Buck-Boost/Flyback Hybrid Converter for Solar Power System Applications

Abstract

This paper proposes a hybrid converter to supply power from solar power source to load. Since power is generated by solar power, which depends on the intensity of solar power, the power generated by the solar power does not keep at a constant power. Therefore, the proposed system needs a battery to balance power between solar power and load. When the proposed one uses the battery to balance powers, the proposed circuit requires a charger and discharger. To simplify the proposed converter, a buck-boost converter and flyback converter can be combined to implement the battery charging and discharging functions. With this approach, the proposed converter can be operated with zero-voltage switching (ZVS) at turn-on transition to reduce switching loss of switch when the proposed one is operated in the discharging mode. In addition, the proposed hybrid converter has several merits, which are less component counts, lighter weight, smaller size and higher conversion efficiency. As compared with the conventional counterparts with hard-switching circuit, the proposed one can increase conversion efficiency of 4% and achieve efficiency of 85% under full load condition when the proposed one is operated in the discharging mode. Experimental results which are obtained from a prototype with output voltage of 10 V and maximum output power 20 W have been implemented to verify its feasibility. It is suitable for an electronic sign indicating LED within 200 W, which is used in the night time.

1. Introduction

Nowadays, due to a drastic increase in the demand for electricity, it leads to rapid and depletion of fossil fuels. In particular, when Taiwan Semicoductor Manufacturing (TSMC) and Google data center were built in Taiwan, electricity demand was increased by 1/3 within 5 years. As a result, the power processor adopts renewable energy sources as its input sources. In the renewable energy sources, such as solar power, wind turbine and fuel cell, they have been widely applied to a switching-mode converter for generating electric power to load [1,2]. They include power generation for grid connection, electric vehicles, water pumps, battery charger and discharger, traffic signals, street-lighting, electronic signs, and so on.

Due to the most recent development of light emitting diodes (LEDs) technology, it possesses many advantages, such as smaller size, longer lifetime, lower maintenance costs and greater strength against breakage [3,4,5,6]. Therefore, LEDs have widely used in our daily lives. They are suitable for indoor and outdoor energy-saving lighting applications, such as automotive taillights, thin film transistor liquid crystal display (TFT-LCD) backlight, traffic signals, streetlights, electronic signs [7,8,9,10]. In particular, the electronic sign or streetlight is used in the night time. It is suitable for solar power sources to supply power when solar power sources are adopted in the electronic sign or streetlight system. That is, the power system uses a charger to store energy from solar power sources to battery in the daytime, while the one adopts a discharger to release energy from battery to LEDs in the night time. The proposed power system simultaneously needs a charger and discharger, as shown in Figure 1.

Since the proposed power system adopts PV sources as its input source, the one needs the charger and discharger for electronic sign or streetlight application. The output voltage of solar power source is less than or greater than that of battery (8 V~12 V). Therefore, it simultaneously needs a step-up and step-down converter, such as buck-boost, ‘cuk, zeta and sepic converter [11,12,13]. As compared with ‘cuk, zeta and sepic converter, buck-boost converter possesses a simpler circuit topology. It is chosen as the charger for battery system, as shown in Figure 2. Since the flyback converter possesses many merits, which are a simpler circuit topology, wider ranges of voltage ratio between input voltage and output voltage and a lower cost, it can be applied to the solar power system or battery system. Therefore, the proposed power system can adopt buck-boost converter and flyback converter to implement battery charging and discharging functions, simultaneously, as shown in Figure 3.

When the proposed power system uses the flyback converter as the discharger, the leakage inductor of transformer will induce a spike voltage across switch. As a result, it will generate an extra switching loss. To avoid this problem, an active clamp circuit can be added into the flyback converter to recover leakage inductor energy [14,15,16,17], as shown in Figure 4. In order to simply circuit topology, switches of the charger and discharger can be respectively integrated, as shown in Figure 5. From Figure 5, the proposed hybrid converter can use a less component count to implement the battery charging and discharging functions, simultaneously. Therefore, the proposed power system can reduce cost, weight and size. Furthermore, the proposed one can be operated in ZVS at turn-on transition to increase conversion efficiency. It is suitable for a PV power system.

2. Derivation of the Proposed Hybrid Converter

The proposed hybrid converter adopts a buck-boost converter as the battery charger and a flyback converter as the battery discharger, as shown in Figure 4. In order to simplify the proposed power system, a bidirectional buck-boost converter is used and an active clamp circuit is introduced into flyback converter to increase conversion efficiency, as shown in Figure 6. From Figure 6, since the battery charger and discharger in the proposed power system are operated in complementary, switch S₁ is added into the proposed one to keep the battery charging and discharging functions. When switch S₁ is regarded as the operational mode switch, switches M₂ and M₃ shown in Figure 6 can be merged as a switch M₂ illustrated in Figure 5, while switches M₁ and M₄ can be merged as a switch M₁. The inductor L₁ can be also merged with the magnetizing inductor L_m of transformer. With this approach, the proposed power system can use a less component count to achieve the battery charging and discharging functions.

When the proposed power system is operated in the charging mode, switch S₁ is turned off. The equivalent circuit of the proposed one is the same as a buck-boost converter, as shown in Figure 7a. In Figure 7a, the magnetizing inductor of transformer T_r is respected as the inductor of the buck-boost one, where topology of the proposed hybrid converter operated in the charging mode is highlighted with thick line. When the proposed one is operated in discharging mode, switch S₁ is turned on, its equivalent circuit is the same as active clamp flyback converter, as shown in Figure 7b. In Figure 7b, the proposed hybrid one is highlighted with thick line. Therefore, the proposed power system can be respectively operated in different modes by the operational conditions of switch S₁.

3. Operational Principle of the Proposed Power System

The proposed hybrid converter can be divided into two operational modes: the charging mode and the discharging mode. Its equivalent circuit of the different operational modes is shown in Figure 7. Since the proposed hybrid converter can be operated in two different modes, its operational principle for each operational mode is also described in the following, respectively.

The charging mode

When the proposed hybrid converter is operated in the charging mode, its operational modes can be divided into 6 modes. The equivalent circuit of each operational mode and conceptual waveforms are plotted in Figure 8 and Figure 9, respectively. The power flow of each operational mode in the proposed hybrid converter is highlighted with thick line, as shown in Figure 9. In the following, each operational mode is briefly described.

Mode 1 [Figure 9a: t₀ ≤ t < t₁]: Before t₀, switch M₁ is in the turn-on state and switch M₂ is in the turn-off state. During this time interval, switch current I_M1 abruptly increases from 0A to the initial value of inductor L_m operated in continuous condition mode (CCM). When t = t₀, switch M₁ is still in the turn-on state, and M₂ is kept in the turn-off state. Since inductance L_m is further greater than L_k, voltage V_PV is approximately applied to inductance L_m. During this time interval, inductor L_m is in the stored energy state. Inductor current I_Lm linearly increases. The charging current I_B equals 0A.

