Hybrid Converter with Multiple Sources for Lithium Battery Charger Applications

Abstract

This paper proposes a hybrid converter with multiple sources for lithium battery charger applications. Since the output voltage of a lithium battery charger is very low, its charger needs a higher step-down voltage for a utility line source or a step-down voltage for PV arrays. In order to implement the battery charger with utility line and PV arrays sources to simultaneously supply power to battery, a flyback converter is selected for utility line sources, and a buck converter is adopted for PV arrays source. Due to leakage inductor of transformer in flyback converter, an active clamp circuit is introduced into flyback converter to recover the energy stored in leakage inductor. In addition, flyback and buck converters can adopt switch integration techniques to simplify circuit structure. With this approach, the proposed hybrid converter has less components, is lighter weight and has smaller size and higher conversion efficiency. Finally, a prototype of the proposed hybrid converter with output voltage of 5 V~8.4 V and output maximum current of 12 A has been implement to verify its feasibility. It is suitable for the lithium battery charger applications.

1. Introduction

Currently, advances in switching power supply technology have created high energy density with lower volume, size and cost. It is widely applied to power systems to generate electric power to load, such as ac/dc converter, dc/dc converter, uninterrupted power supply (UPS), induction heating, electronic ballast, telecom power supplies, light emitting diode drivers and battery charger and dischargers [1,2,3,4,5]. In particular, battery power is rapidly replacing fossil fuel as an energy storage system in a variety of power system application, such as energy storage cabinet system, UPS, electric vehicle, small bikes, garden tools, vacuum cleaners and 3C products [6,7,8,9,10].

In general, battery power is combined with renewable energy sources to generate electric power to load due to zero pollution. In particular, when solar power is regarded as an input power source of power processor, different types of power sources should be merged to transfer less fluctuated and more reliable energy to load due to its intermittent feature. In order to supply power to the battery, a utility line source is selected to help solar power to sustain continuous energy to battery when solar power is functioning with less intense solar radiation. Therefore, solar power sources and utility line sources are simultaneously selected in the proposed power system to increase power reliability for battery charging applications.

When charger is widely used in power systems, various battery types are chosen to achieve storage energy. Since lithium battery possesses high energy density, small size and low self-discharge [11,12,13], it is extensively adopted in portable products. However, the lifetime of lithium battery is easily affected by the charging method. In order to increase life time of lithium battery, many battery charging methods have been proposed [14,15,16]. They include constant trickle current (CTC), constant current (CC) and constant current/constant voltage (CC-CV) charging methods. In these methods, since CTC charging method requires a longer charging time, its applications are limited. Since the CC-CV charging method can reduce charging time, it is suitable for the utility line source system. In addition, battery charger adopts solar power as it input source. To implement maximum power point tracking (MPPT) of solar power, the CC charging method can be used to extract its maximum power. Therefore, CC-CV and CC charging methods are, respectively, adopted in the proposed power system operated in the utility line and solar power source conditions.

In general, a battery cell is connected in series or parallel to form a battery pack for power system applications. Since a battery pack uses a lot of battery cells connected in series, it will result in voltage difference between each battery cell. Therefore, the lifetime and maximum storage capacity of battery pack can be reduced. In order to obtain better lifetime and maximum storage capacity of the battery, a battery pack with two or three battery cells connected in series is usually adopted without a battery equalizer. Its output voltage is less than 13 V. When a battery charger uses the utility line source as its input source, it needs a high step-down converter. Due to the low-level power application of the proposed charger, a flyback or forward converter can be selected as the charging converter. Moreover, a flyback converter has a better circuit and costs less. It is regarded as the charger when the proposed power system is operated in the utility line source condition, as shown in Figure 1. If the proposed one adopts solar power as its input source, a buck converter can be chosen as the charger because of low voltage differences between the output voltage of solar power and the battery, as shown in Figure 2. Therefore, the proposed power system operated in the utility line source condition adopts a flyback converter as its charger, while the proposed one operated in the solar power source condition uses a buck converter as its charger.

The proposed power system can select flyback and buck converters to achieve multiple sources for lithium battery charger applications, as shown in Figure 3. Since transformer T_r in flyback converter exists with leakage inductance L_K, it will induce a spike voltage across switch M₁ when switch M₁ is switched off. In order to recover the energy trapped in leakage inductance L_K, an active clamp circuit is introduced into the flyback converter to increase conversion efficiency [17,18,19,20]. Moreover, a buck converter can adopt a bidirectional circuit to implement the battery charger. For further simplifying circuit topology of the proposed power system, switches of active clamp flyback and bidirectional buck converters can be merged to form a hybrid converter, as shown in Figure 4. In Figure 4, since the utility line source and solar power source conditions are separately operated and their exchange time is very long, switch S₁ with a low speed and low cost is adopted to control operational conditions. In addition, the proposed hybrid converter can use less components and is of lighter volume, smaller size, lower cost and higher conversion efficiency. It is suitable for battery charger systems with multiple sources, such as Ni-Cd, Ni-MH, lead-acid, lithium batteries, etc.

The multiport converter has been widely applied to generate electric power [21,22,23,24,25,26]. In [21], a multi-port converter was used in smart grid for the integration of storage and distributed generator. The authors of [22] proposed a multi-input dc-dc converter to transfer power from different power sources to the load. In order to implement input source of converter with multiple power sources, their component counts were added, and their driving circuits are complex. In [23,24,25,26], they are adopted in PV and battery system for supplying power to load. They possess dual input and single output ports. The proposed hybrid converter is shown in Figure 4. It is similar to three-port converter: dual inputs and single output. Comparison of component counts with the proposed hybrid converter and its counterparts is illustrated in

Table 1. Comparison of component counts with the proposed hybrid converter and its counterparts.

