and increase the normalized switching frequency, thus finally keeping the voltage gain and the output voltage constant. During the whole operation range, LLC 1 is designed to operate at the series resonant frequency point, where its output voltage is almost kept constant.
Before the discussion of the design considerations, the battery charging profile is introduced. The starting voltage value of a battery cell is 3.2 V, the end voltage value is 4.2 V, and the charging current is 2 A. The battery pack is composed of 38 battery cells connected in series. The battery pack charging profile and the voltage distribution between LLC 1 and LLC 2 are shown in Fig. 10. It can be seen that LLC 1 is designed to operate at the series resonant frequency and its output voltage keeps constant. The function decoupling idea is adopted here to further improve the system efficiency. The principle for determining the power distribution between two LLC resonant networks can be described as the following: as shown in Fig. 8, where P in1 and P o1 represent the input power and output power of the LLC 1 , and P in2 and P o2 represent the input power and output power of LLC 2 , and the efficiencies of LLC 1 and LLC 2 are represented by η 1 and η 2 , respectively. Based on the energy conservation law, the following equations can be obtained:
Then, the total output power of the proposed converter can be expressed as follows:
The system efficiency can be derived as follows:
where m 1 and m 2 are the percentile power distributions of LLC 1 and LLC 2 , respectively, and
Based on (13), the system efficiency is related to the parameters m 1 , m 2 , η 1 , and η 2 . In this research, LLC 1 is designed to operate at the series resonant frequency operating point, which is also the best efficiency operating point for an LLC resonant converter; while the responsibility of LLC 2 is to regulate the output of the whole system, so its operating point varies, which will reduce the corresponding efficiency η 2 . This viewpoint is also verified by the efficiency curve of the proposed converter as shown in the experimental results. Therefore, theoretically, to maximize the overall system efficiency, parameter m 1 should be close to 1, which means LLC 1 should handle most of the output power. However, the output voltage of LLC 2 is required to achieve the closed-loop regulation. In addition, a small output voltage of LLC 2 will lead to a high step-down turns ratio when considering the high input voltage (340-380 V), which will degrade the converter efficiency. Overall, the main considerations for the power sharing between two LLC resonant networks are: overall system efficiency, which requires a small output voltage of LLC 2 ; and appropriate turns ratio of LLC 2 , which avoids a very small output voltage. In this research, a compromise between ( 1) and ( 2) is made. The minimum output voltage of LLC 2 is designed to be 20 V, and the percentile power distribution of LLC 1 is 62.5% or 37.5% for LLC 2 .
The specifications of the proposed converter are summarized in Table II. Input voltage equals 360 V, which is selected as the nominal operating point.
1) Design Considerations for LLC 2 : Since LLC 1 is operating at the series resonant frequency, which is much easier to design, the design procedures begin with LLC 2 . The design guidelines for LLC 2 are summarized as follows: First, the secondary diodes can achieve ZCS operation, which requires a switching frequency lower than the series resonant frequency during the whole operation range; and second, the voltage gain of LLC 2 can satisfy the system voltage gain requirement, and the voltage gain is monotonously decreasing with the increase in the normalized switching frequency.
First, in order to guarantee the ZCS operation for secondary diodes, the series resonant frequency operation is designed at the beginning of the CC charge when the resonant inductor reaches its maximum value. Based on the input voltage and output voltage at the beginning of the CC charge, the transformer turns ratio can be calculated as follows:
)
The voltage stress should be considered when designing resonant capacitor C r2 . Equation ( 16) represents the voltage stress on the resonant capacitor. The voltage stress is selected as 400 V, and the resonant capacitor of 24.7 nF is selected. As mentioned above, when the resonant inductor reaches its maximum value, the series resonant frequency should be equal to the switching frequency, which can guarantee the ZCS operation for the secondary diodes during the whole operation range. Based on (17), L r,max equal to 102 μH is calculated and
Next, we need to find the suitable magnetizing inductor value and minimum resonant inductor value to satisfy the system voltage gain requirement. Based on the battery charging profile, the maximum voltage gain is calculated as follows:
V in,min = 160 -170 1.9 × 7.6 170 = 3.38.
(
At the beginning of the CC charge mode, the equivalent load is the smallest one, and this is also the worst condition for the converter to achieve the desired voltage gain. Fig. 11 shows the voltage gain curve of LLC 2 with different resonant inductor and magnetizing inductor values under the worst condition. It can be seen that the voltage gain is monotonously decreasing with the increase in the normalized switching frequency under these conditions, so LLC 2 is operating in region 2. In order to satisfy the system voltage gain requirement, a lower magnetizing inductor is preferred. However, a lower L m results in a high-resonant rms current and high conduction losses. Therefore, a compromised magnetizing inductor value of 120 μH is selected. Then, the minimum resonant inductor value of 27 μH can be found based on Fig. 12 to meet the maximum voltage gain requirement. Up to now, the resonant network for LLC 2 has been finalized: C r2 = 24.7 nF, L r2 = 27-102 μH, and L m2 = 120 μH.