Mode 2 [Figure 9b: t₁ ≤ t < t₂]: At t = t₁, switch M₁ is turned off and switch M₂ is still in the turn-off state. During this time interval, capacitor voltage V_CM2 is discharging from (V_PV + V_B) to 0V, while V_CM1 is charged from 0V to (V_PV + V_B). Within this mode, switch current I_M1 abruptly decreases from the maximum value to 0A, and current I_M2 quickly increases from 0V to the maximum value.

Mode 3 [Figure 9c: t₂ ≤ t < t₃]: At t = t₂, body diode D_M2 is in the forwardly bias state. Energy stored in magnetizing inductor L_m is released through battery and body diode D_M2. Inductor current I_Lm linearly reduces. The battery is in the charging state.

Mode 4 [Figure 9d: t₃ ≤ t < t₄]: At t₃, switch M₂ is turned on and M₁ is kept in the turn-off state. Since body diode D_M2 is forwardly biased before t = t₃, switch M₂ is operated at ZVS at turn-on transition. Energy stored in magnetizing inductor L_m is still in the released energy state. Current I_Lm is equal to charging current I_B, and its value linearly increases.

Mode 5 [Figure 9e: t₄ ≤ t < t₅]: At t = t₄, switch M₂ is turned off, and M₁ is kept at the turn-off state. Since energy stored in inductor current I_Lm is released through battery and body diode D_M2, switch voltage V_M1 is kept at 0V. Capacitor voltage V_CM1 is also kept at (V_PV + V_B). Inductor current I_Lm linearly reduces.

Mode 6 [Figure 9f: t₅ ≤ t < t₆]: At t = t₅, switch M₁ is turned on, and M₂ is kept in the turn-off state. Due to body diode D_M2 is in the forwardly bias state before t = t₅, switch voltage V_M1 abruptly varies from (V_PV + V_B) to 0V, switch voltage V_M2 fast changes from 0V to (V_PV + V_B). Switch current I_M1 suddenly increases to the initial value when the proposed converter is operated in CCM. Switch current I_M2 and battery current I_B simultaneously decreases to 0A. Since this time interval is very short, current I_M1 is kept at the initial value and current I_M2 and battery current I_B are sustained at 0A. When t = t₆, a new switching cycle will start.

The discharging mode

When the proposed hybrid converter is operated in the discharging mode during the night time, PV arrays does not generate power to supply battery. Furthermore, the proposed one with battery is required to supply energy to lighting system. According to the previously requirements, switch S₁ is turned on and PV arrays are not to supply power to load by diode D_B. Its equivalent circuit is implemented by flyback with active clamp circuit, as shown in Figure 7b. When the proposed hybrid converter is formed with the active clamp flyback converter, its operational mode is divided into eight modes. Its key component waveform is illustrated in Figure 10. In addition, equivalent circuit of each operational mode is depicted in Figure 11. In the following, each operational mode is described briefly.

Mode 1 [Figure 11a: t₀ ≤ t < t₁]: Before t₀, switch M₂ is in the turn-on state and switch M₁ is in the turn-off state. Switch current I_M2 fast varies from 0A to the initial value of inductor L_m in the proposed converter operated in CCM. When t = t₀, switch M₂ is still in the turn-on state, and M₁ is kept in the turn-off state. Switch current I_M2 is equal to the initial value of inductor current I_Lm. During this time interval, magnetizing inductor L_m is in the stored energy state. Inductor current I_Lm linearly increases. Since diode D₁ is reversely biased, load power is supplied by output capacitor C_o.

Mode 2 [Figure 11b: t₁ ≤ t < t₂]: At t₁, switch M₂ is turned off and switch M₁ is still in the turn-off state. Since inductor current I_LK must be operated in the continuous condition through capacitor C_M1 and C_DC, Capacitor C_M1 is discharged and its voltage V_M1 varies from (V_o/N + V_B) to 0V. Within this mode, capacitor C_o supplies power to load. Switch current I_M2 abruptly decreases to 0A, while current I_M1 suddenly reduced to the negative maximum value. Capacitor current I_CC also varies from 0V to its maximum value.

Mode 3 [Figure 11c: t₂ ≤ t < t₃]: When t = t₂, body diode D_M1 is forwardly biased and diode D₁ is also in the forwardly bias. Inductor voltage V_Lm is clamped at (−V_o/N). During this time interval, leakage inductor L_k and capacitor C_C form a resonant network. Inductor current I_Lk varies with the resonant form from the maximum value to the negative maximum value. Energy stored in the magnetizing inductor L_m is released through secondary winding of transformer T_r and diode D₁ to load.

Mode 4 [Figure 11d: t₃ ≤ t < t₄]: At t = t₃, switch M₁ is turned on and M₂ is kept in the turn-off state. Because body diode D_M1 is in the forwardly bias state before t = t₃, switch M₁ is operated with ZVS at turn-on transition. Within this mode, inductor L_k and capacitor C_c connects in series to generate the resonance. Inductor current I_Lk is still in the resonant state, and current I_Lm linearly reduce to release the energy stored in the magnetizing inductor L_m.

Mode 5 [Figure 11e: t₄ ≤ t < t₅]: At t₄, switch M₁ is turned off, and M₂ is kept at the turn-off state. Since capacitor C_M1 enters the charging state, capacitor voltage V_M1 varies from 0V to (V_o/N + V_B). Moreover, capacitor voltage V_M2 works in the discharging state, voltage V_M2 change from (V_o/N + V_B) to 0V. Within this mode, energy stored in the magnetizing inductor L_m releases through diode D₁ to load. Inductor current I_Lm linearly reduces.

Mode 6 [Figure 11f: t₅ ≤ t < t₆]: When t = t₅, capacitor voltage V_M1 is clamped at (V_o/N + V_B), while voltage V_M2 is kept at 0V. At the moment, body diode D_M2 is forwardly biased. During this time interval, inductor current I_Lk equals to current I_M2. Their values abruptly varies from the negative maximum value to 0V. The magnetizing inductor L_m is still in the discharging energy state, and its current I_Lm linearly decreases.

Mode 7 [Figure 11g: t₆ ≤ t < t₇]: When t = t₆, switch M₂ is turned on, and switch M₁ is still kept in the turn-off state. Since body diode D_M2 is in the forwardly bias state before t₆, switch M₂ is operated with ZVS at turn-on transition. During this time interval, current I_LK (=I_M2) changes from a negative value to 0V. The magnetizing inductor L_m is still in the released energy state through diode D₁ to load. Its current I_Lm linearly reduces.

Mode 8 [Figure 11h: t₇ ≤ t < t₈]: At t₇, switch M₂ is in the turn-on state and M₁ is in the turn-off state. During this time interval, inductor current I_LK varies from 0A to the initial value. The magnetizing inductor L_m is kept in the released energy state. Therefore, current I_Lm linearly decreases. When operational mode is at the end of mode 8, one new switching cycle will start.

4. Design of the Proposed Hybrid Converter

The proposed hybrid converter includes a charger and discharger. When the proposed one is operated as the charger, its equivalent circuit is the same as buck-boost converter. Moreover, its equivalent circuit is formed with an active clamp flyback converter for the discharger. Since the proposed one is composed with charger and discharger, its design must satisfy requirements of each converter. In the following, each converter is briefly analyzed.