Three-Port Converter	Input Ports	Output Ports	Inductors	Transformers	Switches	Diodes	Capacitors	Extra Switches
M. Kumar, et al. [23]	2	1	2	0	3	3	3	0
H. Wu, et al. [24]	2	1	2	0	3	3	1	0
H. Wu, et al. [25]	2	1	3	0	3	3	1	0
Y-E. Wu, et al. [26]	2	1	1	1	4	2	3	0
The proposed Hybrid converter (Figure 4)	2	1	0	1	3	0	1	1

. From Table 1, it can be observed that the proposed one can implement dual inputs and single output. It only uses one transformer, three switches, one capacitor and one extra switch. Compared with its counterparts, the proposed hybrid converter can reduce component counts to achieve approximately functions.

2. Derivation of the Proposed Hybrid Converter

Since the proposed hybrid converter includes an active clamp flyback and buck converter for battery charging applications, illustrated in Figure 3, it will become a complex circuit structure. In Figure 3, the active clamp flyback and buck converters are operated at different times, and the operational time of each converter is very long. Therefore, two sets of converters can be integrated as a hybrid converter. In the following, a circuit structure derivation is briefly described.

In order to simplify circuit structure of the proposed hybrid converter, diodes D₅ and D₆ shown in Figure 3 are, respectively, changed by switches M_D5 and M_D6 illustrated in Figure 5a. In Figure 5a, when switch M_D5 is moved from the upper regions to the lower loop, which consists of switch M_D5, voltage V_B and inductor L_S, the operation of the proposed power system is not affected, as shown in Figure 5b. If switches M_D5 and M_D6 are operated synchronously, two switches can be merged by switch M_D56. Moreover, inductors L₁ and L_S can be integrated to form inductors L_1S, as shown in Figure 5c.

In order to further simplify the proposed power system, nodes A and A’ are regarded as the same node AA’. Its circuit structure is illustrated in Figure 5d. When the operational condition of the proposed one is operated in the flyback converter condition, switches M₂ and M_D56 are switched on or switched off at the same time. Therefore, the S terminal of switch M₂ connected in node AA’ can be moved to node B. The operation of the proposed one is not affected, as shown in Figure 5e. Since flyback and buck converters are operated at different times and their exchange time is very long, switch S₁ with low speed and low cost can be used to control the operational condition of the proposed power system. Therefore, switches M₂ and M₃ are integrated to form switch M₂₃, as shown in Figure 5f. To simplify component symbol, the component devices of the proposed hybrid converter are renamed, as shown in Figure 4. From Figure 4, it can be observed that proposed hybrid converter can use less component counts to implement battery charger under utility line and solar power sources.

3. Operational Principle of the Proposed Hybrid Converter

The proposed hybrid converter can be operated in the utility line source and solar power source conditions for lithium battery charging applications. When the proposed one is operated in the solar power source condition, its equivalent circuit is illustrated in Figure 6a by the blue line. Figure 6b shows equivalent circuit of the proposed one operated in the utility line source condition by the blue line. In order to explain the operational principle of the proposed one, each converter is briefly described in the following.

A.

The solar power source condition: buck converter

When the proposed hybrid converter is operated in the solar power source condition, its equivalent circuit is shown in Figure 6a. Its equivalent circuit is a buck converter. Since the operational state of the proposed converter is always in continuous conduction mode (CCM) from light load to heavy load, its operational principle with CCM is briefly described. According to the operational principle of the proposed converter operated in the solar power source condition, its operational principle can be divided into five modes. Figure 7 illustrates an equivalent circuit of each operational mode by the blue line. While Figure 8 shows conceptual waveforms of each operational mode over a complete switching cycle. In the following, each operational mode is briefly explained.

Mode 1 (Figure 7a: t₀ ≤ t < t₁): Before t₀, switches M₂ and M₃ are in the off state. Diode D_M3 is in the forward bias state. When t = t₀, switch M₂ is switched on. Since switch current I_DS3 is equal to (–I_B), switch current I_DS2 abruptly increases from 0 A to I_B. Therefore, diode is D_M3 reversely biased. During this time interval, current I_B linearly increases and inductor L_s is in the storage energy state.

Mode 2 (Figure 7b: t₁ ≤ t < t₂): At t₁, switch M₂ is switched off and switch M₃ is kept in the off state. Within this time interval, since inductor current I_B has to be sustained at continuous state, capacitor C_M2 is operated in the charging state, while C_M3 is sustained in the discharging state. Therefore, voltage V_DS2 varies from 0 V to V_PV and voltage V_DS3 changes from V_PV to 0 V.

Mode 3 (Figure 7c: t₂ ≤ t < t₃): When t = t₂, switches M₂ and M₃ are kept in the off state. At the moment, voltage V_DS3 is equal to 0 V. Diode D_M3 is forwardly biased. During this time period, inductor L_s is in the released energy state. Its current, I_B, linearly decreases.

Mode 4 (Figure 7d: t₃ ≤ t < t₄): At t = t₃, switch M₂ is in the off state and M₃ is switched on. Since diode D_M3 is forwardly biased before t = t₃, switch M₂ is operated with zero-voltage switching (ZVS) at the turn-on transition. During this time interval, inductor L_S releases energy to the battery. Its current, I_B, linearly decreases.

Mode 5 (Figure 7e: t₄ ≤ t < t₅): When t = t₄, switch M₂ is in the off state and M₃ is switched off. Within this mode, switch current I_DS3 is a negative value. Diode D_M3 is forwardly biased to release energy stored in inductor L_s to the battery. Inductor current I_B linearly decreases. When the operational mode is at the end of mode 5, one new switching cycle will start.

B.

The utility line source condition: active clamp flyback converter

When the proposed hybrid converter is operated in the utility line source condition, an active clamp flyback converter is used to charge battery. Since the operational state of active clamp flyback converter is always kept in CCM from light load to heavy load, the operational principle of the one is briefly described for CCM operation. According to the operational principle of active clamp flyback converter, its operational mode can be divided into 10 modes. The equivalent circuit of each operational mode is shown in Figure 9 by the blue line, while the conceptual waveforms of each operational mode is illustrated in Figure 10. In the following, each operational mode is briefly explained.