2) Design Considerations for LLC 1 : Clearly, for LLC 1 , it is always operating in region 2. Similarly, based on the voltage stress requirement, a resonant capacitor value of 66 nF is selected. Since LLC 1 is operating at the series resonant frequency point, the resonant inductor L r1 can be calculated based on the following equation So, L r1 = 38 μH is selected. For magnetizing inductor L m1 , the design considerations mainly include two aspects: First, rms value of the resonant network current should be low; and second, total input impedance of the resonant tank should be inductive.
The relationship between magnetizing inductor L m1 and the resonant network rms current is shown in Fig. 12. It can be seen that higher magnetizing inductance value leads to a lower resonant network rms current. In addition, when the magnetizing inductance value is higher than 200 μH, the current decreasing slope becomes low, so L m1 equal to 200 μH is selected. Next, the total input impedance will be examined.
Because of the parallel connection of two LLC resonant networks, the total input impedance can be expressed as follows:
where Z in1 is the input impedance of LLC 1 and Z in2 is the input impedance of LLC 2 .
Since LLC 1 is operating at the series resonant frequency, the input impedance of LLC 1 can be simplified as
For LLC2, the input impedance can be expressed as below
Based on ( 20)-( 22), one can find the relationship among resonant tank input impedances Z in1 , Z in2 , and Z in and the resonant variable inductor L r2 as shown in Fig. 13. Similarly, the worst condition (at the beginning of the CC charge, where the converter is the least inductive) for the converter is checked. It can be seen that during the whole operation range, the total input impedance angle is positive, which means that the converter is operating in inductive region, agreeing with the theoretical analysis. Thus, the primary switches can achieve the ZVS operation. The parameters for LLC 1 are: C r1 = 66 nF, L r1 = 38 μH, and L m1 = 200 μH.
In this part, an experimental prototype is built to verify the theoretical analysis. The experimental setup is shown in Fig. 14. The system mainly includes the following parts: 1) main power circuit; 2) voltage and current sampling circuit, where LV 25-P and LA 25-NP from life energy motion (LEM) are adopted to sample the output voltage and output current, respectively; 3) a control circuit, where LM358 is adopted to form a PI controller, and combined with NPN transistor BD137, a voltage controlled current source is built to provide the dc bias current for the variable inductor; and 4) auxiliary power supply, which is designed to make a control circuit, a voltage sampling circuit, and a driver circuit work. In practice, the leakage inductance of the transformer can be utilized as part of the variable inductor, so the design requirements for transformer are reduced. Circuit parameters and components part numbers are given in Table III.
Similarly to the traditional LLC resonant converter [27], the soft start-up mechanism can be described as follows. The switching frequency during the start-up process is decreased from a high switching frequency (three times higher than the nominal operating frequency) to the nominal switching frequency to reduce the current spike. Fig. 15 shows the soft start-up process of the proposed topology. It can be seen that the output voltage builds smoothly and quickly. The total settling time is about 4 ms. Fig. 16 shows the relationship between the designed variable inductor value and dc bias current. The blue line shows the simulation results by using the model in [21] and the red line shows the obtained experimental results. It can be seen that the experimental results agree with the simulation results, and the dc bias current is set as 0-0.5 A to satisfy the required inductance range.
First, the operation of LLC 1 is tested individually. Fig. 17 shows the open-loop experimental waveforms of the output voltage V o1 , output current I o1 , resonant inductor current i Lr , and resonant tank input voltage V HB of LLC 1 with different output power when input voltage equals 380 V. It can be seen that the output voltage of LLC 1 remains constant at 100 V with different output power, which agrees with the theoretical analysis. Therefore, LLC 1 is designed to operate at the series resonant frequency operating point, where its output voltage almost remains constant with different output power.
Then, the experimental waveforms of the proposed dual halfbridge LLC resonant converter with MC are presented. The experimental waveforms are obtained for V in = 360 V, which is the nominal operating point in this research. Five operating points from the battery charging profile are selected and depicted in Fig. 18.
The left of Fig. 19(a) shows the experimental waveforms of the resonant tank input voltage V HB , input current i tank (which input voltage. So, the converter is operating in inductive region, and the ZVS operation for the primary switches is achieved.