A. Charger: Buck-boost converter

Since the battery charger is adopted with buck-boost converter, its key parameters include duty ratio D₁₁ and inductor L_m. Therefore, duty ratio D₁₁ and inductor L_m are derived in the following.

A.1 Duty ratio D₁₁

In the light day, the proposed hybrid converter is regarded as the charger. The power flows from PV arrays to battery. During switching cycle, battery voltage V_B is almost kept at a constant value. For maximum power point tracking (MPPT) of solar power, the proposed one can regulate the charging current I_B to implement MPPT. The maximum duty ratio D_11(max) can be determined under the minimum output voltage V_PV(min) of solar power and maximum battery voltage V_B(max). Its relationship is expressed as

$$V_{PV\left(min\right)}{D}_{11(max)}{T}_s+\left(-V_{B(max)}\right)\left(1-D_{11(max)}\right)T_s=0,$$

(1)

where T_s represents the period of the proposed hybrid converter. From (1), D_11(max) can be derived by

$$D_{11(max)}=\frac{V_{B(max)}}{V_{PV\left(min\right)+}{V}_{B(max)}}.$$

(2)

In addition, maximum transfer ratio M_11(max) can be obtained as

$$M_{11(max)}=\frac{D_{11(max)}}{1-D_{11(max)}}.$$

(3)

According to the above equations, when type of battery is selected, the maximum charging current I_B(max) can be denoted. Moreover, the charging current I_B can changed from its maximum charging current I_B(max) to 0A by regulating duty ratio D₁₁ of switch M₁. The charging current I_B is determined by MPPT of solar power.

A.2 Inductor L_m

In order to obtain the inductance L_m, the boundary inductance L_mB, which is the inductor value of the proposed converter operated in the boundary of CCM and discontinuous condition mode (DCM). Its conceptual waveforms are illustrated in Figure 12. The average charging current I_B(av) can be determined as

$$I_{B(av)}=\frac{\Delta I_{Lm(max)}(1-D_{11})}{2},$$

(4)

where ΔI_Lm(max) represents a maximum current variation of inductor L_m. In (4), ΔI_Lm(max) can be expressed by

$$\Delta I_{Lm\left(max\right)}=\frac{V_{PV}{D}_{11}{T}_s}{L_{mB}}=\frac{V_B\left(1-D_{11}\right)T_s}{L_{mB}}$$

(5)

where V_PV is the output voltage of solar power and V_B represents the battery voltage. According to (4) and (5), the charging current I_B(av) can be obtained as

$$I_{B(av)}=\frac{{(1-D_{11})}^2{V}_B{T}_s}{{2L}_{mB}}.$$

(6)

Since the maximum charging current I_B(av)max occurs at the maximum battery voltage V_B(max) and the minimum PV voltage V_PV(min), the maximum charging current I_B(av)max can be rewritten with

$$I_{B(av)max}=\frac{{(1-D_{11(min)})}^2{V}_{B(max)}{T}_s}{{2L}_{mB}},$$

(7)

where D_11(min) represents duty ratio from V_B(max) to V_PV(max). Since the charger is always operated in CCM, I_B(av)max can be expressed by K₁I_B(max), where K₁ varies from 0 to 1 and I_B(max) is the maximum charging current. In general, K₁ is set at 0.1~0.3. From (7), it can be seen that inductor L_m1 can be expressed as

$$L_{m1}=\frac{{(1-D_{11(min)})}^2{V}_{B(max)}{T}_s}{{2K}_1{I}_{B(max)}}.$$

(8)

A.3. selection of switches

Figure 7a shows the schematic diagram of the proposed hybrid converter operated in the charging mode. In order to determine voltage and $V_{PV}$ is at the maximum value and battery voltage $V_B$ is at maximum value, voltage ratings of components in the proposed one can be determined. Maximum voltage stresses of $M_1$ and $M_2$ can be determined by

$$V_{M\mathit{1}(max)}{=V}_{M\mathit{2}(max)}{=V}_{PV(max)}{+V}_{B(max)}.$$

(9)

In addition, voltage stress of switch $S_1$ obtained as

$$V_{S\mathit{1}(max)}{=NV}_{B(max)}$$

(10)

When input voltage $V_{pV}$ is at minimum value and battery voltage $V_B$ is at maximum value, the maximum rms current $I_{M(rms)}$ of switch $M_1$ can be illustrated by

$$I_{M\mathit{1}(rms)}=\frac{I_{B(max)}}{\mathit{1}-D_{\mathit{11}(max)}}\sqrt{D_{\mathit{11}(max)}[\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}]}\mathit{,}$$

(11)

where r is defined by ($\raisebox{1ex}{${\Delta I}_{Lm}$}\!\left/ \!\raisebox{-1ex}{$I_{B(max)}$}\right.$). The maximum rms current $I_{M\mathit{2}(rms)}$ of switch $M_2$ can be derived as

$$I_{M\mathit{2}(rms)}{=I}_{B(max)}\sqrt{\frac{[\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}]}{\mathit{1}-D_{\mathit{11}(max)}}}.$$

(12)

Moreover, the maximum rms current $I_{LK(rms)}$ of inductor $L_M$ can be obtained as

$$I_{LK(rms)}=\frac{I_{B(max)}}{\mathit{1}-D_{\mathit{11}(max)}}\sqrt{\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}}.$$

(13)

Discharger: Active clamp flyback converter

When the proposed boost converter is operated in the discharging mode, its equivalent circuit is composed by flyback converter with the active clamp circuit. For design of active clamp flyback converter, the important parameters include duty ratio D₁₂, transformer T_r, active clamp capacitor C_C and output capacitor C_o. In the following, their designs are analyzed briefly.

B.1. Duty ratio D₁₂

When the proposed hybrid converter uses flyback converter with the active clamp circuit to achieve soft-switching features, the active clamp circuit does not affect transfer ratio M₁₂ of the proposed flyback converter. That is, transfer ratio M₁₂ is the same as the conventional one. According to volt-second balance of inductor L_m, the following equation can be obtained by

$$V_B{D}_{\mathit{12}}{T}_s+\left(-\raisebox{1ex}{$V_o$}\!\left/ \!\raisebox{-1ex}{$N$}\right.\right)\left(\mathit{1}-D_{\mathit{12}}\right)T_s=\mathit{0}\mathit{,}$$

(14)

where N (=N₂/N₁) is the turns ratio of transformer T_r. From (9), it can be found that transfer ratio M₁₂ can be represented as

$$M_{\mathit{12}}=\frac{{ND}_{\mathit{12}}}{(\mathit{1}-D_{\mathit{12}})}.$$

(15)

When the output to input voltage transfer ratio M₁₂ is determined, duty ratio D₁₂ can obtained by

$$D_{\mathit{12}}=\frac{V_o}{{NV}_B{+V}_o}.$$

(16)

In the (11), when N, V_o and V_B are specified, duty ratio D₁₂ can be determined.