Mode 1 (Figure 9a: t₀ ≤ t < t₁): Before t₀, switches M₁~M₃ are in the off state, and diodes D_M1 and D_M1 are in the forwardly bias state. When t = t₀, switch M₁ is switched on, and switches M₂ and M₃ are kept in the off state. At the moment, since diode D_M1 is forwardly biased before t₀, switch M₁ is operated with ZVS at turn-on transition. During this time interval, current I_LK varies from a negative value to 0 A. Since current I_DS3 is a negative value, diode D_M3 is in the forwardly bias state. Current I_B linearly decreases and inductor L_m releases energy through transformer T_r and diode D_M3 to the battery.

Mode 2 (Figure 9b: t₁ ≤ t < t₂): At t₁, switch M₁ is kept in the on state, and switches M₂ and M₃ are sustained in the off state. Within this mode, inductor current I_LK varies from 0 A to the initial value, which is the maximum inductor current of inductor L_m operated in CCM. Moreover, since current I_DS3 is kept at the negative value, diode D_M3 is sustained in the forwardly bias state. The magnetizing inductor L_m releases energy to battery.

Mode 3 (Figure 9c: t₂ ≤ t < t₃): When t = t₂, switch M₁ is sustained in the on state, and switches M₂ and M₃ are in the off state. At the moment, inductor current I_LK is equal to current I_Lm. Diode D_M3 is reversely biased. During this time interval, inductor L_m is in the storage energy state. Inductor current I_Lm linearly increases.

Mode 4 (Figure 9d: t₃ ≤ t < t₄): When t = t₃, switch M₁ is switched off, and switches M₂ and M₃ are kept in the off state. During this time interval, since inductor current I_LK has to be kept in the continuous state, capacitor C_M1 is charged, and capacitors C_M2 and C_M3 are simultaneously discharged. Therefore, voltage V_DS1 varies from 0 V to [V_DC + NV_B]. Voltage V_DS3 changes from [(V_DC/N) + V_B] to 0 V, while voltage V_DS2 varies from [(N-1)V_B +(N-1)V_DC/N] to 0 V.

Mode 5 (Figure 9e: t₄ ≤ t < t₅): At t₄, switch M₁~M₃ are kept in the off state. In this moment, voltages V_DS2 and V_DS3 are equal to 0 V. Diode D_M2 and D_M3 are forwardly biased, simultaneously. During this time interval, inductor L_K and capacitor C_C form a resonant network, and they start to generate resonance. Inductor current I_Lm releases energy through transformer T_r and diode D_M3 to battery. I_Lm linearly increases.

Mode 6 (Figure 9f: t₅ ≤ t < t₆): When t = t₅, switch M₁ is sustained in the off state, while switches M₂ and M₃ are simultaneously switched on. At the moment, switches M₂ and M₃ are simultaneously operated with ZVS at the turn-on transition. Within this mode, inductor L_K and capacitor C_C are sustained in the resonant state. Current I_LK with the resonant manner varies from a maximum negative value to 0 A. Inductor L_m is kept in the released energy state. Therefore, inductor current I_Lm linearly increases.

Mode 7 (Figure 9g: t₆ ≤ t < t₇): When t = t₆, switch M₁ is in the off state and switches M₂ and M₃ are kept in the on state. In this moment, current I_LK is equal to 0 A. During this time interval, inductor L_K and capacitor C_C are sustained in the resonant state. Inductor L_m releases energy through transformer T_r and switch M₃ to the battery. Therefore, inductor current I_Lm linearly increases. Since switch current I_DS3 is equal to (I_B–I_DS2), it varies from a negative value to 0 A.

Mode 8 (Figure 9h: t₇ ≤ t < t₈): At t₇, switch M₁ is kept in the off state, while switches M₂ and M₃ are simultaneously sustained in the on state. Within this mode, Inductor L_K and capacitor C_C are kept in the resonant state. Inductor current I_LK with the resonant manner varies from 0 A to the maximum value. Inductor L_m is in the released energy state. Its value linearly increases.

Mode 9 (Figure 9i: t₈ ≤ t < t₉): When t = t₈, switch M₁ is in the off state, while switches M₂ and M₃ are simultaneously switched on. In this mode, current I_DS3 is equal to (−I_B). Diode D_M3 is forwardly biased. Since inductor current I_LK must be kept in the continuous state, capacitor C_M1 is discharged, and capacitor C_M2 is charged. Voltage V_DS1 varies from [V_DC + NV_B] to 0 V, while voltage V_DS2 changes from 0 V to [(N − 1)V_B +(N − 1)V_DC/N]. Inductor L_m is kept in the released energy state.

Mode 10 (Figure 9j: t₉ ≤ t < t₁₀): At t = t₉, switch M₁ ~ M₃ are in the off state. At the moment, voltage V_DS1 is equal to 0 V. Thus, diode D_M1 is forwardly biased. During this time interval, inductor current I_LK varies from the maximum negative value to 0 A. Inductor current L_m is still in the released energy state. When operational mode is at the end of mode 10, one new switching cycle will start.

4. Design of the Proposed Hybrid Converter

Design of the proposed hybrid converter can be divided into two conditions. One is the utility line source condition, and the other is the solar power source condition. In the following, the design of each operational condition is briefly derived.

4.1. The Utility Line Source Condition: Active Clamp Flyback Converter

When the proposed hybrid converter is operated in the utility line source condition, the active clamp flyback converter is adopted to charge lithium battery. Its key parameter design is analyzed in the following.