Similarly, Fig. 19(b) shows the experimental waveforms of operating point B. The output current is constant at 2 A, and the resonant tank input current is lagging behind the input voltage. So, the ZVS operation for the primary switches is achieved.
Fig. 19(c) shows the experimental waveforms of operating point C, which is also the transition point from CC charge mode to CV charge mode. At this operating point, the output current is still kept constant at 2 A, whereas the output voltage reaches its maximum value of 160 V. In addition, the ZVS operation is still maintaining in this condition. seen that the diode current decreases to zero before the commutation occurs. So, the ZCS operation for both diode rectifiers of LLC 1 and LLC 2 are achieved during the whole operation range.
Based on Figs. 19 and20, one can conclude that during the whole operation range the following statements hold.
1) LLC 1 is always operating at the series resonant frequency point. Its output voltage is almost kept constant at 95 V, and its resonant inductor current is lower than 3 A, which agrees with the theoretical analysis. As shown in Fig. 12, by selecting the magnetizing inductor L m1 = 200 μH, the resonant current is below 3 A.
2) The output voltage of LLC 2 increases from 26 to 69 V during the CC charge mode to meet the voltage gain requirement.
3) The proposed converter can achieve CC charge and CV charge. 4) The ZVS operation is achieved for the whole operation range. 5) Since the switching frequency is designed below the series resonant frequency, the ZCS operation is achieved for the rectifiers during the whole operation range. Next, the dynamic response of the proposed converter is investigated. Fig. 21 shows the dynamic response of the proposed converter for different conditions at the CV charge mode: when output power changes from 192 to 64 W; and when input voltage changes from 360 to 380 V. It can be seen that the output voltage remains constant when the output power changes, both the output voltage and output current remain constant when input voltage changes, and the proposed system provides fast dynamic response.
Similarly, Fig. 22 shows the dynamic response at the CC charge mode when output power changes and input voltage changes. It can be seen that the dynamic response of the proposed converter is good. Fig. 23 shows the efficiency curve of the proposed converter. Since the output power level is relatively low, the efficiency is low at light load. However, for higher output power levels, the system efficiency is above 92%, and the maximum measured efficiency is around 95.5% when the output power equals 300 W. In addition, it can be seen that the efficiency of LLC 1 is about 5% higher than that of LLC 2 since LLC 1 is always operating at the series resonant frequency, which is highest efficiency operating point for LLC resonant converters. Its maximum efficiency is measured around 98%. Fig. 24 shows the estimated power loss analysis of the converter when P o = 320 W. It can be seen that since the ZVS operation is achieved for primary switches, only the conduction losses are included; for the secondary diode rectifiers, the ZCS operation is achieved, but the conduction losses cannot be ignored due to the relatively high rms current that flows through the rectifier and the high forward voltage of the diode. In a future work, synchronous rectifier technology, low forward voltage diode, and half-bridge rectifier can be adopted to further improve the system efficiency. For the variable inductor, both the control winding loss and core loss are included.
Table IV shows the comparison results between different control strategies and topologies of an LLC or dual LLC resonant converter. Based on the comparison results, the proposed dual half-bridge LLC resonant converter with MC has the following advantages: 1) fixed switching frequency operation, which simplifies the magnetic components and driver circuits design; 2) no additional switch is required, so no extra loss is generated, and no corresponding control circuit is needed; and 3) by using two LLC resonant networks and the function decoupling idea, the system efficiency can be improved.
In this paper, a dual half-bridge LLC resonant converter with MC for battery charger application is proposed. The half-bridge inverter is shared between two LLC resonant converters, with their inputs connected in parallel, whereas their outputs are connected in series. One of the LLC resonant converters is designed to operate at the series resonant frequency point, where the output voltage is independent of the load. Second LLC resonant converter adopts MC to regulate the output of the system to provide CC charge and CV charge to the battery. In addition, the function decoupling idea is implemented to further improve the system efficiency. Since LLC 1 is operating at the best efficiency operating point, it handles most of the output power, and the main responsibility of LLC 2 is to achieve closed-loop control. By carefully designing the resonant networks, the ZVS operation for primary switches and ZCS operation for the secondary diodes can be guaranteed. Finally, a 320-W experimental prototype is built to verify the theoretical analysis. It can be seen from the experimental waveforms that the proposed converter can achieve CC charge and CV charge and the experimental results agree with the theoretical analysis. Moreover, the proposed converter has good dynamic characteristic.
The main contribution of this paper lies in the following aspects:
1) a new dual-half bridge LLC resonant converter for battery charger application is proposed; 2) constant output voltage and constant output current characteristics of the LLC resonant converter are investigated; and 3) design considerations for an LLC resonant converter with MC are presented.