B.2. Transformer T_r

In order to Design transformer T_r, turns ratio N and the magnetizing inductor L_m are important parameters. Since output current I_o can be determined by inductance L_m and turns ratio N, their conceptual waveforms is shown in Figure 13. From Figure 13, it can be found that the average diode current I_D1(av) is represented by

$$I_{D\mathit{1}(av)}=\frac{\Delta I_{Lm\mathit{2}(max)}(\mathit{1}-D_{\mathit{12}})}{\mathit{2}N},$$

(17)

where $\Delta I_{Lm\mathit{2}\left(max\right)}$ is the variation value of inductor current $I_{Lm\mathit{2}}$. According to operational principle of the proposed hybrid converter, inductor current ΔI_Lm2(max) is obtained with

$$\Delta I_{Lm\mathit{2}(max)}=\frac{V_{B(max)}{D}_{\mathit{12}}{T}_s}{L_{MB\mathit{2}}},$$

(18)

where L_MB2 is the magnetizing inductance of transformer T_r where the proposed hybrid converter is operated in the boundary of DCM and CCM.

Since the proposed one adopts the active clamp circuit to achieve soft-switching features, its magnetizing inductor L_m2 is always operated in CCM. Therefore, the proposed one is designed in CCM under light load condition. The average current I_D1(av) is equal to K₂I_o(max), where K₂ range from 0 to 1 and I_o(max) represents the maximum output current. According to (12) and (13), the magnetizing inductor L_m2 can be determined by

$$L_{m\mathit{2}}=\frac{V_{B(max)}{D}_{\mathit{12}}(\mathit{1}-D_{\mathit{12}}{)T}_s}{{\mathit{2}NK}_{\mathit{2}}{I}_{o(max)}}.$$

(19)

Since the magnetizing inductor L_m is separately operated in the charging and discharging modes, their inductances are derived with different values (L_m1 and L_m2), respectively. In order to design a proper inductance L_m, it is selected with the maximum value between L_m1 and L_m2.

In (10) and (11), when voltage V_B and V_o are specified, turns ratio N is inversely proportional to duty ratio D₁₂.Since a large duty ratio D₁₂ corresponds to a smaller turns ratio N of transformer T_r. That is, lower current stresses are imposed on switches M₁ and M₂. However, in order to tolerate variations of load, battery voltage and component value, it is better to selected an operating ranges as D = 0.35~0.4. When duty ratio D₁₂ is specified, turns ratio N can be determined.

B.3. Active clamp capacitor Cc

When the proposed hybrid converter adopts the active clamp to achieve soft-switching features, the active clamp capacitor C_C can be used to recover energy trapped in leakage inductor L_k and help switch to achieve ZVS features. In order to obtain a wider range of soft-switching features, a half of resonant period is equal to or greater than turn-off time of switch M₂ when capacitor Cc and leakage inductor L_k are formed as the resonant network. Therefore, capacitor Cc must satisfy the following inequality:

$$\mathsf{\pi }\sqrt{L_k{C}_c{}_{}}\ge (1-D_{12}{)T}_s.$$

(20)

According to (15), capacitor C_C can be expressed by

$$C_o\ge \frac{{(1-D_{12})}^2{T}_s{}^2}{{\mathsf{\pi }}^2{L}_k}.$$

(21)

In (10), once leakage inductor L_k is specified, capacitor C_C can be determined.

B.4. Output Capacitor C_o

Since output capacitor C_o is used to reduce ripple of output voltage V_o, its value must be large enough. The ripple voltage ΔV_o across output capacitor C_o is expressed as follows:

$${\Delta V}_o=\frac{I_{o(max)}{D}_{\mathit{12}}{T}_s}{C_o},$$

(22)

where I_o(max) is the maximum output current. Therefore, output capacitor C_O can be determined by

$$C_o=\frac{I_{o(max)}{D}_{\mathit{12}}{T}_s}{\Delta \mathrm{Vo}}.$$

(23)

When the maximum output current I_o(max), duty ratio D₁₂, switching cycle T_S and output ripple voltage ΔV_o are specified, output capacitor C_o can be determined by (18).

B.4. Selection of switches and diode

Figure 7a shows the schematic diagram of the proposed hybrid converter operated in the discharging mode. When battery voltage $V_B$ is under a maximum value situation, voltage rating of components can be determined. Maximum voltage stresses of switch $M_1$ and $M_2$ can be obtained as

$$V_{M\mathit{1}(max)}{=V}_{M\mathit{2}(max)}{=V}_{B(max)}+\frac{V_o}{N}.$$

(24)

Maximum voltage stress $V_{D\mathit{1}(max)}$ of diode $D_{\mathit{1}}$ can be expressed by

$$V_{D\mathit{1}(max)}{=NV}_{B(max)}+ V_o.$$

(25)

When the minimum battery voltage $V_{B(min)}$ and output maximum current $I_{o\left(max\right)}$, the maximum rms current $I_{M\mathit{2}\left(rms\right)}$ can be derived as

$$I_{M\mathit{2}(rms)}=\frac{{NI}_{o(max)}}{\mathit{1}-D_{\mathit{12}(max)}}\sqrt{D_{\mathit{12}(max)}[\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}]}.$$

(26)

The maximum rms current $I_{LM\mathit{2}\left(rms\right)}$ is expressed by

$$I_{M\mathit{2}(rms)}=\frac{{NI}_{o(max)}}{\mathit{1}-D_{\mathit{12}(max)}}\sqrt{\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}}.$$

(27)

Moreover, the maximum rms current $I_{S\mathit{1}\left(rms\right)}{(=I}_{D\mathit{1}\left(rms\right)})$ is indicated by

$$I_{S\mathit{1}(rms)}{=I}_{D\mathit{1}(rms)}{=I}_{o(max)}\sqrt{\frac{[\mathit{1}+\frac{r^{\mathit{2}}}{\mathit{12}}]}{(\mathit{1}-D_{\mathit{12}(max)})}}.$$

(28)

Since switch $M_2$ is turned off, inductor $L_K$ and capacitor $C_c$ form a resonant network. A half resonant period of the resonant network is equal to (1$-{\mathrm{D}}_{\mathit{12}}$) $T_s$. The current waveform of switch $M_1$ varies with cosine wave manner. According to the rms calculation method for the cosine wave, the maximum rms current $I_{M\mathit{1}(rms)}$ can be obtained by

$$I_{M\mathit{1}(rms)}{=I}_{PK}\sqrt{\frac{\mathit{1}-D_{\mathit{12}(max)}}{\mathit{2}}},$$

(29)

where $D_{12(max)}$ is cut the minimum battery voltage $V_{B(min)}$ and $I_{PK}$ expresses the maximum current of inductor $L_{M2}$. When the proposed hybrid converter is operated in the heavy load condition, current $I_{PK}$ is approximately equal to [${NI}_{o(max)}/(1-D_{12\left(max\right)})+\frac{1}{2}{\Delta I}_{Lm\mathit{2}}$].

B.5. Power losses analysis

Since the proposed hybrid converter is operated in the charging mode, the proposed one is operated with hard-switching manner.Its power loss analysis is the same as the conventional buck converter.

The power loss analysis is neglected in this paper. When the proposed one is operated in the discharging mode, the active clamp capacitor $C_c$ can be used to recover the energy strapped in leakage inductor $L_k$ to increase conversion efficiency of the proposed one. Therefore, the power loss analysis is described for the proposed one operated in the discharging mode. When the proposed one is operated in the discharging mode, power loss includes losses of switches, diode and core. In the following, power loss analysis is derived.