4.1.1. Duty Ratio D₁₁

Since the active clamp flyback converter does not affect design of duty ratio D₁₁ and transformer T_r, the designs of D₁₁ and transformer T_r are the same as the conventional flyback converter. According to volt-second balance of magnetizing inductance L_m, the relationship between voltage V_DC and output voltage V_B can be expressed as follows:

$$V_{DC}{D}_{\mathit{11}}{T}_s+\left({-NV}_B\right)\left({\mathit{1}-D}_{\mathit{11}}\right)T_s=\mathit{0}$$

(1)

where N is turns ratio of transformer T_r, V_DC represents the equivalent dc voltage of utility line and T_s expresses the period of switching cycle. From (1), the conversion ratio M₁₁ of the active clamp flyback converter can be indicated by the following.

$$M_{\mathit{11}}=\frac{V_B}{V_{DC}}=\frac{D_{\mathit{11}}}{{N(\mathit{1}-D}_{\mathit{11}})}$$

(2)

When input voltage V_DC and battery voltage V_B are specified, duty ratio D₁₁ can be rewritten as follows.

$$D_{\mathit{11}}=\frac{{NV}_B}{{NV}_B{+V}_{DC}}$$

(3)

In (3), when N is kept at a constant value, the maximum duty ratio D_11(max) is determined under the maximum battery voltage V_B(max) and minimum input voltage V_DC(min). That is, the maximum duty ratio D_11(max) is determined by the following.

$$D_{\mathit{11}\left(\mathit{max}\right)}=\frac{{NV}_{B\left(\mathit{max}\right)}}{{NV}_B{\left(\mathit{max}\right)+V}_{DC\left(\mathit{min}\right)}}$$

(4)

In general, if the maximum duty ratio of a pulse-width modulation integrated circuit (PWM IC) is limited within 0.5, the maximum duty ratio D_11(max) has better selection ranges from 0.35 to 0.4.

4.1.2. Transformer T_r

For the design of transformer T_r, turn ratio N and magnetizing inductance L_m are two key parameters. In (4), when the maximum duty ratio D_11(max), battery voltage V_B(max) and input voltage V_DC(min) are determined, turns ratio N can be rewritten by the following.

$$N=\frac{D_{\mathit{11}\left(\mathit{max}\right)}{V}_{DC\left(\mathit{min}\right)}}{{(\mathit{1}-D}_{\mathit{11}\left(\mathit{max}\right)}{)V}_{B\left(\mathit{max}\right)}}.$$

(5)

In order to design magnetizing inductance L_m, magnetizing inductor current variation ΔI_Lm1 must be determined. In general, when the proposed flyback converter is operated in the boundaries of CCM and discontinuous conduction mode (DCM), average current I_B1(av) can be obtained as the desired reference value. Ratio K₁ of the average current I_B1(av) to the maximum charging current I_B(max) is set. That is, when the proposed converter begins to enter CCM operation, the average current I_B1(av) is equal to K₁I_B(max), where K₁ varies from 0 to 1. Figure 11 plots ideal waveforms of inductor current I_Lm and charging current I_B1 of the proposed one operated at the boundary condition. In Figure 11, the average current I_B1(av) is expressed by the following.

$$I_{B\mathit{1}\left(\mathrm{av}\right)}=\frac{{N\Delta I}_{Lm\mathit{1}}{(\mathit{1}-D}_{\mathit{11}})}{\mathit{2}}.$$

(6)

In Figure 11, current variation ΔI_Lm1 is equal to I_Lm(P). According to operational principle of the proposed flyback converter, current variation ΔI_Lm1 can be derived as follows:

$${\Delta I}_{Lm\mathit{1}}{=I}_{Lm\left(P\right)}=\frac{V_{DC}{D}_{\mathit{11}}{T}_s}{L_{mB\mathit{1}}},$$

(7)

where L_mB1 is the boundary value of magnetizing inductance L_m1 when the proposed flyback converter is operated in the boundary of CCM and DCM. Since the proposed one adopts the active clamp circuit to achieve ZVS operational features under CCM condition, it magnetizing inductance L_m1 is always operated in CCM to increase soft-switching operational ranges. In order to achieve a variety of soft-switching operational ranges, the proposed one begins to enter CCM under light load conditions. From (6) and (7), the magnetizing inductance L_m1 can be expressed as follows.

$$L_{m\mathit{1}}=\frac{{NV}_{DC}{D}_{\mathit{11}}{(\mathit{1}-D}_{\mathit{11}}{)T}_s}{{\mathit{2}K}_{\mathit{1}}{I}_{B\left(\mathit{max}\right)}}.$$

(8)

4.1.3. Capacitor C_c

In the active clamp flyback converter, capacitor C_c is adopted to recover energy stored in leakage inductance L_K and achieve ZVS features of switches. Since inductor L_K and capacitor C_c are connected in series to form a resonant network, half of the resonant period is equal to or greater than the turn-off time of switch M₁ to produce a wider range of soft-switching features. Thus, capacitor C_c has to satisfy the following inequality.

$$\pi \sqrt{L_K{C}_c} \ge { (\mathit{1}-D}_{\mathit{11}}{)T}_s.$$

(9)

In (9), capacitor C_c can be rewritten as follows.

$$C_c \ge \frac{{\left(\mathit{1}-D_{\mathit{11}}\right)}^{\mathit{2}}{T}_s{}^{\mathit{2}}}{{\pi }^{\mathit{2}}{L}_K}$$

(10)

From (5) and (8), magnetizing inductor L_m1 and turn ratio N of transformer T_r can be obtained, and then the turns of primary and secondary windings of transformer T_r can be determined. According to the turns of primary and secondary windings relative to wind transformer T_r, leakage inductance L_K can be measured by the practical wound transformer T_r. When leakage inductance L_K is obtained, capacitor C_c can be also determined by (10).

4.2. The Solar Power Source Condition: Buck Converter

When a battery uses solar power as its input source, the buck converter is regarded as the battery charger, as shown in Figure 6a. To design the proposed buck converter, the key parameters are derived in the following.