(1). Losses of switches

The losses of switches include switching loss and conduction loss. Figure 14 shows the conceptual waveforms of switching losses for switches $M_1$ and $M_2$. Since switches $M_1$ and $M_2$ is operated with ZVS at turn-on transition, their switching loss is only induced at turn-off transition of switches. Therefore, switching losses $P_{soff}$ of switches $M_{\mathit{1}}$ and $M_{\mathit{2}}$ can be expressed by

$$P_{soff}=\frac{\mathit{1}}{{\mathit{2}T}_s}{V}_{M\mathit{1}(max)}{(t}_{off}{I}_{DP})\mathit{,}$$

(30)

where $I_{DP}$ is equal to [${NI}_{o(max)}/(1-D_{12\left(max\right)})+\frac{1}{2}{\Delta I}_{Lm\mathit{2}}$]. The conduction loss of switch $M_{\mathit{1}} ($ or $M_{\mathit{2}}$) can be derived as

$$P_{CD}{=I}_{M(rms)}{}^{\mathit{2}}{R}_{DS(on)}\mathit{,}$$

(31)

where $I_{M(rms)}$ is the rms current of each switch and $R_{DS(on)}$ represses a resistance of switch during turn-on state.

(2). Loss of diode

The loss of diode $D_1$ is generated by the forward voltage $V_F$ when diode $D_1$ is in the forward biased state. The loss $P_{D1}$ can be derived by

$$P_{D\mathit{1}}{=I}_{D\mathit{1}(rms)}{}^{\mathit{2}}{V}_F.$$

(32)

(3). Loss of core

The loss of core includes core loss and copper loss.The core loss of transformer $T_r$ is determined by the maximum flux density $B_m$ and core loss curve of core. The maximum flux density $B_m$ can be determined by

$${\mathrm{B}}_{\mathrm{m}}=\frac{{\mathsf{\mu }}_{\mathrm{o}}{\mathsf{\mu }}_{\mathrm{r}}\mathrm{N}(\frac{{\mathrm{N}\mathrm{I}}_{\mathrm{o}(\max )}}{1-{\mathrm{D}}_{12(\max )}}+\frac{{\Delta \mathrm{I}}_{\mathrm{Lm}2}}{2})}{{(\mathrm{l}}_{\mathrm{e}}{+\mathsf{\mu }}_{\mathrm{r}}{\mathrm{l}}_{\mathrm{g}})},$$

(33)

where N is the turns of primary winding and $l_e$ expresses the effective magnetic path length, $l_g$ indicates air gap length and ${\mu }_r$ permeability. When $B_m$ is determined, the core loss coefficient $C_p$ can be obtained through core loss curve of core. The core loss $P_{CL}$ is determined as

$$P_{CL}{=C}_P{V}_e\mathit{,}$$

(34)

where $V_e$ is the effective core volume of core. Moreover, copper loss $P_{CPL}$ can be derived by

$$P_{CPL}{=I}_{Lm\mathit{2}(rms)}{}^{\mathit{2}}{R}_{dc\mathit{1}}{l}_{m\mathit{1}}{+I}_{D\mathit{1}(rms)}{}^{\mathit{2}}{R}_{dc\mathit{2}}{l}_{m\mathit{2}},$$

(35)

where $R_{dc\mathit{1}}$ is the resistance coefficient of wire gauge of primary winding, ${\mathrm{l}}_{\mathrm{m}1}$ represses the total length of turns of primary winding, $R_{dc\mathit{2}}$ is the resistance coefficient of wire gauge of secondary winding and $l_{m\mathit{2}}$ indicates the total length of turns of secondary winding.

A. Block diagram of control method of the proposed hybrid converter

In order to control the proposed hybrid converter, a microcontroller and pulse-width modulation integrated circuit (PWM IC) are adopted in the proposed systems, as shown in Figure 15. In Figure 15, the microcontroller is used to implement maximum power point tracking (MPPT) of solar power, manages battery charging, controls battery charging current and perform battery protection. Moreover, the PWM IC is adopted to regulate output voltage V_o. For MPPT, this paper uses the perturb-and-observe method to execute the MPPT of solar power. In order to match the MPPT of solar power, charger adopts constant current (CC) method to implement battery charging.

B. Performances comparison between the proposed hybrid converter and the conventional counterpart converter

In general, key components of switching power supply include the switch, diode, magnetic device, capacitor, printed circuit board (PCB), control IC, driving circuit, filter and resistor, and so on. According to the technical report of the Industrial Economics and Knowledge Center (IEK) in Taiwan, cost of each component in switching power supply is illustrated in

Table 1. Total cost analysis of switching power supply (data from Industrial Economics and Knowledge Center (IEK) in Taiwan).

Component	Cost Ratio = (Cost ofEach Item/Total Cost)
switch	20%
capacitor	18%
Magnetic device	16%
diode	10%
PCB	6%
filter	8%
Driving circuit	12%
resistor	5%
Control IC	3%
others	2%

. From Table 1, it can be found that switch, capacitor, magnetic device, diode and driving circuit possess higher cost ratio in the switching power supply.

Table 2. Component count comparison between the proposed hybrid converter and the conventional counterpart converter.

Component	The Conventional Hybrid Buck-Boost/Flyback Hybrid Converter (Figure 4)	The Proposed Hybrid Buck-Boost/Flyback Hybrid Converter (Figure 5)	Cost Ratio decrEase for the Proposed Hybrid Converter
switch	3 pcs	2 pcs	6.7%
Magnetic device	2 pcs	1 pc	8%
diode	2 pcs	1 pc	5%
capacitor	3 pcs	3 pcs	0%
Driving circuit	2 sets	1 sets	6%
Extra device	0 pc	1 pc	−3~−6.7%

lists the component counts comparison between the proposed hybrid converter and the conventional counterpart converter. Since the conventional counterpart converter shown in Figure 4 includes three switches, two magnetic devices, two diodes and two sets of driving circuits, the proposed hybrid converter can reduce component usage and increase an extra switch S₁ usage. When the proposed one reduces one switch usage, it can obtain a cost reduction of 6.7%. In addition, the reduction magnetic device, diode and driving circuit usage of the proposed one can acquire a cost reduction of 8%, 5% and 6%, respectively. In order to reduce component counts, the proposed one increases a cost of 3~6.7%. From Table 2, it can be found that the proposed one can reduce cost of 19–22.7%.

5. Experimental Results

The proposed hybrid converter used solar power as its input source. Specifications of solar power are listed in

Table 3. Specification of the solar power supplied by solar power manufacturer.

Parameter	Values
Maximum power (Pmax)	30 W
Maximum power voltage (Ppv(max))	17.5 V
Maximum power current (Ipv(max))	1.84 A
Open circuit voltage (Voc)	20.9 V
Short circuit current (Isc)	1.94 A

. The following specifications were implemented.