4.2.1. Duty Ratio D₁₂

In Figure 6a, switch M₂ is regarded as the main switch of the proposed buck converter, while switch M₃ is used as the auxiliary switch. According to volt-second balance of inductor L_s, its relationship is expressed by the following:

$${(V}_{PV}{-V}_B{)D}_{\mathit{12}}{T}_s+{(-V}_B{\left)\right(\mathit{1}-D}_{\mathit{12}}{)T}_s=\mathit{0},$$

(11)

where V_PV is output voltage of solar power, V_B represents battery voltage and T_s expresses the period of switching cycle. Conversion ratio M₁₂ of the proposed buck converter can be analyzed as follows.

$$M_{\mathit{12} }=\frac{V_B}{V_{PV}}{=D}_{\mathit{12}}.$$

(12)

From (12), the maximum duty ratio D_12(max) happens at the maximum battery voltage V_B(max) and minimum voltage V_PV(min). Therefore, the maximum duty ratio D_12(max) can be determined by the following.

$$D_{\mathit{12}\left(\mathit{max}\right)}=\frac{V_{B\left(\mathit{max}\right)}}{V_{PV\left(\mathit{min}\right)}}.$$

(13)

When the proposed hybrid converter is operated in the solar power condition, the proposed one can regulate output current with CC method to charge lithium battery and extract maximum output power of solar power. Its duty ratio D₁₂ is limited within D_12(max), as illustrated in (13).

4.2.2. Inductor L_s

Inductor L_s is the inductance of secondary winding of transformer T_r. Its value is equal to (L_m1/N²). Figure 12 shows ideal waveforms of current I_DS2, I_DS3 and I_B2 of the proposed buck converter operated in the boundaries of CCM and DCM. From Figure 12, the average charging current I_B2(av) can be derived by the following:

$$I_{B\mathit{2}\left(av\right)}=\frac{{\Delta I}_{LS}}{\mathit{2}}=\frac{I_{LS\left(P\right)}}{\mathit{2}},$$

(14)

where ΔI_LS is the current variation of inductor L_s, and I_LS(P) expresses the peak current of inductor L_s. Since voltage V_LS across inductor L_s is equal to (V_PV – V_B) during switch M₂ in the on state, current I_LS(P) can be the inductor as follows:

$$I_{LS\left(P\right)}=\frac{{(V}_{PV}{-V}_B)}{L_{SB}}{D}_{\mathit{12}}{T}_S,$$

(15)

where L_SB is the boundary inductance of L_S when the proposed converter is operated in the boundary of CCM and DCM. In (13), when the maximum voltage V_B(max) and minimum voltage V_PV(min) are specified, the maximum duty ratio D_12(max) can be obtained. Therefore, inductor current I_LS(P) can be rewritten as follows.

$$I_{LS\left(P\right)}=\frac{{(V}_{PV\left(\mathit{min}\right)}{-V}_{B\left(\mathit{max}\right)})}{L_{SB}}{D}_{\mathit{12}\left(\mathit{max}\right)}{T}_S.$$

(16)

From (14) and (15), the average current I_B2(av) is as follows.

$$I_{B\mathit{2}\left(av\right)}=\frac{{(V}_{PV\left(\mathit{min}\right)}{-V}_{B\left(\mathit{max}\right)})}{{\mathit{2}L}_{SB}}{D}_{\mathit{12}\left(\mathit{max}\right)}{T}_S.$$

(17)

When the proposed buck converter is operated in the boundary, average current I_B2(av) is set at K₂I_B(max), where K₂ varies from 0 to 1, and I_B(max) expresses the maximum charging current. In general, K₂ has a better selection range under 0.2~0.3. Therefore, inductor L_s can be expressed by the following.

$$Ls=\frac{{(V}_{PV\left(\mathit{min}\right)}{-V}_{B\left(\mathit{max}\right)})}{\mathit{2}{K}_{\mathit{2}}{I}_{B\left(\mathit{max}\right)}}{D}_{\mathit{12}\left(\mathit{max}\right)}{T}_S.$$

(18)

Since inductor L_s is equal to (L_m2/N²), inductor L_m2 can be indicated by the following.

$$L_{m\mathit{2}}=\frac{N^{\mathit{2}}{(V}_{PV\left(\mathit{min}\right)}{-V}_{B\left(\mathit{max}\right)})}{{\mathit{2}K}_{\mathit{2}}{I}_{B\left(\mathit{max}\right)}}{D}_{\mathit{12}\left(\mathit{max}\right)}{T}_S.$$

(19)

In order to design the proposed hybrid converter, inductor L_m of transformer T_r can be determined by inductors L_m1 and L_m2. It can be selected with the larger value between L_m1 and L_m2.

5. Control Circuit of the Proposed Hybrid Converter

The proposed hybrid converter adopts the utility line and solar power as its input source, respectively. In order to achieve a power supply system with multiple sources, the proposed one needs a controller to implement battery charging control and MPPT functions. Figure 13 illustrates the block diagram of the controller for the proposed hybrid converter. In Figure 13, the proposed one is divided into two parts: power circuit and controller. The controller is used to control power circuit for supplying power to battery. Therefore, the controller includes MPPT, power source selection, CC command selection, CC/CV command, PWM generator and battery protection units.

Table 2. Definitions of key parameters in Figure 13 for the controller of the proposed hybrid converter.

Symbol	Definition	Symbol	Definition
VPV	output voltage of solar power	SDI	protection signal of IB ≥ IBP
VPV(min)	minimum output voltage of solar power	SDV	protection signal of VB ≥ VBP
VDC	equivalent dc voltage of utility line	SD	protection signal of battery
VDC(min)	minimum equivalent dc voltage of utility line	SPV	detector signal of VPV ≥ VPV(min)
VB	battery voltage	SDC	detector signal of VDC ≥ VDC(min)
VB(max)	maximum battery voltage	PSP	selector signal of solar power
VBP	voltage protection of battery	PUL	selector signal of utility line
IB	Battery current	M11	gate signal of switch M1 under utility line source
IB(max)	maximum charging current of Battery	M12	gate signal of switch M2 under utility line source
IBP	current protection of battery	M13	gate signal of switch M3 under utility line source
PPV(max)	maximum output power of solar power at present	M21	gate signal of switch M1 under solar power source
IBcom1	current command value under PPV(max)	M22	gate signal of switch M2 under solar power source
IBcom	current command value with CC charging method	M23	gate signal of switch M3 under solar power source
Scc	selecting signal of CC command	M1	gate signal of switch M1
Scm	selecting signal of CC/CV command	M2	gate signal of switch M2
Vref	command signal of PWM generator	M3	gate signal of switch M3
Vf	feedback signal of PWM generator	S1	gate signal of switch S1
SPWM	PWM signal of main switch generator

lists definitions of key parameters in Figure 13, while

Table 3. Operational condition of the proposed hybrid converter for the controller shown.

Controlling Unit		Selection/Judgement Condition					Operational Condition
		Variable	State
Power source selection unit	solar power detector	SPV	High				VPV ≥ VPV(min)
					Low		VPV < VPV(min)
	utility line detector	SDC	High		High		VDC ≥ VDC(min)
				Low		Low	VDC < VDC(min)
	power source selector	PSP	High				under the solar power condition
					Low		Shutdown solar power
		PSP			High		under the solar utility line condition
			Low			Low	Shutdown utility line
CC command selection unit	solar power command	IBcom1					$I_{\mathit{Bcom}\mathit{1}}=\frac{P_{\mathit{PV}\left(\mathit{max}\right)}}{V_B}$
	Charging current selector	Scc	High				IBcom1 ≥ IB(max)
			Low				IBcom1 < IB(max)
	CC command selector	IBcom	Scc = High				IBcom = IB(max)
			Scc = Low				IBcom = IBcom1
CC/CV command unit	Charging mode judgement	Scm	High				VB ≥ VB(max)
			Low				VB < VB(max)
	CC/CV command selector	Vref	Scm = High				Vref = VB(max) under CV operation
			Scm = Low				Vref = IBcom under CC operation
PWM generator unit	Feedback selector	Vf	Scm = High				Vf = VB under CV operation
			Scm = Low				Vf = IB under CC operation
	PWM generator	SPWM					Error value by Vref and Vf
	Gate driver	M11					M11 = SPWM
	under utility	M12					M12$=\overline{S_{\mathit{PWM}}}$
	line source	M13					M13$=\overline{S_{\mathit{PWM}}}$
	Gate driver	M21					turn-off
	under solar	M22					M22 = SPWM
	power source	M23					M23$=\overline{S_{\mathit{PWM}}}$
	PWM signal selector	M1					M1 = PUL M11 + PSP M21
		M2					M2 = PUL M12 + PSP M22
		M3					M3 = PUL M13 + PSP M23
		S1	PSP = High				S1 = Low
			PUL = High				S1 = High
		SD	High				shutdown the proposed hybrid converter
			Low				normal operation
Battery protection unit	IB protection	SDI	High				IB ≥ IBP
			Low				IB < IBP
	VB protection	SDV	High				VB ≥ VBP
			Low				VB < VBP
	battery protection	SD					SD = SDI + SDV

illustrates the operational condition of the proposed hybrid converter. In the following, each control unit is briefly described.

5.1. MPPT Unit

The proposed hybrid converter possesses two operational conditions: the utility line source and solar power source conditions. When the proposed one uses solar power as its input source, it regulates charging current I_B with the CC method to charge the battery and implement MPPT. For implementing MPPT of solar power, the perturb and observe algorithm (P&O) was used for tracking the maximum power point (MPP) of solar power [27]. Since its algorithm is described in [27], it will not be described in this paper. As mentioned above, the MPPT unit in the controller adopts voltage V_PV and current I_PV to obtain the maximum power P_{PV (max)} of solar power.

5.2. CC Command Selection Unit

When the proposed hybrid converter is operated for a battery charger, charging current I_B uses the CC-CV method to supply power to the battery. In order to implement the battery charging function with the CC method, the controller must generate CC command value I_BCOM to regulate charging current I_B. The CC command selection unit is used to generate CC command value I_BCOM. When the maximum power P_PV(max) of solar power is obtained, the solar power command can produce a command value I_BCOM1, which can be expressed by (P_PV(max)/V_B). Since the charging current I_B is limited within I_B(max), charging the current selector can generate control signal S_CC, which is obtained by the relationship between I_BCOM1 and I_B(max). When I_BCOM1 ≥ I_B(max), signal S_CC varies from low levels to high levels. It is used to control the CC command selector, and signal I_BCOM is equal to I_B(max). If I_BCOM1 < I_B(max), signal S_CC is kept at low levels. It can control CC command selector to obtain I_BCOM = I_BCOM1.

Since the battery charging method adopts the CC–CV hybrid method to obtain better charging efficiency, the CC/CV command unit can produce a selecting signal S_Cm to control the battery charger operated in the CC charging mode or the CV charging mode. When voltage V_B is equal to or greater than voltage V_B(max), signal S_Cm varies from low levels to high levels. The proposed battery charger is operated in the CV charging mode. The command value V_ref is equal to V_B(max). Moreover, the feedback selector can induce feedback signal V_f, which is equal to V_B. The error value can be obtained by difference between the command value V_ref and feedback value V_f when signals V_ref and V_f are sent to PWM generator for generating error value. The error value compared with a triangle wave in the PWM generator can produce signal S_PWM to drive switches in the proposed hybrid converter for battery charging. In addition, when V_B < V_B(max), the proposed one is operated in the CC charging mode. Signal V_ref = I_BCOM and V_f = I_B. PWM generator can receive signals V_ref and V_f to generate S_PWM for battery charging.

5.3. PWM Generator Unit

The PWM generator unit includes a feedback selector, PWM generator, gate driver under utility line source, gate driver under solar power source and PWM signal selector. The feedback selector and PWM generator receives command value V_ref and feedback value V_f to generate PWM signal S_PWM for implementing CC or CV charge. The PWM signal S_PWM can be sent to gate driver under utility line source and gate driver under solar power source for generating different PWM signals under different power source to implement battery charger.