A. Charger: Buck-boost converter

• Input voltage V_PV: DC 17.5 V~20.6 V (solar power),
• Switching frequency f_s1: 50 kHz,
• Output voltage V_B: DC 8 V~12 V (lithium battery:3.2 Ah), and
• Maximum charging current I_B(max): 3.2 Ah

B. Discharger: flyback converter

• Input voltage V_B: DC 8 V~12 V (lithium battery:3.2 Ah),
• Switching frequency f_s2: 50 kHz,
• Output voltage V_o: DC 10 V, and
• Maximum output current I_o(max): 2 A.

According to the previously specifications and design of the proposed hybrid converter, inductor L_m, turns ratio N and active clamp capacitor C_C could be determined.

Table 4. Parameters of components in the proposed hybrid converter.

Operational Mode	Design Value				Practical Value (v)	Conditions
	Symbol	Parameter	Equation	Value
The charging mode	Switch $M_{\mathit{1}}$	$V_{M\mathit{1}(max)}$	(9)	33 V	33 V	${\mathrm{V}}_{B(max)}=12\mathrm{V}$ $V_{PV(max)}=20.6\mathrm{V}$ $D_{\mathit{11}(max)}=0.6$ $D_{\mathit{11}(min)}=0.368$ ${\Delta I}_{LM}=0.64\mathrm{A}$, r = 0.2
		$I_{M\mathit{1}(rms)}$	(11)	6.22 A	6.20 A
		$I_{M\mathit{1}(pk)}$		8.32 A	8.07 A
	Switch $M_{\mathit{2}}$	$V_{M\mathit{2}(max)}$	(9)	33 V	33 V	$V_{B(max)}=12\mathrm{V}$ $V_{PV(max)}=20.6\mathrm{V}$ $V_{PV(min)}=8\mathrm{V}$ $D_{\mathit{11}(max)}=0.6$ $D_{\mathit{11}(min)}=0.368$ ${\Delta I}_{Lm}=0.64\mathrm{A}$, r = 0.2
		$I_{M\mathit{2}(rms)}$	(12)	5.07 A	5.06 A
		$I_{M\mathit{2}(pk)}$		8.32 A	8.07 A
	Switch $S_{\mathit{1}}$	$V_{S\mathit{1}(max)}$	(10)	24 V	24 V	N = 2 $V_{B(max)}=12\mathrm{V}$
		$I_{S\mathit{1}(rms)}$		0 A	0 A
		$I_{S\mathit{1}(pk)}$		0 A	0 A
	Inductor $L_{m\mathit{1}}$	$L_{m\mathit{1}}$	(8)	150 µH	660 µH ${\Delta I}_{Lmp}=0.145\mathrm{A}$ $r_p=0.045$ $I_{Lk(rms)} =$ 8 A	$D_{\mathit{11}(min)}=0.368$, $D_{\mathit{11}(max)}=0.6$ K = 0.1, $T_s$= 20 µS, $V_{B(max)}=12\mathrm{V}$, $I_{B(max)}=3.2\mathrm{A}$ ${\Delta I}_{LM}=0.64\mathrm{A}$, r = 0.2
		$I_{LK(rms)}$	(13)	8.01 A
The discharging mode	Switch $M_{\mathit{1}}$	$V_{M\mathit{1}(max)}$	(24)	17 V	17 V	$V_{B(max)}=12\mathrm{V}$, $V_{B(min)}=8\mathrm{V}$ $D_{\mathit{12}(min)}=0.294$, $D_{\mathit{12}(max)}=0.385$ N = 2, $V_o=10\mathrm{V}$, r = 0.2845 $I_{o(max)}=$ 2 A
		$I_{M\mathit{1}(rms)}$	(29)	3.92 A	3.63 A
		$I_{M\mathit{1}(pk)}$		7.07 A	6.56 A
	Switch $M_{\mathit{2}}$	$V_{M\mathit{2}(max)}$	(24)	17 V	17 V	$V_{B(max)}=12\mathrm{V}$ $D_{\mathit{12}(max)}=0.385$ N = 2, $V_o=10\mathrm{V}$, r = 0.2845 $I_{o(max)}=$2 A
		$I_{M\mathit{2}(rms)}$	(26)	1.05 A	4.04 A
		$I_{M\mathit{2}(pk)}$		7.07 A	6.56 A
	Switch $S_{\mathit{1}}$	$V_{S\mathit{1}(max)}$		0 V	0 V	$D_{\mathit{12}(max)}=0.385$ r = 0.2845 $I_{o(max)}=$2 A
		$I_{\mathrm{S}1(rms)}$	(28)	2.56 A	2.55 A
		$I_{S\mathit{1}(pk)}$		3.54 A	3.28 A
	Transformer $T_r$	$L_{m\mathit{2}}$	(19)	62 µA	660 µH ${\Delta I}_{Lmp}=0.107\mathrm{A}$ $r_p=0.027$ $I_{Lm\mathit{2}(rms)}=6.5\mathrm{A}$	$V_{B(max)}=12V$, $D_{\mathit{12}}=0.294$ $K_{\mathit{2}}$ = 0.1,$T_s$ = 20 µS, N = 2 $I_{o\left(max\right)}=2\mathrm{A}$ ${\Delta I}_{Lm\mathit{2}}=1.138\mathrm{A}$, r = 0.2845
		$I_{Lm(rms)}$	(27)	6.53 A
	Capacitor $C_c$	$C_c$	(21)	1.62 µF	1.5 µF	$L_k=12.5\text{ µ}\mathrm{H}$, $D_{\mathit{12}(min)}=0.294$ $T_s$ = 20 µS

illustrates parameters of components of the proposed hybrid converter. According to operational conditions of the proposed one, current and voltage stresses could be determined. From Table 4, it can be obtained that the magnetizing inductor L_m equaled 660 μH and turns ratio N was equal to 2. When transformer T_r was wound with the magnetizing inductor L_m of 660 μH, leakage inductor L_k was measured and its value was 12.5 μH. Therefore, the active capacitor C_C was calculated and its value was 1.62 μF. Capacitor C_C is adopted with 1.5 μF. In addition, current and voltage stresses of the proposed hybrid converter and the conventional counterpart converter are listed in

Table 5. Current and voltage stresses of components between the proposed hybrid converter and the counterpart converter.

Component	The counTerpart Converter Shown in Figure 4			The Proposed Hybrid Converter Shown in Figure 5
	Symbol	Voltage Stress	Current Stress (rms)	Symbol	Voltage Stress	Current Stress (rms)
switches	$M_{\mathit{1}}$	33 V	6.20 A	$M_{\mathit{1}}$	33 V	6.20 A
	$M_{\mathit{2}}$	17 V	4.04 A	$M_{\mathit{2}}$	33 V	5.06 A
	$M_{\mathit{3}}$	17 V	3.63 A	$S_{\mathit{1}}$	24 V	2.55 A
Diodes	$D_{\mathit{1}}$	33 V	5.06 A	$D_{\mathit{1}}$	34 V	2.55 A
	$D_{\mathit{2}}$	34 V	2.55 A

. From Table 5, it can be found that although component stress of the proposed hybrid converter was higher than that of the conventional counterpart converter, it could use fewer component counters to achieve the charging and discharging functions. The switch S₁ could adopt lower current and voltage stresses to change the charging mode or discharging mode of the proposed one. Furthermore, the components of power stage in the proposed hybrid converter were determined as follows:

• Switches M₁, M₂: AoW2918,
• Diode D₁: STPS10L60D,
• Switches S₁: AoW2918,
• Transformer T_r: EE-33 core, and
• Output capacitor C_o: 47 μF/25 V.