In the gate driver under utility line source, the PWM signal S_PWM is sent to this control circuit to generate three PWM signals. The PWM signal M₁₁ is used to drive switch M₁, which is regarded as the main switch. PWM signals M₁₁ and M₁₂ are operated in complementary, while PWM signals M₁₂ and M₁₃ are operated synchronously. Switches M₂ and M₃ are regarded as auxiliary switches and are driven by PWM signals M₁₂ and M₁₃, respectively. In addition, the gate driver under the solar power source can produce three PWM signals, M₂₁, M₂₂ and M₂₃, by PWM signal S_PWM. PWM signal M₂₂ is the main PWM signal for driving switch M₂. The PWM signals M₂₂ and M₂₃ are operated complementarily. Therefore, PWM signal M₂₃ is used to drive auxiliary switch M₃. In this operational condition, signal M₂₁ is switched off. Two pairs of PWM signals (M₁₁, M₁₂, M₁₃) and (M₂₁, M₂₂, M₂₃) are sent to a PWM signal selector to produce PWM signals selector to produce PWM signals M₁, M₂ and M₃. When operational signal P_SP is in the high level, PWM signals, M₁ = M₁₁, M₂ = M₁₂, M₃ = M₁₃, are adopted to drive switches M₁, M₂ and M₃, respectively. During this operational condition, the proposed hybrid converter is operated in the solar power source condition. Switch S₁ is switched off. If operational signal P_UL is in the high level, PWM signals M₁ = M₂₁, M₂ = M₂₂ and M₃ = M₂₃ are used to drive switches M₁, M₂ and M₃ separately. Within this operational condition, utility line source is regarded as the input source of the proposed hybrid converter. Switch S₁ is switched on. Moreover, signal S_D is the shutdown signal of the proposed hybrid converter. When signal S_D is in the high level, the proposed one enters the shutdown condition. During this time interval, battery operational condition is under I_B ≥ I_BP or V_B ≥ V_BP.

5.4. Power Source Selection Unit

A power source selection unit is used to select power source as input source of the proposed hybrid converter. When solar power can supply enough power to battery, the proposed one can use solar power to supply power for the battery. During this operational condition, the solar power detector is in the V_PV ≥ V_PV(min) condition. Signal S_PV is in the high level. Therefore, signal P_SP is under the high level, and signal P_UL is in the low level. If V_PV ≥ V_PV(min) and V_DC ≥ V_{DC (min)}, signals S_PV and S_DC are simultaneously in the high level. When V_PV ≥ V_PV(min) and V_DC ≥ V_{DC (min)}, signals S_PV and S_DC are simultaneously in the high level. Within this operational condition, the powers of solar power and utility line are large enough to supply power to battery. Since the power source in the proposed hybrid converter is a priority selection to solar power, the proposed one is operated in the solar power condition. Signal P_SP is in the high level state. In addition, when V_PV < V_PV(min) and V_DC ≥ V_{DC (min)}, solar power is not enough to supply power to the battery, and the utility line is large enough to supply power to battery. Therefore, a utility line can supply power to the battery. Signal P_UL is in the high level state. When V_PV < V_PV(min) and V_DC < V_{DC (min)}, solar power and utility lines are not enough to supply power to battery, simultaneously. Signals P_SP and P_UL are under the low level state. The proposed hybrid converter is operated in the shutdown condition. The operational condition of the proposed one is listed in Table 3.

5.5. Battery Protection Unit

The battery does not operate in overcurrent and overvoltage conditions. When I_B ≥ I_BP, the charging current I_B is greater than the maximum charging current I_B(max). Signal S_DI is in the high level state, and the proposed hybrid converter must be shut down. If V_B ≥ V_BP, battery voltage V_B is greater than maximum charging voltage V_B(max). Signal S_DV is in the high level state, and the proposed one can be shut down. Therefore, shutdown signal S_D is equal to S_DI + S_DV. When signal S_D is in the high level state, the proposed hybrid converter is operated in the shutdown condition.

6. Experimental Results

The proposed hybrid converter can be operated in the utility line source and solar power source conditions. In order to verify battery charging features, a prototype was implemented with the following specifications:

A. The utility line source condition: active clamp flyback converter

• Input voltage V_DC: DC127~183 V (AC90 V~130 V);
• Switching frequency f_s1: 50 kHz;
• Output voltage V_B: DC5 V~8.4 V (battery pack: 2 series*8 parallel);
• Maximum charging current I_B(max): 12 A.

B. The solar power source condition: buck converter

• Input voltage V_PV: DC30~45 V (solar panel: P_PV(max) = 100 W);
• Switching frequency f_s2: 50 kHz;
• Output voltage V_B: DC5 V~8.4 V (battery pack: 2 series*8 parallel);
• Maximum charging current I_B(max): 12 A.

According to the previous specifications of the proposed hybrid converter operated in different power source conditions, the specifications of solar power is illustrated in

Table 4. Specifications of solar panel.

Parameters	Single Module Value	Series Module Value
Maximum Power PPV(max)	50 W	100 W
Open circuit voltage VDC	22.5 V	45 V
Maximum Power voltage VPV(max)	17.96 V	36 V
Maximum Power current IPV(max)	2.78 A	2.78 A
Short circuit current ISC	3.1 A	3.1 A

, from which it can be observed that maximum output power P_PV(max) = 100 W, maximum power voltage V_PV = 36 V and maximum power current I_PV = 2.78 A. In addition, the battery pack includes 16 sets of battery cells. Specifications of each battery cell are illustrated in

Table 5. Specifications of lithium battery.

Parameters	Single Battery Cell		Battery Pack: 2 Series *8 Parallel
	Rated Value	Practical Value	Rated Value	Practical Value
Rated capacity	3.2 Ah	3.2 Ah	25.6 Ah	25.6 Ah
Nominal voltage VB(NV)	3.6 V	3.6 V	7.2 V	7.2 V
Maximum voltage VB(max)	4.2 V	4.2 V	8.4 V	8.4 V
Protection voltage VBP		4.3 V		8.6 V
Maximum charging current IB(max)	1.625 A	1.5 A	6.5 A	6 A
Protection current IBP		1.6 A		6.4 A
Maximum discharging current IBD(max)	6.4 A		25.6 A
Minimum discharging voltage VB(min)	2.5 V	2.5 V	5 V	5 V

. Two battery cells connected in series are regarded as a string. Eight sets of strings compose battery pack. In Table 5, the voltage of the battery pack varies from 5 V to 8.4 V, and the maximum charging current I_B(max) is equal to 12 A. Therefore, the battery pack is expressed by two series*8 parallel.