Figure 16 shows the photo of the proposed hybrid prototype converter. The hardware dimension of the proposed hybrid converter was about 100 × 60 mm². The circuit layout safety distance was set at 5 mm around outside of each component. According to the requirement of safety distance of each component, circuit layout area comparison between the proposed hybrid converter and the conventional counterpart converter is listed in

Table 6. Layout area comparison between the propose hybrid converter and the conventional counterpart converter.

Component	The Conventional Counterpart Converter Shown in Figure 4			The Proposed Hybrid Converter Shown in Figure 5
	Symbol	Dimension (Length × Width)	Circuit Layout Dimension (Length × Width)	Symbol (Length × Width)	Dimension (Length × Width)	Circuit Layout Dimension (Length × Width)
Switches (head sink dimension Length × width = 15 mm × 10 mm)	Switch $M_{\mathit{1}}$ with heat sink	10 mm × 5 mm $S_{M\mathit{1}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PM\mathit{1}}{=500\mathrm{mm}}^2$	Switch $M_{\mathit{1}}$ with heat sink	10 mm × 5 mm $S_{M\mathit{1}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PM\mathit{1}}{=500\mathrm{mm}}^2$
	Switch $M_{\mathit{2}}$ with heat sink	10 mm × 5 mm $S_{M\mathit{2}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PM\mathit{2}}{=500\mathrm{mm}}^2$	Switch $M_{\mathit{2}}$ with heat sink	10 mm × 5 mm $S_{M\mathit{2}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PM\mathit{2}}{=500\mathrm{mm}}^2$
	Switch $M_{\mathit{3}}$ with heat sink	10 mm × 5 mm $S_{M\mathit{3}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PM\mathit{3}}{=500\mathrm{mm}}^2$	Switch $S_{\mathit{1}}$ without heat sink	10 mm × 5 mm $S_{s\mathit{1}}{=50\mathrm{mm}}^2$	20 mm × 15 mm $S_{PS\mathit{1}}{=300\mathrm{mm}}^2$
Magnetics (EE-33 core)	Inductor $L_{\mathit{1}}$	35 mm × 35 mm $S_{L\mathit{1}}{=1225\mathrm{mm}}^2$	45 mm × 45 mm $S_{PL\mathit{1}}{=2025\mathrm{mm}}^2$	Transformer $T_r$	35 mm × 35 mm $S_{Tr}{=1225\mathrm{mm}}^2$	45 mm × 45 mm $S_{PTr}{=2025\mathrm{mm}}^2$
	Transformer $T_r$	35 mm × 35 mm $S_{Tr}{=1225\mathrm{mm}}^2$	45 mm × 45 mm $S_{PTr}{=2025\mathrm{mm}}^2$
Diodes	Diode $D_{\mathit{1}}$ with heat sink	10 mm × 5 mm $S_{D\mathit{1}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PD\mathit{1}}{=500\mathrm{mm}}^2$	Diode $D_{\mathit{1}}$ with heat sink	10 mm × 5 mm $S_{D\mathit{1}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PD\mathit{1}}{=500\mathrm{mm}}^2$
	Diode $D_{\mathit{2}}$ with heat sink	10 mm × 5 mm $S_{D\mathit{2}}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PD\mathit{2}}{=500\mathrm{mm}}^2$
	Diode $D_B$ with heat sink	10 mm × 5 mm $S_{DB}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PDB}{=500\mathrm{mm}}^2$	Diode $D_B$ with heat sink	10 mm × 5 mm $S_{DB}{=50\mathrm{mm}}^2$	25 mm × 20 mm $S_{PDB}{=500\mathrm{mm}}^2$
others	Fuse, connector, Driving circuit and filter	$S_{PT}$> 1675 ${\mathrm{mm}}^2$		Fuse, connector, Driving circuit and filter	$S_{PT}$ = 1675 ${\mathrm{mm}}^2$
Total circuit layout area $S_{TA}$		$S_{TA}$> 8725 ${\mathrm{mm}}^2$ (=9000 ${\mathrm{mm}}^2$)		$S_{TA}$ = 6000 ${\mathrm{mm}}^2$

. When switch M₁ was adopted with AoW2918, its package wasTO220. According to dimension of TO220 package, component dimension was 10 × 5 mm². In order to consider safety distance between two components, circuit layout dimension was considered with 20 × 15 mm². Although a component with a heat sink could increase its power processing capacity, its circuit layout dimension was increased. The heat sink dimension for TO220 package was 15 × 10 mm². Therefore, switch with heat sink needed 25 × 20 mm² for switch layout dimension. According to the above requirement to layout the proposed hybrid converter and the conventional counterpart converter, their circuit layout area is respectively calculated in the Table 6. From Table 6, it can be found that the proposed hybrid converter needed a circuit layout area of 6000 mm², while the conventional counterpart converter needed that of 9000 mm². Therefore, the proposed one could reduce circuit layout area by 3000 mm². The power density of the proposed one could increase about 1.5 times.

The proposed hybrid converter used solar power to charge the battery with CC. The MPPT and battery charging with CC must be implemented. When solar power was used as input voltage source, the proposed hybrid converter adopted the perturb-and-observe method to implement MPPT. Measured voltage V_PV, current I_PV, and power P_PV waveforms of solar power is shown in Figure 17. Figure 17a illustrates those waveforms under P_PV(max) = 15 W, while Figure 17b plots those waveforms under P_PV(max) = 30 W. From Figure 17, it can be obtained that tracking time T of solar power was about 200 ms. Figure 18 shows measured gate voltage M₁ of switch M₁ and charging current I_B. Since capacitor C_C connected with inductor L_m in series, they formed a resonant network through battery or capacitor C_DC during switch M₁ turn-on or turn-off interval, respectively. The measured charging current I_B varied with a resonant waveform. Figure 18a shows those waveforms under the average charging current I_B(av) = 0.7 A. Moreover, Figure 18b illustrates those waveforms under I_B(av) = 3 A.

Since the proposed hybrid converter was operated in the discharging mode, switches M₁ and M₂ were operated with ZVS at turn-on transition. When the proposed hybrid converter was operated in the discharging mode, measured switch voltages V_M1, V_M2 and currents I_M1, I_M2 waveforms of the proposed hybrid converter are shown in Figure 19. Figure 19a,b show those waveforms under 10% of full-load condition, while Figure 20a,b illustrate those waveforms under 15% of full-load condition. From Figure 19 and Figure 20, it can be found that switch M₁ and M₂ were operated with ZVS at turn-on transition under 10–15% of full-load condition, simultaneously. Figure 21 illustrates measured output voltage V_o and output current I_o under step-load change between 0% of full-load and 100% of full-load conditions, from which it can be obtained that the voltage regulation of output voltage V_o was limited within ±1%.

Comparison of conversion efficiency between flyback converter with hard-switching circuit and with the proposed active clamp circuit from light load to heavy load is shown in Figure 22, illustrating that the efficiency of the proposed converter is higher than that of hard-switching one. Its efficiency was 85% under full-load condition. According to component selection of the proposed hybrid converter, key component parameters are listed in

Table 7. Key component parameters of the proposed hybrid converter.

Component	Part Number	Voltage/Current Ratings Or Formula	Features
			Symbol	Parameter	Values
$M_{\mathit{1}}$, $M_{\mathit{2}}$ $S_{\mathit{1}}$	Aow2918	100 V/90 A	$R_{DS(on)}$	Drain-source On resistance	<7 mΩ
			$t_{on}$	Turn-on transition time	41 nS
			$t_{off}$	Turn-off transition time	54 nS
$D_{\mathit{1}}$	STPS10L60D	60 V/10 A	$V_F$	Forward drop voltage	0.56 V
Transformer $T_r$	TDK EE-33 (PC95 material)	$B_m\mathit{=}\frac{{\mathit{\text{µ}}}_o{\mathit{\text{µ}}}_r{NI}_{pk}}{{(l}_e{+\mathit{\text{µ}}}_r{l}_g)}(\mathrm{T})$ $I_{pk}\mathit{=}\frac{{NI}_{o(max)}}{{1\mathit{-}D}_{\mathit{12}(max)}}+\frac{{\Delta I}_{LM\mathit{2}}}{\mathit{2}}(\mathrm{A})$ µ0: 4π × 10−7($\raisebox{1ex}{$H$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$) IPK: maximum inductor current of primary winding (A) ID(max): output maximum current (A) D12(max): maximum duty cycle of switch M2 ${\Delta I}_{Lm\mathit{2}}$:variation of current ILm2(A) N: turns of primary winding Ae: Effective core volume (m2)	${\mathit{\text{µ}}}_r$	permeability	3300
			$A_e$	Effective cross-sectional area	119 ${\mathrm{mm}}^2$
			$l_e$	Effective magnetic Path length	67.5 mm
			$V_e$	Effective core volume	8030 ${\mathrm{mm}}^3$
			$l_g$	Air gap length	0.8 mm
			$l_{n\mathit{1}}$	Approximate mean length of turn in primary winding	64 mm
			$l_{n\mathit{2}}$	Approximate mean length of turn in secondary winding	72 mm
			AWG#18	Wire gauges of primary and secondary windings	Diameter 1.0 mm
				$R_{dc}:$ resistance	21.4 mΩ/m
			$N_{\mathit{1}}$	turn of primary winding	20 Turns
			$N_{\mathit{2}}$	turn of secondary winding	40 Turns
			$R_{dc\mathit{1}}{l}_{m\mathit{1}}$	Resistance of primary winding	0.027 Ω
			$R_{dc\mathit{2}}{l}_{m\mathit{2}}$	Resistance of secondary winding	0.062 Ω

. Power loss analysis of the proposed hybrid converter under full-load condition is illustrated in

Table 8. Power loss analysis of the proposed hybrid converter under $V_B$ = 12 V and output maximum current $I_{o\left(max\right)}=2\mathrm{A}$.

Component	The Proposed Hybrid Converter		Total Power Losses of Each Component
	Symbol	Power Loss
Driving circuit	$P_{DC}$	$P_{DC}{\mathit{=}I}_{cc}{\text{× }V}_{cc}$ $=17{.7\text{ × }12\text{ × }10}^{-3}=0.21 \mathrm{w}$	$P_{DC}=0.21\mathrm{w}$
Switch $M_{\mathit{1}}$	Switching loss $P_{CM\mathit{1}}$	$P_{CM\mathit{1}}=$0.15 w	$P_{CDM\mathit{1}}=$ 0.24 w
	Conduction loss $P_{DM\mathit{1}}$	$P_{DM\mathit{1}}=$0.09 w
Switch $M_{\mathit{2}}$	Switching loss $P_{CM\mathit{2}}$	$P_{CM\mathit{2}}=$0.15 w	$P_{CDM\mathit{2}}=$ 0.26 w
	Conduction loss $P_{DM\mathit{2}}$	$P_{DM\mathit{2}}=$0.11 w
Switch $S_{\mathit{1}}$	Conduction loss $P_{DS\mathit{1}}$	$P_{DS\mathit{1}}=$0.05 w	$P_{DS\mathit{1}}=$ 0.05 w
Diodes $D_{\mathit{1}}$	Forward drop loss $P_{D\mathit{1}}$	$P_{D\mathit{1}}=$1.43 w	$P_{D1}=$ 1.43 w
Transformer $T_r$	Core loss $P_{cTr}$	$P_{cTr}=$0.88 w	$P_{cpTr}=$ 2.45 w
	Copper loss $P_{cpTr}$	$P_{cpTr}=$1.54 w
Efficiency	86.6%

. Total power losses included switch, diode, transformer and driving circuit in the proposed hybrid one. The driving circuit loss was measured by oscillator and voltage V_cc is 12 V and current I_cc was17.7 mA. The driving circuit loss P_DC was 0.21 W. Since switches M₁ and M₂ were operated with ZVS at turn-on transition, their switching loss only considered switching loss at turn-off transition. According to the maximum operational current and voltage of switch, diode and transformer in the proposed hybrid converter, losses of each component are listed in Table 8. Switch S₁ was one time in the turn-on or turn-off state during a day. Its loss was only conduction loss. According to (33) and Table 4, maximum flux density Bm can be determined and its value was 200 mT. Figure 23 shows the core loss curves of transformer T_r manufactured by PC95 material of TDK. When B_m = 200 mT, core coefficient C_p is equal to 110 mW/cm³. Effective core volume V_e of transformer T_r was equal to 8.03 cm³. The core loss could be determined and its value P_cTr = 0.88 W. In addition, copper loss P_cpTr could be obtained by (35). Since I_D1(rms) = I_S1(rms) = 2.55 A, I_Lm2(rms) = 6.5 A, R_dc1l_m1 = 0.027 Ω and R_dc2l_m2 = 0.062 Ω, copper loss P_cpTr equaled 1.54 W. The conversion efficiency of the proposed hybrid converter operated in the discharging mode was 86.6% under full-load condition. The practical conversion was 85%. The stray loss of the proposed hybrid converter was 1.6%.

6. Conclusions

The proposed hybrid converter is consisted of buck-boost converter and active flyback converter to implement battery charger and discharger. Circuit derivation of the proposed hybrid converter is presented in this paper for decreasing component count. Moreover, operational principle, steady-state analysis, design and power loss analysis of the proposed hybrid converter have been described in detail. As compared with the conventional counterparts with hard-switching circuit, the proposed one can increase conversion efficiency of 4% and achieve efficiency of 85% under full load condition when the proposed one is operated in the discharging mode. In addition, cost and power density comparison between the proposed hybrid converter and the conventional counterpart converter, the proposed hybrid one can reduce cost of 19–22.7% and power density of the proposed one can increase about 1.5 times. An experimental prototype has been implemented for lithium battery of 12 V/3.2 Ah and for LED lighting of 10 V/2 A. It can verify the feasibility of the proposed hybrid converter. It is suitable for solar power applications.