According to the design of the proposed hybrid converter, the key components are listed in

Table 6. Key components of the proposed hybrid converter.

Symbol	Material Type	Power Rating/Value
Switch M1	STF13NM60N	650 V/11 A
Switch M2	STO36N60M6	600 V/30 A
Switch M3	AOW2918	100/90 A
Switch S1	STF13NM60N	650 V/11 A
Capacitor Cc	Mpp Capacitor	0.4 F/400 V
Transformer Tr	EE-33 CORE	Lm = 3.6 mH, LK = 40µH, N = 9

. In order to verify the performances of the proposed hybrid converter, the experimental results are separately measured under solar power and utility line conditions. When solar voltage P_PV = 36 V, the measured switch voltage V_DS and current I_DS waveforms of switches M₂ and M₃ are shown in Figure 14 and Figure 15. Figure 14 shows those waveforms under 25% of the full-load condition, while Figure 15 depicts those waveforms under 100% of the full-load condition. From Figure 14 and Figure 15, it can be observed that the proposed hybrid converter can adopt solar power to charge battery from light load to heavy load. Figure 16 illustrates measured battery voltage V_B and current I_B waveforms under different charging currents. When charging current I_B = 3 A, those waveforms are shown in Figure 16a. In addition, when I_B = 6 A, those waveforms are expressed in Figure 16b. From measured voltage V_B and current I_B waveforms, the proposed hybrid converter operated in the solar power condition can achieve different charging currents under a constant value.

When the proposed hybrid converter uses solar power as its input source, it has to possess a good dynamic response. In order to verify the dynamic response of the proposed hybrid converter, Figure 17 illustrates measured battery voltage V_B and current I_B waveforms under step-load changes between I_B = 0 A and I_B(max) = 12 A. In Figure 17, battery voltage V_B varies within ±1%, from which it can be observed that the proposed hybrid converter operated in the solar power condition has a good dynamic response. Figure 18 shows measured solar power voltage V_PV, current I_PV and power P_PV waveforms under the maximum solar power P_PV(max) = 50 W. In Figure 18, when solar power P_PV varies from 0 W to 50 W, the MPPT time interval is about 330 ms. That is, the proposed hybrid converter can achieve MPPT features. Figure 19 expresses the conversion efficiency curve of the proposed hybrid converter operated in the solar power condition from light load to heavy load. In Figure 19, the maximum conversion efficiency is 95% under 80% of the full-load condition. When the proposed hybrid converter is operated under 100% of full-load condition, its conversion efficiency is about 91%. According to power loss analysis, driving circuit and stray losses are about 21.7% of total power loss. Losses of switches are approximated to 42.7%, while losses of transformer T_r are approximately 35.6%. As mentioned above, the proposed hybrid converter can be operated in the solar power condition to achieve battery charging.

When the proposed hybrid converter adopts the utility line as its input source, some experimental results are measured to verify its feasibility. Figure 20 and Figure 21 illustrate measured switch voltage V_DS and current I_DS of the proposed hybrid converter operated in the utility line condition. Figure 20 shows those waveforms under 45% of the full-load condition, while Figure 21 expresses those waveforms under 100% of the full-load condition. From Figure 20 and Figure 21, it can be observed that switches M₁ and M₂ are operated with ZVS at the turn-on transition. Figure 22 depicts measured battery voltage V_B and current I_B waveforms of the proposed one operated in the utility line condition under different charging currents. Figure 22a shows those waveforms under I_B = 3 A, while Figure 22b illustrates those waveforms under I_B = 6 A. In Figure 22, the charging current I_B can be successfully changed. Measured battery voltage V_B and current I_B waveforms of the proposed one operated in the utility line condition under step-load changes from I_B = 2.4 A to I_B(max) = 12 A are illustrated in Figure 23. Its battery voltage, V_B, can be kept within ±1% to verify a good dynamic response. Figure 24 draws the conversion efficiency curve of the proposed one operated in the utility line condition from light loads to heavy loads. The maximum conversion efficiency is about 93% under 70% of the full-load condition. When the proposed hybrid converter is operated under 100% of the full-load condition, its conversion efficiency is about 89%. According to power loss analysis, driving circuit and stray losses is about 4.3% of total power loss. Losses of switches are approximated to 88.1%, while losses of transformer T_r are approximately 7.6%. As previously experiment results, the proposed hybrid converter can be operated in the utility line condition to achieve battery charging.

7. Conclusions

This paper proposes a hybrid converter using multiple sources to charge lithium battery. The proposed hybrid converter consists of a buck converter and flyback converter to achieve battery charging under different input sources. Compared with its counterparts, the proposed hybrid converter can reduce component counts when the proposed one adds an extra switch with low speed and low cost. In this paper, circuit simplification of the proposed one is described for reducing component counts. In addition, operational principles, steady-state analysis and design of the proposed converter have been described in detail. From experiment results, it can be observed that the proposed hybrid converter can be operated in different input sources, such as the utility line and solar power sources. When the proposed hybrid converter is operated in the solar power condition, it can implement different charging currents and achieve MPPT operations. Moreover, its maximum conversion efficiency is about 95% under 80% of the full-load condition and its conversion efficiency of the full-load condition is about 91%. When the proposed one is operated in the utility line condition, switches M₁ and M₂ can be operated with ZVS at the turn-on transition. Its maximum conversion efficiency is about 93% under 70% of the full-load condition, and its conversion efficiency of the full-load condition is about 89%. An experimental prototype has been implemented for lithium battery charger of 8.4 V/12 A. It can verify the feasibility of the proposed hybrid converter for lithium battery charging under different input sources.